initial commit

README.md

@@ -1,3 +1,44 @@
-# flares
+FLARES (fNIRS Lightweight Analysis, Research, & Evaluation Suite)
+=================================================================
 
-fNIRS Lightweight Analysis, Research, & Evaluation Suite
+FLARES is a lightweight standalone application to extract meaningful data out of .snirf files.
+
+FLARES is free and open-source software that runs on Windows, MacOS, and Linux. Please read the information regarding each operating system below.
+
+Visit the official [FLARES web site](https://research.dezeeuw.ca/flares).
+
+[![Python web site](https://img.shields.io/badge/Made%20with-Python-1f425f.svg)](https://www.python.org)
+
+# For MacOS Users
+
+Due to the cost of an Apple Developer account, the application is not certified by Apple. Once the application is extracted and attempted to be launched for the first time you will get a popup stating:
+
+"Apple could not verify flares.app is free of malware that may harm your Mac or compromise your privacy.", with the options of "Done" or "Move to Trash".
+
+The solution around this is to use finder and navigate to the flares-darwin folder. Once the folder has been located, right click the folder and click the option "New Terminal at Folder". Once the terminal opens, run the following command (you can copy + paste):
+
+```xattr -dr com.apple.quarantine flares.app & pid1=$!; xattr -dr com.apple.quarantine flares_updater.app & pid2=$!; wait $pid1 $pid2; exit```
+
+Once the command has been executed and the text "[Process completed]" appears, you may close the terminal window and attempt to open the application again. If you choose to unrestrict the app through Settings > Privacy & Security, the app may not be able to update correctly in the future.
+
+This only applies for the first time you attempt to run FLARES. Subsequent times, including after updates, will function correctly as-is.
+
+# For Windows Users
+
+Due to the cost of a code signing certificate, the application is not digitally signed. Once the application is extracted and attempted to be launched for the first time you will get a popup stating:
+
+"Windows protected your PC - Microsoft Defender SmartScreen prevented an unrecognized app from starting. Running this app might put your PC at risk.", with the options of" More info" or "Don't run".
+
+The solution around this is to click "More info" and then select "Run anyway".
+
+This only applies for the first time you attempt to run FLARES. Subsequent times, including after updates, will function correctly as-is.
+
+# For Linux Users
+
+There are no conditions for Linux users at this time.
+
+# Licence
+
+FLARES is distributed under the GPL-3.0 license.
+
+Copyright (C) 2025 Tyler de Zeeuw

flares_updater.py

@@ -0,0 +1,255 @@
+"""
+Filename: flares_updater.py
+Description: FLARES updater executable
+
+Author: Tyler de Zeeuw
+License: GPL-3.0
+"""
+
+# Built-in imports
+import os
+import sys
+import time
+import shlex
+import psutil
+import shutil
+import platform
+import subprocess
+from datetime import datetime
+
+PLATFORM_NAME = platform.system().lower()
+
+if PLATFORM_NAME == 'darwin':
+    LOG_FILE = os.path.join(os.path.dirname(sys.executable), "../../../flares_updater.log")
+else:
+    LOG_FILE = os.path.join(os.getcwd(), "flares_updater.log")
+
+
+def log(msg):
+    with open(LOG_FILE, "a", encoding="utf-8") as f:
+        timestamp = datetime.now().strftime("%Y-%m-%d %H:%M:%S")
+        f.write(f"{timestamp} - {msg}\n")
+
+
+def kill_all_processes_by_executable(exe_path):
+    terminated_any = False
+    exe_path = os.path.realpath(exe_path)
+
+    if PLATFORM_NAME == 'windows':
+        for proc in psutil.process_iter(['pid', 'exe']):
+            try:
+                proc_exe = proc.info.get('exe')
+                if proc_exe and os.path.samefile(os.path.realpath(proc_exe), exe_path):
+                    log(f"Terminating process: PID {proc.pid}")
+                    _terminate_process(proc)
+                    terminated_any = True
+            except Exception as e:
+                log(f"Error terminating process (Windows): {e}")
+    elif PLATFORM_NAME == 'linux':
+        for proc in psutil.process_iter(['pid', 'cmdline']):
+            try:
+                cmdline = proc.info.get('cmdline', [])
+                if cmdline:
+                    proc_cmd = os.path.realpath(cmdline[0])
+                    if os.path.samefile(proc_cmd, exe_path):
+                        log(f"Terminating process: PID {proc.pid}")
+                        _terminate_process(proc)
+                        terminated_any = True
+            except Exception as e:
+                log(f"Error terminating process (Linux): {e}")
+
+    if not terminated_any:
+        log(f"No running processes found for {exe_path}")
+    return terminated_any
+
+
+def _terminate_process(proc):
+    try:
+        proc.terminate()
+        proc.wait(timeout=10)
+        log(f"Process {proc.pid} terminated gracefully.")
+    except psutil.TimeoutExpired:
+        log(f"Process {proc.pid} did not terminate in time. Killing forcefully.")
+        proc.kill()
+        proc.wait(timeout=5)
+        log(f"Process {proc.pid} killed.")
+
+
+def wait_for_unlock(path, timeout=100):
+    start_time = time.time()
+    while time.time() - start_time < timeout:
+        try:
+            if os.path.isdir(path):
+                shutil.rmtree(path)
+            else:
+                os.remove(path)
+            log(f"Deleted (after wait): {path}")
+            return
+        except Exception as e:
+            log(f"Still locked: {path} - {e}")
+            time.sleep(1)
+    log(f"Failed to delete after wait: {path}")
+    
+
+def delete_path(path):
+    if os.path.exists(path):
+        try:
+            if os.path.isdir(path):
+                shutil.rmtree(path)
+                log(f"Deleted directory: {path}")
+            else:
+                os.remove(path)
+                log(f"Deleted file: {path}")
+        except Exception as e:
+            log(f"Error deleting {path}: {e}")
+
+
+def copy_update_files(src_folder, dest_folder, updater_name):
+    for item in os.listdir(src_folder):
+        if item.lower() == updater_name.lower():
+            log(f"Skipping updater executable: {item}")
+            continue
+        s = os.path.join(src_folder, item)
+        d = os.path.join(dest_folder, item)
+        delete_path(d)
+        try:
+            if os.path.isdir(s):
+                shutil.copytree(s, d)
+                log(f"Copied folder: {s} -> {d}")
+            else:
+                shutil.copy2(s, d)
+                log(f"Copied file: {s} -> {d}")
+        except Exception as e:
+            log(f"Error copying {s} -> {d}: {e}")
+
+
+def copy_update_files_darwin(src_folder, dest_folder, updater_name):
+
+    updater_name = updater_name + ".app"
+
+    for item in os.listdir(src_folder):
+        if item.lower() == updater_name.lower():
+            log(f"Skipping updater executable: {item}")
+            continue
+        s = os.path.join(src_folder, item)
+        d = os.path.join(dest_folder, item)
+        delete_path(d)
+        try:
+            if os.path.isdir(s):
+                subprocess.check_call(["ditto", s, d])
+                log(f"Copied folder with ditto: {s} -> {d}")
+            else:
+                shutil.copy2(s, d)
+                log(f"Copied file: {s} -> {d}")
+        except Exception as e:
+            log(f"Error copying {s} -> {d}: {e}")
+
+
+def remove_quarantine(app_path):
+    script = f'''
+    do shell script "xattr -d -r com.apple.quarantine {shlex.quote(app_path)}" with administrator privileges with prompt "FLARES needs privileges to finish the update. (1/2)"
+    '''
+    try:
+        subprocess.run(['osascript', '-e', script], check=True)
+        print("✅ Quarantine attribute removed.")
+    except subprocess.CalledProcessError as e:
+        print("❌ Failed to remove quarantine attribute.")
+        print(e)
+
+
+def main():
+    try:
+        log(f"[Updater] sys.argv: {sys.argv}")
+
+        if len(sys.argv) != 3:
+            log("Invalid arguments. Usage: flares_updater <update_folder> <main_app_executable>")
+            sys.exit(1)
+
+        update_folder = sys.argv[1]
+        main_exe = sys.argv[2]
+
+        # Interesting naming convention
+        parent_dir = os.path.dirname(os.path.abspath(main_exe))
+        pparent_dir = os.path.dirname(parent_dir)
+        ppparent_dir = os.path.dirname(pparent_dir)
+        pppparent_dir = os.path.dirname(ppparent_dir)
+
+        updater_name = os.path.basename(sys.argv[0])
+
+        log("Updater started.")
+        log(f"Update folder: {update_folder}")
+        log(f"Main EXE: {main_exe}")
+        log(f"Updater EXE: {updater_name}")
+        if PLATFORM_NAME == 'darwin':
+            log(f"Main App Folder: {ppparent_dir}")
+
+        # Kill all instances of main app
+        kill_all_processes_by_executable(main_exe)
+
+        # Wait until main_exe process is fully gone (polling)
+        for _ in range(20):  # wait max 10 seconds
+            running = False
+            for proc in psutil.process_iter(['exe', 'cmdline']):
+                try:
+                    if PLATFORM_NAME == 'windows':
+                        proc_exe = proc.info.get('exe')
+                        if proc_exe and os.path.samefile(os.path.realpath(proc_exe), os.path.realpath(main_exe)):
+                            running = True
+                            break
+                    elif PLATFORM_NAME == 'linux':
+                        cmdline = proc.info.get('cmdline', [])
+                        if cmdline:
+                            proc_cmd = os.path.realpath(cmdline[0])
+                            if os.path.samefile(proc_cmd, os.path.realpath(main_exe)):
+                                running = True
+                                break
+                except Exception as e:
+                    log(f"Polling error: {e}")
+            if not running:
+                break
+            time.sleep(0.5)
+        else:
+            log("Warning: main executable still running after wait timeout.")
+
+        # Delete old version files
+        if PLATFORM_NAME == 'darwin':
+            log(f'Attempting to delete {ppparent_dir}')
+            delete_path(ppparent_dir)
+            update_folder = os.path.join(sys.argv[1], "flares-darwin")
+            copy_update_files_darwin(update_folder, pppparent_dir, updater_name)
+
+        else:
+            delete_path(main_exe)
+            wait_for_unlock(os.path.join(parent_dir, "_internal"))
+
+            # Copy new files excluding the updater itself
+            copy_update_files(update_folder, parent_dir, updater_name)
+
+    except Exception as e:
+        log(f"Something went wrong: {e}")
+
+    # Relaunch main app
+    try:
+        if PLATFORM_NAME == 'linux':
+            os.chmod(main_exe, 0o755)
+            log("Added executable bit")
+    
+        if PLATFORM_NAME == 'darwin':
+            os.chmod(ppparent_dir, 0o755)
+            log("Added executable bit")
+            remove_quarantine(ppparent_dir)
+            log(f"Removed the quarantine flag on {ppparent_dir}")
+            subprocess.Popen(['open', ppparent_dir, "--args", "--finish-update"])
+        else:
+            subprocess.Popen([main_exe, "--finish-update"], cwd=parent_dir)
+
+        log("Relaunched main app.")
+    except Exception as e:
+        log(f"Failed to relaunch main app: {e}")
+
+    log("Updater completed. Exiting.")
+    sys.exit(0)
+
+
+if __name__ == "__main__":
+    main()

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icons/desktop.ini

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+[LocalizedFileNames]
+updater.png=@updater.png,0

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mne/__init__.py

@@ -0,0 +1,36 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+"""MNE software for MEG and EEG data analysis."""
+# PEP0440 compatible formatted version, see:
+# https://www.python.org/dev/peps/pep-0440/
+#
+# Generic release markers:
+#   X.Y
+#   X.Y.Z   # For bugfix releases
+#
+# Admissible pre-release markers:
+#   X.YaN   # Alpha release
+#   X.YbN   # Beta release
+#   X.YrcN  # Release Candidate
+#   X.Y     # Final release
+#
+# Dev branch marker is: 'X.Y.devN' where N is an integer.
+#
+import lazy_loader as lazy
+
+try:
+    from importlib.metadata import version
+
+    __version__ = version("mne")
+except Exception:
+    __version__ = "0.0.0"
+
+(__getattr__, __dir__, __all__) = lazy.attach_stub(__name__, __file__)
+
+# initialize logging
+from .utils import set_log_level, set_log_file
+
+set_log_level(None, False)
+set_log_file()

mne/__init__.pyi

@@ -0,0 +1,430 @@
+__all__ = [
+    "AcqParserFIF",
+    "Annotations",
+    "BaseEpochs",
+    "BiHemiLabel",
+    "Covariance",
+    "Dipole",
+    "DipoleFixed",
+    "Epochs",
+    "EpochsArray",
+    "Evoked",
+    "EvokedArray",
+    "Forward",
+    "Info",
+    "Label",
+    "MixedSourceEstimate",
+    "MixedVectorSourceEstimate",
+    "Projection",
+    "Report",
+    "SourceEstimate",
+    "SourceMorph",
+    "SourceSpaces",
+    "Transform",
+    "VectorSourceEstimate",
+    "VolSourceEstimate",
+    "VolVectorSourceEstimate",
+    "add_reference_channels",
+    "add_source_space_distances",
+    "annotations_from_events",
+    "apply_forward",
+    "apply_forward_raw",
+    "average_forward_solutions",
+    "beamformer",
+    "channel_indices_by_type",
+    "channel_type",
+    "channels",
+    "chpi",
+    "combine_evoked",
+    "commands",
+    "compute_covariance",
+    "compute_proj_epochs",
+    "compute_proj_evoked",
+    "compute_proj_raw",
+    "compute_rank",
+    "compute_raw_covariance",
+    "compute_source_morph",
+    "concatenate_epochs",
+    "concatenate_events",
+    "concatenate_raws",
+    "convert_forward_solution",
+    "coreg",
+    "count_annotations",
+    "count_events",
+    "create_default_subject",
+    "create_info",
+    "cuda",
+    "datasets",
+    "decimate_surface",
+    "decoding",
+    "defaults",
+    "dig_mri_distances",
+    "dipole",
+    "epochs",
+    "equalize_channels",
+    "event",
+    "events_from_annotations",
+    "export",
+    "extract_label_time_course",
+    "filter",
+    "find_events",
+    "find_layout",
+    "find_stim_steps",
+    "fit_dipole",
+    "forward",
+    "get_config",
+    "get_config_path",
+    "get_head_surf",
+    "get_meg_helmet_surf",
+    "get_montage_volume_labels",
+    "get_volume_labels_from_aseg",
+    "get_volume_labels_from_src",
+    "grade_to_tris",
+    "grade_to_vertices",
+    "grand_average",
+    "grow_labels",
+    "gui",
+    "head_to_mni",
+    "head_to_mri",
+    "inverse_sparse",
+    "io",
+    "label_sign_flip",
+    "labels_to_stc",
+    "make_ad_hoc_cov",
+    "make_bem_model",
+    "make_bem_solution",
+    "make_field_map",
+    "make_fixed_length_epochs",
+    "make_fixed_length_events",
+    "make_forward_dipole",
+    "make_forward_solution",
+    "make_sphere_model",
+    "match_channel_orders",
+    "merge_events",
+    "minimum_norm",
+    "morph_labels",
+    "morph_source_spaces",
+    "open_docs",
+    "open_report",
+    "parse_config",
+    "pick_channels",
+    "pick_channels_cov",
+    "pick_channels_forward",
+    "pick_channels_regexp",
+    "pick_events",
+    "pick_info",
+    "pick_types",
+    "pick_types_forward",
+    "preprocessing",
+    "random_parcellation",
+    "read_annotations",
+    "read_bem_solution",
+    "read_bem_surfaces",
+    "read_cov",
+    "read_dipole",
+    "read_epochs",
+    "read_epochs_eeglab",
+    "read_epochs_fieldtrip",
+    "read_epochs_kit",
+    "read_events",
+    "read_evoked_besa",
+    "read_evoked_fieldtrip",
+    "read_evokeds",
+    "read_evokeds_mff",
+    "read_forward_solution",
+    "read_freesurfer_lut",
+    "read_label",
+    "read_labels_from_annot",
+    "read_lta",
+    "read_morph_map",
+    "read_proj",
+    "read_reject_parameters",
+    "read_source_estimate",
+    "read_source_morph",
+    "read_source_spaces",
+    "read_surface",
+    "read_talxfm",
+    "read_trans",
+    "read_tri",
+    "read_vectorview_selection",
+    "rename_channels",
+    "report",
+    "scale_bem",
+    "scale_labels",
+    "scale_mri",
+    "scale_source_space",
+    "sensitivity_map",
+    "set_bipolar_reference",
+    "set_cache_dir",
+    "set_config",
+    "set_eeg_reference",
+    "set_log_file",
+    "set_log_level",
+    "set_memmap_min_size",
+    "setup_source_space",
+    "setup_volume_source_space",
+    "simulation",
+    "source_space",
+    "spatial_dist_adjacency",
+    "spatial_inter_hemi_adjacency",
+    "spatial_src_adjacency",
+    "spatial_tris_adjacency",
+    "spatio_temporal_dist_adjacency",
+    "spatio_temporal_src_adjacency",
+    "spatio_temporal_tris_adjacency",
+    "split_label",
+    "stats",
+    "stc_near_sensors",
+    "stc_to_label",
+    "surface",
+    "sys_info",
+    "time_frequency",
+    "transform_surface_to",
+    "use_coil_def",
+    "use_log_level",
+    "verbose",
+    "vertex_to_mni",
+    "viz",
+    "what",
+    "whiten_evoked",
+    "write_bem_solution",
+    "write_bem_surfaces",
+    "write_cov",
+    "write_events",
+    "write_evokeds",
+    "write_forward_solution",
+    "write_head_bem",
+    "write_label",
+    "write_labels_to_annot",
+    "write_proj",
+    "write_source_spaces",
+    "write_surface",
+    "write_trans",
+]
+from . import (
+    beamformer,
+    channels,
+    chpi,
+    commands,
+    coreg,
+    cuda,
+    datasets,
+    decoding,
+    defaults,
+    dipole,
+    epochs,
+    event,
+    export,
+    filter,
+    forward,
+    gui,
+    inverse_sparse,
+    io,
+    minimum_norm,
+    preprocessing,
+    report,
+    simulation,
+    source_space,
+    stats,
+    surface,
+    time_frequency,
+    viz,
+)
+from ._fiff.meas_info import Info, create_info
+from ._fiff.pick import (
+    channel_indices_by_type,
+    channel_type,
+    pick_channels,
+    pick_channels_cov,
+    pick_channels_forward,
+    pick_channels_regexp,
+    pick_info,
+    pick_types,
+    pick_types_forward,
+)
+from ._fiff.proj import Projection
+from ._fiff.reference import (
+    add_reference_channels,
+    set_bipolar_reference,
+    set_eeg_reference,
+)
+from ._fiff.what import what
+from ._freesurfer import (
+    get_volume_labels_from_aseg,
+    head_to_mni,
+    head_to_mri,
+    read_freesurfer_lut,
+    read_lta,
+    read_talxfm,
+    vertex_to_mni,
+)
+from .annotations import (
+    Annotations,
+    annotations_from_events,
+    count_annotations,
+    events_from_annotations,
+    read_annotations,
+)
+from .bem import (
+    make_bem_model,
+    make_bem_solution,
+    make_sphere_model,
+    read_bem_solution,
+    read_bem_surfaces,
+    write_bem_solution,
+    write_bem_surfaces,
+    write_head_bem,
+)
+from .channels import (
+    equalize_channels,
+    find_layout,
+    read_vectorview_selection,
+    rename_channels,
+)
+from .coreg import (
+    create_default_subject,
+    scale_bem,
+    scale_labels,
+    scale_mri,
+    scale_source_space,
+)
+from .cov import (
+    Covariance,
+    compute_covariance,
+    compute_raw_covariance,
+    make_ad_hoc_cov,
+    read_cov,
+    whiten_evoked,
+    write_cov,
+)
+from .dipole import Dipole, DipoleFixed, fit_dipole, read_dipole
+from .epochs import (
+    BaseEpochs,
+    Epochs,
+    EpochsArray,
+    concatenate_epochs,
+    make_fixed_length_epochs,
+    read_epochs,
+)
+from .event import (
+    AcqParserFIF,
+    concatenate_events,
+    count_events,
+    find_events,
+    find_stim_steps,
+    make_fixed_length_events,
+    merge_events,
+    pick_events,
+    read_events,
+    write_events,
+)
+from .evoked import Evoked, EvokedArray, combine_evoked, read_evokeds, write_evokeds
+from .forward import (
+    Forward,
+    apply_forward,
+    apply_forward_raw,
+    average_forward_solutions,
+    convert_forward_solution,
+    make_field_map,
+    make_forward_dipole,
+    make_forward_solution,
+    read_forward_solution,
+    use_coil_def,
+    write_forward_solution,
+)
+from .io import (
+    read_epochs_fieldtrip,
+    read_evoked_besa,
+    read_evoked_fieldtrip,
+    read_evokeds_mff,
+)
+from .io.base import concatenate_raws, match_channel_orders
+from .io.eeglab import read_epochs_eeglab
+from .io.kit import read_epochs_kit
+from .label import (
+    BiHemiLabel,
+    Label,
+    grow_labels,
+    label_sign_flip,
+    labels_to_stc,
+    morph_labels,
+    random_parcellation,
+    read_label,
+    read_labels_from_annot,
+    split_label,
+    stc_to_label,
+    write_label,
+    write_labels_to_annot,
+)
+from .misc import parse_config, read_reject_parameters
+from .morph import (
+    SourceMorph,
+    compute_source_morph,
+    grade_to_vertices,
+    read_source_morph,
+)
+from .morph_map import read_morph_map
+from .proj import (
+    compute_proj_epochs,
+    compute_proj_evoked,
+    compute_proj_raw,
+    read_proj,
+    sensitivity_map,
+    write_proj,
+)
+from .rank import compute_rank
+from .report import Report, open_report
+from .source_estimate import (
+    MixedSourceEstimate,
+    MixedVectorSourceEstimate,
+    SourceEstimate,
+    VectorSourceEstimate,
+    VolSourceEstimate,
+    VolVectorSourceEstimate,
+    extract_label_time_course,
+    grade_to_tris,
+    read_source_estimate,
+    spatial_dist_adjacency,
+    spatial_inter_hemi_adjacency,
+    spatial_src_adjacency,
+    spatial_tris_adjacency,
+    spatio_temporal_dist_adjacency,
+    spatio_temporal_src_adjacency,
+    spatio_temporal_tris_adjacency,
+    stc_near_sensors,
+)
+from .source_space._source_space import (
+    SourceSpaces,
+    add_source_space_distances,
+    get_volume_labels_from_src,
+    morph_source_spaces,
+    read_source_spaces,
+    setup_source_space,
+    setup_volume_source_space,
+    write_source_spaces,
+)
+from .surface import (
+    decimate_surface,
+    dig_mri_distances,
+    get_head_surf,
+    get_meg_helmet_surf,
+    get_montage_volume_labels,
+    read_surface,
+    read_tri,
+    write_surface,
+)
+from .transforms import Transform, read_trans, transform_surface_to, write_trans
+from .utils import (
+    get_config,
+    get_config_path,
+    grand_average,
+    open_docs,
+    set_cache_dir,
+    set_config,
+    set_log_file,
+    set_log_level,
+    set_memmap_min_size,
+    sys_info,
+    use_log_level,
+    verbose,
+)

mne/__main__.py

@@ -0,0 +1,8 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from .commands.utils import main
+
+if __name__ == "__main__":
+    main()

mne/_fiff/__init__.py

@@ -0,0 +1,8 @@
+"""Private module for FIF basic I/O routines."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+# All imports should be done directly to submodules, so we don't import
+# anything here or use lazy_loader.

mne/_fiff/_digitization.py

@@ -0,0 +1,605 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import heapq
+from collections import Counter
+
+import numpy as np
+
+from ..utils import Bunch, _check_fname, _validate_type, logger, verbose, warn
+from .constants import FIFF, _coord_frame_named
+from .tag import read_tag
+from .tree import dir_tree_find
+from .write import _safe_name_list, start_and_end_file, write_dig_points
+
+_dig_kind_dict = {
+    "cardinal": FIFF.FIFFV_POINT_CARDINAL,
+    "hpi": FIFF.FIFFV_POINT_HPI,
+    "eeg": FIFF.FIFFV_POINT_EEG,
+    "extra": FIFF.FIFFV_POINT_EXTRA,
+}
+_dig_kind_ints = tuple(sorted(_dig_kind_dict.values()))
+_dig_kind_proper = {
+    "cardinal": "Cardinal",
+    "hpi": "HPI",
+    "eeg": "EEG",
+    "extra": "Extra",
+    "unknown": "Unknown",
+}
+_dig_kind_rev = {val: key for key, val in _dig_kind_dict.items()}
+_cardinal_kind_rev = {1: "LPA", 2: "Nasion", 3: "RPA", 4: "Inion"}
+
+
+def _format_dig_points(dig, enforce_order=False):
+    """Format the dig points nicely."""
+    if enforce_order and dig is not None:
+        # reorder points based on type:
+        # Fiducials/HPI, EEG, extra (headshape)
+        fids_digpoints = []
+        hpi_digpoints = []
+        eeg_digpoints = []
+        extra_digpoints = []
+        head_digpoints = []
+
+        # use a heap to enforce order on FIDS, EEG, Extra
+        for idx, digpoint in enumerate(dig):
+            ident = digpoint["ident"]
+            kind = digpoint["kind"]
+
+            # push onto heap based on 'ident' (for the order) for
+            # each of the possible DigPoint 'kind's
+            # keep track of 'idx' in case of any clashes in
+            # the 'ident' variable, which can occur when
+            # user passes in DigMontage + DigMontage
+            if kind == FIFF.FIFFV_POINT_CARDINAL:
+                heapq.heappush(fids_digpoints, (ident, idx, digpoint))
+            elif kind == FIFF.FIFFV_POINT_HPI:
+                heapq.heappush(hpi_digpoints, (ident, idx, digpoint))
+            elif kind == FIFF.FIFFV_POINT_EEG:
+                heapq.heappush(eeg_digpoints, (ident, idx, digpoint))
+            elif kind == FIFF.FIFFV_POINT_EXTRA:
+                heapq.heappush(extra_digpoints, (ident, idx, digpoint))
+            elif kind == FIFF.FIFFV_POINT_HEAD:
+                heapq.heappush(head_digpoints, (ident, idx, digpoint))
+
+        # now recreate dig based on sorted order
+        fids_digpoints.sort(), hpi_digpoints.sort()
+        eeg_digpoints.sort()
+        extra_digpoints.sort(), head_digpoints.sort()
+        new_dig = []
+        for idx, d in enumerate(
+            fids_digpoints
+            + hpi_digpoints
+            + extra_digpoints
+            + eeg_digpoints
+            + head_digpoints
+        ):
+            new_dig.append(d[-1])
+        dig = new_dig
+
+    return [DigPoint(d) for d in dig] if dig is not None else dig
+
+
+def _get_dig_eeg(dig):
+    return [d for d in dig if d["kind"] == FIFF.FIFFV_POINT_EEG]
+
+
+def _count_points_by_type(dig):
+    """Get the number of points of each type."""
+    occurrences = Counter([d["kind"] for d in dig])
+    return dict(
+        fid=occurrences[FIFF.FIFFV_POINT_CARDINAL],
+        hpi=occurrences[FIFF.FIFFV_POINT_HPI],
+        eeg=occurrences[FIFF.FIFFV_POINT_EEG],
+        extra=occurrences[FIFF.FIFFV_POINT_EXTRA],
+    )
+
+
+_dig_keys = {"kind", "ident", "r", "coord_frame"}
+
+
+class DigPoint(dict):
+    """Container for a digitization point.
+
+    This is a simple subclass of the standard dict type designed to provide
+    a readable string representation.
+
+    Parameters
+    ----------
+    kind : int
+        The kind of channel,
+        e.g. ``FIFFV_POINT_EEG``, ``FIFFV_POINT_CARDINAL``.
+    r : array, shape (3,)
+        3D position in m. and coord_frame.
+    ident : int
+        Number specifying the identity of the point.
+        e.g.  ``FIFFV_POINT_NASION`` if kind is ``FIFFV_POINT_CARDINAL``,
+        or 42 if kind is ``FIFFV_POINT_EEG``.
+    coord_frame : int
+        The coordinate frame used, e.g. ``FIFFV_COORD_HEAD``.
+    """
+
+    def __repr__(self):  # noqa: D105
+        from ..transforms import _coord_frame_name
+
+        if self["kind"] == FIFF.FIFFV_POINT_CARDINAL:
+            id_ = _cardinal_kind_rev.get(self["ident"], "Unknown cardinal")
+        else:
+            id_ = _dig_kind_proper[_dig_kind_rev.get(self["kind"], "unknown")]
+            id_ = f"{id_} #{self['ident']}"
+        id_ = id_.rjust(10)
+        cf = _coord_frame_name(self["coord_frame"])
+        x, y, z = self["r"]
+        if "voxel" in cf:
+            pos = (f"({x:0.1f}, {y:0.1f}, {z:0.1f})").ljust(25)
+        else:
+            pos = (f"({x * 1e3:0.1f}, {y * 1e3:0.1f}, {z * 1e3:0.1f}) mm").ljust(25)
+        return f"<DigPoint | {id_} : {pos} : {cf} frame>"
+
+    # speed up info copy by only deep copying the mutable item
+    def __deepcopy__(self, memodict):
+        """Make a deepcopy."""
+        return DigPoint(
+            kind=self["kind"],
+            r=self["r"].copy(),
+            ident=self["ident"],
+            coord_frame=self["coord_frame"],
+        )
+
+    def __eq__(self, other):  # noqa: D105
+        """Compare two DigPoints.
+
+        Two digpoints are equal if they are the same kind, share the same
+        coordinate frame and position.
+        """
+        my_keys = ["kind", "ident", "coord_frame"]
+        if set(self.keys()) != set(other.keys()):
+            return False
+        elif any(self[_] != other[_] for _ in my_keys):
+            return False
+        else:
+            return np.allclose(self["r"], other["r"])
+
+
+def _read_dig_fif(fid, meas_info, *, return_ch_names=False):
+    """Read digitizer data from a FIFF file."""
+    isotrak = dir_tree_find(meas_info, FIFF.FIFFB_ISOTRAK)
+    dig = None
+    ch_names = None
+    if len(isotrak) == 0:
+        logger.info("Isotrak not found")
+    elif len(isotrak) > 1:
+        warn("Multiple Isotrak found")
+    else:
+        isotrak = isotrak[0]
+        coord_frame = FIFF.FIFFV_COORD_HEAD
+        dig = []
+        for k in range(isotrak["nent"]):
+            kind = isotrak["directory"][k].kind
+            pos = isotrak["directory"][k].pos
+            if kind == FIFF.FIFF_DIG_POINT:
+                tag = read_tag(fid, pos)
+                dig.append(tag.data)
+            elif kind == FIFF.FIFF_MNE_COORD_FRAME:
+                tag = read_tag(fid, pos)
+                coord_frame = _coord_frame_named.get(int(tag.data.item()))
+            elif kind == FIFF.FIFF_MNE_CH_NAME_LIST:
+                tag = read_tag(fid, pos)
+                ch_names = _safe_name_list(tag.data, "read", "ch_names")
+        for d in dig:
+            d["coord_frame"] = coord_frame
+    out = _format_dig_points(dig)
+    if return_ch_names:
+        out = (out, ch_names)
+    return out
+
+
+@verbose
+def write_dig(
+    fname, pts, coord_frame=None, *, ch_names=None, overwrite=False, verbose=None
+):
+    """Write digitization data to a FIF file.
+
+    Parameters
+    ----------
+    fname : path-like
+        Destination file name.
+    pts : iterator of dict
+        Iterator through digitizer points. Each point is a dictionary with
+        the keys 'kind', 'ident' and 'r'.
+    coord_frame : int | str | None
+        If all the points have the same coordinate frame, specify the type
+        here. Can be None (default) if the points could have varying
+        coordinate frames.
+    ch_names : list of str | None
+        Channel names associated with the digitization points, if available.
+
+        .. versionadded:: 1.9
+    %(overwrite)s
+
+        .. versionadded:: 1.0
+    %(verbose)s
+
+        .. versionadded:: 1.0
+    """
+    from ..transforms import _to_const
+
+    fname = _check_fname(fname, overwrite=overwrite)
+    if coord_frame is not None:
+        coord_frame = _to_const(coord_frame)
+        pts_frames = {pt.get("coord_frame", coord_frame) for pt in pts}
+        bad_frames = pts_frames - {coord_frame}
+        if len(bad_frames) > 0:
+            raise ValueError(
+                "Points have coord_frame entries that are incompatible with "
+                f"coord_frame={coord_frame}: {tuple(bad_frames)}."
+            )
+    _validate_type(ch_names, (None, list, tuple), "ch_names")
+    if ch_names is not None:
+        for ci, ch_name in enumerate(ch_names):
+            _validate_type(ch_name, str, f"ch_names[{ci}]")
+
+    with start_and_end_file(fname) as fid:
+        write_dig_points(
+            fid, pts, block=True, coord_frame=coord_frame, ch_names=ch_names
+        )
+
+
+_cardinal_ident_mapping = {
+    FIFF.FIFFV_POINT_NASION: "nasion",
+    FIFF.FIFFV_POINT_LPA: "lpa",
+    FIFF.FIFFV_POINT_RPA: "rpa",
+}
+
+
+def _ensure_fiducials_head(dig):
+    # Ensure that there are all three fiducials in the head coord frame
+    fids = dict()
+    for d in dig:
+        if d["kind"] == FIFF.FIFFV_POINT_CARDINAL:
+            name = _cardinal_ident_mapping.get(d["ident"], None)
+            if name is not None:
+                fids[name] = d
+    radius = None
+    mults = dict(
+        lpa=[-1, 0, 0],
+        rpa=[1, 0, 0],
+        nasion=[0, 1, 0],
+    )
+    for ident, name in _cardinal_ident_mapping.items():
+        if name not in fids:
+            if radius is None:
+                radius = [
+                    np.linalg.norm(d["r"])
+                    for d in dig
+                    if d["coord_frame"] == FIFF.FIFFV_COORD_HEAD
+                    and not np.isnan(d["r"]).any()
+                ]
+                if not radius:
+                    return  # can't complete, no head points
+                radius = np.mean(radius)
+            dig.append(
+                DigPoint(
+                    kind=FIFF.FIFFV_POINT_CARDINAL,
+                    ident=ident,
+                    r=np.array(mults[name], float) * radius,
+                    coord_frame=FIFF.FIFFV_COORD_HEAD,
+                )
+            )
+
+
+# XXXX:
+# This does something really similar to _read_dig_montage_fif but:
+#   - does not check coord_frame
+#   - does not do any operation that implies assumptions with the names
+def _get_data_as_dict_from_dig(dig, exclude_ref_channel=True):
+    """Obtain coordinate data from a Dig.
+
+    Parameters
+    ----------
+    dig : list of dicts
+        A container of DigPoints to be added to the info['dig'].
+
+    Returns
+    -------
+    ch_pos : dict
+        The container of all relevant channel positions inside dig.
+    """
+    # Split up the dig points by category
+    hsp, hpi, elp = list(), list(), list()
+    fids, dig_ch_pos_location = dict(), list()
+    dig = [] if dig is None else dig
+
+    for d in dig:
+        if d["kind"] == FIFF.FIFFV_POINT_CARDINAL:
+            fids[_cardinal_ident_mapping[d["ident"]]] = d["r"]
+        elif d["kind"] == FIFF.FIFFV_POINT_HPI:
+            hpi.append(d["r"])
+            elp.append(d["r"])
+        elif d["kind"] == FIFF.FIFFV_POINT_EXTRA:
+            hsp.append(d["r"])
+        elif d["kind"] == FIFF.FIFFV_POINT_EEG:
+            if d["ident"] != 0 or not exclude_ref_channel:
+                dig_ch_pos_location.append(d["r"])
+
+    dig_coord_frames = set([d["coord_frame"] for d in dig])
+    if len(dig_coord_frames) == 0:
+        dig_coord_frames = set([FIFF.FIFFV_COORD_HEAD])
+    if len(dig_coord_frames) != 1:
+        raise RuntimeError(
+            "Only single coordinate frame in dig is supported, "
+            f"got {dig_coord_frames}"
+        )
+    dig_ch_pos_location = np.array(dig_ch_pos_location)
+    dig_ch_pos_location.shape = (-1, 3)  # empty will be (0, 3)
+    return Bunch(
+        nasion=fids.get("nasion", None),
+        lpa=fids.get("lpa", None),
+        rpa=fids.get("rpa", None),
+        hsp=np.array(hsp) if len(hsp) else None,
+        hpi=np.array(hpi) if len(hpi) else None,
+        elp=np.array(elp) if len(elp) else None,
+        dig_ch_pos_location=dig_ch_pos_location,
+        coord_frame=dig_coord_frames.pop(),
+    )
+
+
+def _get_fid_coords(dig, raise_error=True):
+    fid_coords = Bunch(nasion=None, lpa=None, rpa=None)
+    fid_coord_frames = dict()
+
+    for d in dig:
+        if d["kind"] == FIFF.FIFFV_POINT_CARDINAL:
+            key = _cardinal_ident_mapping[d["ident"]]
+            fid_coords[key] = d["r"]
+            fid_coord_frames[key] = d["coord_frame"]
+
+    if len(fid_coord_frames) > 0 and raise_error:
+        if set(fid_coord_frames.keys()) != set(["nasion", "lpa", "rpa"]):
+            raise ValueError(
+                f"Some fiducial points are missing (got {fid_coord_frames.keys()})."
+            )
+
+        if len(set(fid_coord_frames.values())) > 1:
+            raise ValueError(
+                "All fiducial points must be in the same coordinate system "
+                f"(got {len(fid_coord_frames)})"
+            )
+
+    coord_frame = fid_coord_frames.popitem()[1] if fid_coord_frames else None
+
+    return fid_coords, coord_frame
+
+
+def _coord_frame_const(coord_frame):
+    from ..transforms import _str_to_frame
+
+    if not isinstance(coord_frame, str) or coord_frame not in _str_to_frame:
+        raise ValueError(
+            f"coord_frame must be one of {sorted(_str_to_frame.keys())}, got "
+            f"{coord_frame}"
+        )
+    return _str_to_frame[coord_frame]
+
+
+def _make_dig_points(
+    nasion=None,
+    lpa=None,
+    rpa=None,
+    hpi=None,
+    extra_points=None,
+    dig_ch_pos=None,
+    *,
+    coord_frame="head",
+    add_missing_fiducials=False,
+):
+    """Construct digitizer info for the info.
+
+    Parameters
+    ----------
+    nasion : array-like | numpy.ndarray, shape (3,) | None
+        Point designated as the nasion point.
+    lpa : array-like |  numpy.ndarray, shape (3,) | None
+        Point designated as the left auricular point.
+    rpa : array-like |  numpy.ndarray, shape (3,) | None
+        Point designated as the right auricular point.
+    hpi : array-like | numpy.ndarray, shape (n_points, 3) | None
+        Points designated as head position indicator points.
+    extra_points : array-like | numpy.ndarray, shape (n_points, 3)
+        Points designed as the headshape points.
+    dig_ch_pos : dict
+        Dict of EEG channel positions.
+    coord_frame : str
+        The coordinate frame of the points. Usually this is "unknown"
+        for native digitizer space. Defaults to "head".
+    add_missing_fiducials : bool
+        If True, add fiducials to the dig points if they are not present.
+        Requires that coord_frame='head' and that lpa, nasion, and rpa are all
+        None.
+
+    Returns
+    -------
+    dig : list of dicts
+        A container of DigPoints to be added to the info['dig'].
+    """
+    coord_frame = _coord_frame_const(coord_frame)
+
+    dig = []
+    if lpa is not None:
+        lpa = np.asarray(lpa)
+        if lpa.shape != (3,):
+            raise ValueError(f"LPA should have the shape (3,) instead of {lpa.shape}")
+        dig.append(
+            {
+                "r": lpa,
+                "ident": FIFF.FIFFV_POINT_LPA,
+                "kind": FIFF.FIFFV_POINT_CARDINAL,
+                "coord_frame": coord_frame,
+            }
+        )
+    if nasion is not None:
+        nasion = np.asarray(nasion)
+        if nasion.shape != (3,):
+            raise ValueError(
+                f"Nasion should have the shape (3,) instead of {nasion.shape}"
+            )
+        dig.append(
+            {
+                "r": nasion,
+                "ident": FIFF.FIFFV_POINT_NASION,
+                "kind": FIFF.FIFFV_POINT_CARDINAL,
+                "coord_frame": coord_frame,
+            }
+        )
+    if rpa is not None:
+        rpa = np.asarray(rpa)
+        if rpa.shape != (3,):
+            raise ValueError(f"RPA should have the shape (3,) instead of {rpa.shape}")
+        dig.append(
+            {
+                "r": rpa,
+                "ident": FIFF.FIFFV_POINT_RPA,
+                "kind": FIFF.FIFFV_POINT_CARDINAL,
+                "coord_frame": coord_frame,
+            }
+        )
+    if hpi is not None:
+        hpi = np.asarray(hpi)
+        if hpi.ndim != 2 or hpi.shape[1] != 3:
+            raise ValueError(
+                f"HPI should have the shape (n_points, 3) instead of {hpi.shape}"
+            )
+        for idx, point in enumerate(hpi):
+            dig.append(
+                {
+                    "r": point,
+                    "ident": idx + 1,
+                    "kind": FIFF.FIFFV_POINT_HPI,
+                    "coord_frame": coord_frame,
+                }
+            )
+    if extra_points is not None:
+        extra_points = np.asarray(extra_points)
+        if len(extra_points) and extra_points.shape[1] != 3:
+            raise ValueError(
+                "Points should have the shape (n_points, 3) instead of "
+                f"{extra_points.shape}"
+            )
+        for idx, point in enumerate(extra_points):
+            dig.append(
+                {
+                    "r": point,
+                    "ident": idx + 1,
+                    "kind": FIFF.FIFFV_POINT_EXTRA,
+                    "coord_frame": coord_frame,
+                }
+            )
+    if dig_ch_pos is not None:
+        idents = []
+        use_arange = False
+        for key, value in dig_ch_pos.items():
+            _validate_type(key, str, "dig_ch_pos")
+            try:
+                idents.append(int(key[-3:]))
+            except ValueError:
+                use_arange = True
+            _validate_type(value, (np.ndarray, list, tuple), "dig_ch_pos")
+            value = np.array(value, dtype=float)
+            dig_ch_pos[key] = value
+            if value.shape != (3,):
+                raise RuntimeError(
+                    "The position should be a 1D array of 3 floats. "
+                    f"Provided shape {value.shape}."
+                )
+        if use_arange:
+            idents = np.arange(1, len(dig_ch_pos) + 1)
+        for key, ident in zip(dig_ch_pos, idents):
+            dig.append(
+                {
+                    "r": dig_ch_pos[key],
+                    "ident": int(ident),
+                    "kind": FIFF.FIFFV_POINT_EEG,
+                    "coord_frame": coord_frame,
+                }
+            )
+    if add_missing_fiducials:
+        assert coord_frame == FIFF.FIFFV_COORD_HEAD
+        # These being none is really an assumption that if you have one you
+        # should have all three. But we can relax this later if necessary.
+        assert lpa is None
+        assert rpa is None
+        assert nasion is None
+        _ensure_fiducials_head(dig)
+
+    return _format_dig_points(dig)
+
+
+def _call_make_dig_points(nasion, lpa, rpa, hpi, extra, convert=True):
+    from ..transforms import (
+        Transform,
+        apply_trans,
+        get_ras_to_neuromag_trans,
+    )
+
+    if convert:
+        neuromag_trans = get_ras_to_neuromag_trans(nasion, lpa, rpa)
+        nasion = apply_trans(neuromag_trans, nasion)
+        lpa = apply_trans(neuromag_trans, lpa)
+        rpa = apply_trans(neuromag_trans, rpa)
+
+        if hpi is not None:
+            hpi = apply_trans(neuromag_trans, hpi)
+
+        extra = apply_trans(neuromag_trans, extra).astype(np.float32)
+    else:
+        neuromag_trans = None
+
+    ctf_head_t = Transform(fro="ctf_head", to="head", trans=neuromag_trans)
+
+    info_dig = _make_dig_points(
+        nasion=nasion, lpa=lpa, rpa=rpa, hpi=hpi, extra_points=extra
+    )
+
+    return info_dig, ctf_head_t
+
+
+##############################################################################
+# From artemis123 (we have modified the function a bit)
+def _artemis123_read_pos(nas, lpa, rpa, hpi, extra):
+    # move into MNE head coords
+    dig_points, _ = _call_make_dig_points(nas, lpa, rpa, hpi, extra)
+    return dig_points
+
+
+##############################################################################
+# From bti
+def _make_bti_dig_points(
+    nasion,
+    lpa,
+    rpa,
+    hpi,
+    extra,
+    convert=False,
+    use_hpi=False,
+    bti_dev_t=False,
+    dev_ctf_t=False,
+):
+    from ..transforms import (
+        Transform,
+        combine_transforms,
+        invert_transform,
+    )
+
+    _hpi = hpi if use_hpi else None
+    info_dig, ctf_head_t = _call_make_dig_points(nasion, lpa, rpa, _hpi, extra, convert)
+
+    if convert:
+        t = combine_transforms(
+            invert_transform(bti_dev_t), dev_ctf_t, "meg", "ctf_head"
+        )
+        dev_head_t = combine_transforms(t, ctf_head_t, "meg", "head")
+    else:
+        dev_head_t = Transform("meg", "head", trans=None)
+
+    return info_dig, dev_head_t, ctf_head_t  # ctf_head_t should not be needed

mne/_fiff/compensator.py

@@ -0,0 +1,168 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from ..utils import fill_doc
+from .constants import FIFF
+
+
+def get_current_comp(info):
+    """Get the current compensation in effect in the data."""
+    comp = None
+    first_comp = -1
+    for k, chan in enumerate(info["chs"]):
+        if chan["kind"] == FIFF.FIFFV_MEG_CH:
+            comp = int(chan["coil_type"]) >> 16
+            if first_comp < 0:
+                first_comp = comp
+            elif comp != first_comp:
+                raise ValueError("Compensation is not set equally on all MEG channels")
+    return comp
+
+
+def set_current_comp(info, comp):
+    """Set the current compensation in effect in the data."""
+    comp_now = get_current_comp(info)
+    for k, chan in enumerate(info["chs"]):
+        if chan["kind"] == FIFF.FIFFV_MEG_CH:
+            rem = chan["coil_type"] - (comp_now << 16)
+            chan["coil_type"] = int(rem + (comp << 16))
+
+
+def _make_compensator(info, grade):
+    """Auxiliary function for make_compensator."""
+    for k in range(len(info["comps"])):
+        if info["comps"][k]["kind"] == grade:
+            this_data = info["comps"][k]["data"]
+
+            #   Create the preselector
+            presel = np.zeros((this_data["ncol"], info["nchan"]))
+            for col, col_name in enumerate(this_data["col_names"]):
+                ind = [k for k, ch in enumerate(info["ch_names"]) if ch == col_name]
+                if len(ind) == 0:
+                    raise ValueError(f"Channel {col_name} is not available in data")
+                elif len(ind) > 1:
+                    raise ValueError(f"Ambiguous channel {col_name}")
+                presel[col, ind[0]] = 1.0
+
+            #   Create the postselector (zero entries for channels not found)
+            postsel = np.zeros((info["nchan"], this_data["nrow"]))
+            for c, ch_name in enumerate(info["ch_names"]):
+                ind = [
+                    k for k, ch in enumerate(this_data["row_names"]) if ch == ch_name
+                ]
+                if len(ind) > 1:
+                    raise ValueError(f"Ambiguous channel {ch_name}")
+                elif len(ind) == 1:
+                    postsel[c, ind[0]] = 1.0
+                # else, don't use it at all (postsel[c, ?] = 0.0) by allocation
+            this_comp = np.dot(postsel, np.dot(this_data["data"], presel))
+            return this_comp
+
+    raise ValueError(f"Desired compensation matrix (grade = {grade:d}) not found")
+
+
+@fill_doc
+def make_compensator(info, from_, to, exclude_comp_chs=False):
+    """Return compensation matrix eg. for CTF system.
+
+    Create a compensation matrix to bring the data from one compensation
+    state to another.
+
+    Parameters
+    ----------
+    %(info_not_none)s
+    from_ : int
+        Compensation in the input data.
+    to : int
+        Desired compensation in the output.
+    exclude_comp_chs : bool
+        Exclude compensation channels from the output.
+
+    Returns
+    -------
+    comp : array | None.
+        The compensation matrix. Might be None if no compensation
+        is needed (from == to).
+    """
+    if from_ == to:
+        return None
+
+    #   s_orig = s_from + C1*s_from = (I + C1)*s_from
+    #   s_to   = s_orig - C2*s_orig = (I - C2)*s_orig
+    #   s_to   = (I - C2)*(I + C1)*s_from = (I + C1 - C2 - C2*C1)*s_from
+    if from_ != 0:
+        C1 = _make_compensator(info, from_)
+        comp_from_0 = np.linalg.inv(np.eye(info["nchan"]) - C1)
+    if to != 0:
+        C2 = _make_compensator(info, to)
+        comp_0_to = np.eye(info["nchan"]) - C2
+    if from_ != 0:
+        if to != 0:
+            # This is mathematically equivalent, but has higher numerical
+            # error than using the inverse to always go to zero and back
+            # comp = np.eye(info['nchan']) + C1 - C2 - np.dot(C2, C1)
+            comp = np.dot(comp_0_to, comp_from_0)
+        else:
+            comp = comp_from_0
+    else:
+        # from == 0, to != 0 guaranteed here
+        comp = comp_0_to
+
+    if exclude_comp_chs:
+        pick = [
+            k for k, c in enumerate(info["chs"]) if c["kind"] != FIFF.FIFFV_REF_MEG_CH
+        ]
+
+        if len(pick) == 0:
+            raise ValueError(
+                "Nothing remains after excluding the compensation channels"
+            )
+
+        comp = comp[pick, :]
+
+    return comp
+
+
+# @verbose
+# def compensate_to(data, to, verbose=None):
+#     """
+#     %
+#     % [newdata] = mne_compensate_to(data,to)
+#     %
+#     % Apply compensation to the data as desired
+#     %
+#     """
+#
+#     newdata = data.copy()
+#     now = get_current_comp(newdata['info'])
+#
+#     #   Are we there already?
+#     if now == to:
+#         logger.info('Data are already compensated as desired')
+#
+#     #   Make the compensator and apply it to all data sets
+#     comp = make_compensator(newdata['info'], now, to)
+#     for k in range(len(newdata['evoked'])):
+#         newdata['evoked'][k]['epochs'] = np.dot(comp,
+#                                               newdata['evoked'][k]['epochs'])
+#
+#     #  Update the compensation info in the channel descriptors
+#     newdata['info']['chs'] = set_current_comp(newdata['info']['chs'], to)
+#     return newdata
+
+
+# def set_current_comp(chs, value):
+#     """Set the current compensation value in the channel info structures
+#     """
+#     new_chs = chs
+#
+#     lower_half = int('FFFF', 16) # hex2dec('FFFF')
+#     for k in range(len(chs)):
+#         if chs[k]['kind'] == FIFF.FIFFV_MEG_CH:
+#             coil_type = float(chs[k]['coil_type']) & lower_half
+#             new_chs[k]['coil_type'] = int(coil_type | (value << 16))
+#
+#     return new_chs

mne/_fiff/ctf_comp.py

@@ -0,0 +1,189 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from copy import deepcopy
+
+import numpy as np
+
+from ..utils import _pl, logger, verbose
+from .constants import FIFF
+from .matrix import _read_named_matrix, write_named_matrix
+from .tag import read_tag
+from .tree import dir_tree_find
+from .write import end_block, start_block, write_int
+
+
+def _add_kind(one):
+    """Convert CTF kind to MNE kind."""
+    if one["ctfkind"] == int("47314252", 16):
+        one["kind"] = 1
+    elif one["ctfkind"] == int("47324252", 16):
+        one["kind"] = 2
+    elif one["ctfkind"] == int("47334252", 16):
+        one["kind"] = 3
+    else:
+        one["kind"] = int(one["ctfkind"])
+
+
+def _calibrate_comp(
+    comp, chs, row_names, col_names, mult_keys=("range", "cal"), flip=False
+):
+    """Get row and column cals."""
+    ch_names = [c["ch_name"] for c in chs]
+    row_cals = np.zeros(len(row_names))
+    col_cals = np.zeros(len(col_names))
+    for names, cals, inv in zip(
+        (row_names, col_names), (row_cals, col_cals), (False, True)
+    ):
+        for ii in range(len(cals)):
+            p = ch_names.count(names[ii])
+            if p != 1:
+                raise RuntimeError(
+                    f"Channel {names[ii]} does not appear exactly once "
+                    f"in data, found {p:d} instance{_pl(p)}"
+                )
+            idx = ch_names.index(names[ii])
+            val = chs[idx][mult_keys[0]] * chs[idx][mult_keys[1]]
+            val = float(1.0 / val) if inv else float(val)
+            val = 1.0 / val if flip else val
+            cals[ii] = val
+    comp["rowcals"] = row_cals
+    comp["colcals"] = col_cals
+    comp["data"]["data"] = row_cals[:, None] * comp["data"]["data"] * col_cals[None, :]
+
+
+@verbose
+def read_ctf_comp(fid, node, chs, verbose=None):
+    """Read the CTF software compensation data from the given node.
+
+    Parameters
+    ----------
+    fid : file
+        The file descriptor.
+    node : dict
+        The node in the FIF tree.
+    chs : list
+        The list of channels from info['chs'] to match with
+        compensators that are read.
+    %(verbose)s
+
+    Returns
+    -------
+    compdata : list
+        The compensation data
+    """
+    return _read_ctf_comp(fid, node, chs, None)
+
+
+def _read_ctf_comp(fid, node, chs, ch_names_mapping):
+    """Read the CTF software compensation data from the given node.
+
+    Parameters
+    ----------
+    fid : file
+        The file descriptor.
+    node : dict
+        The node in the FIF tree.
+    chs : list
+        The list of channels from info['chs'] to match with
+        compensators that are read.
+    ch_names_mapping : dict | None
+        The channel renaming to use.
+    %(verbose)s
+
+    Returns
+    -------
+    compdata : list
+        The compensation data
+    """
+    from .meas_info import _rename_comps
+
+    ch_names_mapping = dict() if ch_names_mapping is None else ch_names_mapping
+    compdata = []
+    comps = dir_tree_find(node, FIFF.FIFFB_MNE_CTF_COMP_DATA)
+
+    for node in comps:
+        #   Read the data we need
+        mat = _read_named_matrix(fid, node, FIFF.FIFF_MNE_CTF_COMP_DATA)
+        for p in range(node["nent"]):
+            kind = node["directory"][p].kind
+            pos = node["directory"][p].pos
+            if kind == FIFF.FIFF_MNE_CTF_COMP_KIND:
+                tag = read_tag(fid, pos)
+                break
+        else:
+            raise Exception("Compensation type not found")
+
+        #   Get the compensation kind and map it to a simple number
+        one = dict(ctfkind=tag.data.item())
+        del tag
+        _add_kind(one)
+        for p in range(node["nent"]):
+            kind = node["directory"][p].kind
+            pos = node["directory"][p].pos
+            if kind == FIFF.FIFF_MNE_CTF_COMP_CALIBRATED:
+                tag = read_tag(fid, pos)
+                calibrated = tag.data
+                break
+        else:
+            calibrated = False
+
+        one["save_calibrated"] = bool(calibrated)
+        one["data"] = mat
+        _rename_comps([one], ch_names_mapping)
+        if not calibrated:
+            #   Calibrate...
+            _calibrate_comp(one, chs, mat["row_names"], mat["col_names"])
+        else:
+            one["rowcals"] = np.ones(mat["data"].shape[0], dtype=np.float64)
+            one["colcals"] = np.ones(mat["data"].shape[1], dtype=np.float64)
+
+        compdata.append(one)
+
+    if len(compdata) > 0:
+        logger.info(f"    Read {len(compdata)} compensation matrices")
+
+    return compdata
+
+
+###############################################################################
+# Writing
+
+
+def write_ctf_comp(fid, comps):
+    """Write the CTF compensation data into a fif file.
+
+    Parameters
+    ----------
+    fid : file
+        The open FIF file descriptor
+
+    comps : list
+        The compensation data to write
+    """
+    if len(comps) <= 0:
+        return
+
+    #  This is very simple in fact
+    start_block(fid, FIFF.FIFFB_MNE_CTF_COMP)
+    for comp in comps:
+        start_block(fid, FIFF.FIFFB_MNE_CTF_COMP_DATA)
+        #    Write the compensation kind
+        write_int(fid, FIFF.FIFF_MNE_CTF_COMP_KIND, comp["ctfkind"])
+        if comp.get("save_calibrated", False):
+            write_int(fid, FIFF.FIFF_MNE_CTF_COMP_CALIBRATED, comp["save_calibrated"])
+
+        if not comp.get("save_calibrated", True):
+            # Undo calibration
+            comp = deepcopy(comp)
+            data = (
+                (1.0 / comp["rowcals"][:, None])
+                * comp["data"]["data"]
+                * (1.0 / comp["colcals"][None, :])
+            )
+            comp["data"]["data"] = data
+        write_named_matrix(fid, FIFF.FIFF_MNE_CTF_COMP_DATA, comp["data"])
+        end_block(fid, FIFF.FIFFB_MNE_CTF_COMP_DATA)
+
+    end_block(fid, FIFF.FIFFB_MNE_CTF_COMP)

mne/_fiff/matrix.py

@@ -0,0 +1,137 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from ..utils import logger
+from .constants import FIFF
+from .tag import find_tag, has_tag
+from .write import (
+    end_block,
+    start_block,
+    write_float_matrix,
+    write_int,
+    write_name_list,
+)
+
+
+def _transpose_named_matrix(mat):
+    """Transpose mat inplace (no copy)."""
+    mat["nrow"], mat["ncol"] = mat["ncol"], mat["nrow"]
+    mat["row_names"], mat["col_names"] = mat["col_names"], mat["row_names"]
+    mat["data"] = mat["data"].T
+
+
+def _read_named_matrix(fid, node, matkind, indent="    ", transpose=False):
+    """Read named matrix from the given node.
+
+    Parameters
+    ----------
+    fid : file
+        The opened file descriptor.
+    node : dict
+        The node in the tree.
+    matkind : int
+        The type of matrix.
+    transpose : bool
+        If True, transpose the matrix. Default is False.
+    %(verbose)s
+
+    Returns
+    -------
+    mat: dict
+        The matrix data
+    """
+    #   Descend one level if necessary
+    if node["block"] != FIFF.FIFFB_MNE_NAMED_MATRIX:
+        for k in range(node["nchild"]):
+            if node["children"][k]["block"] == FIFF.FIFFB_MNE_NAMED_MATRIX:
+                if has_tag(node["children"][k], matkind):
+                    node = node["children"][k]
+                    break
+        else:
+            logger.info(
+                f"{indent}Desired named matrix (kind = {matkind}) not available"
+            )
+            return None
+    else:
+        if not has_tag(node, matkind):
+            logger.info(
+                f"{indent}Desired named matrix (kind = {matkind}) not available"
+            )
+            return None
+
+    #   Read everything we need
+    tag = find_tag(fid, node, matkind)
+    if tag is None:
+        raise ValueError("Matrix data missing")
+    else:
+        data = tag.data
+
+    nrow, ncol = data.shape
+    tag = find_tag(fid, node, FIFF.FIFF_MNE_NROW)
+    if tag is not None and tag.data != nrow:
+        raise ValueError(
+            "Number of rows in matrix data and FIFF_MNE_NROW tag do not match"
+        )
+
+    tag = find_tag(fid, node, FIFF.FIFF_MNE_NCOL)
+    if tag is not None and tag.data != ncol:
+        raise ValueError(
+            "Number of columns in matrix data and FIFF_MNE_NCOL tag do not match"
+        )
+
+    tag = find_tag(fid, node, FIFF.FIFF_MNE_ROW_NAMES)
+    row_names = tag.data.split(":") if tag is not None else []
+
+    tag = find_tag(fid, node, FIFF.FIFF_MNE_COL_NAMES)
+    col_names = tag.data.split(":") if tag is not None else []
+
+    mat = dict(
+        nrow=nrow, ncol=ncol, row_names=row_names, col_names=col_names, data=data
+    )
+    if transpose:
+        _transpose_named_matrix(mat)
+    return mat
+
+
+def write_named_matrix(fid, kind, mat):
+    """Write named matrix from the given node.
+
+    Parameters
+    ----------
+    fid : file
+        The opened file descriptor.
+    kind : int
+        The kind of the matrix.
+    matkind : int
+        The type of matrix.
+    """
+    # let's save ourselves from disaster
+    n_tot = mat["nrow"] * mat["ncol"]
+    if mat["data"].size != n_tot:
+        ratio = n_tot / float(mat["data"].size)
+        if n_tot < mat["data"].size and ratio > 0:
+            ratio = 1 / ratio
+        raise ValueError(
+            f"Cannot write matrix: row ({mat['nrow']}) and column ({mat['ncol']}) "
+            f"total element ({n_tot}) mismatch with data size ({mat['data'].size}), "
+            f"appears to be off by a factor of {ratio:g}x"
+        )
+    start_block(fid, FIFF.FIFFB_MNE_NAMED_MATRIX)
+    write_int(fid, FIFF.FIFF_MNE_NROW, mat["nrow"])
+    write_int(fid, FIFF.FIFF_MNE_NCOL, mat["ncol"])
+
+    if len(mat["row_names"]) > 0:
+        # let's prevent unintentional stupidity
+        if len(mat["row_names"]) != mat["nrow"]:
+            raise ValueError('len(mat["row_names"]) != mat["nrow"]')
+        write_name_list(fid, FIFF.FIFF_MNE_ROW_NAMES, mat["row_names"])
+
+    if len(mat["col_names"]) > 0:
+        # let's prevent unintentional stupidity
+        if len(mat["col_names"]) != mat["ncol"]:
+            raise ValueError('len(mat["col_names"]) != mat["ncol"]')
+        write_name_list(fid, FIFF.FIFF_MNE_COL_NAMES, mat["col_names"])
+
+    write_float_matrix(fid, kind, mat["data"])
+    end_block(fid, FIFF.FIFFB_MNE_NAMED_MATRIX)

mne/_fiff/open.py

@@ -0,0 +1,386 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from gzip import GzipFile
+from io import SEEK_SET, BytesIO
+from pathlib import Path
+
+import numpy as np
+from scipy.sparse import issparse
+
+from ..utils import _check_fname, _file_like, _validate_type, logger, verbose, warn
+from .constants import FIFF
+from .tag import Tag, _call_dict_names, _matrix_info, _read_tag_header, read_tag
+from .tree import dir_tree_find, make_dir_tree
+
+
+class _NoCloseRead:
+    """Create a wrapper that will not close when used as a context manager."""
+
+    def __init__(self, fid):
+        self.fid = fid
+
+    def __enter__(self):
+        return self.fid
+
+    def __exit__(self, type_, value, traceback):
+        return
+
+    def close(self):
+        return
+
+    def seek(self, offset, whence=SEEK_SET):
+        return self.fid.seek(offset, whence)
+
+    def read(self, size=-1):
+        return self.fid.read(size)
+
+
+def _fiff_get_fid(fname):
+    """Open a FIF file with no additional parsing."""
+    if _file_like(fname):
+        logger.debug("Using file-like I/O")
+        fid = _NoCloseRead(fname)
+        fid.seek(0)
+    else:
+        _validate_type(fname, Path, "fname", extra="or file-like")
+        if fname.suffixes[-1] == ".gz":
+            logger.debug("Using gzip I/O")
+            fid = GzipFile(fname, "rb")  # Open in binary mode
+        else:
+            logger.debug("Using normal I/O")
+            fid = open(fname, "rb")  # Open in binary mode
+    return fid
+
+
+def _get_next_fname(fid, fname, tree):
+    """Get the next filename in split files."""
+    _validate_type(fname, (Path, None), "fname")
+    nodes_list = dir_tree_find(tree, FIFF.FIFFB_REF)
+    next_fname = None
+    for nodes in nodes_list:
+        next_fname = None
+        for ent in nodes["directory"]:
+            if ent.kind == FIFF.FIFF_REF_ROLE:
+                tag = read_tag(fid, ent.pos)
+                role = int(tag.data.item())
+                if role != FIFF.FIFFV_ROLE_NEXT_FILE:
+                    next_fname = None
+                    break
+            if ent.kind not in (FIFF.FIFF_REF_FILE_NAME, FIFF.FIFF_REF_FILE_NUM):
+                continue
+            # If we can't resolve it, assume/hope it's in the current directory
+            if fname is None:
+                fname = Path().resolve()
+            if ent.kind == FIFF.FIFF_REF_FILE_NAME:
+                tag = read_tag(fid, ent.pos)
+                next_fname = fname.parent / tag.data
+            if ent.kind == FIFF.FIFF_REF_FILE_NUM:
+                # Some files don't have the name, just the number. So
+                # we construct the name from the current name.
+                if next_fname is not None:
+                    continue
+                next_num = read_tag(fid, ent.pos).data.item()
+                base = fname.name
+                idx = base.find(".")
+                idx2 = base.rfind("-")
+                num_str = base[idx2 + 1 : idx]
+                if not num_str.isdigit():
+                    idx2 = -1
+
+                if idx2 < 0 and next_num == 1:
+                    # this is the first file, which may not be numbered
+                    next_fname = (
+                        fname.parent / f"{base[:idx]}-{next_num:d}.{base[idx + 1 :]}"
+                    )
+                    continue
+
+                next_fname = (
+                    fname.parent / f"{base[:idx2]}-{next_num:d}.{base[idx + 1 :]}"
+                )
+        if next_fname is not None:
+            break
+    return next_fname
+
+
+@verbose
+def fiff_open(fname, preload=False, verbose=None):
+    """Open a FIF file.
+
+    Parameters
+    ----------
+    fname : path-like | fid
+        Name of the fif file, or an opened file (will seek back to 0).
+    preload : bool
+        If True, all data from the file is read into a memory buffer. This
+        requires more memory, but can be faster for I/O operations that require
+        frequent seeks.
+    %(verbose)s
+
+    Returns
+    -------
+    fid : file
+        The file descriptor of the open file.
+    tree : fif tree
+        The tree is a complex structure filled with dictionaries,
+        lists and tags.
+    directory : list
+        A list of tags.
+    """
+    fid = _fiff_get_fid(fname)
+    try:
+        return _fiff_open(fname, fid, preload)
+    except Exception:
+        fid.close()
+        raise
+
+
+def _fiff_open(fname, fid, preload):
+    # do preloading of entire file
+    if preload:
+        # note that StringIO objects instantiated this way are read-only,
+        # but that's okay here since we are using mode "rb" anyway
+        with fid as fid_old:
+            fid = BytesIO(fid_old.read())
+
+    tag = _read_tag_header(fid, 0)
+
+    #   Check that this looks like a fif file
+    prefix = f"file {repr(fname)} does not"
+    if tag.kind != FIFF.FIFF_FILE_ID:
+        raise ValueError(f"{prefix} start with a file id tag")
+
+    if tag.type != FIFF.FIFFT_ID_STRUCT:
+        raise ValueError(f"{prefix} start with a file id tag")
+
+    if tag.size != 20:
+        raise ValueError(f"{prefix} start with a file id tag")
+
+    tag = read_tag(fid, tag.next_pos)
+
+    if tag.kind != FIFF.FIFF_DIR_POINTER:
+        raise ValueError(f"{prefix} have a directory pointer")
+
+    #   Read or create the directory tree
+    logger.debug(f"    Creating tag directory for {fname}...")
+
+    dirpos = int(tag.data.item())
+    read_slow = True
+    if dirpos > 0:
+        dir_tag = read_tag(fid, dirpos)
+        if dir_tag is None or dir_tag.data is None:
+            fid.seek(0, 2)  # move to end of file
+            size = fid.tell()
+            extra = "" if size > dirpos else f" > file size {size}"
+            warn(
+                "FIF tag directory missing at the end of the file "
+                f"(at byte {dirpos}{extra}), possibly corrupted file: {fname}"
+            )
+        else:
+            directory = dir_tag.data
+            read_slow = False
+    if read_slow:
+        pos = 0
+        fid.seek(pos, 0)
+        directory = list()
+        while pos is not None:
+            tag = _read_tag_header(fid, pos)
+            if tag is None:
+                break  # HACK : to fix file ending with empty tag...
+            pos = tag.next_pos
+            directory.append(tag)
+
+    tree, _ = make_dir_tree(fid, directory, indent=1)
+
+    logger.debug("[done]")
+
+    #   Back to the beginning
+    fid.seek(0)
+
+    return fid, tree, directory
+
+
+@verbose
+def show_fiff(
+    fname,
+    indent="    ",
+    read_limit=np.inf,
+    max_str=30,
+    output=str,
+    tag=None,
+    *,
+    show_bytes=False,
+    verbose=None,
+):
+    """Show FIFF information.
+
+    This function is similar to mne_show_fiff.
+
+    Parameters
+    ----------
+    fname : path-like
+        Filename to evaluate.
+    indent : str
+        How to indent the lines.
+    read_limit : int
+        Max number of bytes of data to read from a tag. Can be np.inf
+        to always read all data (helps test read completion).
+    max_str : int
+        Max number of characters of string representation to print for
+        each tag's data.
+    output : type
+        Either str or list. str is a convenience output for printing.
+    tag : int | None
+        Provide information about this tag. If None (default), all information
+        is shown.
+    show_bytes : bool
+        If True (default False), print the byte offsets of each tag.
+    %(verbose)s
+
+    Returns
+    -------
+    contents : str
+        The contents of the file.
+    """
+    if output not in [list, str]:
+        raise ValueError("output must be list or str")
+    if isinstance(tag, str):  # command mne show_fiff passes string
+        tag = int(tag)
+    fname = _check_fname(fname, "read", True)
+    f, tree, _ = fiff_open(fname)
+    # This gets set to 0 (unknown) by fiff_open, but FIFFB_ROOT probably
+    # makes more sense for display
+    tree["block"] = FIFF.FIFFB_ROOT
+    with f as fid:
+        out = _show_tree(
+            fid,
+            tree,
+            indent=indent,
+            level=0,
+            read_limit=read_limit,
+            max_str=max_str,
+            tag_id=tag,
+            show_bytes=show_bytes,
+        )
+    if output is str:
+        out = "\n".join(out)
+    return out
+
+
+def _find_type(value, fmts=("FIFF_",), exclude=("FIFF_UNIT",)):
+    """Find matching values."""
+    value = int(value)
+    vals = [
+        k
+        for k, v in FIFF.items()
+        if v == value
+        and any(fmt in k for fmt in fmts)
+        and not any(exc in k for exc in exclude)
+    ]
+    if len(vals) == 0:
+        vals = ["???"]
+    return vals
+
+
+def _show_tree(
+    fid,
+    tree,
+    indent,
+    level,
+    read_limit,
+    max_str,
+    tag_id,
+    *,
+    show_bytes=False,
+):
+    """Show FIFF tree."""
+    this_idt = indent * level
+    next_idt = indent * (level + 1)
+    # print block-level information
+    found_types = "/".join(_find_type(tree["block"], fmts=["FIFFB_"]))
+    out = [f"{this_idt}{str(int(tree['block'])).ljust(4)} = {found_types}"]
+    tag_found = False
+    if tag_id is None or out[0].strip().startswith(str(tag_id)):
+        tag_found = True
+
+    if tree["directory"] is not None:
+        kinds = [ent.kind for ent in tree["directory"]] + [-1]
+        types = [ent.type for ent in tree["directory"]]
+        sizes = [ent.size for ent in tree["directory"]]
+        poss = [ent.pos for ent in tree["directory"]]
+        counter = 0
+        good = True
+        for k, kn, size, pos, type_ in zip(kinds[:-1], kinds[1:], sizes, poss, types):
+            if not tag_found and k != tag_id:
+                continue
+            tag = Tag(kind=k, type=type_, size=size, next=FIFF.FIFFV_NEXT_NONE, pos=pos)
+            if read_limit is None or size <= read_limit:
+                try:
+                    tag = read_tag(fid, pos)
+                except Exception:
+                    good = False
+
+            if kn == k:
+                # don't print if the next item is the same type (count 'em)
+                counter += 1
+            else:
+                if show_bytes:
+                    at = f" @{pos}"
+                else:
+                    at = ""
+                # find the tag type
+                this_type = _find_type(k, fmts=["FIFF_"])
+                # prepend a count if necessary
+                prepend = "x" + str(counter + 1) + ": " if counter > 0 else ""
+                postpend = ""
+                # print tag data nicely
+                if tag.data is not None:
+                    postpend = " = " + str(tag.data)[:max_str]
+                    if isinstance(tag.data, np.ndarray):
+                        if tag.data.size > 1:
+                            postpend += " ... array size=" + str(tag.data.size)
+                    elif isinstance(tag.data, dict):
+                        postpend += " ... dict len=" + str(len(tag.data))
+                    elif isinstance(tag.data, str):
+                        postpend += " ... str len=" + str(len(tag.data))
+                    elif isinstance(tag.data, list | tuple):
+                        postpend += " ... list len=" + str(len(tag.data))
+                    elif issparse(tag.data):
+                        postpend += (
+                            f" ... sparse ({tag.data.getformat()}) shape="
+                            f"{tag.data.shape}"
+                        )
+                    else:
+                        postpend += " ... type=" + str(type(tag.data))
+                postpend = ">" * 20 + f"BAD @{pos}" if not good else postpend
+                matrix_info = _matrix_info(tag)
+                if matrix_info is not None:
+                    _, type_, _, _ = matrix_info
+                type_ = _call_dict_names.get(type_, f"?{type_}?")
+                this_type = "/".join(this_type)
+                out += [
+                    f"{next_idt}{prepend}{str(k).ljust(4)} = "
+                    f"{this_type}{at} ({size}b {type_}) {postpend}"
+                ]
+                out[-1] = out[-1].replace("\n", "¶")
+                counter = 0
+                good = True
+        if tag_id in kinds:
+            tag_found = True
+    if not tag_found:
+        out = [""]
+        level = -1  # removes extra indent
+    # deal with children
+    for branch in tree["children"]:
+        out += _show_tree(
+            fid,
+            branch,
+            indent,
+            level + 1,
+            read_limit,
+            max_str,
+            tag_id,
+            show_bytes=show_bytes,
+        )
+    return out

mne/_fiff/proc_history.py

@@ -0,0 +1,345 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from ..fixes import _csc_array_cast
+from ..utils import _check_fname, warn
+from .constants import FIFF
+from .open import fiff_open, read_tag
+from .tag import _float_item, _int_item, find_tag
+from .tree import dir_tree_find
+from .write import (
+    _safe_name_list,
+    end_block,
+    start_block,
+    write_float,
+    write_float_matrix,
+    write_float_sparse,
+    write_id,
+    write_int,
+    write_int_matrix,
+    write_name_list_sanitized,
+    write_string,
+)
+
+_proc_map = dict(  # ID, caster, writer
+    parent_file_id=(
+        FIFF.FIFF_PARENT_FILE_ID,
+        dict,
+        write_id,
+    ),
+    block_id=(
+        FIFF.FIFF_BLOCK_ID,
+        dict,
+        write_id,
+    ),
+    parent_block_id=(
+        FIFF.FIFF_PARENT_BLOCK_ID,
+        dict,
+        write_id,
+    ),
+    date=(
+        FIFF.FIFF_MEAS_DATE,
+        lambda d: tuple(int(dd) for dd in d),
+        write_int,
+    ),
+    experimenter=(
+        FIFF.FIFF_EXPERIMENTER,
+        str,
+        write_string,
+    ),
+    creator=(
+        FIFF.FIFF_CREATOR,
+        str,
+        write_string,
+    ),
+)
+
+
+def _read_proc_history(fid, tree):
+    """Read processing history from fiff file.
+
+    This function reads the SSS info, the CTC correction and the
+    calibaraions from the SSS processing logs inside af a raw file
+    (C.f. Maxfilter v2.2 manual (October 2010), page 21)::
+
+        104 = {                 900 = proc. history
+          104 = {               901 = proc. record
+            103 = block ID
+            204 = date
+            212 = scientist
+            113 = creator program
+            104 = {             502 = SSS info
+              264 = SSS task
+              263 = SSS coord frame
+              265 = SSS origin
+              266 = SSS ins.order
+              267 = SSS outs.order
+              268 = SSS nr chnls
+              269 = SSS components
+              278 = SSS nfree
+              243 = HPI g limit    0.98
+              244 = HPI dist limit 0.005
+            105 = }             502 = SSS info
+            104 = {             504 = MaxST info
+              264 = SSS task
+              272 = SSST subspace correlation
+              279 = SSST buffer length
+            105 = }
+            104 = {             501 = CTC correction
+              103 = block ID
+              204 = date
+              113 = creator program
+              800 = CTC matrix
+              3417 = proj item chs
+            105 = }             501 = CTC correction
+            104 = {             503 = SSS finecalib.
+              270 = SSS cal chnls
+              271 = SSS cal coeff
+            105 = }             503 = SSS finecalib.
+          105 = }               901 = proc. record
+        105 = }                 900 = proc. history
+    """
+    proc_history = dir_tree_find(tree, FIFF.FIFFB_PROCESSING_HISTORY)
+    out = list()
+    if len(proc_history) > 0:
+        proc_history = proc_history[0]
+        proc_records = dir_tree_find(proc_history, FIFF.FIFFB_PROCESSING_RECORD)
+        for proc_record in proc_records:
+            record = dict()
+            for i_ent in range(proc_record["nent"]):
+                kind = proc_record["directory"][i_ent].kind
+                pos = proc_record["directory"][i_ent].pos
+                for key, (id_, cast, _) in _proc_map.items():
+                    if kind == id_:
+                        tag = read_tag(fid, pos)
+                        record[key] = cast(tag.data)
+                        break
+                else:
+                    warn(f"Unknown processing history item {kind}")
+            record["max_info"] = _read_maxfilter_record(fid, proc_record)
+            iass = dir_tree_find(proc_record, FIFF.FIFFB_IAS)
+            if len(iass) > 0:
+                # XXX should eventually populate this
+                ss = [dict() for _ in range(len(iass))]
+                record["ias"] = ss
+            if len(record["max_info"]) > 0:
+                out.append(record)
+    return out
+
+
+def _write_proc_history(fid, info):
+    """Write processing history to file."""
+    if len(info["proc_history"]) > 0:
+        start_block(fid, FIFF.FIFFB_PROCESSING_HISTORY)
+        for record in info["proc_history"]:
+            start_block(fid, FIFF.FIFFB_PROCESSING_RECORD)
+            for key, (id_, _, writer) in _proc_map.items():
+                if key in record:
+                    writer(fid, id_, record[key])
+            _write_maxfilter_record(fid, record["max_info"])
+            if "ias" in record:
+                for _ in record["ias"]:
+                    start_block(fid, FIFF.FIFFB_IAS)
+                    # XXX should eventually populate this
+                    end_block(fid, FIFF.FIFFB_IAS)
+            end_block(fid, FIFF.FIFFB_PROCESSING_RECORD)
+        end_block(fid, FIFF.FIFFB_PROCESSING_HISTORY)
+
+
+_sss_info_keys = (
+    "job",
+    "frame",
+    "origin",
+    "in_order",
+    "out_order",
+    "nchan",
+    "components",
+    "nfree",
+    "hpi_g_limit",
+    "hpi_dist_limit",
+)
+_sss_info_ids = (
+    FIFF.FIFF_SSS_JOB,
+    FIFF.FIFF_SSS_FRAME,
+    FIFF.FIFF_SSS_ORIGIN,
+    FIFF.FIFF_SSS_ORD_IN,
+    FIFF.FIFF_SSS_ORD_OUT,
+    FIFF.FIFF_SSS_NMAG,
+    FIFF.FIFF_SSS_COMPONENTS,
+    FIFF.FIFF_SSS_NFREE,
+    FIFF.FIFF_HPI_FIT_GOOD_LIMIT,
+    FIFF.FIFF_HPI_FIT_DIST_LIMIT,
+)
+_sss_info_writers = (
+    write_int,
+    write_int,
+    write_float,
+    write_int,
+    write_int,
+    write_int,
+    write_int,
+    write_int,
+    write_float,
+    write_float,
+)
+_sss_info_casters = (
+    _int_item,
+    _int_item,
+    np.array,
+    _int_item,
+    _int_item,
+    _int_item,
+    np.array,
+    _int_item,
+    _float_item,
+    _float_item,
+)
+
+_max_st_keys = ("job", "subspcorr", "buflen")
+_max_st_ids = (FIFF.FIFF_SSS_JOB, FIFF.FIFF_SSS_ST_CORR, FIFF.FIFF_SSS_ST_LENGTH)
+_max_st_writers = (write_int, write_float, write_float)
+_max_st_casters = (_int_item, _float_item, _float_item)
+
+_sss_ctc_keys = ("block_id", "date", "creator", "decoupler")
+_sss_ctc_ids = (
+    FIFF.FIFF_BLOCK_ID,
+    FIFF.FIFF_MEAS_DATE,
+    FIFF.FIFF_CREATOR,
+    FIFF.FIFF_DECOUPLER_MATRIX,
+)
+_sss_ctc_writers = (write_id, write_int, write_string, write_float_sparse)
+_sss_ctc_casters = (dict, np.array, str, _csc_array_cast)
+
+_sss_cal_keys = ("cal_chans", "cal_corrs")
+_sss_cal_ids = (FIFF.FIFF_SSS_CAL_CHANS, FIFF.FIFF_SSS_CAL_CORRS)
+_sss_cal_writers = (write_int_matrix, write_float_matrix)
+_sss_cal_casters = (np.array, np.array)
+
+
+def _read_ctc(fname):
+    """Read cross-talk correction matrix."""
+    fname = _check_fname(fname, overwrite="read", must_exist=True)
+    f, tree, _ = fiff_open(fname)
+    with f as fid:
+        sss_ctc = _read_maxfilter_record(fid, tree)["sss_ctc"]
+        bad_str = f"Invalid cross-talk FIF: {fname}"
+        if len(sss_ctc) == 0:
+            raise ValueError(bad_str)
+        node = dir_tree_find(tree, FIFF.FIFFB_DATA_CORRECTION)[0]
+        comment = find_tag(fid, node, FIFF.FIFF_COMMENT).data
+        if comment != "cross-talk compensation matrix":
+            raise ValueError(bad_str)
+        sss_ctc["creator"] = find_tag(fid, node, FIFF.FIFF_CREATOR).data
+        sss_ctc["date"] = find_tag(fid, node, FIFF.FIFF_MEAS_DATE).data
+    return sss_ctc
+
+
+def _read_maxfilter_record(fid, tree):
+    """Read maxfilter processing record from file."""
+    sss_info_block = dir_tree_find(tree, FIFF.FIFFB_SSS_INFO)  # 502
+    sss_info = dict()
+    if len(sss_info_block) > 0:
+        sss_info_block = sss_info_block[0]
+        for i_ent in range(sss_info_block["nent"]):
+            kind = sss_info_block["directory"][i_ent].kind
+            pos = sss_info_block["directory"][i_ent].pos
+            for key, id_, cast in zip(_sss_info_keys, _sss_info_ids, _sss_info_casters):
+                if kind == id_:
+                    tag = read_tag(fid, pos)
+                    sss_info[key] = cast(tag.data)
+                    break
+
+    max_st_block = dir_tree_find(tree, FIFF.FIFFB_SSS_ST_INFO)  # 504
+    max_st = dict()
+    if len(max_st_block) > 0:
+        max_st_block = max_st_block[0]
+        for i_ent in range(max_st_block["nent"]):
+            kind = max_st_block["directory"][i_ent].kind
+            pos = max_st_block["directory"][i_ent].pos
+            for key, id_, cast in zip(_max_st_keys, _max_st_ids, _max_st_casters):
+                if kind == id_:
+                    tag = read_tag(fid, pos)
+                    max_st[key] = cast(tag.data)
+                    break
+
+    sss_ctc_block = dir_tree_find(tree, FIFF.FIFFB_CHANNEL_DECOUPLER)  # 501
+    sss_ctc = dict()
+    if len(sss_ctc_block) > 0:
+        sss_ctc_block = sss_ctc_block[0]
+        for i_ent in range(sss_ctc_block["nent"]):
+            kind = sss_ctc_block["directory"][i_ent].kind
+            pos = sss_ctc_block["directory"][i_ent].pos
+            for key, id_, cast in zip(_sss_ctc_keys, _sss_ctc_ids, _sss_ctc_casters):
+                if kind == id_:
+                    tag = read_tag(fid, pos)
+                    sss_ctc[key] = cast(tag.data)
+                    break
+            else:
+                if kind == FIFF.FIFF_PROJ_ITEM_CH_NAME_LIST:
+                    tag = read_tag(fid, pos)
+                    chs = _safe_name_list(tag.data, "read", "proj_items_chs")
+                    # This list can null chars in the last entry, e.g.:
+                    # [..., 'MEG2642', 'MEG2643', 'MEG2641\x00 ... \x00']
+                    chs[-1] = chs[-1].split("\x00")[0]
+                    sss_ctc["proj_items_chs"] = chs
+
+    sss_cal_block = dir_tree_find(tree, FIFF.FIFFB_SSS_CAL)  # 503
+    sss_cal = dict()
+    if len(sss_cal_block) > 0:
+        sss_cal_block = sss_cal_block[0]
+        for i_ent in range(sss_cal_block["nent"]):
+            kind = sss_cal_block["directory"][i_ent].kind
+            pos = sss_cal_block["directory"][i_ent].pos
+            for key, id_, cast in zip(_sss_cal_keys, _sss_cal_ids, _sss_cal_casters):
+                if kind == id_:
+                    tag = read_tag(fid, pos)
+                    sss_cal[key] = cast(tag.data)
+                    break
+
+    max_info = dict(sss_info=sss_info, sss_ctc=sss_ctc, sss_cal=sss_cal, max_st=max_st)
+    return max_info
+
+
+def _write_maxfilter_record(fid, record):
+    """Write maxfilter processing record to file."""
+    sss_info = record["sss_info"]
+    if len(sss_info) > 0:
+        start_block(fid, FIFF.FIFFB_SSS_INFO)
+        for key, id_, writer in zip(_sss_info_keys, _sss_info_ids, _sss_info_writers):
+            if key in sss_info:
+                writer(fid, id_, sss_info[key])
+        end_block(fid, FIFF.FIFFB_SSS_INFO)
+
+    max_st = record["max_st"]
+    if len(max_st) > 0:
+        start_block(fid, FIFF.FIFFB_SSS_ST_INFO)
+        for key, id_, writer in zip(_max_st_keys, _max_st_ids, _max_st_writers):
+            if key in max_st:
+                writer(fid, id_, max_st[key])
+        end_block(fid, FIFF.FIFFB_SSS_ST_INFO)
+
+    sss_ctc = record["sss_ctc"]
+    if len(sss_ctc) > 0:  # dict has entries
+        start_block(fid, FIFF.FIFFB_CHANNEL_DECOUPLER)
+        for key, id_, writer in zip(_sss_ctc_keys, _sss_ctc_ids, _sss_ctc_writers):
+            if key in sss_ctc:
+                writer(fid, id_, sss_ctc[key])
+        if "proj_items_chs" in sss_ctc:
+            write_name_list_sanitized(
+                fid,
+                FIFF.FIFF_PROJ_ITEM_CH_NAME_LIST,
+                sss_ctc["proj_items_chs"],
+                "proj_items_chs",
+            )
+        end_block(fid, FIFF.FIFFB_CHANNEL_DECOUPLER)
+
+    sss_cal = record["sss_cal"]
+    if len(sss_cal) > 0:
+        start_block(fid, FIFF.FIFFB_SSS_CAL)
+        for key, id_, writer in zip(_sss_cal_keys, _sss_cal_ids, _sss_cal_writers):
+            if key in sss_cal:
+                writer(fid, id_, sss_cal[key])
+        end_block(fid, FIFF.FIFFB_SSS_CAL)

mne/_fiff/reference.py

@@ -0,0 +1,738 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from ..defaults import DEFAULTS
+from ..utils import (
+    _check_option,
+    _check_preload,
+    _on_missing,
+    _validate_type,
+    fill_doc,
+    logger,
+    pinv,
+    verbose,
+    warn,
+)
+from .constants import FIFF
+from .meas_info import _check_ch_keys
+from .pick import _ELECTRODE_CH_TYPES, pick_channels, pick_channels_forward, pick_types
+from .proj import _has_eeg_average_ref_proj, make_eeg_average_ref_proj, setup_proj
+
+
+def _check_before_reference(inst, ref_from, ref_to, ch_type):
+    """Prepare instance for referencing."""
+    # Check to see that data is preloaded
+    _check_preload(inst, "Applying a reference")
+
+    ch_type = _get_ch_type(inst, ch_type)
+    ch_dict = {**{type_: True for type_ in ch_type}, "meg": False, "ref_meg": False}
+    eeg_idx = pick_types(inst.info, **ch_dict)
+
+    if ref_to is None:
+        ref_to = [inst.ch_names[i] for i in eeg_idx]
+        extra = "EEG channels found"
+    else:
+        extra = "channels supplied"
+    if len(ref_to) == 0:
+        raise ValueError(f"No {extra} to apply the reference to")
+
+    _check_ssp(inst, ref_from + ref_to)
+
+    # If the reference touches EEG/ECoG/sEEG/DBS electrodes, note in the
+    # info that a non-CAR has been applied.
+    ref_to_channels = pick_channels(inst.ch_names, ref_to, ordered=True)
+    if len(np.intersect1d(ref_to_channels, eeg_idx)) > 0:
+        with inst.info._unlock():
+            inst.info["custom_ref_applied"] = FIFF.FIFFV_MNE_CUSTOM_REF_ON
+
+    return ref_to
+
+
+def _check_ssp(inst, ref_items):
+    """Check for SSPs that may block re-referencing."""
+    projs_to_remove = []
+    for i, proj in enumerate(inst.info["projs"]):
+        # Remove any average reference projections
+        if (
+            proj["desc"] == "Average EEG reference"
+            or proj["kind"] == FIFF.FIFFV_PROJ_ITEM_EEG_AVREF
+        ):
+            logger.info("Removing existing average EEG reference projection.")
+            # Don't remove the projection right away, but do this at the end of
+            # this loop.
+            projs_to_remove.append(i)
+
+        # Inactive SSPs may block re-referencing
+        elif (
+            not proj["active"]
+            and len([ch for ch in ref_items if ch in proj["data"]["col_names"]]) > 0
+        ):
+            raise RuntimeError(
+                "Inactive signal space projection (SSP) operators are "
+                "present that operate on sensors involved in the desired "
+                "referencing scheme. These projectors need to be applied "
+                "using the apply_proj() method function before the desired "
+                "reference can be set."
+            )
+
+    for i in projs_to_remove:
+        del inst.info["projs"][i]
+
+    # Need to call setup_proj after changing the projs:
+    inst._projector, _ = setup_proj(inst.info, add_eeg_ref=False, activate=False)
+
+
+def _check_before_dict_reference(inst, ref_dict):
+    """Prepare instance for dict-based referencing."""
+    # Check to see that data is preloaded
+    _check_preload(inst, "Applying a reference")
+
+    # Promote all values to list-like. This simplifies our logic and also helps catch
+    # self-referencing cases like `{"Cz": ["Cz"]}`
+    _refdict = {k: [v] if isinstance(v, str) else list(v) for k, v in ref_dict.items()}
+
+    # Check that keys are strings and values are lists-of-strings
+    key_types = {type(k) for k in _refdict}
+    value_types = {type(v) for val in _refdict.values() for v in val}
+    for elem_name, elem in dict(key=key_types, value=value_types).items():
+        if bad_elem := elem - {str}:
+            raise TypeError(
+                f"{elem_name.capitalize()}s in the ref_channels dict must be strings. "
+                f"Your dict has {elem_name}s of type "
+                f'{", ".join(map(lambda x: x.__name__, bad_elem))}.'
+            )
+
+    # Check that keys are valid channels and values are lists-of-valid-channels
+    ch_set = set(inst.ch_names)
+    bad_ch_set = set(inst.info["bads"])
+    keys = set(_refdict)
+    values = set(sum(_refdict.values(), []))
+    for elem_name, elem in dict(key=keys, value=values).items():
+        if bad_elem := elem - ch_set:
+            raise ValueError(
+                f'ref_channels dict contains invalid {elem_name}(s) '
+                f'({", ".join(bad_elem)}) '
+                "that are not names of channels in the instance."
+            )
+        # Check that values are not bad channels
+        if bad_elem := elem.intersection(bad_ch_set):
+            warn(
+                f"ref_channels dict contains {elem_name}(s) "
+                f"({', '.join(bad_elem)}) "
+                "that are marked as bad channels."
+            )
+
+    _check_ssp(inst, keys.union(values))
+
+    # Check for self-referencing
+    self_ref = [[k] == v for k, v in _refdict.items()]
+    if any(self_ref):
+        which = np.array(list(_refdict))[np.nonzero(self_ref)]
+        for ch in which:
+            warn(f"Channel {ch} is self-referenced, which will nullify the channel.")
+
+    # Check that channel types match. First unpack list-like vals into separate items:
+    pairs = [(k, v) for k in _refdict for v in _refdict[k]]
+    ch_type_map = dict(zip(inst.ch_names, inst.get_channel_types()))
+    mismatch = [ch_type_map[k] != ch_type_map[v] for k, v in pairs]
+    if any(mismatch):
+        mismatch_pairs = np.array(pairs)[mismatch]
+        for k, v in mismatch_pairs:
+            warn(
+                f"Channel {k} ({ch_type_map[k]}) is referenced to channel {v} which is "
+                f"a different channel type ({ch_type_map[v]})."
+            )
+
+    # convert channel names to indices
+    keys_ix = pick_channels(inst.ch_names, list(_refdict), ordered=True)
+    vals_ix = (pick_channels(inst.ch_names, v, ordered=True) for v in _refdict.values())
+    return dict(zip(keys_ix, vals_ix))
+
+
+def _apply_reference(inst, ref_from, ref_to=None, forward=None, ch_type="auto"):
+    """Apply a custom EEG referencing scheme."""
+    ref_to = _check_before_reference(inst, ref_from, ref_to, ch_type)
+
+    # Compute reference
+    if len(ref_from) > 0:
+        # this is guaranteed below, but we should avoid the crazy pick_channels
+        # behavior that [] gives all. Also use ordered=True just to make sure
+        # that all supplied channels actually exist.
+        assert len(ref_to) > 0
+        ref_names = ref_from
+        ref_from = pick_channels(inst.ch_names, ref_from, ordered=True)
+        ref_to = pick_channels(inst.ch_names, ref_to, ordered=True)
+
+        data = inst._data
+        ref_data = data[..., ref_from, :].mean(-2, keepdims=True)
+        data[..., ref_to, :] -= ref_data
+        ref_data = ref_data[..., 0, :]
+
+        # REST
+        if forward is not None:
+            # use ch_sel and the given forward
+            forward = pick_channels_forward(forward, ref_names, ordered=True)
+            # 1-3. Compute a forward (G) and avg-ref'ed data (done above)
+            G = forward["sol"]["data"]
+            assert G.shape[0] == len(ref_names)
+            # 4. Compute the forward (G) and average-reference it (Ga):
+            Ga = G - np.mean(G, axis=0, keepdims=True)
+            # 5. Compute the Ga_inv by SVD
+            Ga_inv = pinv(Ga, rtol=1e-6)
+            # 6. Compute Ra = (G @ Ga_inv) in eq (8) from G and Ga_inv
+            Ra = G @ Ga_inv
+            # 7-8. Compute Vp = Ra @ Va; then Vpa=average(Vp)
+            Vpa = np.mean(Ra @ data[..., ref_from, :], axis=-2, keepdims=True)
+            data[..., ref_to, :] += Vpa
+    else:
+        ref_data = None
+
+    return inst, ref_data
+
+
+def _apply_dict_reference(inst, ref_dict):
+    """Apply a dict-based custom EEG referencing scheme."""
+    # this converts all keys to channel indices and all values to arrays of ch. indices:
+    ref_dict = _check_before_dict_reference(inst, ref_dict)
+
+    data = inst._data
+    orig_data = data.copy()
+    for ref_to, ref_from in ref_dict.items():
+        ref_data = orig_data[..., ref_from, :].mean(-2, keepdims=True)
+        data[..., [ref_to], :] -= ref_data
+
+    with inst.info._unlock():
+        inst.info["custom_ref_applied"] = FIFF.FIFFV_MNE_CUSTOM_REF_ON
+    return inst, None
+
+
+@fill_doc
+def add_reference_channels(inst, ref_channels, copy=True):
+    """Add reference channels to data that consists of all zeros.
+
+    Adds reference channels to data that were not included during recording.
+    This is useful when you need to re-reference your data to different
+    channels. These added channels will consist of all zeros.
+
+    Parameters
+    ----------
+    inst : instance of Raw | Epochs | Evoked
+        Instance of Raw or Epochs with EEG channels and reference channel(s).
+    %(ref_channels)s
+    copy : bool
+        Specifies whether the data will be copied (True) or modified in-place
+        (False). Defaults to True.
+
+    Returns
+    -------
+    inst : instance of Raw | Epochs | Evoked
+        Data with added EEG reference channels.
+
+    Notes
+    -----
+    .. warning::
+        When :ref:`re-referencing <tut-set-eeg-ref>`,
+        make sure to apply the montage using :meth:`mne.io.Raw.set_montage`
+        only after calling this function. Applying a montage will only set
+        locations of channels that exist at the time it is applied.
+    """
+    from ..epochs import BaseEpochs
+    from ..evoked import Evoked
+    from ..io import BaseRaw
+
+    # Check to see that data is preloaded
+    _check_preload(inst, "add_reference_channels")
+    _validate_type(ref_channels, (list, tuple, str), "ref_channels")
+    if isinstance(ref_channels, str):
+        ref_channels = [ref_channels]
+    for ch in ref_channels:
+        if ch in inst.info["ch_names"]:
+            raise ValueError(f"Channel {ch} already specified in inst.")
+
+    # Once CAR is applied (active), don't allow adding channels
+    if _has_eeg_average_ref_proj(inst.info, check_active=True):
+        raise RuntimeError("Average reference already applied to data.")
+
+    if copy:
+        inst = inst.copy()
+
+    if isinstance(inst, BaseRaw | Evoked):
+        data = inst._data
+        refs = np.zeros((len(ref_channels), data.shape[1]))
+        data = np.vstack((data, refs))
+        inst._data = data
+    elif isinstance(inst, BaseEpochs):
+        data = inst._data
+        x, y, z = data.shape
+        refs = np.zeros((x * len(ref_channels), z))
+        data = np.vstack((data.reshape((x * y, z), order="F"), refs))
+        data = data.reshape(x, y + len(ref_channels), z, order="F")
+        inst._data = data
+    else:
+        raise TypeError(
+            f"inst should be Raw, Epochs, or Evoked instead of {type(inst)}."
+        )
+    nchan = len(inst.info["ch_names"])
+
+    if inst.info.get("dig", None) is not None:
+        # A montage has been set. Try to infer location of reference channels.
+        # "zeroth" EEG electrode dig points is reference
+        ref_dig_loc = [
+            dl
+            for dl in inst.info["dig"]
+            if (dl["kind"] == FIFF.FIFFV_POINT_EEG and dl["ident"] == 0)
+        ]
+        if len(ref_channels) > 1 or len(ref_dig_loc) != len(ref_channels):
+            ref_dig_array = np.full(12, np.nan)
+            warn(
+                "Location for this channel is unknown or ambiguous; consider calling "
+                "set_montage() after adding new reference channels if needed. "
+                "Applying a montage will only set locations of channels that "
+                "exist at the time it is applied."
+            )
+        else:  # n_ref_channels == 1 and a single ref digitization exists
+            ref_dig_array = np.concatenate(
+                (ref_dig_loc[0]["r"], ref_dig_loc[0]["r"], np.zeros(6))
+            )
+            # Replace the (possibly new) Ref location for each channel
+            for idx in pick_types(inst.info, meg=False, eeg=True, exclude=[]):
+                inst.info["chs"][idx]["loc"][3:6] = ref_dig_loc[0]["r"]
+    else:
+        # If no montage has ever been set, we cannot even try to infer a location.
+        ref_dig_array = np.full(12, np.nan)
+
+    for ch in ref_channels:
+        chan_info = {
+            "ch_name": ch,
+            "coil_type": FIFF.FIFFV_COIL_EEG,
+            "kind": FIFF.FIFFV_EEG_CH,
+            "logno": nchan + 1,
+            "scanno": nchan + 1,
+            "cal": 1,
+            "range": 1.0,
+            "unit_mul": FIFF.FIFF_UNITM_NONE,
+            "unit": FIFF.FIFF_UNIT_V,
+            "coord_frame": FIFF.FIFFV_COORD_HEAD,
+            "loc": ref_dig_array,
+        }
+        inst.info["chs"].append(chan_info)
+        inst.info._update_redundant()
+    range_ = np.arange(1, len(ref_channels) + 1)
+    if isinstance(inst, BaseRaw):
+        inst._cals = np.hstack((inst._cals, [1] * len(ref_channels)))
+        for pi, picks in enumerate(inst._read_picks):
+            inst._read_picks[pi] = np.concatenate([picks, np.max(picks) + range_])
+    elif isinstance(inst, BaseEpochs):
+        picks = inst.picks
+        inst.picks = np.concatenate([picks, np.max(picks) + range_])
+    inst.info._check_consistency()
+    set_eeg_reference(inst, ref_channels=ref_channels, copy=False, verbose=False)
+    return inst
+
+
+_ref_dict = {
+    FIFF.FIFFV_MNE_CUSTOM_REF_ON: "on",
+    FIFF.FIFFV_MNE_CUSTOM_REF_OFF: "off",
+    FIFF.FIFFV_MNE_CUSTOM_REF_CSD: "CSD",
+}
+
+
+def _check_can_reref(inst):
+    from ..epochs import BaseEpochs
+    from ..evoked import Evoked
+    from ..io import BaseRaw
+
+    _validate_type(inst, (BaseRaw, BaseEpochs, Evoked), "Instance")
+    current_custom = inst.info["custom_ref_applied"]
+    if current_custom not in (
+        FIFF.FIFFV_MNE_CUSTOM_REF_ON,
+        FIFF.FIFFV_MNE_CUSTOM_REF_OFF,
+    ):
+        raise RuntimeError(
+            "Cannot set new reference on data with custom reference type "
+            f"{_ref_dict[current_custom]!r}"
+        )
+
+
+@verbose
+def set_eeg_reference(
+    inst,
+    ref_channels="average",
+    copy=True,
+    projection=False,
+    ch_type="auto",
+    forward=None,
+    *,
+    joint=False,
+    verbose=None,
+):
+    """Specify which reference to use for EEG data.
+
+    Use this function to explicitly specify the desired reference for EEG.
+    This can be either an existing electrode or a new virtual channel.
+    This function will re-reference the data according to the desired
+    reference.
+
+    Note that it is also possible to re-reference the signal using a
+    Laplacian (LAP) "reference-free" transformation using the
+    :func:`.compute_current_source_density` function.
+
+    Parameters
+    ----------
+    inst : instance of Raw | Epochs | Evoked
+        Instance of Raw or Epochs with EEG channels and reference channel(s).
+    %(ref_channels_set_eeg_reference)s
+    copy : bool
+        Specifies whether the data will be copied (True) or modified in-place
+        (False). Defaults to True.
+    %(projection_set_eeg_reference)s
+    %(ch_type_set_eeg_reference)s
+    %(forward_set_eeg_reference)s
+    %(joint_set_eeg_reference)s
+    %(verbose)s
+
+    Returns
+    -------
+    inst : instance of Raw | Epochs | Evoked
+        Data with EEG channels re-referenced. If ``ref_channels="average"`` and
+        ``projection=True`` a projection will be added instead of directly
+        re-referencing the data.
+    ref_data : array
+        Array of reference data subtracted from EEG channels. This will be
+        ``None`` if ``projection=True``, or if ``ref_channels`` is ``"REST"`` or a
+        :class:`dict`.
+    %(set_eeg_reference_see_also_notes)s
+    """
+    from ..forward import Forward
+
+    _check_can_reref(inst)
+
+    if isinstance(ref_channels, dict):
+        logger.info("Applying a custom dict-based reference.")
+        return _apply_dict_reference(inst, ref_channels)
+
+    ch_type = _get_ch_type(inst, ch_type)
+
+    if projection:  # average reference projector
+        if ref_channels != "average":
+            raise ValueError(
+                'Setting projection=True is only supported for ref_channels="average", '
+                f"got {ref_channels!r}."
+            )
+        # We need verbose='error' here in case we add projs sequentially
+        if _has_eeg_average_ref_proj(inst.info, ch_type=ch_type, verbose="error"):
+            warn(
+                "An average reference projection was already added. The data "
+                "has been left untouched."
+            )
+        else:
+            # Creating an average reference may fail. In this case, make
+            # sure that the custom_ref_applied flag is left untouched.
+            custom_ref_applied = inst.info["custom_ref_applied"]
+
+            try:
+                with inst.info._unlock():
+                    inst.info["custom_ref_applied"] = FIFF.FIFFV_MNE_CUSTOM_REF_OFF
+                if joint:
+                    inst.add_proj(
+                        make_eeg_average_ref_proj(
+                            inst.info, ch_type=ch_type, activate=False
+                        )
+                    )
+                else:
+                    for this_ch_type in ch_type:
+                        inst.add_proj(
+                            make_eeg_average_ref_proj(
+                                inst.info, ch_type=this_ch_type, activate=False
+                            )
+                        )
+            except Exception:
+                with inst.info._unlock():
+                    inst.info["custom_ref_applied"] = custom_ref_applied
+                raise
+            # If the data has been preloaded, projections will no
+            # longer be automatically applied.
+            if inst.preload:
+                logger.info(
+                    "Average reference projection was added, "
+                    "but has not been applied yet. Use the "
+                    "apply_proj method to apply it."
+                )
+        return inst, None
+    del projection  # not used anymore
+
+    inst = inst.copy() if copy else inst
+    ch_dict = {**{type_: True for type_ in ch_type}, "meg": False, "ref_meg": False}
+    ch_sel = [inst.ch_names[i] for i in pick_types(inst.info, **ch_dict)]
+
+    if ref_channels == "REST":
+        _validate_type(forward, Forward, 'forward when ref_channels="REST"')
+    else:
+        forward = None  # signal to _apply_reference not to do REST
+
+    if ref_channels in ("average", "REST"):
+        logger.info(f"Applying {ref_channels} reference.")
+        ref_channels = ch_sel
+
+    if ref_channels == []:
+        logger.info("EEG data marked as already having the desired reference.")
+    else:
+        logger.info(
+            "Applying a custom "
+            f"{tuple(DEFAULTS['titles'][type_] for type_ in ch_type)} "
+            "reference."
+        )
+
+    return _apply_reference(inst, ref_channels, ch_sel, forward, ch_type=ch_type)
+
+
+def _get_ch_type(inst, ch_type):
+    _validate_type(ch_type, (str, list, tuple), "ch_type")
+    valid_ch_types = ("auto",) + _ELECTRODE_CH_TYPES
+    if isinstance(ch_type, str):
+        _check_option("ch_type", ch_type, valid_ch_types)
+        if ch_type != "auto":
+            ch_type = [ch_type]
+    elif isinstance(ch_type, list | tuple):
+        for type_ in ch_type:
+            _validate_type(type_, str, "ch_type")
+            _check_option("ch_type", type_, valid_ch_types[1:])
+        ch_type = list(ch_type)
+
+    # if ch_type is 'auto', search through list to find first reasonable
+    # reference-able channel type.
+    if ch_type == "auto":
+        for type_ in _ELECTRODE_CH_TYPES:
+            if type_ in inst:
+                ch_type = [type_]
+                logger.info(
+                    f"{DEFAULTS['titles'][type_]} channel type selected for "
+                    "re-referencing"
+                )
+                break
+        # if auto comes up empty, or the user specifies a bad ch_type.
+        else:
+            raise ValueError("No EEG, ECoG, sEEG or DBS channels found to rereference.")
+    return ch_type
+
+
+@verbose
+def set_bipolar_reference(
+    inst,
+    anode,
+    cathode,
+    ch_name=None,
+    ch_info=None,
+    drop_refs=True,
+    copy=True,
+    on_bad="warn",
+    verbose=None,
+):
+    """Re-reference selected channels using a bipolar referencing scheme.
+
+    A bipolar reference takes the difference between two channels (the anode
+    minus the cathode) and adds it as a new virtual channel. The original
+    channels will be dropped by default.
+
+    Multiple anodes and cathodes can be specified, in which case multiple
+    virtual channels will be created. The 1st cathode will be subtracted
+    from the 1st anode, the 2nd cathode from the 2nd anode, etc.
+
+    By default, the virtual channels will be annotated with channel-info and
+    -location of the anodes and coil types will be set to EEG_BIPOLAR.
+
+    Parameters
+    ----------
+    inst : instance of Raw | Epochs | Evoked
+        Data containing the unreferenced channels.
+    anode : str | list of str
+        The name(s) of the channel(s) to use as anode in the bipolar reference.
+    cathode : str | list of str
+        The name(s) of the channel(s) to use as cathode in the bipolar
+        reference.
+    ch_name : str | list of str | None
+        The channel name(s) for the virtual channel(s) containing the resulting
+        signal. By default, bipolar channels are named after the anode and
+        cathode, but it is recommended to supply a more meaningful name.
+    ch_info : dict | list of dict | None
+        This parameter can be used to supply a dictionary (or a dictionary for
+        each bipolar channel) containing channel information to merge in,
+        overwriting the default values. Defaults to None.
+    drop_refs : bool
+        Whether to drop the anode/cathode channels from the instance.
+    copy : bool
+        Whether to operate on a copy of the data (True) or modify it in-place
+        (False). Defaults to True.
+    on_bad : str
+        If a bipolar channel is created from a bad anode or a bad cathode, mne
+        warns if on_bad="warns", raises ValueError if on_bad="raise", and does
+        nothing if on_bad="ignore". For "warn" and "ignore", the new bipolar
+        channel will be marked as bad. Defaults to on_bad="warns".
+    %(verbose)s
+
+    Returns
+    -------
+    inst : instance of Raw | Epochs | Evoked
+        Data with the specified channels re-referenced.
+
+    See Also
+    --------
+    set_eeg_reference : Convenience function for creating an EEG reference.
+
+    Notes
+    -----
+    1. If the anodes contain any EEG channels, this function removes
+       any pre-existing average reference projections.
+
+    2. During source localization, the EEG signal should have an average
+       reference.
+
+    3. The data must be preloaded.
+
+    .. versionadded:: 0.9.0
+    """
+    from ..epochs import BaseEpochs, EpochsArray
+    from ..evoked import EvokedArray
+    from ..io import BaseRaw, RawArray
+    from .meas_info import create_info
+
+    _check_can_reref(inst)
+    if not isinstance(anode, list):
+        anode = [anode]
+
+    if not isinstance(cathode, list):
+        cathode = [cathode]
+
+    if len(anode) != len(cathode):
+        raise ValueError(
+            f"Number of anodes (got {len(anode)}) must equal the number "
+            f"of cathodes (got {len(cathode)})."
+        )
+
+    if ch_name is None:
+        ch_name = [f"{a}-{c}" for (a, c) in zip(anode, cathode)]
+    elif not isinstance(ch_name, list):
+        ch_name = [ch_name]
+    if len(ch_name) != len(anode):
+        raise ValueError(
+            "Number of channel names must equal the number of "
+            f"anodes/cathodes (got {len(ch_name)})."
+        )
+
+    # Check for duplicate channel names (it is allowed to give the name of the
+    # anode or cathode channel, as they will be replaced).
+    for ch, a, c in zip(ch_name, anode, cathode):
+        if ch not in [a, c] and ch in inst.ch_names:
+            raise ValueError(
+                f'There is already a channel named "{ch}", please '
+                "specify a different name for the bipolar "
+                "channel using the ch_name parameter."
+            )
+
+    if ch_info is None:
+        ch_info = [{} for _ in anode]
+    elif not isinstance(ch_info, list):
+        ch_info = [ch_info]
+    if len(ch_info) != len(anode):
+        raise ValueError(
+            "Number of channel info dictionaries must equal the "
+            "number of anodes/cathodes."
+        )
+
+    if copy:
+        inst = inst.copy()
+
+    anode = _check_before_reference(
+        inst, ref_from=cathode, ref_to=anode, ch_type="auto"
+    )
+
+    # Create bipolar reference channels by multiplying the data
+    # (channels x time) with a matrix (n_virtual_channels x channels)
+    # and add them to the instance.
+    multiplier = np.zeros((len(anode), len(inst.ch_names)))
+    for idx, (a, c) in enumerate(zip(anode, cathode)):
+        multiplier[idx, inst.ch_names.index(a)] = 1
+        multiplier[idx, inst.ch_names.index(c)] = -1
+
+    ref_info = create_info(
+        ch_names=ch_name,
+        sfreq=inst.info["sfreq"],
+        ch_types=inst.get_channel_types(picks=anode),
+    )
+
+    # Update "chs" in Reference-Info.
+    for ch_idx, (an, info) in enumerate(zip(anode, ch_info)):
+        _check_ch_keys(info, ch_idx, name="ch_info", check_min=False)
+        an_idx = inst.ch_names.index(an)
+        # Copy everything from anode (except ch_name).
+        an_chs = {k: v for k, v in inst.info["chs"][an_idx].items() if k != "ch_name"}
+        ref_info["chs"][ch_idx].update(an_chs)
+        # Set coil-type to bipolar.
+        ref_info["chs"][ch_idx]["coil_type"] = FIFF.FIFFV_COIL_EEG_BIPOLAR
+        # Update with info from ch_info-parameter.
+        ref_info["chs"][ch_idx].update(info)
+
+    # Set other info-keys from original instance.
+    pick_info = {
+        k: v
+        for k, v in inst.info.items()
+        if k not in ["chs", "ch_names", "bads", "nchan", "sfreq"]
+    }
+
+    with ref_info._unlock():
+        ref_info.update(pick_info)
+
+    # Rereferencing of data.
+    ref_data = multiplier @ inst._data
+
+    if isinstance(inst, BaseRaw):
+        ref_inst = RawArray(ref_data, ref_info, first_samp=inst.first_samp, copy=None)
+    elif isinstance(inst, BaseEpochs):
+        ref_inst = EpochsArray(
+            ref_data,
+            ref_info,
+            events=inst.events,
+            tmin=inst.tmin,
+            event_id=inst.event_id,
+            metadata=inst.metadata,
+        )
+    else:
+        ref_inst = EvokedArray(
+            ref_data,
+            ref_info,
+            tmin=inst.tmin,
+            comment=inst.comment,
+            nave=inst.nave,
+            kind="average",
+        )
+
+    # Add referenced instance to original instance.
+    inst.add_channels([ref_inst], force_update_info=True)
+
+    # Handle bad channels.
+    bad_bipolar_chs = []
+    for ch_idx, (a, c) in enumerate(zip(anode, cathode)):
+        if a in inst.info["bads"] or c in inst.info["bads"]:
+            bad_bipolar_chs.append(ch_name[ch_idx])
+
+    # Add warnings if bad channels are present.
+    if bad_bipolar_chs:
+        msg = f"Bipolar channels are based on bad channels: {bad_bipolar_chs}."
+        _on_missing(on_bad, msg)
+        inst.info["bads"] += bad_bipolar_chs
+
+    added_channels = ", ".join([name for name in ch_name])
+    logger.info(f"Added the following bipolar channels:\n{added_channels}")
+
+    for attr_name in ["picks", "_projector"]:
+        setattr(inst, attr_name, None)
+
+    # Drop remaining channels.
+    if drop_refs:
+        drop_channels = list((set(anode) | set(cathode)) & set(inst.ch_names))
+        inst.drop_channels(drop_channels)
+
+    return inst

mne/_fiff/tag.py

@@ -0,0 +1,523 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import html
+import re
+import struct
+from dataclasses import dataclass
+from functools import partial
+from typing import Any
+
+import numpy as np
+from scipy.sparse import csc_array, csr_array
+
+from ..utils import _check_option, warn
+from ..utils.numerics import _julian_to_date
+from .constants import (
+    FIFF,
+    _ch_coil_type_named,
+    _ch_kind_named,
+    _ch_unit_mul_named,
+    _ch_unit_named,
+    _dig_cardinal_named,
+    _dig_kind_named,
+)
+
+##############################################################################
+# HELPERS
+
+
+@dataclass
+class Tag:
+    """Tag in FIF tree structure."""
+
+    kind: int
+    type: int
+    size: int
+    next: int
+    pos: int
+    data: Any = None
+
+    def __eq__(self, tag):  # noqa: D105
+        return int(
+            self.kind == tag.kind
+            and self.type == tag.type
+            and self.size == tag.size
+            and self.next == tag.next
+            and self.pos == tag.pos
+            and self.data == tag.data
+        )
+
+    @property
+    def next_pos(self):
+        """The next tag position."""
+        if self.next == FIFF.FIFFV_NEXT_SEQ:  # 0
+            return self.pos + 16 + self.size
+        elif self.next > 0:
+            return self.next
+        else:  # self.next should be -1 if we get here
+            return None  # safest to return None so that things like fid.seek die
+
+
+def _frombuffer_rows(fid, tag_size, dtype=None, shape=None, rlims=None):
+    """Get a range of rows from a large tag."""
+    if shape is not None:
+        item_size = np.dtype(dtype).itemsize
+        if not len(shape) == 2:
+            raise ValueError("Only implemented for 2D matrices")
+        want_shape = np.prod(shape)
+        have_shape = tag_size // item_size
+        if want_shape != have_shape:
+            raise ValueError(
+                f"Wrong shape specified, requested {want_shape} but got "
+                f"{have_shape}"
+            )
+        if not len(rlims) == 2:
+            raise ValueError("rlims must have two elements")
+        n_row_out = rlims[1] - rlims[0]
+        if n_row_out <= 0:
+            raise ValueError("rlims must yield at least one output")
+        row_size = item_size * shape[1]
+        # # of bytes to skip at the beginning, # to read, where to end
+        start_skip = int(rlims[0] * row_size)
+        read_size = int(n_row_out * row_size)
+        end_pos = int(fid.tell() + tag_size)
+        # Move the pointer ahead to the read point
+        fid.seek(start_skip, 1)
+        # Do the reading
+        out = np.frombuffer(fid.read(read_size), dtype=dtype)
+        # Move the pointer ahead to the end of the tag
+        fid.seek(end_pos)
+    else:
+        out = np.frombuffer(fid.read(tag_size), dtype=dtype)
+    return out
+
+
+def _loc_to_coil_trans(loc):
+    """Convert loc vector to coil_trans."""
+    assert loc.shape[-1] == 12
+    coil_trans = np.zeros(loc.shape[:-1] + (4, 4))
+    coil_trans[..., :3, 3] = loc[..., :3]
+    coil_trans[..., :3, :3] = np.reshape(
+        loc[..., 3:], loc.shape[:-1] + (3, 3)
+    ).swapaxes(-1, -2)
+    coil_trans[..., -1, -1] = 1.0
+    return coil_trans
+
+
+def _coil_trans_to_loc(coil_trans):
+    """Convert coil_trans to loc."""
+    coil_trans = coil_trans.astype(np.float64)
+    return np.roll(coil_trans.T[:, :3], 1, 0).flatten()
+
+
+def _loc_to_eeg_loc(loc):
+    """Convert a loc to an EEG loc."""
+    if not np.isfinite(loc[:3]).all():
+        raise RuntimeError("Missing EEG channel location")
+    if np.isfinite(loc[3:6]).all() and (loc[3:6]).any():
+        return np.array([loc[0:3], loc[3:6]]).T
+    else:
+        return loc[0:3][:, np.newaxis].copy()
+
+
+##############################################################################
+# READING FUNCTIONS
+
+# None of these functions have docstring because it's more compact that way,
+# and hopefully it's clear what they do by their names and variable values.
+# See ``read_tag`` for variable descriptions. Return values are implied
+# by the function names.
+
+
+def _read_tag_header(fid, pos):
+    """Read only the header of a Tag."""
+    fid.seek(pos, 0)
+    s = fid.read(16)
+    if len(s) != 16:
+        where = fid.tell() - len(s)
+        extra = f" in file {fid.name}" if hasattr(fid, "name") else ""
+        warn(f"Invalid tag with only {len(s)}/16 bytes at position {where}{extra}")
+        return None
+    # struct.unpack faster than np.frombuffer, saves ~10% of time some places
+    kind, type_, size, next_ = struct.unpack(">iIii", s)
+    return Tag(kind, type_, size, next_, pos)
+
+
+def _read_matrix(fid, tag, shape, rlims):
+    """Read a matrix (dense or sparse) tag."""
+    # This should be easy to implement (see _frombuffer_rows)
+    # if we need it, but for now, it's not...
+    if shape is not None or rlims is not None:
+        raise ValueError("Row reading not implemented for matrices yet")
+
+    matrix_coding, matrix_type, bit, dtype = _matrix_info(tag)
+
+    pos = tag.pos + 16
+    fid.seek(pos + tag.size - 4, 0)
+    if matrix_coding == "dense":
+        # Find dimensions and return to the beginning of tag data
+        ndim = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+        fid.seek(-(ndim + 1) * 4, 1)
+        dims = np.frombuffer(fid.read(4 * ndim), dtype=">i4")[::-1]
+        #
+        # Back to where the data start
+        #
+        fid.seek(pos, 0)
+
+        if ndim > 3:
+            raise Exception(
+                "Only 2 or 3-dimensional matrices are supported at this time"
+            )
+
+        data = fid.read(int(bit * dims.prod()))
+        data = np.frombuffer(data, dtype=dtype)
+        # Note: we need the non-conjugate transpose here
+        if matrix_type == FIFF.FIFFT_COMPLEX_FLOAT:
+            data = data.view(">c8")
+        elif matrix_type == FIFF.FIFFT_COMPLEX_DOUBLE:
+            data = data.view(">c16")
+        data.shape = dims
+    else:
+        # Find dimensions and return to the beginning of tag data
+        ndim = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+        fid.seek(-(ndim + 2) * 4, 1)
+        dims = np.frombuffer(fid.read(4 * (ndim + 1)), dtype=">i4")
+        if ndim != 2:
+            raise Exception("Only two-dimensional matrices are supported at this time")
+
+        # Back to where the data start
+        fid.seek(pos, 0)
+        nnz = int(dims[0])
+        nrow = int(dims[1])
+        ncol = int(dims[2])
+        # We need to make a copy so that we can own the data, otherwise we get:
+        #     _sparsetools.csr_sort_indices(len(self.indptr) - 1, self.indptr,
+        # E   ValueError: WRITEBACKIFCOPY base is read-only
+        data = np.frombuffer(fid.read(bit * nnz), dtype=dtype).astype(np.float32)
+        shape = (dims[1], dims[2])
+        if matrix_coding == "sparse CCS":
+            tmp_indices = fid.read(4 * nnz)
+            indices = np.frombuffer(tmp_indices, dtype=">i4")
+            tmp_ptr = fid.read(4 * (ncol + 1))
+            indptr = np.frombuffer(tmp_ptr, dtype=">i4")
+            swap = nrow
+            klass = csc_array
+        else:
+            assert matrix_coding == "sparse RCS", matrix_coding
+            tmp_indices = fid.read(4 * nnz)
+            indices = np.frombuffer(tmp_indices, dtype=">i4")
+            tmp_ptr = fid.read(4 * (nrow + 1))
+            indptr = np.frombuffer(tmp_ptr, dtype=">i4")
+            swap = ncol
+            klass = csr_array
+        if indptr[-1] > len(indices) or np.any(indptr < 0):
+            # There was a bug in MNE-C that caused some data to be
+            # stored without byte swapping
+            indices = np.concatenate(
+                (
+                    np.frombuffer(tmp_indices[: 4 * (swap + 1)], dtype=">i4"),
+                    np.frombuffer(tmp_indices[4 * (swap + 1) :], dtype="<i4"),
+                )
+            )
+            indptr = np.frombuffer(tmp_ptr, dtype="<i4")
+        data = klass((data, indices, indptr), shape=shape)
+    return data
+
+
+def _read_simple(fid, tag, shape, rlims, dtype):
+    """Read simple datatypes from tag (typically used with partial)."""
+    return _frombuffer_rows(fid, tag.size, dtype=dtype, shape=shape, rlims=rlims)
+
+
+def _read_string(fid, tag, shape, rlims):
+    """Read a string tag."""
+    # Always decode to ISO 8859-1 / latin1 (FIFF standard).
+    d = _frombuffer_rows(fid, tag.size, dtype=">c", shape=shape, rlims=rlims)
+    string = str(d.tobytes().decode("latin1", "ignore"))
+    if re.search(r"&#[0-9a-fA-F]{6};", string):
+        string = html.unescape(string)
+    return string
+
+
+def _read_complex_float(fid, tag, shape, rlims):
+    """Read complex float tag."""
+    # data gets stored twice as large
+    if shape is not None:
+        shape = (shape[0], shape[1] * 2)
+    d = _frombuffer_rows(fid, tag.size, dtype=">f4", shape=shape, rlims=rlims)
+    d = d.view(">c8")
+    return d
+
+
+def _read_complex_double(fid, tag, shape, rlims):
+    """Read complex double tag."""
+    # data gets stored twice as large
+    if shape is not None:
+        shape = (shape[0], shape[1] * 2)
+    d = _frombuffer_rows(fid, tag.size, dtype=">f8", shape=shape, rlims=rlims)
+    d = d.view(">c16")
+    return d
+
+
+def _read_id_struct(fid, tag, shape, rlims):
+    """Read ID struct tag."""
+    return dict(
+        version=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        machid=np.frombuffer(fid.read(8), dtype=">i4"),
+        secs=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        usecs=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+    )
+
+
+def _read_dig_point_struct(fid, tag, shape, rlims):
+    """Read dig point struct tag."""
+    kind = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+    kind = _dig_kind_named.get(kind, kind)
+    ident = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+    if kind == FIFF.FIFFV_POINT_CARDINAL:
+        ident = _dig_cardinal_named.get(ident, ident)
+    return dict(
+        kind=kind,
+        ident=ident,
+        r=np.frombuffer(fid.read(12), dtype=">f4"),
+        coord_frame=FIFF.FIFFV_COORD_UNKNOWN,
+    )
+
+
+def _read_coord_trans_struct(fid, tag, shape, rlims):
+    """Read coord trans struct tag."""
+    from ..transforms import Transform
+
+    fro = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+    to = int(np.frombuffer(fid.read(4), dtype=">i4").item())
+    rot = np.frombuffer(fid.read(36), dtype=">f4").reshape(3, 3)
+    move = np.frombuffer(fid.read(12), dtype=">f4")
+    trans = np.r_[np.c_[rot, move], np.array([[0], [0], [0], [1]]).T]
+    data = Transform(fro, to, trans)
+    fid.seek(48, 1)  # Skip over the inverse transformation
+    return data
+
+
+_ch_coord_dict = {
+    FIFF.FIFFV_MEG_CH: FIFF.FIFFV_COORD_DEVICE,
+    FIFF.FIFFV_REF_MEG_CH: FIFF.FIFFV_COORD_DEVICE,
+    FIFF.FIFFV_EEG_CH: FIFF.FIFFV_COORD_HEAD,
+    FIFF.FIFFV_ECOG_CH: FIFF.FIFFV_COORD_HEAD,
+    FIFF.FIFFV_SEEG_CH: FIFF.FIFFV_COORD_HEAD,
+    FIFF.FIFFV_DBS_CH: FIFF.FIFFV_COORD_HEAD,
+    FIFF.FIFFV_FNIRS_CH: FIFF.FIFFV_COORD_HEAD,
+}
+
+
+def _read_ch_info_struct(fid, tag, shape, rlims):
+    """Read channel info struct tag."""
+    d = dict(
+        scanno=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        logno=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        kind=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        range=float(np.frombuffer(fid.read(4), dtype=">f4").item()),
+        cal=float(np.frombuffer(fid.read(4), dtype=">f4").item()),
+        coil_type=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        # deal with really old OSX Anaconda bug by casting to float64
+        loc=np.frombuffer(fid.read(48), dtype=">f4").astype(np.float64),
+        # unit and exponent
+        unit=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+        unit_mul=int(np.frombuffer(fid.read(4), dtype=">i4").item()),
+    )
+    # channel name
+    ch_name = np.frombuffer(fid.read(16), dtype=">c")
+    ch_name = ch_name[: np.argmax(ch_name == b"")].tobytes()
+    d["ch_name"] = ch_name.decode()
+    # coil coordinate system definition
+    _update_ch_info_named(d)
+    return d
+
+
+def _update_ch_info_named(d):
+    d["coord_frame"] = _ch_coord_dict.get(d["kind"], FIFF.FIFFV_COORD_UNKNOWN)
+    d["kind"] = _ch_kind_named.get(d["kind"], d["kind"])
+    d["coil_type"] = _ch_coil_type_named.get(d["coil_type"], d["coil_type"])
+    d["unit"] = _ch_unit_named.get(d["unit"], d["unit"])
+    d["unit_mul"] = _ch_unit_mul_named.get(d["unit_mul"], d["unit_mul"])
+
+
+def _read_old_pack(fid, tag, shape, rlims):
+    """Read old pack tag."""
+    offset = float(np.frombuffer(fid.read(4), dtype=">f4").item())
+    scale = float(np.frombuffer(fid.read(4), dtype=">f4").item())
+    data = np.frombuffer(fid.read(tag.size - 8), dtype=">i2")
+    data = data * scale  # to float64
+    data += offset
+    return data
+
+
+def _read_dir_entry_struct(fid, tag, shape, rlims):
+    """Read dir entry struct tag."""
+    pos = tag.pos + 16
+    entries = list()
+    for offset in range(1, tag.size // 16):
+        ent = _read_tag_header(fid, pos + offset * 16)
+        # The position of the real tag on disk is stored in the "next" entry within the
+        # directory, so we need to overwrite ent.pos. For safety let's also overwrite
+        # ent.next to point nowhere
+        ent.pos, ent.next = ent.next, FIFF.FIFFV_NEXT_NONE
+        entries.append(ent)
+    return entries
+
+
+def _read_julian(fid, tag, shape, rlims):
+    """Read julian tag."""
+    return _julian_to_date(int(np.frombuffer(fid.read(4), dtype=">i4").item()))
+
+
+# Read types call dict
+_call_dict = {
+    FIFF.FIFFT_STRING: _read_string,
+    FIFF.FIFFT_COMPLEX_FLOAT: _read_complex_float,
+    FIFF.FIFFT_COMPLEX_DOUBLE: _read_complex_double,
+    FIFF.FIFFT_ID_STRUCT: _read_id_struct,
+    FIFF.FIFFT_DIG_POINT_STRUCT: _read_dig_point_struct,
+    FIFF.FIFFT_COORD_TRANS_STRUCT: _read_coord_trans_struct,
+    FIFF.FIFFT_CH_INFO_STRUCT: _read_ch_info_struct,
+    FIFF.FIFFT_OLD_PACK: _read_old_pack,
+    FIFF.FIFFT_DIR_ENTRY_STRUCT: _read_dir_entry_struct,
+    FIFF.FIFFT_JULIAN: _read_julian,
+}
+_call_dict_names = {
+    FIFF.FIFFT_STRING: "str",
+    FIFF.FIFFT_COMPLEX_FLOAT: "c8",
+    FIFF.FIFFT_COMPLEX_DOUBLE: "c16",
+    FIFF.FIFFT_ID_STRUCT: "ids",
+    FIFF.FIFFT_DIG_POINT_STRUCT: "dps",
+    FIFF.FIFFT_COORD_TRANS_STRUCT: "cts",
+    FIFF.FIFFT_CH_INFO_STRUCT: "cis",
+    FIFF.FIFFT_OLD_PACK: "op_",
+    FIFF.FIFFT_DIR_ENTRY_STRUCT: "dir",
+    FIFF.FIFFT_JULIAN: "jul",
+    FIFF.FIFFT_VOID: "nul",  # 0
+}
+
+#  Append the simple types
+_simple_dict = {
+    FIFF.FIFFT_BYTE: ">B",
+    FIFF.FIFFT_SHORT: ">i2",
+    FIFF.FIFFT_INT: ">i4",
+    FIFF.FIFFT_USHORT: ">u2",
+    FIFF.FIFFT_UINT: ">u4",
+    FIFF.FIFFT_FLOAT: ">f4",
+    FIFF.FIFFT_DOUBLE: ">f8",
+    FIFF.FIFFT_DAU_PACK16: ">i2",
+}
+for key, dtype in _simple_dict.items():
+    _call_dict[key] = partial(_read_simple, dtype=dtype)
+    _call_dict_names[key] = dtype
+
+
+def read_tag(fid, pos, shape=None, rlims=None):
+    """Read a Tag from a file at a given position.
+
+    Parameters
+    ----------
+    fid : file
+        The open FIF file descriptor.
+    pos : int
+        The position of the Tag in the file.
+    shape : tuple | None
+        If tuple, the shape of the stored matrix. Only to be used with
+        data stored as a vector (not implemented for matrices yet).
+    rlims : tuple | None
+        If tuple, the first (inclusive) and last (exclusive) rows to retrieve.
+        Note that data are assumed to be stored row-major in the file. Only to
+        be used with data stored as a vector (not implemented for matrices
+        yet).
+
+    Returns
+    -------
+    tag : Tag
+        The Tag read.
+    """
+    tag = _read_tag_header(fid, pos)
+    if tag is None:
+        return tag
+    if tag.size > 0:
+        if _matrix_info(tag) is not None:
+            tag.data = _read_matrix(fid, tag, shape, rlims)
+        else:
+            #   All other data types
+            try:
+                fun = _call_dict[tag.type]
+            except KeyError:
+                raise Exception(f"Unimplemented tag data type {tag.type}") from None
+            tag.data = fun(fid, tag, shape, rlims)
+    return tag
+
+
+def find_tag(fid, node, findkind):
+    """Find Tag in an open FIF file descriptor.
+
+    Parameters
+    ----------
+    fid : file-like
+        Open file.
+    node : dict
+        Node to search.
+    findkind : int
+        Tag kind to find.
+
+    Returns
+    -------
+    tag : instance of Tag
+        The first tag found.
+    """
+    if node["directory"] is not None:
+        for subnode in node["directory"]:
+            if subnode.kind == findkind:
+                return read_tag(fid, subnode.pos)
+    return None
+
+
+def has_tag(node, kind):
+    """Check if the node contains a Tag of a given kind."""
+    for d in node["directory"]:
+        if d.kind == kind:
+            return True
+    return False
+
+
+def _rename_list(bads, ch_names_mapping):
+    return [ch_names_mapping.get(bad, bad) for bad in bads]
+
+
+def _int_item(x):
+    return int(x.item())
+
+
+def _float_item(x):
+    return float(x.item())
+
+
+def _matrix_info(tag):
+    matrix_coding = tag.type & 0xFFFF0000
+    if matrix_coding == 0 or tag.size == 0:
+        return None
+    matrix_type = tag.type & 0x0000FFFF
+    matrix_coding_dict = {
+        FIFF.FIFFT_MATRIX: "dense",
+        FIFF.FIFFT_MATRIX | FIFF.FIFFT_SPARSE_CCS_MATRIX: "sparse CCS",
+        FIFF.FIFFT_MATRIX | FIFF.FIFFT_SPARSE_RCS_MATRIX: "sparse RCS",
+    }
+    _check_option("matrix_coding", matrix_coding, list(matrix_coding_dict))
+    matrix_coding = matrix_coding_dict[matrix_coding]
+    matrix_bit_dtype = {
+        FIFF.FIFFT_INT: (4, ">i4"),
+        FIFF.FIFFT_JULIAN: (4, ">i4"),
+        FIFF.FIFFT_FLOAT: (4, ">f4"),
+        FIFF.FIFFT_DOUBLE: (8, ">f8"),
+        FIFF.FIFFT_COMPLEX_FLOAT: (8, ">f4"),
+        FIFF.FIFFT_COMPLEX_DOUBLE: (16, ">f8"),
+    }
+    _check_option("matrix_type", matrix_type, list(matrix_bit_dtype))
+    bit, dtype = matrix_bit_dtype[matrix_type]
+    return matrix_coding, matrix_type, bit, dtype

mne/_fiff/tree.py

@@ -0,0 +1,108 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+
+from ..utils import logger, verbose
+from .constants import FIFF
+from .tag import read_tag
+
+
+def dir_tree_find(tree, kind):
+    """Find nodes of the given kind from a directory tree structure.
+
+    Parameters
+    ----------
+    tree : dict
+        Directory tree.
+    kind : int
+        Kind to find.
+
+    Returns
+    -------
+    nodes : list
+        List of matching nodes.
+    """
+    nodes = []
+
+    if isinstance(tree, list):
+        for t in tree:
+            nodes += dir_tree_find(t, kind)
+    else:
+        #   Am I desirable myself?
+        if tree["block"] == kind:
+            nodes.append(tree)
+
+        #   Search the subtrees
+        for child in tree["children"]:
+            nodes += dir_tree_find(child, kind)
+    return nodes
+
+
+@verbose
+def make_dir_tree(fid, directory, start=0, indent=0, verbose=None):
+    """Create the directory tree structure."""
+    if directory[start].kind == FIFF.FIFF_BLOCK_START:
+        tag = read_tag(fid, directory[start].pos)
+        block = tag.data.item()
+    else:
+        block = 0
+
+    start_separate = False
+
+    this = start
+
+    tree = dict()
+    tree["block"] = block
+    tree["id"] = None
+    tree["parent_id"] = None
+    tree["nent"] = 0
+    tree["nchild"] = 0
+    tree["directory"] = directory[this]
+    tree["children"] = []
+
+    while this < len(directory):
+        if directory[this].kind == FIFF.FIFF_BLOCK_START:
+            if this != start:
+                if not start_separate:
+                    start_separate = True
+                    logger.debug("    " * indent + f"start {{ {block}")
+                child, this = make_dir_tree(fid, directory, this, indent + 1)
+                tree["nchild"] += 1
+                tree["children"].append(child)
+        elif directory[this].kind == FIFF.FIFF_BLOCK_END:
+            tag = read_tag(fid, directory[start].pos)
+            if tag.data == block:
+                break
+        else:
+            tree["nent"] += 1
+            if tree["nent"] == 1:
+                tree["directory"] = list()
+            tree["directory"].append(directory[this])
+
+            #  Add the id information if available
+            if block == 0:
+                if directory[this].kind == FIFF.FIFF_FILE_ID:
+                    tag = read_tag(fid, directory[this].pos)
+                    tree["id"] = tag.data
+            else:
+                if directory[this].kind == FIFF.FIFF_BLOCK_ID:
+                    tag = read_tag(fid, directory[this].pos)
+                    tree["id"] = tag.data
+                elif directory[this].kind == FIFF.FIFF_PARENT_BLOCK_ID:
+                    tag = read_tag(fid, directory[this].pos)
+                    tree["parent_id"] = tag.data
+
+        this += 1
+
+    # Eliminate the empty directory
+    if tree["nent"] == 0:
+        tree["directory"] = None
+
+    content = f"block = {tree['block']} nent = {tree['nent']} nchild = {tree['nchild']}"
+    if start_separate:
+        logger.debug("    " * indent + f"end }} {content}")
+    else:
+        logger.debug("    " * indent + content)
+    last = this
+    return tree, last

mne/_fiff/utils.py

@@ -0,0 +1,331 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import os
+import os.path as op
+from pathlib import Path
+
+import numpy as np
+
+from .constants import FIFF
+from .meas_info import _get_valid_units
+
+
+def _check_orig_units(orig_units):
+    """Check original units from a raw file.
+
+    Units that are close to a valid_unit but not equal can be remapped to fit
+    into the valid_units. All other units that are not valid will be replaced
+    with "n/a".
+
+    Parameters
+    ----------
+    orig_units : dict
+        Dictionary mapping channel names to their units as specified in
+        the header file. Example: {'FC1': 'nV'}
+
+    Returns
+    -------
+    orig_units_remapped : dict
+        Dictionary mapping channel names to their VALID units as specified in
+        the header file. Invalid units are now labeled "n/a".
+        Example: {'FC1': 'nV', 'Hfp3erz': 'n/a'}
+    """
+    if orig_units is None:
+        return
+    valid_units = _get_valid_units()
+    valid_units_lowered = [unit.lower() for unit in valid_units]
+    orig_units_remapped = dict(orig_units)
+    for ch_name, unit in orig_units.items():
+        # Be lenient: we ignore case for now.
+        if unit.lower() in valid_units_lowered:
+            continue
+
+        # Common "invalid units" can be remapped to their valid equivalent
+        remap_dict = dict()
+        remap_dict["uv"] = "µV"
+        remap_dict["μv"] = "µV"  # greek letter mu vs micro sign. use micro
+        remap_dict["\x83\xeav"] = "µV"  # for shift-jis mu, use micro
+        if unit.lower() in remap_dict:
+            orig_units_remapped[ch_name] = remap_dict[unit.lower()]
+            continue
+
+        # Some units cannot be saved, they are invalid: assign "n/a"
+        orig_units_remapped[ch_name] = "n/a"
+
+    return orig_units_remapped
+
+
+def _find_channels(ch_names, ch_type="EOG"):
+    """Find EOG channel."""
+    substrings = (ch_type,)
+    substrings = [s.upper() for s in substrings]
+    if ch_type == "EOG":
+        substrings = ("EOG", "EYE")
+    eog_idx = [
+        idx
+        for idx, ch in enumerate(ch_names)
+        if any(substring in ch.upper() for substring in substrings)
+    ]
+    return eog_idx
+
+
+def _mult_cal_one(data_view, one, idx, cals, mult):
+    """Take a chunk of raw data, multiply by mult or cals, and store."""
+    one = np.asarray(one, dtype=data_view.dtype)
+    assert data_view.shape[1] == one.shape[1], (
+        data_view.shape[1],
+        one.shape[1],
+    )  # noqa: E501
+    if mult is not None:
+        assert mult.ndim == one.ndim == 2
+        data_view[:] = mult @ one[idx]
+    else:
+        assert cals is not None
+        if isinstance(idx, slice):
+            data_view[:] = one[idx]
+        else:
+            # faster than doing one = one[idx]
+            np.take(one, idx, axis=0, out=data_view)
+        data_view *= cals
+
+
+def _blk_read_lims(start, stop, buf_len):
+    """Deal with indexing in the middle of a data block.
+
+    Parameters
+    ----------
+    start : int
+        Starting index.
+    stop : int
+        Ending index (exclusive).
+    buf_len : int
+        Buffer size in samples.
+
+    Returns
+    -------
+    block_start_idx : int
+        The first block to start reading from.
+    r_lims : list
+        The read limits.
+    d_lims : list
+        The write limits.
+
+    Notes
+    -----
+    Consider this example::
+
+        >>> start, stop, buf_len = 2, 27, 10
+
+                    +---------+---------+---------
+    File structure: |  buf0   |   buf1  |   buf2  |
+                    +---------+---------+---------
+    File time:      0        10        20        30
+                    +---------+---------+---------
+    Requested time:   2                       27
+
+                    |                             |
+                blockstart                    blockstop
+                      |                        |
+                    start                    stop
+
+    We need 27 - 2 = 25 samples (per channel) to store our data, and
+    we need to read from 3 buffers (30 samples) to get all of our data.
+
+    On all reads but the first, the data we read starts at
+    the first sample of the buffer. On all reads but the last,
+    the data we read ends on the last sample of the buffer.
+
+    We call ``this_data`` the variable that stores the current buffer's data,
+    and ``data`` the variable that stores the total output.
+
+    On the first read, we need to do this::
+
+        >>> data[0:buf_len-2] = this_data[2:buf_len]  # doctest: +SKIP
+
+    On the second read, we need to do::
+
+        >>> data[1*buf_len-2:2*buf_len-2] = this_data[0:buf_len]  # doctest: +SKIP
+
+    On the final read, we need to do::
+
+        >>> data[2*buf_len-2:3*buf_len-2-3] = this_data[0:buf_len-3]  # doctest: +SKIP
+
+    This function encapsulates this logic to allow a loop over blocks, where
+    data is stored using the following limits::
+
+        >>> data[d_lims[ii, 0]:d_lims[ii, 1]] = this_data[r_lims[ii, 0]:r_lims[ii, 1]]  # doctest: +SKIP
+
+    """  # noqa: E501
+    # this is used to deal with indexing in the middle of a sampling period
+    assert all(isinstance(x, int) for x in (start, stop, buf_len))
+    block_start_idx = start // buf_len
+    block_start = block_start_idx * buf_len
+    last_used_samp = stop - 1
+    block_stop = last_used_samp - last_used_samp % buf_len + buf_len
+    read_size = block_stop - block_start
+    n_blk = read_size // buf_len + (read_size % buf_len != 0)
+    start_offset = start - block_start
+    end_offset = block_stop - stop
+    d_lims = np.empty((n_blk, 2), int)
+    r_lims = np.empty((n_blk, 2), int)
+    for bi in range(n_blk):
+        # Triage start (sidx) and end (eidx) indices for
+        # data (d) and read (r)
+        if bi == 0:
+            d_sidx = 0
+            r_sidx = start_offset
+        else:
+            d_sidx = bi * buf_len - start_offset
+            r_sidx = 0
+        if bi == n_blk - 1:
+            d_eidx = stop - start
+            r_eidx = buf_len - end_offset
+        else:
+            d_eidx = (bi + 1) * buf_len - start_offset
+            r_eidx = buf_len
+        d_lims[bi] = [d_sidx, d_eidx]
+        r_lims[bi] = [r_sidx, r_eidx]
+    return block_start_idx, r_lims, d_lims
+
+
+def _file_size(fname):
+    """Get the file size in bytes."""
+    with open(fname, "rb") as f:
+        f.seek(0, os.SEEK_END)
+        return f.tell()
+
+
+def _read_segments_file(
+    raw,
+    data,
+    idx,
+    fi,
+    start,
+    stop,
+    cals,
+    mult,
+    dtype,
+    n_channels=None,
+    offset=0,
+    trigger_ch=None,
+):
+    """Read a chunk of raw data."""
+    if n_channels is None:
+        n_channels = raw._raw_extras[fi]["orig_nchan"]
+
+    n_bytes = np.dtype(dtype).itemsize
+    # data_offset and data_left count data samples (channels x time points),
+    # not bytes.
+    data_offset = n_channels * start * n_bytes + offset
+    data_left = (stop - start) * n_channels
+
+    # Read up to 100 MB of data at a time, block_size is in data samples
+    block_size = ((int(100e6) // n_bytes) // n_channels) * n_channels
+    block_size = min(data_left, block_size)
+    with open(raw.filenames[fi], "rb", buffering=0) as fid:
+        fid.seek(data_offset)
+        # extract data in chunks
+        for sample_start in np.arange(0, data_left, block_size) // n_channels:
+            count = min(block_size, data_left - sample_start * n_channels)
+            block = np.fromfile(fid, dtype, count)
+            if block.size != count:
+                raise RuntimeError(
+                    f"Incorrect number of samples ({block.size} != {count}), please "
+                    "report this error to MNE-Python developers"
+                )
+            block = block.reshape(n_channels, -1, order="F")
+            n_samples = block.shape[1]  # = count // n_channels
+            sample_stop = sample_start + n_samples
+            if trigger_ch is not None:
+                stim_ch = trigger_ch[start:stop][sample_start:sample_stop]
+                block = np.vstack((block, stim_ch))
+            data_view = data[:, sample_start:sample_stop]
+            _mult_cal_one(data_view, block, idx, cals, mult)
+
+
+def read_str(fid, count=1):
+    """Read string from a binary file in a python version compatible way."""
+    dtype = np.dtype(f">S{count}")
+    string = fid.read(dtype.itemsize)
+    data = np.frombuffer(string, dtype=dtype)[0]
+    bytestr = b"".join([data[0 : data.index(b"\x00") if b"\x00" in data else count]])
+
+    return str(bytestr.decode("ascii"))  # Return native str type for Py2/3
+
+
+def _create_chs(ch_names, cals, ch_coil, ch_kind, eog, ecg, emg, misc):
+    """Initialize info['chs'] for eeg channels."""
+    chs = list()
+    for idx, ch_name in enumerate(ch_names):
+        if ch_name in eog or idx in eog:
+            coil_type = FIFF.FIFFV_COIL_NONE
+            kind = FIFF.FIFFV_EOG_CH
+        elif ch_name in ecg or idx in ecg:
+            coil_type = FIFF.FIFFV_COIL_NONE
+            kind = FIFF.FIFFV_ECG_CH
+        elif ch_name in emg or idx in emg:
+            coil_type = FIFF.FIFFV_COIL_NONE
+            kind = FIFF.FIFFV_EMG_CH
+        elif ch_name in misc or idx in misc:
+            coil_type = FIFF.FIFFV_COIL_NONE
+            kind = FIFF.FIFFV_MISC_CH
+        else:
+            coil_type = ch_coil
+            kind = ch_kind
+
+        chan_info = {
+            "cal": cals[idx],
+            "logno": idx + 1,
+            "scanno": idx + 1,
+            "range": 1.0,
+            "unit_mul": FIFF.FIFF_UNITM_NONE,
+            "ch_name": ch_name,
+            "unit": FIFF.FIFF_UNIT_V,
+            "coord_frame": FIFF.FIFFV_COORD_HEAD,
+            "coil_type": coil_type,
+            "kind": kind,
+            "loc": np.zeros(12),
+        }
+        if coil_type == FIFF.FIFFV_COIL_EEG:
+            chan_info["loc"][:3] = np.nan
+        chs.append(chan_info)
+    return chs
+
+
+def _construct_bids_filename(base, ext, part_idx, validate=True):
+    """Construct a BIDS compatible filename for split files."""
+    # insert index in filename
+    dirname = op.dirname(base)
+    base = op.basename(base)
+    deconstructed_base = base.split("_")
+    if len(deconstructed_base) < 2 and validate:
+        raise ValueError(
+            "Filename base must end with an underscore followed "
+            f"by the modality (e.g., _eeg or _meg), got {base}"
+        )
+    suffix = deconstructed_base[-1]
+    base = "_".join(deconstructed_base[:-1])
+    use_fname = f"{base}_split-{part_idx + 1:02}_{suffix}{ext}"
+    if dirname:
+        use_fname = op.join(dirname, use_fname)
+    return use_fname
+
+
+def _make_split_fnames(fname, n_splits, split_naming):
+    """Make a list of split filenames."""
+    if n_splits == 1:
+        fname = Path(fname)
+        return [fname]
+    res = []
+    base, ext = op.splitext(fname)
+    for i in range(n_splits):
+        if split_naming == "neuromag":
+            path = Path(f"{base}-{i:d}{ext}" if i else fname)
+            res.append(path)
+        else:
+            assert split_naming == "bids"
+            path = Path(_construct_bids_filename(base, ext, i))
+            res.append(path)
+    return res

mne/_fiff/what.py

@@ -0,0 +1,70 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from collections import OrderedDict
+from inspect import signature
+
+from ..utils import _check_fname, logger
+
+
+def what(fname):
+    """Try to determine the type of the FIF file.
+
+    Parameters
+    ----------
+    fname : path-like
+        The filename. Should end in ``.fif`` or ``.fif.gz``.
+
+    Returns
+    -------
+    what : str | None
+        The type of the file. Will be 'unknown' if it could not be determined.
+
+    Notes
+    -----
+    .. versionadded:: 0.19
+    """
+    from ..bem import read_bem_solution, read_bem_surfaces
+    from ..cov import read_cov
+    from ..epochs import read_epochs
+    from ..event import read_events
+    from ..evoked import read_evokeds
+    from ..forward import read_forward_solution
+    from ..io import read_raw_fif
+    from ..minimum_norm import read_inverse_operator
+    from ..preprocessing import read_ica
+    from ..proj import read_proj
+    from ..source_space import read_source_spaces
+    from ..transforms import read_trans
+    from .meas_info import read_fiducials
+
+    fname = _check_fname(fname, overwrite="read", must_exist=True)
+    checks = OrderedDict()
+    checks["raw"] = read_raw_fif
+    checks["ica"] = read_ica
+    checks["epochs"] = read_epochs
+    checks["evoked"] = read_evokeds
+    checks["forward"] = read_forward_solution
+    checks["inverse"] = read_inverse_operator
+    checks["src"] = read_source_spaces
+    checks["bem solution"] = read_bem_solution
+    checks["bem surfaces"] = read_bem_surfaces
+    checks["cov"] = read_cov
+    checks["transform"] = read_trans
+    checks["events"] = read_events
+    checks["fiducials"] = read_fiducials
+    checks["proj"] = read_proj
+    for what, func in checks.items():
+        args = signature(func).parameters
+        assert "verbose" in args, func
+        kwargs = dict(verbose="error")
+        if "preload" in args:
+            kwargs["preload"] = False
+        try:
+            func(fname, **kwargs)
+        except Exception as exp:
+            logger.debug(f"Not {what}: {exp}")
+        else:
+            return what
+    return "unknown"

mne/_fiff/write.py

@@ -0,0 +1,454 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import datetime
+import os.path as op
+import re
+import time
+import uuid
+from contextlib import contextmanager
+from gzip import GzipFile
+
+import numpy as np
+from scipy.sparse import csc_array, csr_array
+
+from ..utils import _file_like, _validate_type, logger
+from ..utils.numerics import _date_to_julian
+from .constants import FIFF
+
+# We choose a "magic" date to store (because meas_date is obligatory)
+# to treat as meas_date=None. This one should be impossible for systems
+# to write -- the second field is microseconds, so anything >= 1e6
+# should be moved into the first field (seconds).
+DATE_NONE = (0, 2**31 - 1)
+
+
+def _write(fid, data, kind, data_size, FIFFT_TYPE, dtype):
+    """Write data."""
+    if isinstance(data, np.ndarray):
+        data_size *= data.size
+
+    # XXX for string types the data size is used as
+    # computed in ``write_string``.
+
+    fid.write(np.array(kind, dtype=">i4").tobytes())
+    fid.write(np.array(FIFFT_TYPE, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+    fid.write(np.array(data, dtype=dtype).tobytes())
+
+
+def _get_split_size(split_size):
+    """Convert human-readable bytes to machine-readable bytes."""
+    if isinstance(split_size, str):
+        exp = dict(MB=20, GB=30).get(split_size[-2:], None)
+        if exp is None:
+            raise ValueError('split_size has to end with either "MB" or "GB"')
+        split_size = int(float(split_size[:-2]) * 2**exp)
+
+    if split_size > 2147483648:
+        raise ValueError("split_size cannot be larger than 2GB")
+    return split_size
+
+
+_NEXT_FILE_BUFFER = 1048576  # 2 ** 20 extra cushion for last post-data tags
+
+
+def write_nop(fid, last=False):
+    """Write a FIFF_NOP."""
+    fid.write(np.array(FIFF.FIFF_NOP, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFT_VOID, dtype=">i4").tobytes())
+    fid.write(np.array(0, dtype=">i4").tobytes())
+    next_ = FIFF.FIFFV_NEXT_NONE if last else FIFF.FIFFV_NEXT_SEQ
+    fid.write(np.array(next_, dtype=">i4").tobytes())
+
+
+INT32_MAX = 2147483647
+
+
+def write_int(fid, kind, data):
+    """Write a 32-bit integer tag to a fif file."""
+    data_size = 4
+    data = np.asarray(data)
+    if data.dtype.kind not in "uib" and data.size > 0:
+        raise TypeError(
+            f"Cannot safely write data kind {kind} with dtype {data.dtype} as int",
+        )
+    max_val = data.max() if data.size > 0 else 0
+    if max_val > INT32_MAX:
+        raise TypeError(
+            f"Value {max_val} exceeds maximum allowed ({INT32_MAX}) for tag {kind}"
+        )
+    data = data.astype(">i4").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_INT, ">i4")
+
+
+def write_double(fid, kind, data):
+    """Write a double-precision floating point tag to a fif file."""
+    data_size = 8
+    data = np.array(data, dtype=">f8").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_DOUBLE, ">f8")
+
+
+def write_float(fid, kind, data):
+    """Write a single-precision floating point tag to a fif file."""
+    data_size = 4
+    data = np.array(data, dtype=">f4").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_FLOAT, ">f4")
+
+
+def write_dau_pack16(fid, kind, data):
+    """Write a dau_pack16 tag to a fif file."""
+    data_size = 2
+    data = np.array(data, dtype=">i2").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_DAU_PACK16, ">i2")
+
+
+def write_complex64(fid, kind, data):
+    """Write a 64 bit complex floating point tag to a fif file."""
+    data_size = 8
+    data = np.array(data, dtype=">c8").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_COMPLEX_FLOAT, ">c8")
+
+
+def write_complex128(fid, kind, data):
+    """Write a 128 bit complex floating point tag to a fif file."""
+    data_size = 16
+    data = np.array(data, dtype=">c16").T
+    _write(fid, data, kind, data_size, FIFF.FIFFT_COMPLEX_FLOAT, ">c16")
+
+
+def write_julian(fid, kind, data):
+    """Write a Julian-formatted date to a FIF file."""
+    assert isinstance(data, datetime.date), type(data)
+    data_size = 4
+    jd = _date_to_julian(data)
+    data = np.array(jd, dtype=">i4")
+    _write(fid, data, kind, data_size, FIFF.FIFFT_JULIAN, ">i4")
+
+
+def write_string(fid, kind, data):
+    """Write a string tag."""
+    try:
+        str_data = str(data).encode("latin1")
+    except UnicodeEncodeError:
+        str_data = str(data).encode("latin1", errors="xmlcharrefreplace")
+    data_size = len(str_data)  # therefore compute size here
+    if data_size > 0:
+        _write(fid, str_data, kind, data_size, FIFF.FIFFT_STRING, ">S")
+
+
+def write_name_list(fid, kind, data):
+    """Write a colon-separated list of names.
+
+    Parameters
+    ----------
+    data : list of strings
+    """
+    write_string(fid, kind, ":".join(data))
+
+
+def write_name_list_sanitized(fid, kind, lst, name):
+    """Write a sanitized, colon-separated list of names."""
+    write_string(fid, kind, _safe_name_list(lst, "write", name))
+
+
+def _safe_name_list(lst, operation, name):
+    if operation == "write":
+        assert isinstance(lst, list | tuple | np.ndarray), type(lst)
+        if any("{COLON}" in val for val in lst):
+            raise ValueError(f'The substring "{{COLON}}" in {name} not supported.')
+        return ":".join(val.replace(":", "{COLON}") for val in lst)
+    else:
+        # take a sanitized string and return a list of strings
+        assert operation == "read"
+        assert lst is None or isinstance(lst, str)
+        if not lst:  # None or empty string
+            return []
+        return [val.replace("{COLON}", ":") for val in lst.split(":")]
+
+
+def write_float_matrix(fid, kind, mat):
+    """Write a single-precision floating-point matrix tag."""
+    _write_matrix_data(fid, kind, mat, FIFF.FIFFT_FLOAT)
+
+
+def write_double_matrix(fid, kind, mat):
+    """Write a double-precision floating-point matrix tag."""
+    _write_matrix_data(fid, kind, mat, FIFF.FIFFT_DOUBLE)
+
+
+def write_int_matrix(fid, kind, mat):
+    """Write integer 32 matrix tag."""
+    _write_matrix_data(fid, kind, mat, FIFF.FIFFT_INT)
+
+
+def write_complex_float_matrix(fid, kind, mat):
+    """Write complex 64 matrix tag."""
+    _write_matrix_data(fid, kind, mat, FIFF.FIFFT_COMPLEX_FLOAT)
+
+
+def write_complex_double_matrix(fid, kind, mat):
+    """Write complex 128 matrix tag."""
+    _write_matrix_data(fid, kind, mat, FIFF.FIFFT_COMPLEX_DOUBLE)
+
+
+def _write_matrix_data(fid, kind, mat, data_type):
+    dtype = {
+        FIFF.FIFFT_FLOAT: ">f4",
+        FIFF.FIFFT_DOUBLE: ">f8",
+        FIFF.FIFFT_COMPLEX_FLOAT: ">c8",
+        FIFF.FIFFT_COMPLEX_DOUBLE: ">c16",
+        FIFF.FIFFT_INT: ">i4",
+    }[data_type]
+    dtype = np.dtype(dtype)
+    data_size = dtype.itemsize * mat.size + 4 * (mat.ndim + 1)
+    matrix_type = data_type | FIFF.FIFFT_MATRIX
+    fid.write(np.array(kind, dtype=">i4").tobytes())
+    fid.write(np.array(matrix_type, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+    fid.write(np.array(mat, dtype=dtype).tobytes())
+    dims = np.empty(mat.ndim + 1, dtype=np.int32)
+    dims[: mat.ndim] = mat.shape[::-1]
+    dims[-1] = mat.ndim
+    fid.write(np.array(dims, dtype=">i4").tobytes())
+    check_fiff_length(fid)
+
+
+def get_machid():
+    """Get (mostly) unique machine ID.
+
+    Returns
+    -------
+    ids : array (length 2, int32)
+        The machine identifier used in MNE.
+    """
+    mac = f"{uuid.getnode():012x}".encode()  # byte conversion for Py3
+    mac = re.findall(b"..", mac)  # split string
+    mac += [b"00", b"00"]  # add two more fields
+
+    # Convert to integer in reverse-order (for some reason)
+    from codecs import encode
+
+    mac = b"".join([encode(h, "hex_codec") for h in mac[::-1]])
+    ids = np.flipud(np.frombuffer(mac, np.int32, count=2))
+    return ids
+
+
+def get_new_file_id():
+    """Create a new file ID tag."""
+    secs, usecs = divmod(time.time(), 1.0)
+    secs, usecs = int(secs), int(usecs * 1e6)
+    return {
+        "machid": get_machid(),
+        "version": FIFF.FIFFC_VERSION,
+        "secs": secs,
+        "usecs": usecs,
+    }
+
+
+def write_id(fid, kind, id_=None):
+    """Write fiff id."""
+    id_ = _generate_meas_id() if id_ is None else id_
+
+    data_size = 5 * 4  # The id comprises five integers
+    fid.write(np.array(kind, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFT_ID_STRUCT, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+
+    # Collect the bits together for one write
+    arr = np.array(
+        [id_["version"], id_["machid"][0], id_["machid"][1], id_["secs"], id_["usecs"]],
+        dtype=">i4",
+    )
+    fid.write(arr.tobytes())
+
+
+def start_block(fid, kind):
+    """Write a FIFF_BLOCK_START tag."""
+    write_int(fid, FIFF.FIFF_BLOCK_START, kind)
+
+
+def end_block(fid, kind):
+    """Write a FIFF_BLOCK_END tag."""
+    write_int(fid, FIFF.FIFF_BLOCK_END, kind)
+
+
+def start_file(fname, id_=None):
+    """Open a fif file for writing and writes the compulsory header tags.
+
+    Parameters
+    ----------
+    fname : path-like | fid
+        The name of the file to open. It is recommended
+        that the name ends with .fif or .fif.gz. Can also be an
+        already opened file.
+    id_ : dict | None
+        ID to use for the FIFF_FILE_ID.
+    """
+    if _file_like(fname):
+        logger.debug(f"Writing using {type(fname)} I/O")
+        fid = fname
+        fid.seek(0)
+    else:
+        fname = str(fname)
+        if op.splitext(fname)[1].lower() == ".gz":
+            logger.debug("Writing using gzip")
+            # defaults to compression level 9, which is barely smaller but much
+            # slower. 2 offers a good compromise.
+            fid = GzipFile(fname, "wb", compresslevel=2)
+        else:
+            logger.debug("Writing using normal I/O")
+            fid = open(fname, "wb")
+    #   Write the compulsory items
+    write_id(fid, FIFF.FIFF_FILE_ID, id_)
+    write_int(fid, FIFF.FIFF_DIR_POINTER, -1)
+    write_int(fid, FIFF.FIFF_FREE_LIST, -1)
+    return fid
+
+
+@contextmanager
+def start_and_end_file(fname, id_=None):
+    """Start and (if successfully written) close the file."""
+    with start_file(fname, id_=id_) as fid:
+        yield fid
+        end_file(fid)  # we only hit this line if the yield does not err
+
+
+def check_fiff_length(fid, close=True):
+    """Ensure our file hasn't grown too large to work properly."""
+    if fid.tell() > 2147483648:  # 2 ** 31, FIFF uses signed 32-bit locations
+        if close:
+            fid.close()
+        raise OSError(
+            "FIFF file exceeded 2GB limit, please split file, reduce"
+            " split_size (if possible), or save to a different "
+            "format"
+        )
+
+
+def end_file(fid):
+    """Write the closing tags to a fif file and closes the file."""
+    write_nop(fid, last=True)
+    check_fiff_length(fid)
+    fid.close()
+
+
+def write_coord_trans(fid, trans):
+    """Write a coordinate transformation structure."""
+    data_size = 4 * 2 * 12 + 4 * 2
+    fid.write(np.array(FIFF.FIFF_COORD_TRANS, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFT_COORD_TRANS_STRUCT, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+    fid.write(np.array(trans["from"], dtype=">i4").tobytes())
+    fid.write(np.array(trans["to"], dtype=">i4").tobytes())
+
+    #   The transform...
+    rot = trans["trans"][:3, :3]
+    move = trans["trans"][:3, 3]
+    fid.write(np.array(rot, dtype=">f4").tobytes())
+    fid.write(np.array(move, dtype=">f4").tobytes())
+
+    #   ...and its inverse
+    trans_inv = np.linalg.inv(trans["trans"])
+    rot = trans_inv[:3, :3]
+    move = trans_inv[:3, 3]
+    fid.write(np.array(rot, dtype=">f4").tobytes())
+    fid.write(np.array(move, dtype=">f4").tobytes())
+
+
+def write_ch_info(fid, ch):
+    """Write a channel information record to a fif file."""
+    data_size = 4 * 13 + 4 * 7 + 16
+
+    fid.write(np.array(FIFF.FIFF_CH_INFO, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFT_CH_INFO_STRUCT, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+
+    #   Start writing fiffChInfoRec
+    fid.write(np.array(ch["scanno"], dtype=">i4").tobytes())
+    fid.write(np.array(ch["logno"], dtype=">i4").tobytes())
+    fid.write(np.array(ch["kind"], dtype=">i4").tobytes())
+    fid.write(np.array(ch["range"], dtype=">f4").tobytes())
+    fid.write(np.array(ch["cal"], dtype=">f4").tobytes())
+    fid.write(np.array(ch["coil_type"], dtype=">i4").tobytes())
+    fid.write(np.array(ch["loc"], dtype=">f4").tobytes())  # writing 12 values
+
+    #   unit and unit multiplier
+    fid.write(np.array(ch["unit"], dtype=">i4").tobytes())
+    fid.write(np.array(ch["unit_mul"], dtype=">i4").tobytes())
+
+    #   Finally channel name
+    ch_name = ch["ch_name"][:15]
+    fid.write(np.array(ch_name, dtype=">c").tobytes())
+    fid.write(b"\0" * (16 - len(ch_name)))
+
+
+def write_dig_points(fid, dig, block=False, coord_frame=None, *, ch_names=None):
+    """Write a set of digitizer data points into a fif file."""
+    if dig is not None:
+        data_size = 5 * 4
+        if block:
+            start_block(fid, FIFF.FIFFB_ISOTRAK)
+        if coord_frame is not None:
+            write_int(fid, FIFF.FIFF_MNE_COORD_FRAME, coord_frame)
+        for d in dig:
+            fid.write(np.array(FIFF.FIFF_DIG_POINT, ">i4").tobytes())
+            fid.write(np.array(FIFF.FIFFT_DIG_POINT_STRUCT, ">i4").tobytes())
+            fid.write(np.array(data_size, dtype=">i4").tobytes())
+            fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, ">i4").tobytes())
+            #   Start writing fiffDigPointRec
+            fid.write(np.array(d["kind"], ">i4").tobytes())
+            fid.write(np.array(d["ident"], ">i4").tobytes())
+            fid.write(np.array(d["r"][:3], ">f4").tobytes())
+        if ch_names is not None:
+            write_name_list_sanitized(
+                fid, FIFF.FIFF_MNE_CH_NAME_LIST, ch_names, "ch_names"
+            )
+        if block:
+            end_block(fid, FIFF.FIFFB_ISOTRAK)
+
+
+def write_float_sparse_rcs(fid, kind, mat):
+    """Write a single-precision sparse compressed row matrix tag."""
+    return write_float_sparse(fid, kind, mat, fmt="csr")
+
+
+def write_float_sparse(fid, kind, mat, fmt="auto"):
+    """Write a single-precision floating-point sparse matrix tag."""
+    if fmt == "auto":
+        fmt = "csr" if isinstance(mat, csr_array) else "csc"
+    need = csr_array if fmt == "csr" else csc_array
+    matrix_type = getattr(FIFF, f"FIFFT_SPARSE_{fmt[-1].upper()}CS_MATRIX")
+    _validate_type(mat, need, "sparse")
+    matrix_type = matrix_type | FIFF.FIFFT_MATRIX | FIFF.FIFFT_FLOAT
+    nnzm = mat.nnz
+    nrow = mat.shape[0]
+    data_size = 4 * nnzm + 4 * nnzm + 4 * (nrow + 1) + 4 * 4
+
+    fid.write(np.array(kind, dtype=">i4").tobytes())
+    fid.write(np.array(matrix_type, dtype=">i4").tobytes())
+    fid.write(np.array(data_size, dtype=">i4").tobytes())
+    fid.write(np.array(FIFF.FIFFV_NEXT_SEQ, dtype=">i4").tobytes())
+
+    fid.write(np.array(mat.data, dtype=">f4").tobytes())
+    fid.write(np.array(mat.indices, dtype=">i4").tobytes())
+    fid.write(np.array(mat.indptr, dtype=">i4").tobytes())
+
+    dims = [nnzm, mat.shape[0], mat.shape[1], 2]
+    fid.write(np.array(dims, dtype=">i4").tobytes())
+    check_fiff_length(fid)
+
+
+def _generate_meas_id():
+    """Generate a new meas_id dict."""
+    id_ = dict()
+    id_["version"] = FIFF.FIFFC_VERSION
+    id_["machid"] = get_machid()
+    id_["secs"], id_["usecs"] = DATE_NONE
+    return id_

mne/_freesurfer.py

@@ -0,0 +1,854 @@
+"""Freesurfer handling functions."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import os.path as op
+from gzip import GzipFile
+from pathlib import Path
+
+import numpy as np
+
+from ._fiff.constants import FIFF
+from ._fiff.meas_info import read_fiducials
+from .surface import _read_mri_surface, read_surface
+from .transforms import (
+    Transform,
+    _ensure_trans,
+    apply_trans,
+    combine_transforms,
+    invert_transform,
+    read_ras_mni_t,
+)
+from .utils import (
+    _check_fname,
+    _check_option,
+    _import_nibabel,
+    _validate_type,
+    get_subjects_dir,
+    logger,
+    verbose,
+)
+
+
+def _check_subject_dir(subject, subjects_dir):
+    """Check that the Freesurfer subject directory is as expected."""
+    subjects_dir = Path(get_subjects_dir(subjects_dir, raise_error=True))
+    for img_name in ("T1", "brain", "aseg"):
+        if not (subjects_dir / subject / "mri" / f"{img_name}.mgz").is_file():
+            raise ValueError(
+                "Freesurfer recon-all subject folder "
+                "is incorrect or improperly formatted, "
+                f"got {subjects_dir / subject}"
+            )
+    return subjects_dir / subject
+
+
+def _get_aseg(aseg, subject, subjects_dir):
+    """Check that the anatomical segmentation file exists and load it."""
+    nib = _import_nibabel("load aseg")
+    subjects_dir = Path(get_subjects_dir(subjects_dir, raise_error=True))
+    if aseg == "auto":  # use aparc+aseg if auto
+        aseg = _check_fname(
+            subjects_dir / subject / "mri" / "aparc+aseg.mgz",
+            overwrite="read",
+            must_exist=False,
+        )
+        if not aseg:  # if doesn't exist use wmparc
+            aseg = subjects_dir / subject / "mri" / "wmparc.mgz"
+    else:
+        aseg = subjects_dir / subject / "mri" / f"{aseg}.mgz"
+    _check_fname(aseg, overwrite="read", must_exist=True)
+    aseg = nib.load(aseg)
+    aseg_data = np.array(aseg.dataobj)
+    return aseg, aseg_data
+
+
+def _reorient_image(img, axcodes="RAS"):
+    """Reorient an image to a given orientation.
+
+    Parameters
+    ----------
+    img : instance of SpatialImage
+        The MRI image.
+    axcodes : tuple | str
+        The axis codes specifying the orientation, e.g. "RAS".
+        See :func:`nibabel.orientations.aff2axcodes`.
+
+    Returns
+    -------
+    img_data : ndarray
+        The reoriented image data.
+    vox_ras_t : ndarray
+        The new transform from the new voxels to surface RAS.
+
+    Notes
+    -----
+    .. versionadded:: 0.24
+    """
+    nib = _import_nibabel("reorient MRI image")
+    orig_data = np.array(img.dataobj).astype(np.float32)
+    # reorient data to RAS
+    ornt = nib.orientations.axcodes2ornt(
+        nib.orientations.aff2axcodes(img.affine)
+    ).astype(int)
+    ras_ornt = nib.orientations.axcodes2ornt(axcodes)
+    ornt_trans = nib.orientations.ornt_transform(ornt, ras_ornt)
+    img_data = nib.orientations.apply_orientation(orig_data, ornt_trans)
+    orig_mgh = nib.MGHImage(orig_data, img.affine)
+    aff_trans = nib.orientations.inv_ornt_aff(ornt_trans, img.shape)
+    vox_ras_t = np.dot(orig_mgh.header.get_vox2ras_tkr(), aff_trans)
+    return img_data, vox_ras_t
+
+
+def _mri_orientation(orientation):
+    """Get MRI orientation information from an image.
+
+    Parameters
+    ----------
+    orientation : str
+        Orientation that you want. Can be "axial", "sagittal", or "coronal".
+
+    Returns
+    -------
+    axis : int
+        The dimension of the axis to take slices over when plotting.
+    x : int
+        The dimension of the x axis.
+    y : int
+        The dimension of the y axis.
+
+    Notes
+    -----
+    .. versionadded:: 0.21
+    .. versionchanged:: 0.24
+    """
+    _check_option("orientation", orientation, ("coronal", "axial", "sagittal"))
+    axis = dict(coronal=1, axial=2, sagittal=0)[orientation]
+    x, y = sorted(set([0, 1, 2]).difference(set([axis])))
+    return axis, x, y
+
+
+def _get_mri_info_data(mri, data):
+    # Read the segmentation data using nibabel
+    if data:
+        _import_nibabel("load MRI atlas data")
+    out = dict()
+    _, out["vox_mri_t"], out["mri_ras_t"], dims, _, mgz = _read_mri_info(
+        mri, return_img=True
+    )
+    out.update(
+        mri_width=dims[0], mri_height=dims[1], mri_depth=dims[1], mri_volume_name=mri
+    )
+    if data:
+        assert mgz is not None
+        out["mri_vox_t"] = invert_transform(out["vox_mri_t"])
+        out["data"] = np.asarray(mgz.dataobj)
+    return out
+
+
+def _get_mgz_header(fname):
+    """Adapted from nibabel to quickly extract header info."""
+    fname = _check_fname(fname, overwrite="read", must_exist=True, name="MRI image")
+    if fname.suffix != ".mgz":
+        raise OSError("Filename must end with .mgz")
+    header_dtd = [
+        ("version", ">i4"),
+        ("dims", ">i4", (4,)),
+        ("type", ">i4"),
+        ("dof", ">i4"),
+        ("goodRASFlag", ">i2"),
+        ("delta", ">f4", (3,)),
+        ("Mdc", ">f4", (3, 3)),
+        ("Pxyz_c", ">f4", (3,)),
+    ]
+    header_dtype = np.dtype(header_dtd)
+    with GzipFile(fname, "rb") as fid:
+        hdr_str = fid.read(header_dtype.itemsize)
+    header = np.ndarray(shape=(), dtype=header_dtype, buffer=hdr_str)
+    # dims
+    dims = header["dims"].astype(int)
+    dims = dims[:3] if len(dims) == 4 else dims
+    # vox2ras_tkr
+    delta = header["delta"]
+    ds = np.array(delta, float)
+    ns = np.array(dims * ds) / 2.0
+    v2rtkr = np.array(
+        [
+            [-ds[0], 0, 0, ns[0]],
+            [0, 0, ds[2], -ns[2]],
+            [0, -ds[1], 0, ns[1]],
+            [0, 0, 0, 1],
+        ],
+        dtype=np.float32,
+    )
+    # ras2vox
+    d = np.diag(delta)
+    pcrs_c = dims / 2.0
+    Mdc = header["Mdc"].T
+    pxyz_0 = header["Pxyz_c"] - np.dot(Mdc, np.dot(d, pcrs_c))
+    M = np.eye(4, 4)
+    M[0:3, 0:3] = np.dot(Mdc, d)
+    M[0:3, 3] = pxyz_0.T
+    header = dict(dims=dims, vox2ras_tkr=v2rtkr, vox2ras=M, zooms=header["delta"])
+    return header
+
+
+def _get_atlas_values(vol_info, rr):
+    # Transform MRI coordinates (where our surfaces live) to voxels
+    rr_vox = apply_trans(vol_info["mri_vox_t"], rr)
+    good = (
+        (rr_vox >= -0.5) & (rr_vox < np.array(vol_info["data"].shape, int) - 0.5)
+    ).all(-1)
+    idx = np.round(rr_vox[good].T).astype(np.int64)
+    values = np.full(rr.shape[0], np.nan)
+    values[good] = vol_info["data"][tuple(idx)]
+    return values
+
+
+def get_volume_labels_from_aseg(mgz_fname, return_colors=False, atlas_ids=None):
+    """Return a list of names and colors of segmented volumes.
+
+    Parameters
+    ----------
+    mgz_fname : path-like
+        Filename to read. Typically ``aseg.mgz`` or some variant in the
+        freesurfer pipeline.
+    return_colors : bool
+        If True returns also the labels colors.
+    atlas_ids : dict | None
+        A lookup table providing a mapping from region names (str) to ID values
+        (int). Can be None to use the standard Freesurfer LUT.
+
+        .. versionadded:: 0.21.0
+
+    Returns
+    -------
+    label_names : list of str
+        The names of segmented volumes included in this mgz file.
+    label_colors : list of str
+        The RGB colors of the labels included in this mgz file.
+
+    See Also
+    --------
+    read_freesurfer_lut
+
+    Notes
+    -----
+    .. versionchanged:: 0.21.0
+       The label names are now sorted in the same order as their corresponding
+       values in the MRI file.
+
+    .. versionadded:: 0.9.0
+    """
+    nib = _import_nibabel("load MRI atlas data")
+    mgz_fname = _check_fname(
+        mgz_fname, overwrite="read", must_exist=True, name="mgz_fname"
+    )
+    atlas = nib.load(mgz_fname)
+    data = np.asarray(atlas.dataobj)  # don't need float here
+    want = np.unique(data)
+    if atlas_ids is None:
+        atlas_ids, colors = read_freesurfer_lut()
+    elif return_colors:
+        raise ValueError("return_colors must be False if atlas_ids are provided")
+    # restrict to the ones in the MRI, sorted by label name
+    keep = np.isin(list(atlas_ids.values()), want)
+    keys = sorted(
+        (key for ki, key in enumerate(atlas_ids.keys()) if keep[ki]),
+        key=lambda x: atlas_ids[x],
+    )
+    if return_colors:
+        colors = [colors[k] for k in keys]
+        out = keys, colors
+    else:
+        out = keys
+    return out
+
+
+##############################################################################
+# Head to MRI volume conversion
+
+
+@verbose
+def head_to_mri(
+    pos,
+    subject,
+    mri_head_t,
+    subjects_dir=None,
+    *,
+    kind="mri",
+    unscale=False,
+    verbose=None,
+):
+    """Convert pos from head coordinate system to MRI ones.
+
+    Parameters
+    ----------
+    pos : array, shape (n_pos, 3)
+        The coordinates (in m) in head coordinate system.
+    %(subject)s
+    mri_head_t : instance of Transform
+        MRI<->Head coordinate transformation.
+    %(subjects_dir)s
+    kind : str
+        The  MRI coordinate frame kind, can be ``'mri'`` (default) for
+        FreeSurfer surface RAS or ``'ras'`` (default in 1.2) to use MRI RAS
+        (scanner RAS).
+
+        .. versionadded:: 1.2
+    unscale : bool
+        For surrogate MRIs (e.g., scaled using ``mne coreg``), if True
+        (default False), use the MRI scaling parameters to obtain points in
+        the original/surrogate subject's MRI space.
+
+        .. versionadded:: 1.2
+    %(verbose)s
+
+    Returns
+    -------
+    coordinates : array, shape (n_pos, 3)
+        The MRI RAS coordinates (in mm) of pos.
+
+    Notes
+    -----
+    This function requires nibabel.
+    """
+    from .coreg import read_mri_cfg
+
+    _validate_type(kind, str, "kind")
+    _check_option("kind", kind, ("ras", "mri"))
+    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
+    t1_fname = subjects_dir / subject / "mri" / "T1.mgz"
+    head_mri_t = _ensure_trans(mri_head_t, "head", "mri")
+    if kind == "ras":
+        _, _, mri_ras_t, _, _ = _read_mri_info(t1_fname)
+        head_ras_t = combine_transforms(head_mri_t, mri_ras_t, "head", "ras")
+        head_dest_t = head_ras_t
+    else:
+        assert kind == "mri"
+        head_dest_t = head_mri_t
+    pos_dest = apply_trans(head_dest_t, pos)
+    # unscale if requested
+    if unscale:
+        params = read_mri_cfg(subject, subjects_dir)
+        pos_dest /= params["scale"]
+    pos_dest *= 1e3  # mm
+    return pos_dest
+
+
+##############################################################################
+# Surface to MNI conversion
+
+
+@verbose
+def vertex_to_mni(vertices, hemis, subject, subjects_dir=None, verbose=None):
+    """Convert the array of vertices for a hemisphere to MNI coordinates.
+
+    Parameters
+    ----------
+    vertices : int, or list of int
+        Vertex number(s) to convert.
+    hemis : int, or list of int
+        Hemisphere(s) the vertices belong to.
+    %(subject)s
+    subjects_dir : str, or None
+        Path to ``SUBJECTS_DIR`` if it is not set in the environment.
+    %(verbose)s
+
+    Returns
+    -------
+    coordinates : array, shape (n_vertices, 3)
+        The MNI coordinates (in mm) of the vertices.
+    """
+    singleton = False
+    if not isinstance(vertices, list) and not isinstance(vertices, np.ndarray):
+        singleton = True
+        vertices = [vertices]
+
+    if not isinstance(hemis, list) and not isinstance(hemis, np.ndarray):
+        hemis = [hemis] * len(vertices)
+
+    if not len(hemis) == len(vertices):
+        raise ValueError("hemi and vertices must match in length")
+
+    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
+
+    surfs = [subjects_dir / subject / "surf" / f"{h}.white" for h in ["lh", "rh"]]
+
+    # read surface locations in MRI space
+    rr = [read_surface(s)[0] for s in surfs]
+
+    # take point locations in MRI space and convert to MNI coordinates
+    xfm = read_talxfm(subject, subjects_dir)
+    xfm["trans"][:3, 3] *= 1000.0  # m->mm
+    data = np.array([rr[h][v, :] for h, v in zip(hemis, vertices)])
+    if singleton:
+        data = data[0]
+    return apply_trans(xfm["trans"], data)
+
+
+##############################################################################
+# Volume to MNI conversion
+
+
+@verbose
+def head_to_mni(pos, subject, mri_head_t, subjects_dir=None, verbose=None):
+    """Convert pos from head coordinate system to MNI ones.
+
+    Parameters
+    ----------
+    pos : array, shape (n_pos, 3)
+        The coordinates (in m) in head coordinate system.
+    %(subject)s
+    mri_head_t : instance of Transform
+        MRI<->Head coordinate transformation.
+    %(subjects_dir)s
+    %(verbose)s
+
+    Returns
+    -------
+    coordinates : array, shape (n_pos, 3)
+        The MNI coordinates (in mm) of pos.
+
+    Notes
+    -----
+    This function requires either nibabel.
+    """
+    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
+
+    # before we go from head to MRI (surface RAS)
+    head_mni_t = combine_transforms(
+        _ensure_trans(mri_head_t, "head", "mri"),
+        read_talxfm(subject, subjects_dir),
+        "head",
+        "mni_tal",
+    )
+    return apply_trans(head_mni_t, pos) * 1000.0
+
+
+@verbose
+def get_mni_fiducials(subject, subjects_dir=None, verbose=None):
+    """Estimate fiducials for a subject.
+
+    Parameters
+    ----------
+    %(subject)s
+    %(subjects_dir)s
+    %(verbose)s
+
+    Returns
+    -------
+    fids_mri : list
+        List of estimated fiducials (each point in a dict), in the order
+        LPA, nasion, RPA.
+
+    Notes
+    -----
+    This takes the ``fsaverage-fiducials.fif`` file included with MNE—which
+    contain the LPA, nasion, and RPA for the ``fsaverage`` subject—and
+    transforms them to the given FreeSurfer subject's MRI space.
+    The MRI of ``fsaverage`` is already in MNI Talairach space, so applying
+    the inverse of the given subject's MNI Talairach affine transformation
+    (``$SUBJECTS_DIR/$SUBJECT/mri/transforms/talairach.xfm``) is used
+    to estimate the subject's fiducial locations.
+
+    For more details about the coordinate systems and transformations involved,
+    see https://surfer.nmr.mgh.harvard.edu/fswiki/CoordinateSystems and
+    :ref:`tut-source-alignment`.
+    """
+    # Eventually we might want to allow using the MNI Talairach with-skull
+    # transformation rather than the standard brain-based MNI Talaranch
+    # transformation, and/or project the points onto the head surface
+    # (if available).
+    fname_fids_fs = (
+        Path(__file__).parent / "data" / "fsaverage" / "fsaverage-fiducials.fif"
+    )
+
+    # Read fsaverage fiducials file and subject Talairach.
+    fids, coord_frame = read_fiducials(fname_fids_fs)
+    assert coord_frame == FIFF.FIFFV_COORD_MRI
+    if subject == "fsaverage":
+        return fids  # special short-circuit for fsaverage
+    mni_mri_t = invert_transform(read_talxfm(subject, subjects_dir))
+    for f in fids:
+        f["r"] = apply_trans(mni_mri_t, f["r"])
+    return fids
+
+
+@verbose
+def estimate_head_mri_t(subject, subjects_dir=None, verbose=None):
+    """Estimate the head->mri transform from fsaverage fiducials.
+
+    A subject's fiducials can be estimated given a Freesurfer ``recon-all``
+    by transforming ``fsaverage`` fiducials using the inverse Talairach
+    transform, see :func:`mne.coreg.get_mni_fiducials`.
+
+    Parameters
+    ----------
+    %(subject)s
+    %(subjects_dir)s
+    %(verbose)s
+
+    Returns
+    -------
+    %(trans_not_none)s
+    """
+    from .channels.montage import compute_native_head_t, make_dig_montage
+
+    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
+    lpa, nasion, rpa = get_mni_fiducials(subject, subjects_dir)
+    montage = make_dig_montage(
+        lpa=lpa["r"], nasion=nasion["r"], rpa=rpa["r"], coord_frame="mri"
+    )
+    return invert_transform(compute_native_head_t(montage))
+
+
+def _get_affine_from_lta_info(lines):
+    """Get the vox2ras affine from lta file info."""
+    volume_data = np.loadtxt([line.split("=")[1] for line in lines])
+    # get the size of the volume (number of voxels), slice resolution.
+    # the matrix of directional cosines and the ras at the center of the bore
+    dims, deltas, dir_cos, center_ras = (
+        volume_data[0],
+        volume_data[1],
+        volume_data[2:5],
+        volume_data[5],
+    )
+    dir_cos_delta = dir_cos.T * deltas
+    vol_center = (dir_cos_delta @ dims[:3]) / 2
+    affine = np.eye(4)
+    affine[:3, :3] = dir_cos_delta
+    affine[:3, 3] = center_ras - vol_center
+    return affine
+
+
+@verbose
+def read_lta(fname, verbose=None):
+    """Read a Freesurfer linear transform array file.
+
+    Parameters
+    ----------
+    fname : path-like
+        The transform filename.
+    %(verbose)s
+
+    Returns
+    -------
+    affine : ndarray
+        The affine transformation described by the lta file.
+    """
+    _check_fname(fname, "read", must_exist=True)
+    with open(fname) as fid:
+        lines = fid.readlines()
+    # 0 is linear vox2vox, 1 is linear ras2ras
+    trans_type = int(lines[0].split("=")[1].strip()[0])
+    assert trans_type in (0, 1)
+    affine = np.loadtxt(lines[5:9])
+    if trans_type == 1:
+        return affine
+
+    src_affine = _get_affine_from_lta_info(lines[12:18])
+    dst_affine = _get_affine_from_lta_info(lines[21:27])
+
+    # don't compute if src and dst are already identical
+    if np.allclose(src_affine, dst_affine):
+        return affine
+
+    ras2ras = src_affine @ np.linalg.inv(affine) @ np.linalg.inv(dst_affine)
+    affine = np.linalg.inv(np.linalg.inv(src_affine) @ ras2ras @ src_affine)
+    return affine
+
+
+@verbose
+def read_talxfm(subject, subjects_dir=None, verbose=None):
+    """Compute MRI-to-MNI transform from FreeSurfer talairach.xfm file.
+
+    Parameters
+    ----------
+    %(subject)s
+    %(subjects_dir)s
+    %(verbose)s
+
+    Returns
+    -------
+    mri_mni_t : instance of Transform
+        The affine transformation from MRI to MNI space for the subject.
+    """
+    # Adapted from freesurfer m-files. Altered to deal with Norig
+    # and Torig correctly
+    subjects_dir = get_subjects_dir(subjects_dir)
+    # Setup the RAS to MNI transform
+    ras_mni_t = read_ras_mni_t(subject, subjects_dir)
+    ras_mni_t["trans"][:3, 3] /= 1000.0  # mm->m
+
+    # We want to get from Freesurfer surface RAS ('mri') to MNI ('mni_tal').
+    # This file only gives us RAS (non-zero origin) ('ras') to MNI ('mni_tal').
+    # Se we need to get the ras->mri transform from the MRI headers.
+
+    # To do this, we get Norig and Torig
+    # (i.e. vox_ras_t and vox_mri_t, respectively)
+    path = subjects_dir / subject / "mri" / "orig.mgz"
+    if not path.is_file():
+        path = subjects_dir / subject / "mri" / "T1.mgz"
+    if not path.is_file():
+        raise OSError(f"mri not found: {path}")
+    _, _, mri_ras_t, _, _ = _read_mri_info(path)
+    mri_mni_t = combine_transforms(mri_ras_t, ras_mni_t, "mri", "mni_tal")
+    return mri_mni_t
+
+
+def _check_mri(mri, subject, subjects_dir) -> str:
+    """Check whether an mri exists in the Freesurfer subject directory."""
+    _validate_type(mri, "path-like", mri)
+    mri = Path(mri)
+    if mri.is_file() and mri.name != mri:
+        return str(mri)
+    elif not mri.is_file():
+        if subject is None:
+            raise FileNotFoundError(
+                f"MRI file {mri!r} not found and no subject provided."
+            )
+        subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
+        mri = subjects_dir / subject / "mri" / mri
+        if not mri.is_file():
+            raise FileNotFoundError(
+                f"MRI file {mri!r} not found in the subjects directory "
+                f"{subjects_dir!r} for subject {subject}."
+            )
+    if mri.name == mri:
+        raise OSError(
+            f"Ambiguous filename - found {mri!r} in current folder. "
+            "If this is correct prefix name with relative or absolute path."
+        )
+    return str(mri)
+
+
+def _read_mri_info(path, units="m", return_img=False, use_nibabel=False):
+    # This is equivalent but 100x slower, so only use nibabel if we need to
+    # (later):
+    if use_nibabel:
+        nib = _import_nibabel()
+        hdr = nib.load(path).header
+        n_orig = hdr.get_vox2ras()
+        t_orig = hdr.get_vox2ras_tkr()
+        dims = hdr.get_data_shape()
+        zooms = hdr.get_zooms()[:3]
+    else:
+        hdr = _get_mgz_header(path)
+        n_orig = hdr["vox2ras"]
+        t_orig = hdr["vox2ras_tkr"]
+        dims = hdr["dims"]
+        zooms = hdr["zooms"]
+
+    # extract the MRI_VOXEL to RAS (non-zero origin) transform
+    vox_ras_t = Transform("mri_voxel", "ras", n_orig)
+
+    # extract the MRI_VOXEL to MRI transform
+    vox_mri_t = Transform("mri_voxel", "mri", t_orig)
+
+    # construct the MRI to RAS (non-zero origin) transform
+    mri_ras_t = combine_transforms(invert_transform(vox_mri_t), vox_ras_t, "mri", "ras")
+
+    assert units in ("m", "mm")
+    if units == "m":
+        conv = np.array([[1e-3, 1e-3, 1e-3, 1]]).T
+        # scaling and translation terms
+        vox_ras_t["trans"] *= conv
+        vox_mri_t["trans"] *= conv
+        # just the translation term
+        mri_ras_t["trans"][:, 3:4] *= conv
+
+    out = (vox_ras_t, vox_mri_t, mri_ras_t, dims, zooms)
+    if return_img:
+        nibabel = _import_nibabel()
+        out += (nibabel.load(path),)
+    return out
+
+
+def read_freesurfer_lut(fname=None):
+    """Read a Freesurfer-formatted LUT.
+
+    Parameters
+    ----------
+    fname : path-like | None
+        The filename. Can be None to read the standard Freesurfer LUT.
+
+    Returns
+    -------
+    atlas_ids : dict
+        Mapping from label names to IDs.
+    colors : dict
+        Mapping from label names to colors.
+    """
+    lut = _get_lut(fname)
+    names, ids = lut["name"], lut["id"]
+    colors = np.array([lut["R"], lut["G"], lut["B"], lut["A"]], float).T
+    atlas_ids = dict(zip(names, ids))
+    colors = dict(zip(names, colors))
+    return atlas_ids, colors
+
+
+def _get_lut(fname=None):
+    """Get a FreeSurfer LUT."""
+    if fname is None:
+        fname = Path(__file__).parent / "data" / "FreeSurferColorLUT.txt"
+    _check_fname(fname, "read", must_exist=True)
+    dtype = [
+        ("id", "<i8"),
+        ("name", "U"),
+        ("R", "<i8"),
+        ("G", "<i8"),
+        ("B", "<i8"),
+        ("A", "<i8"),
+    ]
+    lut = {d[0]: list() for d in dtype}
+    with open(fname) as fid:
+        for line in fid:
+            line = line.strip()
+            if line.startswith("#") or not line:
+                continue
+            line = line.split()
+            if len(line) != len(dtype):
+                raise RuntimeError(f"LUT is improperly formatted: {fname}")
+            for d, part in zip(dtype, line):
+                lut[d[0]].append(part)
+    lut = {d[0]: np.array(lut[d[0]], dtype=d[1]) for d in dtype}
+    assert len(lut["name"]) > 0
+    lut["name"] = [str(name) for name in lut["name"]]
+    return lut
+
+
+@verbose
+def _get_head_surface(surf, subject, subjects_dir, bem=None, verbose=None):
+    """Get a head surface from the Freesurfer subject directory.
+
+    Parameters
+    ----------
+    surf : str
+        The name of the surface 'auto', 'head', 'outer_skin', 'head-dense'
+        or 'seghead'.
+    %(subject)s
+    %(subjects_dir)s
+    bem : mne.bem.ConductorModel | None
+        The conductor model that stores information about the head surface.
+    %(verbose)s
+
+    Returns
+    -------
+    head_surf : dict | None
+        A dictionary with keys 'rr', 'tris', 'ntri', 'use_tris', 'np'
+        and 'coord_frame' that store information for mesh plotting and other
+        useful information about the head surface.
+
+    Notes
+    -----
+    .. versionadded: 0.24
+    """
+    from .bem import _bem_find_surface, read_bem_surfaces
+
+    _check_option("surf", surf, ("auto", "head", "outer_skin", "head-dense", "seghead"))
+    if surf in ("auto", "head", "outer_skin"):
+        if bem is not None:
+            try:
+                return _bem_find_surface(bem, "head")
+            except RuntimeError:
+                logger.info(
+                    "Could not find the surface for "
+                    "head in the provided BEM model, "
+                    "looking in the subject directory."
+                )
+    if subject is None:
+        if surf == "auto":
+            return
+        raise ValueError(
+            "To plot the head surface, the BEM/sphere"
+            " model must contain a head surface "
+            'or "subject" must be provided (got '
+            "None)"
+        )
+    subject_dir = op.join(get_subjects_dir(subjects_dir, raise_error=True), subject)
+    if surf in ("head-dense", "seghead"):
+        try_fnames = [
+            op.join(subject_dir, "bem", f"{subject}-head-dense.fif"),
+            op.join(subject_dir, "surf", "lh.seghead"),
+        ]
+    else:
+        try_fnames = [
+            op.join(subject_dir, "bem", "outer_skin.surf"),
+            op.join(subject_dir, "bem", "flash", "outer_skin.surf"),
+            op.join(subject_dir, "bem", f"{subject}-head-sparse.fif"),
+            op.join(subject_dir, "bem", f"{subject}-head.fif"),
+        ]
+    for fname in try_fnames:
+        if op.exists(fname):
+            logger.info(f"Using {op.basename(fname)} for head surface.")
+            if op.splitext(fname)[-1] == ".fif":
+                return read_bem_surfaces(fname, on_defects="warn")[0]
+            else:
+                return _read_mri_surface(fname)
+    raise OSError(
+        "No head surface found for subject "
+        f"{subject} after trying:\n" + "\n".join(try_fnames)
+    )
+
+
+@verbose
+def _get_skull_surface(surf, subject, subjects_dir, bem=None, verbose=None):
+    """Get a skull surface from the Freesurfer subject directory.
+
+    Parameters
+    ----------
+    surf : str
+        The name of the surface 'outer' or 'inner'.
+    %(subject)s
+    %(subjects_dir)s
+    bem : mne.bem.ConductorModel | None
+        The conductor model that stores information about the skull surface.
+    %(verbose)s
+
+    Returns
+    -------
+    skull_surf : dict | None
+        A dictionary with keys 'rr', 'tris', 'ntri', 'use_tris', 'np'
+        and 'coord_frame' that store information for mesh plotting and other
+        useful information about the head surface.
+
+    Notes
+    -----
+    .. versionadded: 0.24
+    """
+    from .bem import _bem_find_surface
+
+    if bem is not None:
+        try:
+            return _bem_find_surface(bem, surf + "_skull")
+        except RuntimeError:
+            logger.info(
+                "Could not find the surface for "
+                "skull in the provided BEM model, "
+                "looking in the subject directory."
+            )
+    subjects_dir = Path(get_subjects_dir(subjects_dir, raise_error=True))
+    fname = _check_fname(
+        subjects_dir / subject / "bem" / (surf + "_skull.surf"),
+        overwrite="read",
+        must_exist=True,
+        name=f"{surf} skull surface",
+    )
+    return _read_mri_surface(fname)
+
+
+def _estimate_talxfm_rigid(subject, subjects_dir):
+    from .coreg import _trans_from_params, fit_matched_points
+
+    xfm = read_talxfm(subject, subjects_dir)
+    # XYZ+origin + halfway
+    pts_tal = np.concatenate([np.eye(4)[:, :3], np.eye(3) * 0.5])
+    pts_subj = apply_trans(invert_transform(xfm), pts_tal)
+    # we fit with scaling enabled, but then discard it (we just need
+    # the rigid-body components)
+    params = fit_matched_points(pts_subj, pts_tal, scale=3, out="params")
+    rigid = _trans_from_params((True, True, False), params[:6])
+    return rigid

mne/_ola.py

@@ -0,0 +1,463 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+from scipy.signal import get_window
+
+from .utils import _ensure_int, logger, verbose
+
+###############################################################################
+# Class for interpolation between adjacent points
+
+
+class _Interp2:
+    r"""Interpolate between two points.
+
+    Parameters
+    ----------
+    control_points : array, shape (n_changes,)
+        The control points (indices) to use.
+    values : callable | array, shape (n_changes, ...)
+        Callable that takes the control point and returns a list of
+        arrays that must be interpolated.
+    interp : str
+        Can be 'zero', 'linear', 'hann', or 'cos2' (same as hann).
+
+    Notes
+    -----
+    This will process data using overlapping windows of potentially
+    different sizes to achieve a constant output value using different
+    2-point interpolation schemes. For example, for linear interpolation,
+    and window sizes of 6 and 17, this would look like::
+
+        1 _     _
+          |\   / '-.           .-'
+          | \ /     '-.     .-'
+          |  x         |-.-|
+          | / \     .-'     '-.
+          |/   \_.-'           '-.
+        0 +----|----|----|----|---
+          0    5   10   15   20   25
+
+    """
+
+    def __init__(self, control_points, values, interp="hann"):
+        # set up interpolation
+        self.control_points = np.array(control_points, int).ravel()
+        if not np.array_equal(np.unique(self.control_points), self.control_points):
+            raise ValueError("Control points must be sorted and unique")
+        if len(self.control_points) == 0:
+            raise ValueError("Must be at least one control point")
+        if not (self.control_points >= 0).all():
+            raise ValueError(
+                f"All control points must be positive (got {self.control_points[:3]})"
+            )
+        if isinstance(values, np.ndarray):
+            values = [values]
+        if isinstance(values, list | tuple):
+            for v in values:
+                if not (v is None or isinstance(v, np.ndarray)):
+                    raise TypeError(
+                        'All entries in "values" must be ndarray or None, got '
+                        f"{type(v)}"
+                    )
+                if v is not None and v.shape[0] != len(self.control_points):
+                    raise ValueError(
+                        "Values, if provided, must be the same length as the number of "
+                        f"control points ({len(self.control_points)}), got {v.shape[0]}"
+                    )
+            use_values = values
+
+            def val(pt):
+                idx = np.where(control_points == pt)[0][0]
+                return [v[idx] if v is not None else None for v in use_values]
+
+            values = val
+        self.values = values
+        self.n_last = None
+        self._position = 0  # start at zero
+        self._left_idx = 0
+        self._left = self._right = self._use_interp = None
+        known_types = ("cos2", "linear", "zero", "hann")
+        if interp not in known_types:
+            raise ValueError(f'interp must be one of {known_types}, got "{interp}"')
+        self._interp = interp
+
+    def feed_generator(self, n_pts):
+        """Feed data and get interpolators as a generator."""
+        self.n_last = 0
+        n_pts = _ensure_int(n_pts, "n_pts")
+        original_position = self._position
+        stop = self._position + n_pts
+        logger.debug(f"Feed {n_pts} ({self._position}-{stop})")
+        used = np.zeros(n_pts, bool)
+        if self._left is None:  # first one
+            logger.debug(f"  Eval @ 0 ({self.control_points[0]})")
+            self._left = self.values(self.control_points[0])
+            if len(self.control_points) == 1:
+                self._right = self._left
+        n_used = 0
+
+        # Left zero-order hold condition
+        if self._position < self.control_points[self._left_idx]:
+            n_use = min(self.control_points[self._left_idx] - self._position, n_pts)
+            logger.debug(f"  Left ZOH {n_use}")
+            this_sl = slice(None, n_use)
+            assert used[this_sl].size == n_use
+            assert not used[this_sl].any()
+            used[this_sl] = True
+            yield [this_sl, self._left, None, None]
+            self._position += n_use
+            n_used += n_use
+            self.n_last += 1
+
+        # Standard interpolation condition
+        stop_right_idx = np.where(self.control_points >= stop)[0]
+        if len(stop_right_idx) == 0:
+            stop_right_idx = [len(self.control_points) - 1]
+        stop_right_idx = stop_right_idx[0]
+        left_idxs = np.arange(self._left_idx, stop_right_idx)
+        self.n_last += max(len(left_idxs) - 1, 0)
+        for bi, left_idx in enumerate(left_idxs):
+            if left_idx != self._left_idx or self._right is None:
+                if self._right is not None:
+                    assert left_idx == self._left_idx + 1
+                    self._left = self._right
+                    self._left_idx += 1
+                    self._use_interp = None  # need to recreate it
+                eval_pt = self.control_points[self._left_idx + 1]
+                logger.debug(f"  Eval @ {self._left_idx + 1} ({eval_pt})")
+                self._right = self.values(eval_pt)
+            assert self._right is not None
+            left_point = self.control_points[self._left_idx]
+            right_point = self.control_points[self._left_idx + 1]
+            if self._use_interp is None:
+                interp_span = right_point - left_point
+                if self._interp == "zero":
+                    self._use_interp = None
+                elif self._interp == "linear":
+                    self._use_interp = np.linspace(
+                        1.0, 0.0, interp_span, endpoint=False
+                    )
+                else:  # self._interp in ('cos2', 'hann'):
+                    self._use_interp = np.cos(
+                        np.linspace(0, np.pi / 2.0, interp_span, endpoint=False)
+                    )
+                    self._use_interp *= self._use_interp
+            n_use = min(stop, right_point) - self._position
+            if n_use > 0:
+                logger.debug(
+                    f"  Interp {self._interp} {n_use} ({left_point}-{right_point})"
+                )
+                interp_start = self._position - left_point
+                assert interp_start >= 0
+                if self._use_interp is None:
+                    this_interp = None
+                else:
+                    this_interp = self._use_interp[interp_start : interp_start + n_use]
+                    assert this_interp.size == n_use
+                this_sl = slice(n_used, n_used + n_use)
+                assert used[this_sl].size == n_use
+                assert not used[this_sl].any()
+                used[this_sl] = True
+                yield [this_sl, self._left, self._right, this_interp]
+                self._position += n_use
+                n_used += n_use
+
+        # Right zero-order hold condition
+        if self.control_points[self._left_idx] <= self._position:
+            n_use = stop - self._position
+            if n_use > 0:
+                logger.debug(f"  Right ZOH {n_use}")
+                this_sl = slice(n_pts - n_use, None)
+                assert not used[this_sl].any()
+                used[this_sl] = True
+                assert self._right is not None
+                yield [this_sl, self._right, None, None]
+                self._position += n_use
+                n_used += n_use
+                self.n_last += 1
+        assert self._position == stop
+        assert n_used == n_pts
+        assert used.all()
+        assert self._position == original_position + n_pts
+
+    def feed(self, n_pts):
+        """Feed data and get interpolated values."""
+        # Convenience function for assembly
+        out_arrays = None
+        for o in self.feed_generator(n_pts):
+            if out_arrays is None:
+                out_arrays = [
+                    np.empty(v.shape + (n_pts,)) if v is not None else None
+                    for v in o[1]
+                ]
+            for ai, arr in enumerate(out_arrays):
+                if arr is not None:
+                    if o[3] is None:
+                        arr[..., o[0]] = o[1][ai][..., np.newaxis]
+                    else:
+                        arr[..., o[0]] = o[1][ai][..., np.newaxis] * o[3] + o[2][ai][
+                            ..., np.newaxis
+                        ] * (1.0 - o[3])
+        assert out_arrays is not None
+        return out_arrays
+
+
+###############################################################################
+# Constant overlap-add processing class
+
+
+def _check_store(store):
+    if isinstance(store, np.ndarray):
+        store = [store]
+    if isinstance(store, list | tuple) and all(
+        isinstance(s, np.ndarray) for s in store
+    ):
+        store = _Storer(*store)
+    if not callable(store):
+        raise TypeError(f"store must be callable, got type {type(store)}")
+    return store
+
+
+class _COLA:
+    r"""Constant overlap-add processing helper.
+
+    Parameters
+    ----------
+    process : callable
+        A function that takes a chunk of input data with shape
+        ``(n_channels, n_samples)`` and processes it.
+    store : callable | ndarray
+        A function that takes a completed chunk of output data.
+        Can also be an ``ndarray``, in which case it is treated as the
+        output data in which to store the results.
+    n_total : int
+        The total number of samples.
+    n_samples : int
+        The number of samples per window.
+    n_overlap : int
+        The overlap between windows.
+    window : str
+        The window to use. Default is "hann".
+    tol : float
+        The tolerance for COLA checking.
+
+    Notes
+    -----
+    This will process data using overlapping windows to achieve a constant
+    output value. For example, for ``n_total=27``, ``n_samples=10``,
+    ``n_overlap=5`` and ``window='triang'``::
+
+        1 _____               _______
+          |    \   /\   /\   /
+          |     \ /  \ /  \ /
+          |      x    x    x
+          |     / \  / \  / \
+          |    /   \/   \/   \
+        0 +----|----|----|----|----|-
+          0    5   10   15   20   25
+
+    This produces four windows: the first three are the requested length
+    (10 samples) and the last one is longer (12 samples). The first and last
+    window are asymmetric.
+    """
+
+    @verbose
+    def __init__(
+        self,
+        process,
+        store,
+        n_total,
+        n_samples,
+        n_overlap,
+        sfreq,
+        window="hann",
+        tol=1e-10,
+        *,
+        verbose=None,
+    ):
+        n_samples = _ensure_int(n_samples, "n_samples")
+        n_overlap = _ensure_int(n_overlap, "n_overlap")
+        n_total = _ensure_int(n_total, "n_total")
+        if n_samples <= 0:
+            raise ValueError(f"n_samples must be > 0, got {n_samples}")
+        if n_overlap < 0:
+            raise ValueError(f"n_overlap must be >= 0, got {n_overlap}")
+        if n_total < 0:
+            raise ValueError(f"n_total must be >= 0, got {n_total}")
+        self._n_samples = int(n_samples)
+        self._n_overlap = int(n_overlap)
+        del n_samples, n_overlap
+        if n_total < self._n_samples:
+            raise ValueError(
+                f"Number of samples per window ({self._n_samples}) must be at "
+                f"most the total number of samples ({n_total})"
+            )
+        if not callable(process):
+            raise TypeError(f"process must be callable, got type {type(process)}")
+        self._process = process
+        self._step = self._n_samples - self._n_overlap
+        self._store = _check_store(store)
+        self._idx = 0
+        self._in_buffers = self._out_buffers = None
+
+        # Create our window boundaries
+        window_name = window if isinstance(window, str) else "custom"
+        self._window = get_window(
+            window, self._n_samples, fftbins=(self._n_samples - 1) % 2
+        )
+        self._window /= _check_cola(
+            self._window, self._n_samples, self._step, window_name, tol=tol
+        )
+        self.starts = np.arange(0, n_total - self._n_samples + 1, self._step)
+        self.stops = self.starts + self._n_samples
+        delta = n_total - self.stops[-1]
+        self.stops[-1] = n_total
+        sfreq = float(sfreq)
+        pl = "s" if len(self.starts) != 1 else ""
+        logger.info(
+            f"    Processing {len(self.starts):4d} data chunk{pl} of (at least) "
+            f"{self._n_samples / sfreq:0.1f} s with "
+            f"{self._n_overlap / sfreq:0.1f} s overlap and {window_name} windowing"
+        )
+        del window, window_name
+        if delta > 0:
+            logger.info(
+                f"    The final {delta / sfreq} s will be lumped into the final window"
+            )
+
+    @property
+    def _in_offset(self):
+        """Compute from current processing window start and buffer len."""
+        return self.starts[self._idx] + self._in_buffers[0].shape[-1]
+
+    @verbose
+    def feed(self, *datas, verbose=None, **kwargs):
+        """Pass in a chunk of data."""
+        # Append to our input buffer
+        if self._in_buffers is None:
+            self._in_buffers = [None] * len(datas)
+        if len(datas) != len(self._in_buffers):
+            raise ValueError(
+                f"Got {len(datas)} array(s), needed {len(self._in_buffers)}"
+            )
+        for di, data in enumerate(datas):
+            if not isinstance(data, np.ndarray) or data.ndim < 1:
+                raise TypeError(
+                    f"data entry {di} must be an 2D ndarray, got {type(data)}"
+                )
+            if self._in_buffers[di] is None:
+                # In practice, users can give large chunks, so we use
+                # dynamic allocation of the in buffer. We could save some
+                # memory allocation by only ever processing max_len at once,
+                # but this would increase code complexity.
+                self._in_buffers[di] = np.empty(data.shape[:-1] + (0,), data.dtype)
+            if (
+                data.shape[:-1] != self._in_buffers[di].shape[:-1]
+                or self._in_buffers[di].dtype != data.dtype
+            ):
+                raise TypeError(
+                    f"data must dtype {self._in_buffers[di].dtype} and "
+                    f"shape[:-1]=={self._in_buffers[di].shape[:-1]}, got dtype "
+                    f"{data.dtype} shape[:-1]={data.shape[:-1]}"
+                )
+            logger.debug(
+                f"    + Appending {self._in_offset:d}->"
+                f"{self._in_offset + data.shape[-1]:d}"
+            )
+            self._in_buffers[di] = np.concatenate([self._in_buffers[di], data], -1)
+            if self._in_offset > self.stops[-1]:
+                raise ValueError(
+                    f"data (shape {data.shape}) exceeded expected total buffer size ("
+                    f"{self._in_offset} > {self.stops[-1]})"
+                )
+        # Check to see if we can process the next chunk and dump outputs
+        while self._idx < len(self.starts) and self._in_offset >= self.stops[self._idx]:
+            start, stop = self.starts[self._idx], self.stops[self._idx]
+            this_len = stop - start
+            this_window = self._window.copy()
+            if self._idx == len(self.starts) - 1:
+                this_window = np.pad(
+                    self._window, (0, this_len - len(this_window)), "constant"
+                )
+                for offset in range(self._step, len(this_window), self._step):
+                    n_use = len(this_window) - offset
+                    this_window[offset:] += self._window[:n_use]
+            if self._idx == 0:
+                for offset in range(self._n_samples - self._step, 0, -self._step):
+                    this_window[:offset] += self._window[-offset:]
+            logger.debug(f"    * Processing {start}->{stop}")
+            this_proc = [in_[..., :this_len].copy() for in_ in self._in_buffers]
+            if not all(
+                proc.shape[-1] == this_len == this_window.size for proc in this_proc
+            ):
+                raise RuntimeError("internal indexing error")
+            outs = self._process(*this_proc, **kwargs)
+            if self._out_buffers is None:
+                max_len = np.max(self.stops - self.starts)
+                self._out_buffers = [
+                    np.zeros(o.shape[:-1] + (max_len,), o.dtype) for o in outs
+                ]
+            for oi, out in enumerate(outs):
+                out *= this_window
+                self._out_buffers[oi][..., : stop - start] += out
+            self._idx += 1
+            if self._idx < len(self.starts):
+                next_start = self.starts[self._idx]
+            else:
+                next_start = self.stops[-1]
+            delta = next_start - self.starts[self._idx - 1]
+            for di in range(len(self._in_buffers)):
+                self._in_buffers[di] = self._in_buffers[di][..., delta:]
+            logger.debug(f"    - Shifting input/output buffers by {delta:d} samples")
+            self._store(*[o[..., :delta] for o in self._out_buffers])
+            for ob in self._out_buffers:
+                ob[..., :-delta] = ob[..., delta:]
+                ob[..., -delta:] = 0.0
+
+
+def _check_cola(win, nperseg, step, window_name, tol=1e-10):
+    """Check whether the Constant OverLap Add (COLA) constraint is met."""
+    # adapted from SciPy
+    binsums = np.sum(
+        [win[ii * step : (ii + 1) * step] for ii in range(nperseg // step)], axis=0
+    )
+    if nperseg % step != 0:
+        binsums[: nperseg % step] += win[-(nperseg % step) :]
+    const = np.median(binsums)
+    deviation = np.max(np.abs(binsums - const))
+    if deviation > tol:
+        raise ValueError(
+            f"segment length {nperseg:d} with step {step:d} for {window_name} window "
+            "type does not provide a constant output "
+            f"({100 * deviation / const:g}% deviation)"
+        )
+    return const
+
+
+class _Storer:
+    """Store data in chunks."""
+
+    def __init__(self, *outs, picks=None):
+        for oi, out in enumerate(outs):
+            if not isinstance(out, np.ndarray) or out.ndim < 1:
+                raise TypeError(f"outs[oi] must be >= 1D ndarray, got {out}")
+        self.outs = outs
+        self.idx = 0
+        self.picks = picks
+
+    def __call__(self, *outs):
+        if len(outs) != len(self.outs) or not all(
+            out.shape[-1] == outs[0].shape[-1] for out in outs
+        ):
+            raise ValueError("Bad outs")
+        idx = (Ellipsis,)
+        if self.picks is not None:
+            idx += (self.picks,)
+        stop = self.idx + outs[0].shape[-1]
+        idx += (slice(self.idx, stop),)
+        for o1, o2 in zip(self.outs, outs):
+            o1[idx] = o2
+        self.idx = stop

mne/baseline.py

@@ -0,0 +1,224 @@
+"""Utility functions to baseline-correct data."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from .utils import _check_option, _validate_type, logger, verbose
+
+
+def _log_rescale(baseline, mode="mean"):
+    """Log the rescaling method."""
+    if baseline is not None:
+        _check_option(
+            "mode",
+            mode,
+            ["logratio", "ratio", "zscore", "mean", "percent", "zlogratio"],
+        )
+        msg = f"Applying baseline correction (mode: {mode})"
+    else:
+        msg = "No baseline correction applied"
+    return msg
+
+
+@verbose
+def rescale(data, times, baseline, mode="mean", copy=True, picks=None, verbose=None):
+    """Rescale (baseline correct) data.
+
+    Parameters
+    ----------
+    data : array
+        It can be of any shape. The only constraint is that the last
+        dimension should be time.
+    times : 1D array
+        Time instants is seconds.
+    %(baseline_rescale)s
+    mode : 'mean' | 'ratio' | 'logratio' | 'percent' | 'zscore' | 'zlogratio'
+        Perform baseline correction by
+
+        - subtracting the mean of baseline values ('mean')
+        - dividing by the mean of baseline values ('ratio')
+        - dividing by the mean of baseline values and taking the log
+          ('logratio')
+        - subtracting the mean of baseline values followed by dividing by
+          the mean of baseline values ('percent')
+        - subtracting the mean of baseline values and dividing by the
+          standard deviation of baseline values ('zscore')
+        - dividing by the mean of baseline values, taking the log, and
+          dividing by the standard deviation of log baseline values
+          ('zlogratio')
+
+    copy : bool
+        Whether to return a new instance or modify in place.
+    picks : list of int | None
+        Data to process along the axis=-2 (None, default, processes all).
+    %(verbose)s
+
+    Returns
+    -------
+    data_scaled: array
+        Array of same shape as data after rescaling.
+    """
+    if copy:
+        data = data.copy()
+    if verbose is not False:
+        msg = _log_rescale(baseline, mode)
+        logger.info(msg)
+    if baseline is None or data.shape[-1] == 0:
+        return data
+
+    bmin, bmax = baseline
+    if bmin is None:
+        imin = 0
+    else:
+        imin = np.where(times >= bmin)[0]
+        if len(imin) == 0:
+            raise ValueError(
+                f"bmin is too large ({bmin}), it exceeds the largest time value"
+            )
+        imin = int(imin[0])
+    if bmax is None:
+        imax = len(times)
+    else:
+        imax = np.where(times <= bmax)[0]
+        if len(imax) == 0:
+            raise ValueError(
+                f"bmax is too small ({bmax}), it is smaller than the smallest time "
+                "value"
+            )
+        imax = int(imax[-1]) + 1
+    if imin >= imax:
+        raise ValueError(
+            f"Bad rescaling slice ({imin}:{imax}) from time values {bmin}, {bmax}"
+        )
+
+    # technically this is inefficient when `picks` is given, but assuming
+    # that we generally pick most channels for rescaling, it's not so bad
+    mean = np.mean(data[..., imin:imax], axis=-1, keepdims=True)
+
+    if mode == "mean":
+
+        def fun(d, m):
+            d -= m
+
+    elif mode == "ratio":
+
+        def fun(d, m):
+            d /= m
+
+    elif mode == "logratio":
+
+        def fun(d, m):
+            d /= m
+            np.log10(d, out=d)
+
+    elif mode == "percent":
+
+        def fun(d, m):
+            d -= m
+            d /= m
+
+    elif mode == "zscore":
+
+        def fun(d, m):
+            d -= m
+            d /= np.std(d[..., imin:imax], axis=-1, keepdims=True)
+
+    elif mode == "zlogratio":
+
+        def fun(d, m):
+            d /= m
+            np.log10(d, out=d)
+            d /= np.std(d[..., imin:imax], axis=-1, keepdims=True)
+
+    if picks is None:
+        fun(data, mean)
+    else:
+        for pi in picks:
+            fun(data[..., pi, :], mean[..., pi, :])
+    return data
+
+
+def _check_baseline(baseline, times, sfreq, on_baseline_outside_data="raise"):
+    """Check if the baseline is valid and adjust it if requested.
+
+    ``None`` values inside ``baseline`` will be replaced with ``times[0]`` and
+    ``times[-1]``.
+
+    Parameters
+    ----------
+    baseline : array-like, shape (2,) | None
+        Beginning and end of the baseline period, in seconds. If ``None``,
+        assume no baseline and return immediately.
+    times : array
+        The time points.
+    sfreq : float
+        The sampling rate.
+    on_baseline_outside_data : 'raise' | 'info' | 'adjust'
+        What to do if the baseline period exceeds the data.
+        If ``'raise'``, raise an exception (default).
+        If ``'info'``, log an info message.
+        If ``'adjust'``, adjust the baseline such that it is within the data range.
+
+    Returns
+    -------
+    (baseline_tmin, baseline_tmax) | None
+        The baseline with ``None`` values replaced with times, and with adjusted times
+        if ``on_baseline_outside_data='adjust'``; or ``None``, if ``baseline`` is
+        ``None``.
+    """
+    if baseline is None:
+        return None
+
+    _validate_type(baseline, "array-like")
+    baseline = tuple(baseline)
+
+    if len(baseline) != 2:
+        raise ValueError(
+            f"baseline must have exactly two elements (got {len(baseline)})."
+        )
+
+    tmin, tmax = times[0], times[-1]
+    tstep = 1.0 / float(sfreq)
+
+    # check default value of baseline and `tmin=0`
+    if baseline == (None, 0) and tmin == 0:
+        raise ValueError(
+            "Baseline interval is only one sample. Use `baseline=(0, 0)` if this is "
+            "desired."
+        )
+
+    baseline_tmin, baseline_tmax = baseline
+
+    if baseline_tmin is None:
+        baseline_tmin = tmin
+    baseline_tmin = float(baseline_tmin)
+
+    if baseline_tmax is None:
+        baseline_tmax = tmax
+    baseline_tmax = float(baseline_tmax)
+
+    if baseline_tmin > baseline_tmax:
+        raise ValueError(
+            f"Baseline min ({baseline_tmin}) must be less than baseline max ("
+            f"{baseline_tmax})"
+        )
+
+    if (baseline_tmin < tmin - tstep) or (baseline_tmax > tmax + tstep):
+        msg = (
+            f"Baseline interval [{baseline_tmin}, {baseline_tmax}] s is outside of "
+            f"epochs data [{tmin}, {tmax}] s. Epochs were probably cropped."
+        )
+        if on_baseline_outside_data == "raise":
+            raise ValueError(msg)
+        elif on_baseline_outside_data == "info":
+            logger.info(msg)
+        elif on_baseline_outside_data == "adjust":
+            if baseline_tmin < tmin - tstep:
+                baseline_tmin = tmin
+            if baseline_tmax > tmax + tstep:
+                baseline_tmax = tmax
+
+    return baseline_tmin, baseline_tmax

mne/beamformer/__init__.py

@@ -0,0 +1,8 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+"""Beamformers for source localization."""
+import lazy_loader as lazy
+
+(__getattr__, __dir__, __all__) = lazy.attach_stub(__name__, __file__)

mne/beamformer/__init__.pyi

@@ -0,0 +1,34 @@
+__all__ = [
+    "Beamformer",
+    "apply_dics",
+    "apply_dics_csd",
+    "apply_dics_epochs",
+    "apply_dics_tfr_epochs",
+    "apply_lcmv",
+    "apply_lcmv_cov",
+    "apply_lcmv_epochs",
+    "apply_lcmv_raw",
+    "make_dics",
+    "make_lcmv",
+    "make_lcmv_resolution_matrix",
+    "rap_music",
+    "read_beamformer",
+    "trap_music",
+]
+from ._compute_beamformer import Beamformer, read_beamformer
+from ._dics import (
+    apply_dics,
+    apply_dics_csd,
+    apply_dics_epochs,
+    apply_dics_tfr_epochs,
+    make_dics,
+)
+from ._lcmv import (
+    apply_lcmv,
+    apply_lcmv_cov,
+    apply_lcmv_epochs,
+    apply_lcmv_raw,
+    make_lcmv,
+)
+from ._rap_music import rap_music, trap_music
+from .resolution_matrix import make_lcmv_resolution_matrix

mne/beamformer/_compute_beamformer.py

@@ -0,0 +1,603 @@
+"""Functions shared between different beamformer types."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+from copy import deepcopy
+
+import numpy as np
+
+from .._fiff.proj import Projection, make_projector
+from ..cov import Covariance, make_ad_hoc_cov
+from ..forward.forward import _restrict_forward_to_src_sel, is_fixed_orient
+from ..minimum_norm.inverse import _get_vertno, _prepare_forward
+from ..source_space._source_space import label_src_vertno_sel
+from ..time_frequency.csd import CrossSpectralDensity
+from ..utils import (
+    _check_option,
+    _check_src_normal,
+    _import_h5io_funcs,
+    _pl,
+    _reg_pinv,
+    _sym_mat_pow,
+    check_fname,
+    logger,
+    verbose,
+    warn,
+)
+
+
+def _check_proj_match(proj, filters):
+    """Check whether SSP projections in data and spatial filter match."""
+    proj_data, _, _ = make_projector(proj, filters["ch_names"])
+    if not np.allclose(
+        proj_data, filters["proj"], atol=np.finfo(float).eps, rtol=1e-13
+    ):
+        raise ValueError(
+            "The SSP projections present in the data "
+            "do not match the projections used when "
+            "calculating the spatial filter."
+        )
+
+
+def _check_src_type(filters):
+    """Check whether src_type is in filters and set custom warning."""
+    if "src_type" not in filters:
+        filters["src_type"] = None
+    warn_text = (
+        "The spatial filter does not contain src_type and a robust "
+        "guess of src_type is not possible without src. Consider "
+        "recomputing the filter."
+    )
+    return filters, warn_text
+
+
+def _prepare_beamformer_input(
+    info,
+    forward,
+    label=None,
+    pick_ori=None,
+    noise_cov=None,
+    rank=None,
+    pca=False,
+    loose=None,
+    combine_xyz="fro",
+    exp=None,
+    limit=None,
+    allow_fixed_depth=True,
+    limit_depth_chs=False,
+):
+    """Input preparation common for LCMV, DICS, and RAP-MUSIC."""
+    _check_option("pick_ori", pick_ori, ("normal", "max-power", "vector", None))
+
+    # Restrict forward solution to selected vertices
+    if label is not None:
+        _, src_sel = label_src_vertno_sel(label, forward["src"])
+        forward = _restrict_forward_to_src_sel(forward, src_sel)
+
+    if loose is None:
+        loose = 0.0 if is_fixed_orient(forward) else 1.0
+    # TODO: Deduplicate with _check_one_ch_type, should not be necessary
+    # (DICS hits this code path, LCMV does not)
+    if noise_cov is None:
+        noise_cov = make_ad_hoc_cov(info, std=1.0)
+    (
+        forward,
+        info_picked,
+        gain,
+        _,
+        orient_prior,
+        _,
+        trace_GRGT,
+        noise_cov,
+        whitener,
+    ) = _prepare_forward(
+        forward,
+        info,
+        noise_cov,
+        "auto",
+        loose,
+        rank=rank,
+        pca=pca,
+        use_cps=True,
+        exp=exp,
+        limit_depth_chs=limit_depth_chs,
+        combine_xyz=combine_xyz,
+        limit=limit,
+        allow_fixed_depth=allow_fixed_depth,
+    )
+    is_free_ori = not is_fixed_orient(forward)  # could have been changed
+    nn = forward["source_nn"]
+    if is_free_ori:  # take Z coordinate
+        nn = nn[2::3]
+    nn = nn.copy()
+    vertno = _get_vertno(forward["src"])
+    if forward["surf_ori"]:
+        nn[...] = [0, 0, 1]  # align to local +Z coordinate
+    if pick_ori is not None and not is_free_ori:
+        raise ValueError(
+            f"Normal or max-power orientation (got {pick_ori!r}) can only be picked "
+            "when a forward operator with free orientation is used."
+        )
+    if pick_ori == "normal" and not forward["surf_ori"]:
+        raise ValueError(
+            "Normal orientation can only be picked when a forward operator oriented in "
+            "surface coordinates is used."
+        )
+    _check_src_normal(pick_ori, forward["src"])
+    del forward, info
+
+    # Undo the scaling that MNE prefers
+    scale = np.sqrt((noise_cov["eig"] > 0).sum() / trace_GRGT)
+    gain /= scale
+    if orient_prior is not None:
+        orient_std = np.sqrt(orient_prior)
+    else:
+        orient_std = np.ones(gain.shape[1])
+
+    # Get the projector
+    proj, _, _ = make_projector(info_picked["projs"], info_picked["ch_names"])
+    return (is_free_ori, info_picked, proj, vertno, gain, whitener, nn, orient_std)
+
+
+def _reduce_leadfield_rank(G):
+    """Reduce the rank of the leadfield."""
+    # decompose lead field
+    u, s, v = np.linalg.svd(G, full_matrices=False)
+
+    # backproject, omitting one direction (equivalent to setting the smallest
+    # singular value to zero)
+    G = np.matmul(u[:, :, :-1], s[:, :-1, np.newaxis] * v[:, :-1, :])
+
+    return G
+
+
+def _sym_inv_sm(x, reduce_rank, inversion, sk):
+    """Symmetric inversion with single- or matrix-style inversion."""
+    if x.shape[1:] == (1, 1):
+        with np.errstate(divide="ignore", invalid="ignore"):
+            x_inv = 1.0 / x
+        x_inv[~np.isfinite(x_inv)] = 1.0
+    else:
+        assert x.shape[1:] == (3, 3)
+        if inversion == "matrix":
+            x_inv = _sym_mat_pow(x, -1, reduce_rank=reduce_rank)
+            # Reapply source covariance after inversion
+            x_inv *= sk[:, :, np.newaxis]
+            x_inv *= sk[:, np.newaxis, :]
+        else:
+            # Invert for each dipole separately using plain division
+            diags = np.diagonal(x, axis1=1, axis2=2)
+            assert not reduce_rank  # guaranteed earlier
+            with np.errstate(divide="ignore"):
+                diags = 1.0 / diags
+            # set the diagonal of each 3x3
+            x_inv = np.zeros_like(x)
+            for k in range(x.shape[0]):
+                this = diags[k]
+                # Reapply source covariance after inversion
+                this *= sk[k] * sk[k]
+                x_inv[k].flat[::4] = this
+    return x_inv
+
+
+def _compute_beamformer(
+    G,
+    Cm,
+    reg,
+    n_orient,
+    weight_norm,
+    pick_ori,
+    reduce_rank,
+    rank,
+    inversion,
+    nn,
+    orient_std,
+    whitener,
+):
+    """Compute a spatial beamformer filter (LCMV or DICS).
+
+    For more detailed information on the parameters, see the docstrings of
+    `make_lcmv` and `make_dics`.
+
+    Parameters
+    ----------
+    G : ndarray, shape (n_dipoles, n_channels)
+        The leadfield.
+    Cm : ndarray, shape (n_channels, n_channels)
+        The data covariance matrix.
+    reg : float
+        Regularization parameter.
+    n_orient : int
+        Number of dipole orientations defined at each source point
+    weight_norm : None | 'unit-noise-gain' | 'nai'
+        The weight normalization scheme to use.
+    pick_ori : None | 'normal' | 'max-power'
+        The source orientation to compute the beamformer in.
+    reduce_rank : bool
+        Whether to reduce the rank by one during computation of the filter.
+    rank : dict | None | 'full' | 'info'
+        See compute_rank.
+    inversion : 'matrix' | 'single'
+        The inversion scheme to compute the weights.
+    nn : ndarray, shape (n_dipoles, 3)
+        The source normals.
+    orient_std : ndarray, shape (n_dipoles,)
+        The std of the orientation prior used in weighting the lead fields.
+    whitener : ndarray, shape (n_channels, n_channels)
+        The whitener.
+
+    Returns
+    -------
+    W : ndarray, shape (n_dipoles, n_channels)
+        The beamformer filter weights.
+    """
+    _check_option(
+        "weight_norm",
+        weight_norm,
+        ["unit-noise-gain-invariant", "unit-noise-gain", "nai", None],
+    )
+
+    # Whiten the data covariance
+    Cm = whitener @ Cm @ whitener.T.conj()
+    # Restore to properly Hermitian as large whitening coefs can have bad
+    # rounding error
+    Cm[:] = (Cm + Cm.T.conj()) / 2.0
+
+    assert Cm.shape == (G.shape[0],) * 2
+    s, _ = np.linalg.eigh(Cm)
+    if not (s >= -s.max() * 1e-7).all():
+        # This shouldn't ever happen, but just in case
+        warn(
+            "data covariance does not appear to be positive semidefinite, "
+            "results will likely be incorrect"
+        )
+    # Tikhonov regularization using reg parameter to control for
+    # trade-off between spatial resolution and noise sensitivity
+    # eq. 25 in Gross and Ioannides, 1999 Phys. Med. Biol. 44 2081
+    Cm_inv, loading_factor, rank = _reg_pinv(Cm, reg, rank)
+
+    assert orient_std.shape == (G.shape[1],)
+    n_sources = G.shape[1] // n_orient
+    assert nn.shape == (n_sources, 3)
+
+    logger.info(f"Computing beamformer filters for {n_sources} source{_pl(n_sources)}")
+    n_channels = G.shape[0]
+    assert n_orient in (3, 1)
+    Gk = np.reshape(G.T, (n_sources, n_orient, n_channels)).transpose(0, 2, 1)
+    assert Gk.shape == (n_sources, n_channels, n_orient)
+    sk = np.reshape(orient_std, (n_sources, n_orient))
+    del G, orient_std
+
+    _check_option("reduce_rank", reduce_rank, (True, False))
+
+    # inversion of the denominator
+    _check_option("inversion", inversion, ("matrix", "single"))
+    if (
+        inversion == "single"
+        and n_orient > 1
+        and pick_ori == "vector"
+        and weight_norm == "unit-noise-gain-invariant"
+    ):
+        raise ValueError(
+            'Cannot use pick_ori="vector" with inversion="single" and '
+            'weight_norm="unit-noise-gain-invariant"'
+        )
+    if reduce_rank and inversion == "single":
+        raise ValueError(
+            'reduce_rank cannot be used with inversion="single"; '
+            'consider using inversion="matrix" if you have a '
+            "rank-deficient forward model (i.e., from a sphere "
+            "model with MEG channels), otherwise consider using "
+            "reduce_rank=False"
+        )
+    if n_orient > 1:
+        _, Gk_s, _ = np.linalg.svd(Gk, full_matrices=False)
+        assert Gk_s.shape == (n_sources, n_orient)
+        if not reduce_rank and (Gk_s[:, 0] > 1e6 * Gk_s[:, 2]).any():
+            raise ValueError(
+                "Singular matrix detected when estimating spatial filters. "
+                "Consider reducing the rank of the forward operator by using "
+                "reduce_rank=True."
+            )
+        del Gk_s
+
+    #
+    # 1. Reduce rank of the lead field
+    #
+    if reduce_rank:
+        Gk = _reduce_leadfield_rank(Gk)
+
+    def _compute_bf_terms(Gk, Cm_inv):
+        bf_numer = np.matmul(Gk.swapaxes(-2, -1).conj(), Cm_inv)
+        bf_denom = np.matmul(bf_numer, Gk)
+        return bf_numer, bf_denom
+
+    #
+    # 2. Reorient lead field in direction of max power or normal
+    #
+    if pick_ori == "max-power":
+        assert n_orient == 3
+        _, bf_denom = _compute_bf_terms(Gk, Cm_inv)
+        if weight_norm is None:
+            ori_numer = np.eye(n_orient)[np.newaxis]
+            ori_denom = bf_denom
+        else:
+            # compute power, cf Sekihara & Nagarajan 2008, eq. 4.47
+            ori_numer = bf_denom
+            # Cm_inv should be Hermitian so no need for .T.conj()
+            ori_denom = np.matmul(
+                np.matmul(Gk.swapaxes(-2, -1).conj(), Cm_inv @ Cm_inv), Gk
+            )
+        ori_denom_inv = _sym_inv_sm(ori_denom, reduce_rank, inversion, sk)
+        ori_pick = np.matmul(ori_denom_inv, ori_numer)
+        assert ori_pick.shape == (n_sources, n_orient, n_orient)
+
+        # pick eigenvector that corresponds to maximum eigenvalue:
+        eig_vals, eig_vecs = np.linalg.eig(ori_pick.real)  # not Hermitian!
+        # sort eigenvectors by eigenvalues for picking:
+        order = np.argsort(np.abs(eig_vals), axis=-1)
+        # eig_vals = np.take_along_axis(eig_vals, order, axis=-1)
+        max_power_ori = eig_vecs[np.arange(len(eig_vecs)), :, order[:, -1]]
+        assert max_power_ori.shape == (n_sources, n_orient)
+
+        # set the (otherwise arbitrary) sign to match the normal
+        signs = np.sign(np.sum(max_power_ori * nn, axis=1, keepdims=True))
+        signs[signs == 0] = 1.0
+        max_power_ori *= signs
+
+        # Compute the lead field for the optimal orientation,
+        # and adjust numer/denom
+        Gk = np.matmul(Gk, max_power_ori[..., np.newaxis])
+        n_orient = 1
+    else:
+        max_power_ori = None
+        if pick_ori == "normal":
+            Gk = Gk[..., 2:3]
+            n_orient = 1
+
+    #
+    # 3. Compute numerator and denominator of beamformer formula (unit-gain)
+    #
+
+    bf_numer, bf_denom = _compute_bf_terms(Gk, Cm_inv)
+    assert bf_denom.shape == (n_sources,) + (n_orient,) * 2
+    assert bf_numer.shape == (n_sources, n_orient, n_channels)
+    del Gk  # lead field has been adjusted and should not be used anymore
+
+    #
+    # 4. Invert the denominator
+    #
+
+    # Here W is W_ug, i.e.:
+    # G.T @ Cm_inv / (G.T @ Cm_inv @ G)
+    bf_denom_inv = _sym_inv_sm(bf_denom, reduce_rank, inversion, sk)
+    assert bf_denom_inv.shape == (n_sources, n_orient, n_orient)
+    W = np.matmul(bf_denom_inv, bf_numer)
+    assert W.shape == (n_sources, n_orient, n_channels)
+    del bf_denom_inv, sk
+
+    #
+    # 5. Re-scale filter weights according to the selected weight_norm
+    #
+
+    # Weight normalization is done by computing, for each source::
+    #
+    #     W_ung = W_ug / sqrt(W_ug @ W_ug.T)
+    #
+    # with W_ung referring to the unit-noise-gain (weight normalized) filter
+    # and W_ug referring to the above-calculated unit-gain filter stored in W.
+
+    if weight_norm is not None:
+        # Three different ways to calculate the normalization factors here.
+        # Only matters when in vector mode, as otherwise n_orient == 1 and
+        # they are all equivalent.
+        #
+        # In MNE < 0.21, we just used the Frobenius matrix norm:
+        #
+        #    noise_norm = np.linalg.norm(W, axis=(1, 2), keepdims=True)
+        #    assert noise_norm.shape == (n_sources, 1, 1)
+        #    W /= noise_norm
+        #
+        # Sekihara 2008 says to use sqrt(diag(W_ug @ W_ug.T)), which is not
+        # rotation invariant:
+        if weight_norm in ("unit-noise-gain", "nai"):
+            noise_norm = np.matmul(W, W.swapaxes(-2, -1).conj()).real
+            noise_norm = np.reshape(  # np.diag operation over last two axes
+                noise_norm, (n_sources, -1, 1)
+            )[:, :: n_orient + 1]
+            np.sqrt(noise_norm, out=noise_norm)
+            noise_norm[noise_norm == 0] = np.inf
+            assert noise_norm.shape == (n_sources, n_orient, 1)
+            W /= noise_norm
+        else:
+            assert weight_norm == "unit-noise-gain-invariant"
+            # Here we use sqrtm. The shortcut:
+            #
+            #    use = W
+            #
+            # ... does not match the direct route (it is rotated!), so we'll
+            # use the direct one to match FieldTrip:
+            use = bf_numer
+            inner = np.matmul(use, use.swapaxes(-2, -1).conj())
+            W = np.matmul(_sym_mat_pow(inner, -0.5), use)
+            noise_norm = 1.0
+
+        if weight_norm == "nai":
+            # Estimate noise level based on covariance matrix, taking the
+            # first eigenvalue that falls outside the signal subspace or the
+            # loading factor used during regularization, whichever is largest.
+            if rank > len(Cm):
+                # Covariance matrix is full rank, no noise subspace!
+                # Use the loading factor as noise ceiling.
+                if loading_factor == 0:
+                    raise RuntimeError(
+                        "Cannot compute noise subspace with a full-rank "
+                        "covariance matrix and no regularization. Try "
+                        "manually specifying the rank of the covariance "
+                        "matrix or using regularization."
+                    )
+                noise = loading_factor
+            else:
+                noise, _ = np.linalg.eigh(Cm)
+                noise = noise[-rank]
+                noise = max(noise, loading_factor)
+            W /= np.sqrt(noise)
+
+    W = W.reshape(n_sources * n_orient, n_channels)
+    logger.info("Filter computation complete")
+    return W, max_power_ori
+
+
+def _compute_power(Cm, W, n_orient):
+    """Use beamformer filters to compute source power.
+
+    Parameters
+    ----------
+    Cm : ndarray, shape (n_channels, n_channels)
+        Data covariance matrix or CSD matrix.
+    W : ndarray, shape (nvertices*norient, nchannels)
+        Beamformer weights.
+
+    Returns
+    -------
+    power : ndarray, shape (nvertices,)
+        Source power.
+    """
+    n_sources = W.shape[0] // n_orient
+
+    Wk = W.reshape(n_sources, n_orient, W.shape[1])
+    source_power = np.trace(
+        (Wk @ Cm @ Wk.conj().transpose(0, 2, 1)).real, axis1=1, axis2=2
+    )
+
+    return source_power
+
+
+class Beamformer(dict):
+    """A computed beamformer.
+
+    Notes
+    -----
+    .. versionadded:: 0.17
+    """
+
+    def copy(self):
+        """Copy the beamformer.
+
+        Returns
+        -------
+        beamformer : instance of Beamformer
+            A deep copy of the beamformer.
+        """
+        return deepcopy(self)
+
+    def __repr__(self):  # noqa: D105
+        n_verts = sum(len(v) for v in self["vertices"])
+        n_channels = len(self["ch_names"])
+        if self["subject"] is None:
+            subject = "unknown"
+        else:
+            subject = f'"{self["subject"]}"'
+        out = "<Beamformer | {}, subject {}, {} vert, {} ch".format(
+            self["kind"],
+            subject,
+            n_verts,
+            n_channels,
+        )
+        if self["pick_ori"] is not None:
+            out += f', {self["pick_ori"]} ori'
+        if self["weight_norm"] is not None:
+            out += f', {self["weight_norm"]} norm'
+        if self.get("inversion") is not None:
+            out += f', {self["inversion"]} inversion'
+        if "rank" in self:
+            out += f', rank {self["rank"]}'
+        out += ">"
+        return out
+
+    @verbose
+    def save(self, fname, overwrite=False, verbose=None):
+        """Save the beamformer filter.
+
+        Parameters
+        ----------
+        fname : path-like
+            The filename to use to write the HDF5 data.
+            Should end in ``'-lcmv.h5'`` or ``'-dics.h5'``.
+        %(overwrite)s
+        %(verbose)s
+        """
+        _, write_hdf5 = _import_h5io_funcs()
+
+        ending = f'-{self["kind"].lower()}.h5'
+        check_fname(fname, self["kind"], (ending,))
+        csd_orig = None
+        try:
+            if "csd" in self:
+                csd_orig = self["csd"]
+                self["csd"] = self["csd"].__getstate__()
+            write_hdf5(fname, self, overwrite=overwrite, title="mnepython")
+        finally:
+            if csd_orig is not None:
+                self["csd"] = csd_orig
+
+
+def read_beamformer(fname):
+    """Read a beamformer filter.
+
+    Parameters
+    ----------
+    fname : path-like
+        The filename of the HDF5 file.
+
+    Returns
+    -------
+    filter : instance of Beamformer
+        The beamformer filter.
+    """
+    read_hdf5, _ = _import_h5io_funcs()
+    beamformer = read_hdf5(fname, title="mnepython")
+    if "csd" in beamformer:
+        beamformer["csd"] = CrossSpectralDensity(**beamformer["csd"])
+    # h5io seems to cast `bool` to `int` on round-trip, probably a bug
+    # we should fix at some point (if possible -- could be HDF5 limitation)
+    for key in ("normalize_fwd", "is_free_ori", "is_ssp"):
+        if key in beamformer:
+            beamformer[key] = bool(beamformer[key])
+    for key in ("data_cov", "noise_cov"):
+        if beamformer.get(key) is not None:
+            for pi, p in enumerate(beamformer[key]["projs"]):
+                p = Projection(**p)
+                p["active"] = bool(p["active"])
+                beamformer[key]["projs"][pi] = p
+            beamformer[key] = Covariance(
+                *[
+                    beamformer[key].get(arg)
+                    for arg in (
+                        "data",
+                        "names",
+                        "bads",
+                        "projs",
+                        "nfree",
+                        "eig",
+                        "eigvec",
+                        "method",
+                        "loglik",
+                    )
+                ]
+            )
+    return Beamformer(beamformer)
+
+
+def _proj_whiten_data(M, proj, filters):
+    if filters.get("is_ssp", True):
+        # check whether data and filter projs match
+        _check_proj_match(proj, filters)
+        if filters["whitener"] is None:
+            M = np.dot(filters["proj"], M)
+
+    if filters["whitener"] is not None:
+        M = np.dot(filters["whitener"], M)
+    return M

mne/beamformer/_dics.py

@@ -0,0 +1,648 @@
+"""Dynamic Imaging of Coherent Sources (DICS)."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from .._fiff.pick import pick_channels, pick_info
+from ..channels import equalize_channels
+from ..forward import _subject_from_forward
+from ..minimum_norm.inverse import _check_depth, _check_reference, combine_xyz
+from ..rank import compute_rank
+from ..source_estimate import _get_src_type, _make_stc
+from ..time_frequency import EpochsTFR
+from ..time_frequency.tfr import _check_tfr_complex
+from ..utils import (
+    _check_channels_spatial_filter,
+    _check_one_ch_type,
+    _check_option,
+    _check_rank,
+    _validate_type,
+    logger,
+    verbose,
+    warn,
+)
+from ._compute_beamformer import (
+    Beamformer,
+    _check_src_type,
+    _compute_beamformer,
+    _compute_power,
+    _prepare_beamformer_input,
+    _proj_whiten_data,
+)
+
+
+@verbose
+def make_dics(
+    info,
+    forward,
+    csd,
+    reg=0.05,
+    noise_csd=None,
+    label=None,
+    pick_ori=None,
+    rank=None,
+    weight_norm=None,
+    reduce_rank=False,
+    depth=1.0,
+    real_filter=True,
+    inversion="matrix",
+    verbose=None,
+):
+    """Compute a Dynamic Imaging of Coherent Sources (DICS) spatial filter.
+
+    This is a beamformer filter that can be used to estimate the source power
+    at a specific frequency range :footcite:`GrossEtAl2001`. It does this by
+    constructing a spatial filter for each source point.
+    The computation of these filters is very similar to those of the LCMV
+    beamformer (:func:`make_lcmv`), but instead of operating on a covariance
+    matrix, the CSD matrix is used. When applying these filters to a CSD matrix
+    (see :func:`apply_dics_csd`), the source power can be estimated for each
+    source point.
+
+    Parameters
+    ----------
+    %(info_not_none)s
+    forward : instance of Forward
+        Forward operator.
+    csd : instance of CrossSpectralDensity
+        The data cross-spectral density (CSD) matrices. A source estimate is
+        performed for each frequency or frequency-bin defined in the CSD
+        object.
+    reg : float
+        The regularization to apply to the cross-spectral density before
+        computing the inverse.
+    noise_csd : instance of CrossSpectralDensity | None
+        Noise cross-spectral density (CSD) matrices. If provided, whitening
+        will be done. The noise CSDs need to have been computed for the same
+        frequencies as the data CSDs. Providing noise CSDs is mandatory if you
+        mix sensor types, e.g. gradiometers with magnetometers or EEG with
+        MEG.
+
+        .. versionadded:: 0.20
+    label : Label | None
+        Restricts the solution to a given label.
+    %(pick_ori_bf)s
+    %(rank_none)s
+
+        .. versionadded:: 0.17
+    %(weight_norm)s
+
+        Defaults to ``None``, in which case no normalization is performed.
+    %(reduce_rank)s
+    %(depth)s
+    real_filter : bool
+        If ``True``, take only the real part of the cross-spectral-density
+        matrices to compute real filters.
+
+        .. versionchanged:: 0.23
+            Version 0.23 an earlier used ``real_filter=False`` as the default,
+            as of version 0.24 ``True`` is the default.
+    %(inversion_bf)s
+
+        .. versionchanged:: 0.21
+           Default changed to ``'matrix'``.
+    %(verbose)s
+
+    Returns
+    -------
+    filters : instance of Beamformer
+        Dictionary containing filter weights from DICS beamformer.
+        Contains the following keys:
+
+            'kind' : str
+                The type of beamformer, in this case 'DICS'.
+            'weights' : ndarray, shape (n_frequencies, n_weights)
+                For each frequency, the filter weights of the beamformer.
+            'csd' : instance of CrossSpectralDensity
+                The data cross-spectral density matrices used to compute the
+                beamformer.
+            'ch_names' : list of str
+                Channels used to compute the beamformer.
+            'proj' : ndarray, shape (n_channels, n_channels)
+                Projections used to compute the beamformer.
+            'vertices' : list of ndarray
+                Vertices for which the filter weights were computed.
+            'n_sources' : int
+                Number of source location for which the filter weight were
+                computed.
+            'subject' : str
+                The subject ID.
+            'pick-ori' : None | 'max-power' | 'normal' | 'vector'
+                The orientation in which the beamformer filters were computed.
+            'inversion' : 'single' | 'matrix'
+                Whether the spatial filters were computed for each dipole
+                separately or jointly for all dipoles at each vertex using a
+                matrix inversion.
+            'weight_norm' : None | 'unit-noise-gain'
+                The normalization of the weights.
+            'src_type' : str
+                Type of source space.
+            'source_nn' : ndarray, shape (n_sources, 3)
+                For each source location, the surface normal.
+            'is_free_ori' : bool
+                Whether the filter was computed in a fixed direction
+                (pick_ori='max-power', pick_ori='normal') or not.
+            'whitener' : None | ndarray, shape (n_channels, n_channels)
+                Whitening matrix, provided if whitening was applied to the
+                covariance matrix and leadfield during computation of the
+                beamformer weights.
+            'max-power-ori' : ndarray, shape (n_sources, 3) | None
+                When pick_ori='max-power', this fields contains the estimated
+                direction of maximum power at each source location.
+
+    See Also
+    --------
+    apply_dics_csd
+
+    Notes
+    -----
+    The original reference is :footcite:`GrossEtAl2001`. See
+    :footcite:`vanVlietEtAl2018` for a tutorial style paper on the topic.
+
+    The DICS beamformer is very similar to the LCMV (:func:`make_lcmv`)
+    beamformer and many of the parameters are shared. However,
+    :func:`make_dics` and :func:`make_lcmv` currently have different defaults
+    for these parameters, which were settled on separately through extensive
+    practical use case testing (but not necessarily exhaustive parameter space
+    searching), and it remains to be seen how functionally interchangeable they
+    could be.
+
+    The default setting reproduce the DICS beamformer as described in
+    :footcite:`vanVlietEtAl2018`::
+
+        inversion='single', weight_norm=None, depth=1.
+
+    To use the :func:`make_lcmv` defaults, use::
+
+        inversion='matrix', weight_norm='unit-noise-gain-invariant', depth=None
+
+    For more information about ``real_filter``, see the
+    supplemental information from :footcite:`HippEtAl2011`.
+
+    References
+    ----------
+    .. footbibliography::
+    """  # noqa: E501
+    rank = _check_rank(rank)
+    _check_option("pick_ori", pick_ori, [None, "vector", "normal", "max-power"])
+    _check_option("inversion", inversion, ["single", "matrix"])
+    _validate_type(weight_norm, (str, None), "weight_norm")
+
+    frequencies = [np.mean(freq_bin) for freq_bin in csd.frequencies]
+    n_freqs = len(frequencies)
+
+    _, _, allow_mismatch = _check_one_ch_type("dics", info, forward, csd, noise_csd)
+    # remove bads so that equalize_channels only keeps all good
+    info = pick_info(info, pick_channels(info["ch_names"], [], info["bads"]))
+    info, forward, csd = equalize_channels([info, forward, csd])
+
+    csd, noise_csd = _prepare_noise_csd(csd, noise_csd, real_filter)
+
+    depth = _check_depth(depth, "depth_sparse")
+    if inversion == "single":
+        depth["combine_xyz"] = False
+
+    (
+        is_free_ori,
+        info,
+        proj,
+        vertices,
+        G,
+        whitener,
+        nn,
+        orient_std,
+    ) = _prepare_beamformer_input(
+        info,
+        forward,
+        label,
+        pick_ori,
+        noise_cov=noise_csd,
+        rank=rank,
+        pca=False,
+        **depth,
+    )
+
+    # Compute ranks
+    csd_int_rank = []
+    if not allow_mismatch:
+        noise_rank = compute_rank(noise_csd, info=info, rank=rank)
+    for i in range(len(frequencies)):
+        csd_rank = compute_rank(
+            csd.get_data(index=i, as_cov=True), info=info, rank=rank
+        )
+        if not allow_mismatch:
+            for key in csd_rank:
+                if key not in noise_rank or csd_rank[key] != noise_rank[key]:
+                    raise ValueError(
+                        f"{key} data rank ({csd_rank[key]}) did not match the noise "
+                        f"rank ({noise_rank.get(key, None)})"
+                    )
+        csd_int_rank.append(sum(csd_rank.values()))
+
+    del noise_csd
+    ch_names = list(info["ch_names"])
+
+    logger.info("Computing DICS spatial filters...")
+    Ws = []
+    max_oris = []
+    for i, freq in enumerate(frequencies):
+        if n_freqs > 1:
+            logger.info(
+                "    computing DICS spatial filter at "
+                f"{round(freq, 2)} Hz ({i + 1}/{n_freqs})"
+            )
+
+        Cm = csd.get_data(index=i)
+
+        # XXX: Weird that real_filter happens *before* whitening, which could
+        # make things complex again...?
+        if real_filter:
+            Cm = Cm.real
+
+        # compute spatial filter
+        n_orient = 3 if is_free_ori else 1
+        W, max_power_ori = _compute_beamformer(
+            G,
+            Cm,
+            reg,
+            n_orient,
+            weight_norm,
+            pick_ori,
+            reduce_rank,
+            rank=csd_int_rank[i],
+            inversion=inversion,
+            nn=nn,
+            orient_std=orient_std,
+            whitener=whitener,
+        )
+        Ws.append(W)
+        max_oris.append(max_power_ori)
+
+    Ws = np.array(Ws)
+    if pick_ori == "max-power":
+        max_oris = np.array(max_oris)
+    else:
+        max_oris = None
+
+    src_type = _get_src_type(forward["src"], vertices)
+    subject = _subject_from_forward(forward)
+    is_free_ori = is_free_ori if pick_ori in [None, "vector"] else False
+    n_sources = np.sum([len(v) for v in vertices])
+
+    filters = Beamformer(
+        kind="DICS",
+        weights=Ws,
+        csd=csd,
+        ch_names=ch_names,
+        proj=proj,
+        vertices=vertices,
+        n_sources=n_sources,
+        subject=subject,
+        pick_ori=pick_ori,
+        inversion=inversion,
+        weight_norm=weight_norm,
+        src_type=src_type,
+        source_nn=forward["source_nn"].copy(),
+        is_free_ori=is_free_ori,
+        whitener=whitener,
+        max_power_ori=max_oris,
+    )
+
+    return filters
+
+
+def _prepare_noise_csd(csd, noise_csd, real_filter):
+    if noise_csd is not None:
+        csd, noise_csd = equalize_channels([csd, noise_csd])
+        # Use the same noise CSD for all frequencies
+        if len(noise_csd.frequencies) > 1:
+            noise_csd = noise_csd.mean()
+        noise_csd = noise_csd.get_data(as_cov=True)
+        if real_filter:
+            noise_csd["data"] = noise_csd["data"].real
+    return csd, noise_csd
+
+
+def _apply_dics(data, filters, info, tmin, tfr=False):
+    """Apply DICS spatial filter to data for source reconstruction."""
+    if isinstance(data, np.ndarray) and data.ndim == (2 + tfr):
+        data = [data]
+        one_epoch = True
+    else:
+        one_epoch = False
+
+    Ws = filters["weights"]
+    one_freq = len(Ws) == 1
+
+    subject = filters["subject"]
+    # compatibility with 0.16, add src_type as None if not present:
+    filters, warn_text = _check_src_type(filters)
+
+    for i, M in enumerate(data):
+        if not one_epoch:
+            logger.info(f"Processing epoch : {i + 1}")
+
+        # Apply SSPs
+        if not tfr:  # save computation, only compute once
+            M_w = _proj_whiten_data(M, info["projs"], filters)
+
+        stcs = []
+        for j, W in enumerate(Ws):
+            if tfr:  # must compute for each frequency
+                M_w = _proj_whiten_data(M[:, j], info["projs"], filters)
+
+            # project to source space using beamformer weights
+            sol = np.dot(W, M_w)
+
+            if filters["is_free_ori"] and filters["pick_ori"] != "vector":
+                logger.info("combining the current components...")
+                sol = combine_xyz(sol)
+
+            tstep = 1.0 / info["sfreq"]
+
+            stcs.append(
+                _make_stc(
+                    sol,
+                    vertices=filters["vertices"],
+                    src_type=filters["src_type"],
+                    tmin=tmin,
+                    tstep=tstep,
+                    subject=subject,
+                    vector=(filters["pick_ori"] == "vector"),
+                    source_nn=filters["source_nn"],
+                    warn_text=warn_text,
+                )
+            )
+        if one_freq:
+            yield stcs[0]
+        else:
+            yield stcs
+
+    logger.info("[done]")
+
+
+@verbose
+def apply_dics(evoked, filters, verbose=None):
+    """Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights.
+
+    Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights
+    on evoked data.
+
+    .. warning:: The result of this function is meant as an intermediate step
+                 for further processing (such as computing connectivity). If
+                 you are interested in estimating source time courses, use an
+                 LCMV beamformer (:func:`make_lcmv`, :func:`apply_lcmv`)
+                 instead. If you are interested in estimating spectral power at
+                 the source level, use :func:`apply_dics_csd`.
+    .. warning:: This implementation has not been heavily tested so please
+                 report any issues or suggestions.
+
+    Parameters
+    ----------
+    evoked : Evoked
+        Evoked data to apply the DICS beamformer weights to.
+    filters : instance of Beamformer
+        DICS spatial filter (beamformer weights)
+        Filter weights returned from :func:`make_dics`.
+    %(verbose)s
+
+    Returns
+    -------
+    stc : SourceEstimate | VolSourceEstimate | list
+        Source time courses. If the DICS beamformer has been computed for more
+        than one frequency, a list is returned containing for each frequency
+        the corresponding time courses.
+
+    See Also
+    --------
+    apply_dics_epochs
+    apply_dics_tfr_epochs
+    apply_dics_csd
+    """  # noqa: E501
+    _check_reference(evoked)
+
+    info = evoked.info
+    data = evoked.data
+    tmin = evoked.times[0]
+
+    sel = _check_channels_spatial_filter(evoked.ch_names, filters)
+    data = data[sel]
+
+    stc = _apply_dics(data=data, filters=filters, info=info, tmin=tmin)
+
+    return next(stc)
+
+
+@verbose
+def apply_dics_epochs(epochs, filters, return_generator=False, verbose=None):
+    """Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights.
+
+    Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights
+    on single trial data.
+
+    .. warning:: The result of this function is meant as an intermediate step
+                 for further processing (such as computing connectivity). If
+                 you are interested in estimating source time courses, use an
+                 LCMV beamformer (:func:`make_lcmv`, :func:`apply_lcmv`)
+                 instead. If you are interested in estimating spectral power at
+                 the source level, use :func:`apply_dics_csd`.
+    .. warning:: This implementation has not been heavily tested so please
+                 report any issue or suggestions.
+
+    Parameters
+    ----------
+    epochs : Epochs
+        Single trial epochs.
+    filters : instance of Beamformer
+        DICS spatial filter (beamformer weights)
+        Filter weights returned from :func:`make_dics`. The DICS filters must
+        have been computed for a single frequency only.
+    return_generator : bool
+        Return a generator object instead of a list. This allows iterating
+        over the stcs without having to keep them all in memory.
+    %(verbose)s
+
+    Returns
+    -------
+    stc: list | generator of (SourceEstimate | VolSourceEstimate)
+        The source estimates for all epochs.
+
+    See Also
+    --------
+    apply_dics
+    apply_dics_tfr_epochs
+    apply_dics_csd
+    """
+    _check_reference(epochs)
+
+    if len(filters["weights"]) > 1:
+        raise ValueError(
+            "This function only works on DICS beamformer weights that have "
+            "been computed for a single frequency. When calling make_dics(), "
+            "make sure to use a CSD object with only a single frequency (or "
+            "frequency-bin) defined."
+        )
+
+    info = epochs.info
+    tmin = epochs.times[0]
+
+    sel = _check_channels_spatial_filter(epochs.ch_names, filters)
+    data = epochs.get_data(sel)
+
+    stcs = _apply_dics(data=data, filters=filters, info=info, tmin=tmin)
+
+    if not return_generator:
+        stcs = list(stcs)
+
+    return stcs
+
+
+@verbose
+def apply_dics_tfr_epochs(epochs_tfr, filters, return_generator=False, verbose=None):
+    """Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights.
+
+    Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights
+    on single trial time-frequency data.
+
+    Parameters
+    ----------
+    epochs_tfr : EpochsTFR
+        Single trial time-frequency epochs.
+    filters : instance of Beamformer
+        DICS spatial filter (beamformer weights)
+        Filter weights returned from :func:`make_dics`.
+    return_generator : bool
+        Return a generator object instead of a list. This allows iterating
+        over the stcs without having to keep them all in memory.
+    %(verbose)s
+
+    Returns
+    -------
+    stcs : list of list of (SourceEstimate | VectorSourceEstimate | VolSourceEstimate)
+        The source estimates for all epochs (outside list) and for
+        all frequencies (inside list).
+
+    See Also
+    --------
+    apply_dics
+    apply_dics_epochs
+    apply_dics_csd
+    """  # noqa E501
+    _validate_type(epochs_tfr, EpochsTFR)
+    _check_tfr_complex(epochs_tfr)
+
+    if filters["pick_ori"] == "vector":
+        warn(
+            "Using a vector solution to compute power will lead to "
+            "inaccurate directions (only in the first quadrent) "
+            "because power is a strictly positive (squared) metric. "
+            "Using singular value decomposition (SVD) to determine "
+            "the direction is not yet supported in MNE."
+        )
+
+    sel = _check_channels_spatial_filter(epochs_tfr.ch_names, filters)
+    data = epochs_tfr.data[:, sel, :, :]
+
+    stcs = _apply_dics(data, filters, epochs_tfr.info, epochs_tfr.tmin, tfr=True)
+    if not return_generator:
+        stcs = [[stc for stc in tfr_stcs] for tfr_stcs in stcs]
+    return stcs
+
+
+@verbose
+def apply_dics_csd(csd, filters, verbose=None):
+    """Apply Dynamic Imaging of Coherent Sources (DICS) beamformer weights.
+
+    Apply a previously computed DICS beamformer to a cross-spectral density
+    (CSD) object to estimate source power in time and frequency windows
+    specified in the CSD object :footcite:`GrossEtAl2001`.
+
+    .. note:: Only power can computed from the cross-spectral density, not
+              complex phase-amplitude, so vector DICS filters will be
+              converted to scalar source estimates since power is strictly
+              positive and so 3D directions cannot be combined meaningfully
+              (the direction would be confined to the positive quadrant).
+
+    Parameters
+    ----------
+    csd : instance of CrossSpectralDensity
+        The data cross-spectral density (CSD) matrices. A source estimate is
+        performed for each frequency or frequency-bin defined in the CSD
+        object.
+    filters : instance of Beamformer
+        DICS spatial filter (beamformer weights)
+        Filter weights returned from `make_dics`.
+    %(verbose)s
+
+    Returns
+    -------
+    stc : SourceEstimate
+        Source power with frequency instead of time.
+    frequencies : list of float
+        The frequencies for which the source power has been computed. If the
+        data CSD object defines frequency-bins instead of exact frequencies,
+        the mean of each bin is returned.
+
+    See Also
+    --------
+    apply_dics
+    apply_dics_epochs
+    apply_dics_tfr_epochs
+
+    References
+    ----------
+    .. footbibliography::
+    """  # noqa: E501
+    ch_names = filters["ch_names"]
+    vertices = filters["vertices"]
+    n_orient = 3 if filters["is_free_ori"] else 1
+    subject = filters["subject"]
+    whitener = filters["whitener"]
+    n_sources = filters["n_sources"]
+
+    # If CSD is summed over multiple frequencies, take the average frequency
+    frequencies = [np.mean(dfreq) for dfreq in csd.frequencies]
+    n_freqs = len(frequencies)
+
+    source_power = np.zeros((n_sources, len(csd.frequencies)))
+
+    # Ensure the CSD is in the same order as the weights
+    csd_picks = [csd.ch_names.index(ch) for ch in ch_names]
+
+    logger.info("Computing DICS source power...")
+    for i, freq in enumerate(frequencies):
+        if n_freqs > 1:
+            logger.info(
+                "    applying DICS spatial filter at "
+                f"{round(freq, 2)} Hz ({i + 1}/{n_freqs})"
+            )
+
+        Cm = csd.get_data(index=i)
+        Cm = Cm[csd_picks, :][:, csd_picks]
+        W = filters["weights"][i]
+
+        # Whiten the CSD
+        Cm = np.dot(whitener, np.dot(Cm, whitener.conj().T))
+
+        source_power[:, i] = _compute_power(Cm, W, n_orient)
+
+    logger.info("[done]")
+
+    # compatibility with 0.16, add src_type as None if not present:
+    filters, warn_text = _check_src_type(filters)
+
+    return (
+        _make_stc(
+            source_power,
+            vertices=vertices,
+            src_type=filters["src_type"],
+            tmin=0.0,
+            tstep=1.0,
+            subject=subject,
+            warn_text=warn_text,
+        ),
+        frequencies,
+    )

mne/beamformer/_lcmv.py

@@ -0,0 +1,503 @@
+"""Compute Linearly constrained minimum variance (LCMV) beamformer."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from .._fiff.meas_info import _simplify_info
+from .._fiff.pick import pick_channels_cov, pick_info
+from ..forward import _subject_from_forward
+from ..minimum_norm.inverse import _check_depth, _check_reference, combine_xyz
+from ..rank import compute_rank
+from ..source_estimate import _get_src_type, _make_stc
+from ..utils import (
+    _check_channels_spatial_filter,
+    _check_info_inv,
+    _check_one_ch_type,
+    logger,
+    verbose,
+)
+from ._compute_beamformer import (
+    Beamformer,
+    _check_src_type,
+    _compute_beamformer,
+    _compute_power,
+    _prepare_beamformer_input,
+    _proj_whiten_data,
+)
+
+
+@verbose
+def make_lcmv(
+    info,
+    forward,
+    data_cov,
+    reg=0.05,
+    noise_cov=None,
+    label=None,
+    pick_ori=None,
+    rank="info",
+    weight_norm="unit-noise-gain-invariant",
+    reduce_rank=False,
+    depth=None,
+    inversion="matrix",
+    verbose=None,
+):
+    """Compute LCMV spatial filter.
+
+    Parameters
+    ----------
+    %(info_not_none)s
+        Specifies the channels to include. Bad channels (in ``info['bads']``)
+        are not used.
+    forward : instance of Forward
+        Forward operator.
+    data_cov : instance of Covariance
+        The data covariance.
+    reg : float
+        The regularization for the whitened data covariance.
+    noise_cov : instance of Covariance
+        The noise covariance. If provided, whitening will be done. Providing a
+        noise covariance is mandatory if you mix sensor types, e.g.
+        gradiometers with magnetometers or EEG with MEG.
+
+        .. note::
+            If ``noise_cov`` is ``None`` and ``weight_norm='unit-noise-gain'``,
+            the unit noise is assumed to be 1 in SI units, e.g., 1 T for
+            magnetometers, 1 V for EEG, so resulting amplitudes will be tiny.
+            Consider using :func:`mne.make_ad_hoc_cov` to provide a
+            ``noise_cov`` to set noise values that are more reasonable for
+            neural data or using ``weight_norm='nai'`` for weight-normalized
+            beamformer output that is scaled by a noise estimate.
+    label : instance of Label
+        Restricts the LCMV solution to a given label.
+    %(pick_ori_bf)s
+
+        - ``'vector'``
+            Keeps the currents for each direction separate
+    %(rank_info)s
+    %(weight_norm)s
+
+        Defaults to ``'unit-noise-gain-invariant'``.
+    %(reduce_rank)s
+    %(depth)s
+
+        .. versionadded:: 0.18
+    %(inversion_bf)s
+
+        .. versionadded:: 0.21
+    %(verbose)s
+
+    Returns
+    -------
+    filters : instance of Beamformer
+        Dictionary containing filter weights from LCMV beamformer.
+        Contains the following keys:
+
+            'kind' : str
+                The type of beamformer, in this case 'LCMV'.
+            'weights' : array
+                The filter weights of the beamformer.
+            'data_cov' : instance of Covariance
+                The data covariance matrix used to compute the beamformer.
+            'noise_cov' : instance of Covariance | None
+                The noise covariance matrix used to compute the beamformer.
+            'whitener' : None | ndarray, shape (n_channels, n_channels)
+                Whitening matrix, provided if whitening was applied to the
+                covariance matrix and leadfield during computation of the
+                beamformer weights.
+            'weight_norm' : str | None
+                Type of weight normalization used to compute the filter
+                weights.
+            'pick-ori' : None | 'max-power' | 'normal' | 'vector'
+                The orientation in which the beamformer filters were computed.
+            'ch_names' : list of str
+                Channels used to compute the beamformer.
+            'proj' : array
+                Projections used to compute the beamformer.
+            'is_ssp' : bool
+                If True, projections were applied prior to filter computation.
+            'vertices' : list
+                Vertices for which the filter weights were computed.
+            'is_free_ori' : bool
+                If True, the filter was computed with free source orientation.
+            'n_sources' : int
+                Number of source location for which the filter weight were
+                computed.
+            'src_type' : str
+                Type of source space.
+            'source_nn' : ndarray, shape (n_sources, 3)
+                For each source location, the surface normal.
+            'proj' : ndarray, shape (n_channels, n_channels)
+                Projections used to compute the beamformer.
+            'subject' : str
+                The subject ID.
+            'rank' : int
+                The rank of the data covariance matrix used to compute the
+                beamformer weights.
+            'max-power-ori' : ndarray, shape (n_sources, 3) | None
+                When pick_ori='max-power', this fields contains the estimated
+                direction of maximum power at each source location.
+            'inversion' : 'single' | 'matrix'
+                Whether the spatial filters were computed for each dipole
+                separately or jointly for all dipoles at each vertex using a
+                matrix inversion.
+
+    Notes
+    -----
+    The original reference is :footcite:`VanVeenEtAl1997`.
+
+    To obtain the Sekihara unit-noise-gain vector beamformer, you should use
+    ``weight_norm='unit-noise-gain', pick_ori='vector'`` followed by
+    :meth:`vec_stc.project('pca', src) <mne.VectorSourceEstimate.project>`.
+
+    .. versionchanged:: 0.21
+       The computations were extensively reworked, and the default for
+       ``weight_norm`` was set to ``'unit-noise-gain-invariant'``.
+
+    References
+    ----------
+    .. footbibliography::
+    """
+    # check number of sensor types present in the data and ensure a noise cov
+    info = _simplify_info(info, keep=("proc_history",))
+    noise_cov, _, allow_mismatch = _check_one_ch_type(
+        "lcmv", info, forward, data_cov, noise_cov
+    )
+    # XXX we need this extra picking step (can't just rely on minimum norm's
+    # because there can be a mismatch. Should probably add an extra arg to
+    # _prepare_beamformer_input at some point (later)
+    picks = _check_info_inv(info, forward, data_cov, noise_cov)
+    info = pick_info(info, picks)
+    data_rank = compute_rank(data_cov, rank=rank, info=info)
+    noise_rank = compute_rank(noise_cov, rank=rank, info=info)
+    for key in data_rank:
+        if (
+            key not in noise_rank or data_rank[key] != noise_rank[key]
+        ) and not allow_mismatch:
+            raise ValueError(
+                f"{key} data rank ({data_rank[key]}) did not match the noise rank ("
+                f"{noise_rank.get(key, None)})"
+            )
+    del noise_rank
+    rank = data_rank
+    logger.info(f"Making LCMV beamformer with rank {rank}")
+    del data_rank
+    depth = _check_depth(depth, "depth_sparse")
+    if inversion == "single":
+        depth["combine_xyz"] = False
+
+    (
+        is_free_ori,
+        info,
+        proj,
+        vertno,
+        G,
+        whitener,
+        nn,
+        orient_std,
+    ) = _prepare_beamformer_input(
+        info,
+        forward,
+        label,
+        pick_ori,
+        noise_cov=noise_cov,
+        rank=rank,
+        pca=False,
+        **depth,
+    )
+    ch_names = list(info["ch_names"])
+
+    data_cov = pick_channels_cov(data_cov, include=ch_names)
+    Cm = data_cov._get_square()
+    if "estimator" in data_cov:
+        del data_cov["estimator"]
+    rank_int = sum(rank.values())
+    del rank
+
+    # compute spatial filter
+    n_orient = 3 if is_free_ori else 1
+    W, max_power_ori = _compute_beamformer(
+        G,
+        Cm,
+        reg,
+        n_orient,
+        weight_norm,
+        pick_ori,
+        reduce_rank,
+        rank_int,
+        inversion=inversion,
+        nn=nn,
+        orient_std=orient_std,
+        whitener=whitener,
+    )
+
+    # get src type to store with filters for _make_stc
+    src_type = _get_src_type(forward["src"], vertno)
+
+    # get subject to store with filters
+    subject_from = _subject_from_forward(forward)
+
+    # Is the computed beamformer a scalar or vector beamformer?
+    is_free_ori = is_free_ori if pick_ori in [None, "vector"] else False
+    is_ssp = bool(info["projs"])
+
+    filters = Beamformer(
+        kind="LCMV",
+        weights=W,
+        data_cov=data_cov,
+        noise_cov=noise_cov,
+        whitener=whitener,
+        weight_norm=weight_norm,
+        pick_ori=pick_ori,
+        ch_names=ch_names,
+        proj=proj,
+        is_ssp=is_ssp,
+        vertices=vertno,
+        is_free_ori=is_free_ori,
+        n_sources=forward["nsource"],
+        src_type=src_type,
+        source_nn=forward["source_nn"].copy(),
+        subject=subject_from,
+        rank=rank_int,
+        max_power_ori=max_power_ori,
+        inversion=inversion,
+    )
+
+    return filters
+
+
+def _apply_lcmv(data, filters, info, tmin):
+    """Apply LCMV spatial filter to data for source reconstruction."""
+    if isinstance(data, np.ndarray) and data.ndim == 2:
+        data = [data]
+        return_single = True
+    else:
+        return_single = False
+
+    W = filters["weights"]
+
+    for i, M in enumerate(data):
+        if len(M) != len(filters["ch_names"]):
+            raise ValueError("data and picks must have the same length")
+
+        if not return_single:
+            logger.info(f"Processing epoch : {i + 1}")
+
+        M = _proj_whiten_data(M, info["projs"], filters)
+
+        # project to source space using beamformer weights
+        vector = False
+        if filters["is_free_ori"]:
+            sol = np.dot(W, M)
+            if filters["pick_ori"] == "vector":
+                vector = True
+            else:
+                logger.info("combining the current components...")
+                sol = combine_xyz(sol)
+        else:
+            # Linear inverse: do computation here or delayed
+            if M.shape[0] < W.shape[0] and filters["pick_ori"] != "max-power":
+                sol = (W, M)
+            else:
+                sol = np.dot(W, M)
+
+        tstep = 1.0 / info["sfreq"]
+
+        # compatibility with 0.16, add src_type as None if not present:
+        filters, warn_text = _check_src_type(filters)
+
+        yield _make_stc(
+            sol,
+            vertices=filters["vertices"],
+            tmin=tmin,
+            tstep=tstep,
+            subject=filters["subject"],
+            vector=vector,
+            source_nn=filters["source_nn"],
+            src_type=filters["src_type"],
+            warn_text=warn_text,
+        )
+
+    logger.info("[done]")
+
+
+@verbose
+def apply_lcmv(evoked, filters, *, verbose=None):
+    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.
+
+    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
+    on evoked data.
+
+    Parameters
+    ----------
+    evoked : Evoked
+        Evoked data to invert.
+    filters : instance of Beamformer
+        LCMV spatial filter (beamformer weights).
+        Filter weights returned from :func:`make_lcmv`.
+    %(verbose)s
+
+    Returns
+    -------
+    stc : SourceEstimate | VolSourceEstimate | VectorSourceEstimate
+        Source time courses.
+
+    See Also
+    --------
+    make_lcmv, apply_lcmv_raw, apply_lcmv_epochs, apply_lcmv_cov
+
+    Notes
+    -----
+    .. versionadded:: 0.18
+    """
+    _check_reference(evoked)
+
+    info = evoked.info
+    data = evoked.data
+    tmin = evoked.times[0]
+
+    sel = _check_channels_spatial_filter(evoked.ch_names, filters)
+    data = data[sel]
+
+    stc = _apply_lcmv(data=data, filters=filters, info=info, tmin=tmin)
+
+    return next(stc)
+
+
+@verbose
+def apply_lcmv_epochs(epochs, filters, *, return_generator=False, verbose=None):
+    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.
+
+    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
+    on single trial data.
+
+    Parameters
+    ----------
+    epochs : Epochs
+        Single trial epochs.
+    filters : instance of Beamformer
+        LCMV spatial filter (beamformer weights)
+        Filter weights returned from :func:`make_lcmv`.
+    return_generator : bool
+         Return a generator object instead of a list. This allows iterating
+         over the stcs without having to keep them all in memory.
+    %(verbose)s
+
+    Returns
+    -------
+    stc: list | generator of (SourceEstimate | VolSourceEstimate)
+        The source estimates for all epochs.
+
+    See Also
+    --------
+    make_lcmv, apply_lcmv_raw, apply_lcmv, apply_lcmv_cov
+    """
+    _check_reference(epochs)
+
+    info = epochs.info
+    tmin = epochs.times[0]
+
+    sel = _check_channels_spatial_filter(epochs.ch_names, filters)
+    data = epochs.get_data(sel)
+    stcs = _apply_lcmv(data=data, filters=filters, info=info, tmin=tmin)
+
+    if not return_generator:
+        stcs = [s for s in stcs]
+
+    return stcs
+
+
+@verbose
+def apply_lcmv_raw(raw, filters, start=None, stop=None, *, verbose=None):
+    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.
+
+    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
+    on raw data.
+
+    Parameters
+    ----------
+    raw : mne.io.Raw
+        Raw data to invert.
+    filters : instance of Beamformer
+        LCMV spatial filter (beamformer weights).
+        Filter weights returned from :func:`make_lcmv`.
+    start : int
+        Index of first time sample (index not time is seconds).
+    stop : int
+        Index of first time sample not to include (index not time is seconds).
+    %(verbose)s
+
+    Returns
+    -------
+    stc : SourceEstimate | VolSourceEstimate
+        Source time courses.
+
+    See Also
+    --------
+    make_lcmv, apply_lcmv_epochs, apply_lcmv, apply_lcmv_cov
+    """
+    _check_reference(raw)
+
+    info = raw.info
+
+    sel = _check_channels_spatial_filter(raw.ch_names, filters)
+    data, times = raw[sel, start:stop]
+    tmin = times[0]
+
+    stc = _apply_lcmv(data=data, filters=filters, info=info, tmin=tmin)
+
+    return next(stc)
+
+
+@verbose
+def apply_lcmv_cov(data_cov, filters, verbose=None):
+    """Apply Linearly Constrained  Minimum Variance (LCMV) beamformer weights.
+
+    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
+    to a data covariance matrix to estimate source power.
+
+    Parameters
+    ----------
+    data_cov : instance of Covariance
+        Data covariance matrix.
+    filters : instance of Beamformer
+        LCMV spatial filter (beamformer weights).
+        Filter weights returned from :func:`make_lcmv`.
+    %(verbose)s
+
+    Returns
+    -------
+    stc : SourceEstimate | VolSourceEstimate
+        Source power.
+
+    See Also
+    --------
+    make_lcmv, apply_lcmv, apply_lcmv_epochs, apply_lcmv_raw
+    """
+    sel = _check_channels_spatial_filter(data_cov.ch_names, filters)
+    sel_names = [data_cov.ch_names[ii] for ii in sel]
+    data_cov = pick_channels_cov(data_cov, sel_names)
+
+    n_orient = filters["weights"].shape[0] // filters["n_sources"]
+    # Need to project and whiten along both dimensions
+    data = _proj_whiten_data(data_cov["data"].T, data_cov["projs"], filters)
+    data = _proj_whiten_data(data.T, data_cov["projs"], filters)
+    del data_cov
+    source_power = _compute_power(data, filters["weights"], n_orient)
+
+    # compatibility with 0.16, add src_type as None if not present:
+    filters, warn_text = _check_src_type(filters)
+
+    return _make_stc(
+        source_power,
+        vertices=filters["vertices"],
+        src_type=filters["src_type"],
+        tmin=0.0,
+        tstep=1.0,
+        subject=filters["subject"],
+        source_nn=filters["source_nn"],
+        warn_text=warn_text,
+    )

mne/beamformer/_rap_music.py

@@ -0,0 +1,315 @@
+"""Compute a Recursively Applied and Projected MUltiple Signal Classification (RAP-MUSIC)."""  # noqa
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+from scipy import linalg
+
+from .._fiff.pick import pick_channels_forward, pick_info
+from ..fixes import _safe_svd
+from ..forward import convert_forward_solution, is_fixed_orient
+from ..inverse_sparse.mxne_inverse import _make_dipoles_sparse
+from ..minimum_norm.inverse import _log_exp_var
+from ..utils import _check_info_inv, fill_doc, logger, verbose
+from ._compute_beamformer import _prepare_beamformer_input
+
+
+@fill_doc
+def _apply_rap_music(
+    data, info, times, forward, noise_cov, n_dipoles=2, picks=None, use_trap=False
+):
+    """RAP-MUSIC or TRAP-MUSIC for evoked data.
+
+    Parameters
+    ----------
+    data : array, shape (n_channels, n_times)
+        Evoked data.
+    %(info_not_none)s
+    times : array
+        Times.
+    forward : instance of Forward
+        Forward operator.
+    noise_cov : instance of Covariance
+        The noise covariance.
+    n_dipoles : int
+        The number of dipoles to estimate. The default value is 2.
+    picks : list of int
+        Caller ensures this is a list of int.
+    use_trap : bool
+        Use the TRAP-MUSIC variant if True (default False).
+
+    Returns
+    -------
+    dipoles : list of instances of Dipole
+        The dipole fits.
+    explained_data : array | None
+        Data explained by the dipoles using a least square fitting with the
+        selected active dipoles and their estimated orientation.
+    """
+    info = pick_info(info, picks)
+    del picks
+    # things are much simpler if we avoid surface orientation
+    align = forward["source_nn"].copy()
+    if forward["surf_ori"] and not is_fixed_orient(forward):
+        forward = convert_forward_solution(forward, surf_ori=False)
+    is_free_ori, info, _, _, G, whitener, _, _ = _prepare_beamformer_input(
+        info, forward, noise_cov=noise_cov, rank=None
+    )
+    forward = pick_channels_forward(forward, info["ch_names"], ordered=True)
+    del info
+
+    # whiten the data (leadfield already whitened)
+    M = np.dot(whitener, data)
+    del data
+
+    _, eig_vectors = linalg.eigh(np.dot(M, M.T))
+    phi_sig = eig_vectors[:, -n_dipoles:]
+
+    n_orient = 3 if is_free_ori else 1
+    G.shape = (G.shape[0], -1, n_orient)
+    gain = forward["sol"]["data"].copy()
+    gain.shape = G.shape
+    n_channels = G.shape[0]
+    A = np.empty((n_channels, n_dipoles))
+    gain_dip = np.empty((n_channels, n_dipoles))
+    oris = np.empty((n_dipoles, 3))
+    poss = np.empty((n_dipoles, 3))
+
+    G_proj = G.copy()
+    phi_sig_proj = phi_sig.copy()
+
+    idxs = list()
+    for k in range(n_dipoles):
+        subcorr_max = -1.0
+        source_idx, source_ori, source_pos = 0, [0, 0, 0], [0, 0, 0]
+        for i_source in range(G.shape[1]):
+            Gk = G_proj[:, i_source]
+            subcorr, ori = _compute_subcorr(Gk, phi_sig_proj)
+            if subcorr > subcorr_max:
+                subcorr_max = subcorr
+                source_idx = i_source
+                source_ori = ori
+                source_pos = forward["source_rr"][i_source]
+                if n_orient == 3 and align is not None:
+                    surf_normal = forward["source_nn"][3 * i_source + 2]
+                    # make sure ori is aligned to the surface orientation
+                    source_ori *= np.sign(source_ori @ surf_normal) or 1.0
+                if n_orient == 1:
+                    source_ori = forward["source_nn"][i_source]
+
+        idxs.append(source_idx)
+        if n_orient == 3:
+            Ak = np.dot(G[:, source_idx], source_ori)
+        else:
+            Ak = G[:, source_idx, 0]
+        A[:, k] = Ak
+        oris[k] = source_ori
+        poss[k] = source_pos
+
+        logger.info(f"source {k + 1} found: p = {source_idx}")
+        if n_orient == 3:
+            logger.info("ori = {} {} {}".format(*tuple(oris[k])))
+
+        projection = _compute_proj(A[:, : k + 1])
+        G_proj = np.einsum("ab,bso->aso", projection, G)
+        phi_sig_proj = np.dot(projection, phi_sig)
+        if use_trap:
+            phi_sig_proj = phi_sig_proj[:, -(n_dipoles - k) :]
+    del G, G_proj
+
+    sol = linalg.lstsq(A, M)[0]
+    if n_orient == 3:
+        X = sol[:, np.newaxis] * oris[:, :, np.newaxis]
+        X.shape = (-1, len(times))
+    else:
+        X = sol
+
+    gain_active = gain[:, idxs]
+    if n_orient == 3:
+        gain_dip = (oris * gain_active).sum(-1)
+        idxs = np.array(idxs)
+        active_set = np.array([[3 * idxs, 3 * idxs + 1, 3 * idxs + 2]]).T.ravel()
+    else:
+        gain_dip = gain_active[:, :, 0]
+        active_set = idxs
+    gain_active = whitener @ gain_active.reshape(gain.shape[0], -1)
+    assert gain_active.shape == (n_channels, X.shape[0])
+
+    explained_data = gain_dip @ sol
+    M_estimate = whitener @ explained_data
+    _log_exp_var(M, M_estimate)
+    tstep = np.median(np.diff(times)) if len(times) > 1 else 1.0
+    dipoles = _make_dipoles_sparse(
+        X, active_set, forward, times[0], tstep, M, gain_active, active_is_idx=True
+    )
+    for dipole, ori in zip(dipoles, oris):
+        signs = np.sign((dipole.ori * ori).sum(-1, keepdims=True))
+        dipole.ori *= signs
+        dipole.amplitude *= signs[:, 0]
+    logger.info("[done]")
+    return dipoles, explained_data
+
+
+def _compute_subcorr(G, phi_sig):
+    """Compute the subspace correlation."""
+    Ug, Sg, Vg = _safe_svd(G, full_matrices=False)
+    # Now we look at the actual rank of the forward fields
+    # in G and handle the fact that it might be rank defficient
+    # eg. when using MEG and a sphere model for which the
+    # radial component will be truly 0.
+    rank = np.sum(Sg > (Sg[0] * 1e-6))
+    if rank == 0:
+        return 0, np.zeros(len(G))
+    rank = max(rank, 2)  # rank cannot be 1
+    Ug, Sg, Vg = Ug[:, :rank], Sg[:rank], Vg[:rank]
+    tmp = np.dot(Ug.T.conjugate(), phi_sig)
+    Uc, Sc, _ = _safe_svd(tmp, full_matrices=False)
+    X = np.dot(Vg.T / Sg[None, :], Uc[:, 0])  # subcorr
+    return Sc[0], X / np.linalg.norm(X)
+
+
+def _compute_proj(A):
+    """Compute the orthogonal projection operation for a manifold vector A."""
+    U, _, _ = _safe_svd(A, full_matrices=False)
+    return np.identity(A.shape[0]) - np.dot(U, U.T.conjugate())
+
+
+def _rap_music(evoked, forward, noise_cov, n_dipoles, return_residual, use_trap):
+    """RAP-/TRAP-MUSIC implementation."""
+    info = evoked.info
+    data = evoked.data
+    times = evoked.times
+
+    picks = _check_info_inv(info, forward, data_cov=None, noise_cov=noise_cov)
+
+    data = data[picks]
+
+    dipoles, explained_data = _apply_rap_music(
+        data, info, times, forward, noise_cov, n_dipoles, picks, use_trap
+    )
+
+    if return_residual:
+        residual = evoked.copy().pick([info["ch_names"][p] for p in picks])
+        residual.data -= explained_data
+        active_projs = [p for p in residual.info["projs"] if p["active"]]
+        for p in active_projs:
+            p["active"] = False
+        residual.add_proj(active_projs, remove_existing=True)
+        residual.apply_proj()
+        return dipoles, residual
+    else:
+        return dipoles
+
+
+@verbose
+def rap_music(
+    evoked,
+    forward,
+    noise_cov,
+    n_dipoles=5,
+    return_residual=False,
+    *,
+    verbose=None,
+):
+    """RAP-MUSIC source localization method.
+
+    Compute Recursively Applied and Projected MUltiple SIgnal Classification
+    (RAP-MUSIC) :footcite:`MosherLeahy1999,MosherLeahy1996` on evoked data.
+
+    .. note:: The goodness of fit (GOF) of all the returned dipoles is the
+              same and corresponds to the GOF of the full set of dipoles.
+
+    Parameters
+    ----------
+    evoked : instance of Evoked
+        Evoked data to localize.
+    forward : instance of Forward
+        Forward operator.
+    noise_cov : instance of Covariance
+        The noise covariance.
+    n_dipoles : int
+        The number of dipoles to look for. The default value is 5.
+    return_residual : bool
+        If True, the residual is returned as an Evoked instance.
+    %(verbose)s
+
+    Returns
+    -------
+    dipoles : list of instance of Dipole
+        The dipole fits.
+    residual : instance of Evoked
+        The residual a.k.a. data not explained by the dipoles.
+        Only returned if return_residual is True.
+
+    See Also
+    --------
+    mne.fit_dipole
+    mne.beamformer.trap_music
+
+    Notes
+    -----
+    .. versionadded:: 0.9.0
+
+    References
+    ----------
+    .. footbibliography::
+    """
+    return _rap_music(evoked, forward, noise_cov, n_dipoles, return_residual, False)
+
+
+@verbose
+def trap_music(
+    evoked,
+    forward,
+    noise_cov,
+    n_dipoles=5,
+    return_residual=False,
+    *,
+    verbose=None,
+):
+    """TRAP-MUSIC source localization method.
+
+    Compute Truncated Recursively Applied and Projected MUltiple SIgnal Classification
+    (TRAP-MUSIC) :footcite:`Makela2018` on evoked data.
+
+    .. note:: The goodness of fit (GOF) of all the returned dipoles is the
+              same and corresponds to the GOF of the full set of dipoles.
+
+    Parameters
+    ----------
+    evoked : instance of Evoked
+        Evoked data to localize.
+    forward : instance of Forward
+        Forward operator.
+    noise_cov : instance of Covariance
+        The noise covariance.
+    n_dipoles : int
+        The number of dipoles to look for. The default value is 5.
+    return_residual : bool
+        If True, the residual is returned as an Evoked instance.
+    %(verbose)s
+
+    Returns
+    -------
+    dipoles : list of instance of Dipole
+        The dipole fits.
+    residual : instance of Evoked
+        The residual a.k.a. data not explained by the dipoles.
+        Only returned if return_residual is True.
+
+    See Also
+    --------
+    mne.fit_dipole
+    mne.beamformer.rap_music
+
+    Notes
+    -----
+    .. versionadded:: 1.4
+
+    References
+    ----------
+    .. footbibliography::
+    """
+    return _rap_music(evoked, forward, noise_cov, n_dipoles, return_residual, True)

mne/beamformer/resolution_matrix.py

@@ -0,0 +1,86 @@
+"""Compute resolution matrix for beamformers."""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from .._fiff.pick import pick_channels, pick_channels_forward, pick_info
+from ..evoked import EvokedArray
+from ..utils import fill_doc, logger
+from ._lcmv import apply_lcmv
+
+
+@fill_doc
+def make_lcmv_resolution_matrix(filters, forward, info):
+    """Compute resolution matrix for LCMV beamformer.
+
+    Parameters
+    ----------
+    filters : instance of Beamformer
+         Dictionary containing filter weights from LCMV beamformer
+         (see mne.beamformer.make_lcmv).
+    forward : instance of Forward
+        Forward Solution with leadfield matrix.
+    %(info_not_none)s Used to compute LCMV filters.
+
+    Returns
+    -------
+    resmat : array, shape (n_dipoles_lcmv, n_dipoles_fwd)
+        Resolution matrix (filter matrix multiplied to leadfield from
+        forward solution). Numbers of rows (n_dipoles_lcmv) and columns
+        (n_dipoles_fwd) may differ by a factor depending on orientation
+        constraints of filter and forward solution, respectively (e.g. factor 3
+        for free dipole orientation versus factor 1 for scalar beamformers).
+    """
+    # don't include bad channels from noise covariance matrix
+    bads_filt = filters["noise_cov"]["bads"]
+    ch_names = filters["noise_cov"]["names"]
+
+    # good channels
+    ch_names = [c for c in ch_names if (c not in bads_filt)]
+
+    # adjust channels in forward solution
+    forward = pick_channels_forward(forward, ch_names, ordered=True)
+
+    # get leadfield matrix from forward solution
+    leadfield = forward["sol"]["data"]
+
+    # get the filter weights for beamformer as matrix
+    filtmat = _get_matrix_from_lcmv(filters, forward, info)
+
+    # compute resolution matrix
+    resmat = filtmat.dot(leadfield)
+
+    logger.info(f"Dimensions of LCMV resolution matrix: {resmat.shape}.")
+
+    return resmat
+
+
+def _get_matrix_from_lcmv(filters, forward, info, verbose=None):
+    """Get inverse matrix for LCMV beamformer.
+
+    Returns
+    -------
+    invmat : array, shape (n_dipoles, n_channels)
+        Inverse matrix associated with LCMV beamformer filters.
+    """
+    # number of channels for identity matrix
+    info = pick_info(info, pick_channels(info["ch_names"], filters["ch_names"]))
+    n_chs = len(info["ch_names"])
+
+    # create identity matrix as input for inverse operator
+    # set elements to zero for non-selected channels
+    id_mat = np.eye(n_chs)
+
+    # convert identity matrix to evoked data type (pretending it's an epochs
+    evo_ident = EvokedArray(id_mat, info=info, tmin=0.0)
+
+    # apply beamformer to identity matrix
+    stc_lcmv = apply_lcmv(evo_ident, filters, verbose=verbose)
+
+    # turn source estimate into numpsy array
+    invmat = stc_lcmv.data
+
+    return invmat

mne/channels/__init__.py

@@ -0,0 +1,12 @@
+"""Module dedicated to manipulation of channels.
+
+Can be used for setting of sensor locations used for processing and plotting.
+"""
+
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import lazy_loader as lazy
+
+(__getattr__, __dir__, __all__) = lazy.attach_stub(__name__, __file__)

mne/channels/__init__.pyi

@@ -0,0 +1,78 @@
+__all__ = [
+    "DigMontage",
+    "Layout",
+    "_EEG_SELECTIONS",
+    "_SELECTIONS",
+    "_divide_to_regions",
+    "combine_channels",
+    "compute_dev_head_t",
+    "compute_native_head_t",
+    "equalize_channels",
+    "find_ch_adjacency",
+    "find_layout",
+    "fix_mag_coil_types",
+    "generate_2d_layout",
+    "get_builtin_ch_adjacencies",
+    "get_builtin_montages",
+    "make_1020_channel_selections",
+    "make_dig_montage",
+    "make_eeg_layout",
+    "make_grid_layout",
+    "make_standard_montage",
+    "read_ch_adjacency",
+    "read_custom_montage",
+    "read_dig_captrak",
+    "read_dig_dat",
+    "read_dig_egi",
+    "read_dig_fif",
+    "read_dig_hpts",
+    "read_dig_localite",
+    "read_dig_polhemus_isotrak",
+    "read_layout",
+    "read_polhemus_fastscan",
+    "read_vectorview_selection",
+    "rename_channels",
+    "transform_to_head",
+    "unify_bad_channels",
+]
+from .channels import (
+    _EEG_SELECTIONS,
+    _SELECTIONS,
+    _divide_to_regions,
+    combine_channels,
+    equalize_channels,
+    find_ch_adjacency,
+    fix_mag_coil_types,
+    get_builtin_ch_adjacencies,
+    make_1020_channel_selections,
+    read_ch_adjacency,
+    read_vectorview_selection,
+    rename_channels,
+    unify_bad_channels,
+)
+from .layout import (
+    Layout,
+    find_layout,
+    generate_2d_layout,
+    make_eeg_layout,
+    make_grid_layout,
+    read_layout,
+)
+from .montage import (
+    DigMontage,
+    compute_dev_head_t,
+    compute_native_head_t,
+    get_builtin_montages,
+    make_dig_montage,
+    make_standard_montage,
+    read_custom_montage,
+    read_dig_captrak,
+    read_dig_dat,
+    read_dig_egi,
+    read_dig_fif,
+    read_dig_hpts,
+    read_dig_localite,
+    read_dig_polhemus_isotrak,
+    read_polhemus_fastscan,
+    transform_to_head,
+)

mne/channels/_dig_montage_utils.py

@@ -0,0 +1,96 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import numpy as np
+
+from ..utils import Bunch, _check_fname, _soft_import, warn
+
+
+def _read_dig_montage_egi(
+    fname,
+    _scaling,
+    _all_data_kwargs_are_none,
+):
+    if not _all_data_kwargs_are_none:
+        raise ValueError(
+            "hsp, hpi, elp, point_names, fif must all be None if egi is not None"
+        )
+    _check_fname(fname, overwrite="read", must_exist=True)
+    defusedxml = _soft_import("defusedxml", "reading EGI montages")
+    root = defusedxml.ElementTree.parse(fname).getroot()
+    ns = root.tag[root.tag.index("{") : root.tag.index("}") + 1]
+    sensors = root.find(f"{ns}sensorLayout/{ns}sensors")
+    fids = dict()
+    dig_ch_pos = dict()
+
+    fid_name_map = {
+        "Nasion": "nasion",
+        "Right periauricular point": "rpa",
+        "Left periauricular point": "lpa",
+    }
+
+    for s in sensors:
+        name, number, kind = s[0].text, int(s[1].text), int(s[2].text)
+        coordinates = np.array([float(s[3].text), float(s[4].text), float(s[5].text)])
+
+        coordinates *= _scaling
+
+        # EEG Channels
+        if kind == 0:
+            dig_ch_pos[f"EEG {number:03d}"] = coordinates
+        # Reference
+        elif kind == 1:
+            dig_ch_pos[f"EEG {len(dig_ch_pos) + 1:03d}"] = coordinates
+        # Fiducials
+        elif kind == 2:
+            fid_name = fid_name_map[name]
+            fids[fid_name] = coordinates
+        # Unknown
+        else:
+            warn(
+                f"Unknown sensor type {kind} detected. Skipping sensor..."
+                "Proceed with caution!"
+            )
+
+    return Bunch(
+        # EGI stuff
+        nasion=fids["nasion"],
+        lpa=fids["lpa"],
+        rpa=fids["rpa"],
+        ch_pos=dig_ch_pos,
+        coord_frame="unknown",
+    )
+
+
+def _parse_brainvision_dig_montage(fname, scale):
+    FID_NAME_MAP = {"Nasion": "nasion", "RPA": "rpa", "LPA": "lpa"}
+    defusedxml = _soft_import("defusedxml", "reading BrainVision montages")
+    root = defusedxml.ElementTree.parse(fname).getroot()
+    sensors = root.find("CapTrakElectrodeList")
+
+    fids, dig_ch_pos = dict(), dict()
+
+    for s in sensors:
+        name = s.find("Name").text
+
+        is_fid = name in FID_NAME_MAP
+        coordinates = scale * np.array(
+            [float(s.find("X").text), float(s.find("Y").text), float(s.find("Z").text)]
+        )
+
+        # Fiducials
+        if is_fid:
+            fids[FID_NAME_MAP[name]] = coordinates
+        # EEG Channels
+        else:
+            dig_ch_pos[name] = coordinates
+
+    return dict(
+        # BVCT stuff
+        nasion=fids["nasion"],
+        lpa=fids["lpa"],
+        rpa=fids["rpa"],
+        ch_pos=dig_ch_pos,
+        coord_frame="unknown",
+    )

mne/channels/_standard_montage_utils.py

@@ -0,0 +1,421 @@
+# Authors: The MNE-Python contributors.
+# License: BSD-3-Clause
+# Copyright the MNE-Python contributors.
+
+import csv
+import os.path as op
+from collections import OrderedDict
+from functools import partial
+
+import numpy as np
+
+from .._freesurfer import get_mni_fiducials
+from ..transforms import _sph_to_cart
+from ..utils import _pl, _soft_import, warn
+from . import __file__ as _CHANNELS_INIT_FILE
+from .montage import make_dig_montage
+
+MONTAGE_PATH = op.join(op.dirname(_CHANNELS_INIT_FILE), "data", "montages")
+
+_str = "U100"
+
+
+# In standard_1020, T9=LPA, T10=RPA, Nasion is the same as Iz with a
+# sign-flipped Y value
+
+
+def _egi_256(head_size):
+    fname = op.join(MONTAGE_PATH, "EGI_256.csd")
+    montage = _read_csd(fname, head_size)
+    ch_pos = montage._get_ch_pos()
+
+    # For this cap, the Nasion is the frontmost electrode,
+    # LPA/RPA we approximate by putting 75% of the way (toward the front)
+    # between the two electrodes that are halfway down the ear holes
+    nasion = ch_pos["E31"]
+    lpa = 0.75 * ch_pos["E67"] + 0.25 * ch_pos["E94"]
+    rpa = 0.75 * ch_pos["E219"] + 0.25 * ch_pos["E190"]
+
+    fids_montage = make_dig_montage(
+        coord_frame="unknown",
+        nasion=nasion,
+        lpa=lpa,
+        rpa=rpa,
+    )
+
+    montage += fids_montage  # add fiducials to montage
+
+    return montage
+
+
+def _easycap(basename, head_size):
+    fname = op.join(MONTAGE_PATH, basename)
+    montage = _read_theta_phi_in_degrees(fname, head_size, add_fiducials=True)
+    return montage
+
+
+def _hydrocel(basename, head_size):
+    fname = op.join(MONTAGE_PATH, basename)
+    return _read_sfp(fname, head_size)
+
+
+def _str_names(ch_names):
+    return [str(ch_name) for ch_name in ch_names]
+
+
+def _safe_np_loadtxt(fname, **kwargs):
+    out = np.genfromtxt(fname, **kwargs)
+    ch_names = _str_names(out["f0"])
+    others = tuple(out[f"f{ii}"] for ii in range(1, len(out.dtype.fields)))
+    return (ch_names,) + others
+
+
+def _biosemi(basename, head_size):
+    fname = op.join(MONTAGE_PATH, basename)
+    fid_names = ("Nz", "LPA", "RPA")
+    return _read_theta_phi_in_degrees(fname, head_size, fid_names)
+
+
+def _mgh_or_standard(basename, head_size, coord_frame="unknown"):
+    fid_names = ("Nz", "LPA", "RPA")
+    fname = op.join(MONTAGE_PATH, basename)
+
+    ch_names_, pos = [], []
+    with open(fname) as fid:
+        # Ignore units as we will scale later using the norms anyway
+        for line in fid:
+            if "Positions\n" in line:
+                break
+        pos = []
+        for line in fid:
+            if "Labels\n" in line:
+                break
+            pos.append(list(map(float, line.split())))
+        for line in fid:
+            if not line or not set(line) - {" "}:
+                break
+            ch_names_.append(line.strip(" ").strip("\n"))
+
+    pos = np.array(pos) / 1000.0
+    ch_pos = _check_dupes_odict(ch_names_, pos)
+    nasion, lpa, rpa = (ch_pos.pop(n) for n in fid_names)
+    if head_size is None:
+        scale = 1.0
+    else:
+        scale = head_size / np.median(np.linalg.norm(pos, axis=1))
+    for value in ch_pos.values():
+        value *= scale
+    # if we are in MRI/MNI coordinates, we need to replace nasion, LPA, and RPA
+    # with those of fsaverage for ``trans='fsaverage'`` to work
+    if coord_frame == "mri":
+        lpa, nasion, rpa = (x["r"].copy() for x in get_mni_fiducials("fsaverage"))
+    nasion *= scale
+    lpa *= scale
+    rpa *= scale
+
+    return make_dig_montage(
+        ch_pos=ch_pos, coord_frame=coord_frame, nasion=nasion, lpa=lpa, rpa=rpa
+    )
+
+
+standard_montage_look_up_table = {
+    "EGI_256": _egi_256,
+    "easycap-M1": partial(_easycap, basename="easycap-M1.txt"),
+    "easycap-M10": partial(_easycap, basename="easycap-M10.txt"),
+    "easycap-M43": partial(_easycap, basename="easycap-M43.txt"),
+    "GSN-HydroCel-128": partial(_hydrocel, basename="GSN-HydroCel-128.sfp"),
+    "GSN-HydroCel-129": partial(_hydrocel, basename="GSN-HydroCel-129.sfp"),
+    "GSN-HydroCel-256": partial(_hydrocel, basename="GSN-HydroCel-256.sfp"),
+    "GSN-HydroCel-257": partial(_hydrocel, basename="GSN-HydroCel-257.sfp"),
+    "GSN-HydroCel-32": partial(_hydrocel, basename="GSN-HydroCel-32.sfp"),
+    "GSN-HydroCel-64_1.0": partial(_hydrocel, basename="GSN-HydroCel-64_1.0.sfp"),
+    "GSN-HydroCel-65_1.0": partial(_hydrocel, basename="GSN-HydroCel-65_1.0.sfp"),
+    "biosemi128": partial(_biosemi, basename="biosemi128.txt"),
+    "biosemi16": partial(_biosemi, basename="biosemi16.txt"),
+    "biosemi160": partial(_biosemi, basename="biosemi160.txt"),
+    "biosemi256": partial(_biosemi, basename="biosemi256.txt"),
+    "biosemi32": partial(_biosemi, basename="biosemi32.txt"),
+    "biosemi64": partial(_biosemi, basename="biosemi64.txt"),
+    "mgh60": partial(_mgh_or_standard, basename="mgh60.elc", coord_frame="mri"),
+    "mgh70": partial(_mgh_or_standard, basename="mgh70.elc", coord_frame="mri"),
+    "standard_1005": partial(
+        _mgh_or_standard, basename="standard_1005.elc", coord_frame="mri"
+    ),
+    "standard_1020": partial(
+        _mgh_or_standard, basename="standard_1020.elc", coord_frame="mri"
+    ),
+    "standard_alphabetic": partial(
+        _mgh_or_standard, basename="standard_alphabetic.elc", coord_frame="mri"
+    ),
+    "standard_postfixed": partial(
+        _mgh_or_standard, basename="standard_postfixed.elc", coord_frame="mri"
+    ),
+    "standard_prefixed": partial(
+        _mgh_or_standard, basename="standard_prefixed.elc", coord_frame="mri"
+    ),
+    "standard_primed": partial(
+        _mgh_or_standard, basename="standard_primed.elc", coord_frame="mri"
+    ),
+    "artinis-octamon": partial(
+        _mgh_or_standard, coord_frame="mri", basename="artinis-octamon.elc"
+    ),
+    "artinis-brite23": partial(
+        _mgh_or_standard, coord_frame="mri", basename="artinis-brite23.elc"
+    ),
+    "brainproducts-RNP-BA-128": partial(
+        _easycap, basename="brainproducts-RNP-BA-128.txt"
+    ),
+}
+
+
+def _read_sfp(fname, head_size):
+    """Read .sfp BESA/EGI files."""
+    # fname has been already checked
+    fid_names = ("FidNz", "FidT9", "FidT10")
+    options = dict(dtype=(_str, "f4", "f4", "f4"))
+    ch_names, xs, ys, zs = _safe_np_loadtxt(fname, **options)
+    # deal with "headshape"
+    mask = np.array([ch_name == "headshape" for ch_name in ch_names], bool)
+    hsp = np.stack([xs[mask], ys[mask], zs[mask]], axis=-1)
+    mask = ~mask
+    pos = np.stack([xs[mask], ys[mask], zs[mask]], axis=-1)
+    ch_names = [ch_name for ch_name, m in zip(ch_names, mask) if m]
+    ch_pos = _check_dupes_odict(ch_names, pos)
+    del xs, ys, zs, ch_names
+    # no one grants that fid names are there.
+    nasion, lpa, rpa = (ch_pos.pop(n, None) for n in fid_names)
+
+    if head_size is not None:
+        scale = head_size / np.median(np.linalg.norm(pos, axis=-1))
+        for value in ch_pos.values():
+            value *= scale
+        nasion = nasion * scale if nasion is not None else None
+        lpa = lpa * scale if lpa is not None else None
+        rpa = rpa * scale if rpa is not None else None
+
+    return make_dig_montage(
+        ch_pos=ch_pos, coord_frame="unknown", nasion=nasion, rpa=rpa, lpa=lpa, hsp=hsp
+    )
+
+
+def _read_csd(fname, head_size):
+    # Label, Theta, Phi, Radius, X, Y, Z, off sphere surface
+    options = dict(
+        comments="//", dtype=(_str, "f4", "f4", "f4", "f4", "f4", "f4", "f4")
+    )
+    ch_names, _, _, _, xs, ys, zs, _ = _safe_np_loadtxt(fname, **options)
+    pos = np.stack([xs, ys, zs], axis=-1)
+
+    if head_size is not None:
+        pos *= head_size / np.median(np.linalg.norm(pos, axis=1))
+
+    return make_dig_montage(ch_pos=_check_dupes_odict(ch_names, pos))
+
+
+def _check_dupes_odict(ch_names, pos):
+    """Warn if there are duplicates, then turn to ordered dict."""
+    ch_names = list(ch_names)
+    dups = OrderedDict((ch_name, ch_names.count(ch_name)) for ch_name in ch_names)
+    dups = OrderedDict((ch_name, count) for ch_name, count in dups.items() if count > 1)
+    n = len(dups)
+    if n:
+        dups = ", ".join(f"{ch_name} ({count})" for ch_name, count in dups.items())
+        warn(
+            f"Duplicate channel position{_pl(n)} found, the last will be "
+            f"used for {dups}"
+        )
+    return OrderedDict(zip(ch_names, pos))
+
+
+def _read_elc(fname, head_size):
+    """Read .elc files.
+
+    The `.elc` files are so-called "asa electrode files". ASA here stands for
+    Advances Source Analysis, and is a software package developed and sold by
+    the ANT Neuro company. They provide a device for sensor digitization, called
+    'xensor', which produces the `.elc` files.
+
+    Parameters
+    ----------
+    fname : str
+        File extension is expected to be '.elc'.
+    head_size : float | None
+        The size of the head in [m]. If none, returns the values read from the
+        file with no modification.
+
+    Returns
+    -------
+    montage : instance of DigMontage
+        The montage units are [m].
+    """
+    fid_names = ("Nz", "LPA", "RPA")
+
+    with open(fname) as fid:
+        # Read units
+        # _read_elc does require to detect the units. (see _mgh_or_standard)
+        for line in fid:
+            if "UnitPosition" in line:
+                units = line.split()[1]
+                scale = dict(m=1.0, mm=1e-3)[units]
+                break
+        else:
+            raise RuntimeError(f"Could not detect units in file {fname}")
+        for line in fid:
+            if "Positions\n" in line:
+                break
+
+        # Read positions
+        new_style = False
+        pos = []
+        for line in fid:
+            if "Labels\n" in line:
+                break
+            if ":" in line:
+                # Of the 'new' format: `E01 : 5.288 -3.658 119.693`
+                pos.append(list(map(float, line.split(":")[1].split())))
+                new_style = True
+            else:
+                # Of the 'old' format: `5.288 -3.658 119.693`
+                pos.append(list(map(float, line.split())))
+
+        # Read labels
+        ch_names_ = []
+        for line in fid:
+            if not line or not set(line) - {" "}:
+                break
+            if new_style:
+                # Not sure how this format would deal with spaces in channel labels,
+                # but none of my test files had this, so let's wait until it comes up.
+                parsed = line.strip(" ").strip("\n").split()
+            else:
+                parsed = [line.strip(" ").strip("\n")]
+            ch_names_.extend(parsed)
+
+    pos = np.array(pos) * scale
+    if head_size is not None:
+        pos *= head_size / np.median(np.linalg.norm(pos, axis=1))
+
+    ch_pos = _check_dupes_odict(ch_names_, pos)
+    nasion, lpa, rpa = (ch_pos.pop(n, None) for n in fid_names)
+
+    return make_dig_montage(
+        ch_pos=ch_pos, coord_frame="unknown", nasion=nasion, lpa=lpa, rpa=rpa
+    )
+
+
+def _read_theta_phi_in_degrees(fname, head_size, fid_names=None, add_fiducials=False):
+    ch_names, theta, phi = _safe_np_loadtxt(
+        fname, skip_header=1, dtype=(_str, "i4", "i4")
+    )
+    if add_fiducials:
+        # Add fiducials based on 10/20 spherical coordinate definitions
+        # http://chgd.umich.edu/wp-content/uploads/2014/06/
+        # 10-20_system_positioning.pdf
+        # extrapolated from other sensor coordinates in the Easycap layouts
+        # https://www.easycap.de/wp-content/uploads/2018/02/
+        # Easycap-Equidistant-Layouts.pdf
+        assert fid_names is None
+        fid_names = ["Nasion", "LPA", "RPA"]
+        ch_names.extend(fid_names)
+        theta = np.append(theta, [115, -115, 115])
+        phi = np.append(phi, [90, 0, 0])
+
+    radii = np.full(len(phi), head_size)
+    pos = _sph_to_cart(np.array([radii, np.deg2rad(phi), np.deg2rad(theta)]).T)
+    ch_pos = _check_dupes_odict(ch_names, pos)
+
+    nasion, lpa, rpa = None, None, None
+    if fid_names is not None:
+        nasion, lpa, rpa = (ch_pos.pop(n, None) for n in fid_names)
+
+    return make_dig_montage(
+        ch_pos=ch_pos, coord_frame="unknown", nasion=nasion, lpa=lpa, rpa=rpa
+    )
+
+
+def _read_elp_besa(fname, head_size):
+    # This .elp is not the same as polhemus elp. see _read_isotrak_elp_points
+    dtype = np.dtype("S8, S8, f8, f8, f8")
+    data = np.loadtxt(fname, dtype=dtype)
+
+    ch_names = data["f1"].astype(str).tolist()
+    az = data["f2"]
+    horiz = data["f3"]
+    radius = np.abs(az / 180.0)
+    az = np.deg2rad(np.array([h if a >= 0.0 else 180 + h for h, a in zip(horiz, az)]))
+    pol = radius * np.pi
+    rad = data["f4"] / 100
+    pos = _sph_to_cart(np.array([rad, az, pol]).T)
+
+    if head_size is not None:
+        pos *= head_size / np.median(np.linalg.norm(pos, axis=1))
+
+    ch_pos = _check_dupes_odict(ch_names, pos)
+
+    fid_names = ("Nz", "LPA", "RPA")
+    # No one grants that the fid names actually exist.
+    nasion, lpa, rpa = (ch_pos.pop(n, None) for n in fid_names)
+
+    return make_dig_montage(ch_pos=ch_pos, nasion=nasion, lpa=lpa, rpa=rpa)
+
+
+def _read_brainvision(fname, head_size):
+    # 'BrainVision Electrodes File' format
+    # Based on BrainVision Analyzer coordinate system: Defined between
+    # standard electrode positions: X-axis from T7 to T8, Y-axis from Oz to
+    # Fpz, Z-axis orthogonal from XY-plane through Cz, fit to a sphere if
+    # idealized (when radius=1), specified in millimeters
+    defusedxml = _soft_import("defusedxml", "reading BrainVision montages")
+    root = defusedxml.ElementTree.parse(fname).getroot()
+    ch_names = [s.text for s in root.findall("./Electrode/Name")]
+    theta = [float(s.text) for s in root.findall("./Electrode/Theta")]
+    pol = np.deg2rad(np.array(theta))
+    phi = [float(s.text) for s in root.findall("./Electrode/Phi")]
+    az = np.deg2rad(np.array(phi))
+    rad = [float(s.text) for s in root.findall("./Electrode/Radius")]
+    rad = np.array(rad)  # specified in mm
+    pos = _sph_to_cart(np.array([rad, az, pol]).T)
+
+    if head_size is not None:
+        pos *= head_size / np.median(np.linalg.norm(pos, axis=1))
+
+    return make_dig_montage(ch_pos=_check_dupes_odict(ch_names, pos))
+
+
+def _read_xyz(fname):
+    """Import EEG channel locations from CSV, TSV, or XYZ files.
+
+    CSV and TSV files should have columns 4 columns containing
+    ch_name, x, y, and z. Each row represents one channel.
+    XYZ files should have 5 columns containing
+    count, x, y, z, and ch_name. Each row represents one channel
+    CSV files should be separated by commas, TSV and XYZ files should be
+    separated by tabs.
+
+    Parameters
+    ----------
+    fname : str
+        Name of the file to read channel locations from.
+
+    Returns
+    -------
+    montage : instance of DigMontage
+        The montage.
+    """
+    ch_names = []
+    pos = []
+    file_format = op.splitext(fname)[1].lower()
+    with open(fname) as f:
+        if file_format != ".xyz":
+            f.readline()  # skip header
+        delimiter = "," if file_format == ".csv" else "\t"
+        for row in csv.reader(f, delimiter=delimiter):
+            if file_format == ".xyz":
+                _, x, y, z, ch_name, *_ = row
+                ch_name = ch_name.strip()  # deals with variable tab size
+            else:
+                ch_name, x, y, z, *_ = row
+            ch_names.append(ch_name)
+            pos.append((x, y, z))
+    d = _check_dupes_odict(ch_names, np.array(pos, dtype=float))
+    return make_dig_montage(ch_pos=d)

mne/channels/data/layouts/CTF-275.lout

@@ -0,0 +1,276 @@
+  -42.27    42.33   -39.99    31.80
+001    -4.09    10.91     4.00     3.00 MLC11-2622
+002    -7.25     8.87     4.00     3.00 MLC12-2622
+003   -10.79     7.43     4.00     3.00 MLC13-2622
+004   -14.40     5.31     4.00     3.00 MLC14-2622
+005   -17.45     2.88     4.00     3.00 MLC15-2622
+006   -19.94    -0.21     4.00     3.00 MLC16-2622
+007   -22.30    -3.88     4.00     3.00 MLC17-2622
+008    -7.70     5.16     4.00     3.00 MLC21-2622
+009   -11.18     3.69     4.00     3.00 MLC22-2622
+010   -14.17     1.40     4.00     3.00 MLC23-2622
+011   -16.42    -1.52     4.00     3.00 MLC24-2622
+012   -18.64    -4.88     4.00     3.00 MLC25-2622
+013   -12.55    -2.00     4.00     3.00 MLC31-2622
+014   -15.13    -5.41     4.00     3.00 MLC32-2622
+015    -9.57     0.28     4.00     3.00 MLC41-2622
+016   -11.51    -5.56     4.00     3.00 MLC42-2622
+017    -4.04     4.58     4.00     3.00 MLC51-2622
+018    -6.04     1.35     4.00     3.00 MLC52-2622
+019    -8.79    -3.34     4.00     3.00 MLC53-2622
+020    -8.32    -7.10     4.00     3.00 MLC54-2622
+021    -6.60   -10.22     4.00     3.00 MLC55-2622
+022    -4.01    -1.76     4.00     3.00 MLC61-2622
+023    -5.55    -4.97     4.00     3.00 MLC62-2622
+024    -3.74    -8.12     4.00     3.00 MLC63-2622
+025    -7.63    28.14     4.00     3.00 MLF11-2622
+026   -12.92    27.01     4.00     3.00 MLF12-2622
+027   -18.14    25.41     4.00     3.00 MLF13-2622
+028   -23.34    23.65     4.00     3.00 MLF14-2622
+029    -4.64    25.47     4.00     3.00 MLF21-2622
+030    -9.22    24.68     4.00     3.00 MLF22-2622
+031   -13.60    23.41     4.00     3.00 MLF23-2622
+032   -18.31    21.53     4.00     3.00 MLF24-2622
+033   -22.68    19.69     4.00     3.00 MLF25-2622
+034    -6.57    22.14     4.00     3.00 MLF31-2622
+035   -10.75    21.22     4.00     3.00 MLF32-2622
+036   -15.16    19.49     4.00     3.00 MLF33-2622
+037   -19.01    17.57     4.00     3.00 MLF34-2622
+038   -22.93    15.25     4.00     3.00 MLF35-2622
+039    -4.25    19.38     4.00     3.00 MLF41-2622
+040    -8.17    18.80     4.00     3.00 MLF42-2622
+041   -12.29    17.37     4.00     3.00 MLF43-2622
+042   -15.93    15.49     4.00     3.00 MLF44-2622
+043   -19.89    13.39     4.00     3.00 MLF45-2622
+044   -24.12    10.50     4.00     3.00 MLF46-2622
+045    -5.48    16.15     4.00     3.00 MLF51-2622
+046    -9.58    15.10     4.00     3.00 MLF52-2622
+047   -13.17    13.43     4.00     3.00 MLF53-2622
+048   -16.66    11.39     4.00     3.00 MLF54-2622
+049   -20.76     9.06     4.00     3.00 MLF55-2622
+050   -24.71     5.73     4.00     3.00 MLF56-2622
+051    -7.17    12.78     4.00     3.00 MLF61-2622
+052   -10.58    11.08     4.00     3.00 MLF62-2622
+053   -13.93     9.16     4.00     3.00 MLF63-2622
+054   -17.37     7.29     4.00     3.00 MLF64-2622
+055   -20.83     4.87     4.00     3.00 MLF65-2622
+056   -23.40     1.59     4.00     3.00 MLF66-2622
+057   -25.90    -2.51     4.00     3.00 MLF67-2622
+058    -6.96   -27.32     4.00     3.00 MLO11-2622
+059   -11.88   -25.97     4.00     3.00 MLO12-2622
+060   -16.48   -23.69     4.00     3.00 MLO13-2622
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+336	-1.963487	1.749684	0.069221	0.051916	COMNT
+337	1.963487	1.749684	0.069221	0.051916	SCALE

mne/channels/data/layouts/EGI256.lout

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mne/channels/data/layouts/GeodesicHeadWeb-280.lout

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mne/channels/data/layouts/KIT-125.lout

@@ -0,0 +1,126 @@
+   -0.50     0.50    -0.50     0.50
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mne/channels/data/layouts/KIT-157.lout

@@ -0,0 +1,158 @@
+-42.19	43.52	-41.7	28.71
+001     9.78   -14.18     4.00     3.00 MEG 001
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+004     8.08   -21.05     4.00     3.00 MEG 004
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+006    15.80   -16.63     4.00     3.00 MEG 006
+007    10.21   -12.01     4.00     3.00 MEG 007
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mne/channels/data/layouts/KIT-160.lay

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+162	-0.547000000	-0.5000000000	0.03188472676	0.02713339699	SCALE

mne/channels/data/layouts/KIT-AD.lout

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mne/channels/data/layouts/KIT-AS-2008.lout

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mne/channels/data/layouts/KIT-UMD-3.lout

@@ -0,0 +1,158 @@
+  -25.00    28.00   -21.35    23.75
+000   -23.42    20.48     3.20     2.40 MEG 001
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mne/channels/data/layouts/Neuromag_122.lout

@@ -0,0 +1,123 @@
+-3	28	-17	15
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+9	21.9673		3.613717	2	1.5	MEG 009
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mne/channels/data/layouts/Vectorview-all.lout

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mne/channels/data/layouts/Vectorview-grad.lout

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mne/channels/data/layouts/Vectorview-grad_norm.lout

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mne/channels/data/layouts/Vectorview-mag.lout

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mne/channels/data/layouts/biosemi.lay

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+34	0.496189	1.527114	0.290000	0.230000	Fp2
+35	0.943808	1.299041	0.290000	0.230000	AF8
+36	0.545830	1.170536	0.290000	0.230000	AF4
+37	0.000000	1.204277	0.290000	0.230000	AFz
+38	0.000000	0.802851	0.290000	0.230000	Fz
+39	0.326906	0.809121	0.290000	0.230000	F2
+40	0.659023	0.813825	0.290000	0.230000	F4
+41	0.987913	0.858779	0.290000	0.230000	F6
+42	1.299041	0.943808	0.290000	0.230000	F8
+43	1.527114	0.496189	0.290000	0.230000	FT8
+44	1.173172	0.450338	0.290000	0.230000	FC6
+45	0.770517	0.409691	0.290000	0.230000	FC4
+46	0.394923	0.394923	0.290000	0.230000	FC2
+47	0.000000	0.401426	0.290000	0.230000	FCz
+48	0.000000	0.000000	0.290000	0.230000	Cz
+49	0.401426	0.000000	0.290000	0.230000	C2
+50	0.802851	0.000000	0.290000	0.230000	C4
+51	1.204277	0.000000	0.290000	0.230000	C6
+52	1.605703	0.000000	0.290000	0.230000	T8
+53	1.527114	-0.496189	0.290000	0.230000	TP8
+54	1.173172	-0.450338	0.290000	0.230000	CP6
+55	0.770517	-0.409691	0.290000	0.230000	CP4
+56	0.394923	-0.394923	0.290000	0.230000	CP2
+57	0.326906	-0.809121	0.290000	0.230000	P2
+58	0.659023	-0.813825	0.290000	0.230000	P4
+59	0.987913	-0.858779	0.290000	0.230000	P6
+60	1.299041	-0.943808	0.290000	0.230000	P8
+61	1.537550	-1.290157	0.290000	0.230000	P10
+62	0.943808	-1.299041	0.290000	0.230000	PO8
+63	0.545830	-1.170536	0.290000	0.230000	PO4
+64	0.496189	-1.527114	0.290000	0.230000	O2

mne/channels/data/layouts/magnesWH3600.lout

@@ -0,0 +1,249 @@
+  -42.19    43.52   -41.70    28.71
+001    -1.28    -5.13     4.00     3.00 MEG 001
+002    -1.22    -1.43     4.00     3.00 MEG 002
+003    -1.37     2.53     4.00     3.00 MEG 003
+004    -1.36     5.90     4.00     3.00 MEG 004
+005    -1.45     9.27     4.00     3.00 MEG 005
+006    -4.89     9.36     4.00     3.00 MEG 006
+007    -5.20     5.86     4.00     3.00 MEG 007
+008    -5.26     2.40     4.00     3.00 MEG 008
+009    -5.34    -1.29     4.00     3.00 MEG 009
+010    -5.12    -5.08     4.00     3.00 MEG 010
+011    -4.73    -8.47     4.00     3.00 MEG 011
+012    -1.31    -8.81     4.00     3.00 MEG 012
+013     2.04    -8.49     4.00     3.00 MEG 013
+014     2.54    -5.16     4.00     3.00 MEG 014
+015     2.69    -1.43     4.00     3.00 MEG 015
+016     2.62     2.56     4.00     3.00 MEG 016
+017     2.50     5.89     4.00     3.00 MEG 017
+018     2.10     9.34     4.00     3.00 MEG 018
+019    -1.45    12.55     4.00     3.00 MEG 019
+020    -5.76    12.42     4.00     3.00 MEG 020
+021    -8.30     9.98     4.00     3.00 MEG 021
+022    -9.16     5.97     4.00     3.00 MEG 022
+023    -9.32     2.49     4.00     3.00 MEG 023
+024    -9.42    -1.32     4.00     3.00 MEG 024
+025    -9.13    -5.11     4.00     3.00 MEG 025
+026    -8.43    -9.18     4.00     3.00 MEG 026
+027    -5.45   -12.10     4.00     3.00 MEG 027
+028    -1.40   -12.51     4.00     3.00 MEG 028
+029     2.64   -12.08     4.00     3.00 MEG 029
+030     5.77    -9.29     4.00     3.00 MEG 030
+031     6.50    -5.19     4.00     3.00 MEG 031
+032     6.85    -1.37     4.00     3.00 MEG 032
+033     6.70     2.65     4.00     3.00 MEG 033
+034     6.46     6.18     4.00     3.00 MEG 034
+035     5.61    10.08     4.00     3.00 MEG 035
+036     2.95    12.49     4.00     3.00 MEG 036
+037    -1.47    15.77     4.00     3.00 MEG 037
+038    -5.48    15.52     4.00     3.00 MEG 038
+039    -8.97    13.31     4.00     3.00 MEG 039
+040   -11.91    10.42     4.00     3.00 MEG 040
+041   -12.96     6.84     4.00     3.00 MEG 041
+042   -13.39     3.21     4.00     3.00 MEG 042
+043   -13.58    -0.70     4.00     3.00 MEG 043
+044   -13.08    -4.42     4.00     3.00 MEG 044
+045   -12.52    -8.05     4.00     3.00 MEG 045
+046   -11.13   -11.34     4.00     3.00 MEG 046
+047    -8.45   -14.21     4.00     3.00 MEG 047
+048    -5.08   -15.56     4.00     3.00 MEG 048
+049    -1.60   -16.17     4.00     3.00 MEG 049
+050     2.22   -15.61     4.00     3.00 MEG 050
+051     5.63   -14.28     4.00     3.00 MEG 051
+052     8.38   -11.70     4.00     3.00 MEG 052
+053     9.89    -8.24     4.00     3.00 MEG 053
+054    10.43    -4.42     4.00     3.00 MEG 054
+055    10.94    -0.62     4.00     3.00 MEG 055
+056    10.72     3.35     4.00     3.00 MEG 056
+057    10.22     7.01     4.00     3.00 MEG 057
+058     9.04    10.61     4.00     3.00 MEG 058
+059     6.20    13.42     4.00     3.00 MEG 059
+060     2.52    15.65     4.00     3.00 MEG 060
+061    -1.53    18.91     4.00     3.00 MEG 061
+062    -5.68    18.61     4.00     3.00 MEG 062
+063    -9.46    16.89     4.00     3.00 MEG 063
+064   -12.95    14.48     4.00     3.00 MEG 064
+065   -15.67    11.24     4.00     3.00 MEG 065
+066   -17.06     7.05     4.00     3.00 MEG 066
+067   -17.65     3.16     4.00     3.00 MEG 067
+068   -17.98    -1.20     4.00     3.00 MEG 068
+069   -17.13    -5.53     4.00     3.00 MEG 069
+070   -16.60    -9.33     4.00     3.00 MEG 070
+071   -14.32   -12.91     4.00     3.00 MEG 071
+072   -11.85   -15.75     4.00     3.00 MEG 072
+073    -8.78   -17.93     4.00     3.00 MEG 073
+074    -5.30   -19.40     4.00     3.00 MEG 074
+075    -1.58   -19.85     4.00     3.00 MEG 075
+076     2.41   -19.42     4.00     3.00 MEG 076
+077     5.94   -18.13     4.00     3.00 MEG 077
+078     9.16   -15.98     4.00     3.00 MEG 078
+079    11.79   -13.08     4.00     3.00 MEG 079
+080    13.62    -9.59     4.00     3.00 MEG 080
+081    14.57    -5.64     4.00     3.00 MEG 081
+082    15.42    -1.35     4.00     3.00 MEG 082
+083    15.05     3.30     4.00     3.00 MEG 083
+084    14.29     7.20     4.00     3.00 MEG 084
+085    12.81    11.43     4.00     3.00 MEG 085
+086     9.96    14.67     4.00     3.00 MEG 086
+087     6.46    17.06     4.00     3.00 MEG 087
+088     2.60    18.73     4.00     3.00 MEG 088
+089    -1.60    22.21     4.00     3.00 MEG 089
+090    -5.83    21.82     4.00     3.00 MEG 090
+091    -9.75    20.43     4.00     3.00 MEG 091
+092   -13.45    18.45     4.00     3.00 MEG 092
+093   -16.67    15.62     4.00     3.00 MEG 093
+094   -19.33    12.13     4.00     3.00 MEG 094
+095   -20.94     7.82     4.00     3.00 MEG 095
+096   -21.81     3.65     4.00     3.00 MEG 096
+097   -22.23    -1.27     4.00     3.00 MEG 097
+098   -21.14    -5.87     4.00     3.00 MEG 098
+099   -20.30    -9.97     4.00     3.00 MEG 099
+100   -18.46   -13.84     4.00     3.00 MEG 100
+101   -16.07   -17.08     4.00     3.00 MEG 101
+102   -12.88   -19.71     4.00     3.00 MEG 102
+103    -9.34   -21.89     4.00     3.00 MEG 103
+104    -5.64   -23.02     4.00     3.00 MEG 104
+105    -1.72   -23.54     4.00     3.00 MEG 105
+106     2.48   -23.24     4.00     3.00 MEG 106
+107     6.42   -22.00     4.00     3.00 MEG 107
+108     9.86   -20.19     4.00     3.00 MEG 108
+109    13.22   -17.32     4.00     3.00 MEG 109
+110    15.75   -14.15     4.00     3.00 MEG 110
+111    17.67   -10.19     4.00     3.00 MEG 111
+112    18.65    -6.08     4.00     3.00 MEG 112
+113    19.69    -1.27     4.00     3.00 MEG 113
+114    19.27     3.70     4.00     3.00 MEG 114
+115    18.30     8.05     4.00     3.00 MEG 115
+116    16.46    12.48     4.00     3.00 MEG 116
+117    13.74    15.93     4.00     3.00 MEG 117
+118    10.41    18.72     4.00     3.00 MEG 118
+119     6.64    20.69     4.00     3.00 MEG 119
+120     2.67    22.02     4.00     3.00 MEG 120
+121    -1.74    25.41     4.00     3.00 MEG 121
+122    -6.59    24.84     4.00     3.00 MEG 122
+123   -11.16    23.37     4.00     3.00 MEG 123
+124   -15.46    21.07     4.00     3.00 MEG 124
+125   -19.25    17.84     4.00     3.00 MEG 125
+126   -22.45    13.89     4.00     3.00 MEG 126
+127   -24.89     8.96     4.00     3.00 MEG 127
+128   -26.13     4.36     4.00     3.00 MEG 128
+129   -26.65    -1.22     4.00     3.00 MEG 129
+130   -25.30    -6.36     4.00     3.00 MEG 130
+131   -24.16   -11.45     4.00     3.00 MEG 131
+132   -21.98   -15.88     4.00     3.00 MEG 132
+133   -18.81   -19.82     4.00     3.00 MEG 133
+134   -15.20   -22.99     4.00     3.00 MEG 134
+135   -11.11   -25.29     4.00     3.00 MEG 135
+136    -6.51   -26.74     4.00     3.00 MEG 136
+137    -1.86   -27.28     4.00     3.00 MEG 137
+138     3.17   -26.90     4.00     3.00 MEG 138
+139     7.79   -25.55     4.00     3.00 MEG 139
+140    12.07   -23.15     4.00     3.00 MEG 140
+141    15.93   -20.09     4.00     3.00 MEG 141
+142    19.04   -16.25     4.00     3.00 MEG 142
+143    21.39   -11.67     4.00     3.00 MEG 143
+144    22.75    -6.58     4.00     3.00 MEG 144
+145    23.99    -1.23     4.00     3.00 MEG 145
+146    23.36     4.49     4.00     3.00 MEG 146
+147    22.02     9.37     4.00     3.00 MEG 147
+148    19.51    14.31     4.00     3.00 MEG 148
+149    16.20    18.23     4.00     3.00 MEG 149
+150    12.16    21.54     4.00     3.00 MEG 150
+151     7.85    23.69     4.00     3.00 MEG 151
+152     3.16    25.01     4.00     3.00 MEG 152
+153   -23.01    18.82     4.00     3.00 MEG 153
+154   -26.06    15.31     4.00     3.00 MEG 154
+155   -28.76    10.18     4.00     3.00 MEG 155
+156   -31.71     3.39     4.00     3.00 MEG 156
+157   -32.05    -2.89     4.00     3.00 MEG 157
+158   -31.42    -8.67     4.00     3.00 MEG 158
+159   -26.22   -15.24     4.00     3.00 MEG 159
+160   -23.31   -19.72     4.00     3.00 MEG 160
+161   -19.33   -23.66     4.00     3.00 MEG 161
+162   -14.75   -26.73     4.00     3.00 MEG 162
+163    -9.92   -28.91     4.00     3.00 MEG 163
+164    -4.52   -30.10     4.00     3.00 MEG 164
+165     1.25   -30.15     4.00     3.00 MEG 165
+166     6.17   -29.40     4.00     3.00 MEG 166
+167    11.43   -27.39     4.00     3.00 MEG 167
+168    16.20   -24.37     4.00     3.00 MEG 168
+169    20.37   -20.27     4.00     3.00 MEG 169
+170    23.54   -15.56     4.00     3.00 MEG 170
+171    28.66    -8.94     4.00     3.00 MEG 171
+172    29.46    -3.00     4.00     3.00 MEG 172
+173    29.04     3.51     4.00     3.00 MEG 173
+174    25.94    10.77     4.00     3.00 MEG 174
+175    23.08    15.80     4.00     3.00 MEG 175
+176    19.78    19.54     4.00     3.00 MEG 176
+177   -26.70    20.52     4.00     3.00 MEG 177
+178   -29.66    16.81     4.00     3.00 MEG 178
+179   -32.55    11.68     4.00     3.00 MEG 179
+180   -32.47   -13.23     4.00     3.00 MEG 180
+181   -27.63   -19.12     4.00     3.00 MEG 181
+182   -23.75   -23.89     4.00     3.00 MEG 182
+183   -18.94   -27.77     4.00     3.00 MEG 183
+184   -13.64   -30.59     4.00     3.00 MEG 184
+185    -7.93   -32.70     4.00     3.00 MEG 185
+186    -2.12   -33.31     4.00     3.00 MEG 186
+187     4.06   -32.74     4.00     3.00 MEG 187
+188    10.04   -31.14     4.00     3.00 MEG 188
+189    15.57   -28.41     4.00     3.00 MEG 189
+190    20.44   -24.69     4.00     3.00 MEG 190
+191    24.62   -19.81     4.00     3.00 MEG 191
+192    29.49   -13.87     4.00     3.00 MEG 192
+193    29.48    12.54     4.00     3.00 MEG 193
+194    26.49    17.54     4.00     3.00 MEG 194
+195    23.28    21.40     4.00     3.00 MEG 195
+196   -36.84     4.15     4.00     3.00 MEG 196
+197   -37.22    -3.16     4.00     3.00 MEG 197
+198   -36.14    -9.68     4.00     3.00 MEG 198
+199   -28.42   -23.63     4.00     3.00 MEG 199
+200   -23.68   -28.05     4.00     3.00 MEG 200
+201   -18.03   -31.89     4.00     3.00 MEG 201
+202   -11.97   -34.42     4.00     3.00 MEG 202
+203    -5.32   -35.88     4.00     3.00 MEG 203
+204     1.03   -36.08     4.00     3.00 MEG 204
+205     7.92   -35.00     4.00     3.00 MEG 205
+206    13.99   -32.64     4.00     3.00 MEG 206
+207    19.78   -29.06     4.00     3.00 MEG 207
+208    24.79   -24.52     4.00     3.00 MEG 208
+209    33.39   -10.13     4.00     3.00 MEG 209
+210    34.62    -3.11     4.00     3.00 MEG 210
+211    34.23     4.57     4.00     3.00 MEG 211
+212   -32.38    19.14     4.00     3.00 MEG 212
+213   -35.90    13.21     4.00     3.00 MEG 213
+214   -36.70   -14.70     4.00     3.00 MEG 214
+215   -32.93   -22.44     4.00     3.00 MEG 215
+216   -28.17   -28.07     4.00     3.00 MEG 216
+217   -22.65   -32.41     4.00     3.00 MEG 217
+218   -16.53   -35.71     4.00     3.00 MEG 218
+219    -9.52   -37.92     4.00     3.00 MEG 219
+220    -2.58   -38.82     4.00     3.00 MEG 220
+221     4.65   -38.54     4.00     3.00 MEG 221
+222    11.78   -36.65     4.00     3.00 MEG 222
+223    18.43   -33.60     4.00     3.00 MEG 223
+224    24.26   -29.21     4.00     3.00 MEG 224
+225    29.52   -23.44     4.00     3.00 MEG 225
+226    33.73   -15.36     4.00     3.00 MEG 226
+227    33.02    14.20     4.00     3.00 MEG 227
+228    29.24    19.93     4.00     3.00 MEG 228
+229   -36.80    18.24     4.00     3.00 MEG 229
+230   -40.03    12.76     4.00     3.00 MEG 230
+231   -41.35     5.03     4.00     3.00 MEG 231
+232   -41.79    -3.17     4.00     3.00 MEG 232
+233   -40.48   -10.59     4.00     3.00 MEG 233
+234   -32.92   -26.79     4.00     3.00 MEG 234
+235   -27.40   -32.12     4.00     3.00 MEG 235
+236   -20.92   -36.72     4.00     3.00 MEG 236
+237   -14.11   -39.49     4.00     3.00 MEG 237
+238    -6.76   -41.18     4.00     3.00 MEG 238
+239     1.45   -41.40     4.00     3.00 MEG 239
+240     8.96   -40.25     4.00     3.00 MEG 240
+241    16.27   -37.84     4.00     3.00 MEG 241
+242    22.75   -33.68     4.00     3.00 MEG 242
+243    29.08   -28.20     4.00     3.00 MEG 243
+244    37.59   -11.05     4.00     3.00 MEG 244
+245    39.12    -3.16     4.00     3.00 MEG 245
+246    38.59     5.47     4.00     3.00 MEG 246
+247    37.16    13.60     4.00     3.00 MEG 247
+248    33.62    18.93     4.00     3.00 MEG 248

mne/channels/data/montages/EGI_256.csd

@@ -0,0 +1,258 @@
+// MatLab   Sphere coordinates [degrees]         Cartesian coordinates
+// Label       Theta       Phi    Radius         X         Y         Z       off sphere surface
+      E1      37.700     -14.000       1.000    0.7677    0.5934   -0.2419  -0.00000000000000011
+      E2      44.600      -0.880       1.000    0.7119    0.7021   -0.0154   0.00000000000000000
+      E3      51.700      11.000       1.000    0.6084    0.7704    0.1908   0.00000000000000000
+      E4      58.200      21.800       1.000    0.4893    0.7891    0.3714  -0.00000000000000011
+      E5      64.200      33.600       1.000    0.3625    0.7499    0.5534   0.00000000000000000
+      E6      70.800      45.500       1.000    0.2305    0.6619    0.7133  -0.00000000000000022
+      E7      77.200      56.700       1.000    0.1216    0.5354    0.8358   0.00000000000000000
+      E8      90.000      67.700       1.000    0.0000    0.3795    0.9252   0.00000000000000000
+      E9     127.300      78.300       1.000   -0.1229    0.1613    0.9792   0.00000000000000000
+     E10      51.200      -9.080       1.000    0.6188    0.7696   -0.1578   0.00000000000000000
+     E11      58.800       2.370       1.000    0.5176    0.8546    0.0414   0.00000000000000000
+     E12      66.800      14.300       1.000    0.3817    0.8907    0.2470  -0.00000000000000011
+     E13      73.800      25.200       1.000    0.2524    0.8689    0.4258   0.00000000000000022
+     E14      81.360      36.400       1.000    0.1209    0.7958    0.5934   0.00000000000000022
+     E15      90.000      46.900       1.000    0.0000    0.6833    0.7302   0.00000000000000000
+     E16     102.800      56.700       1.000   -0.1216    0.5354    0.8358   0.00000000000000000
+     E17     128.200      66.600       1.000   -0.2456    0.3121    0.9178  -0.00000000000000011
+     E18      66.600      -4.970       1.000    0.3957    0.9143   -0.0866  -0.00000000000000011
+     E19      74.000       4.680       1.000    0.2747    0.9581    0.0816  -0.00000000000000011
+     E20      81.960      15.700       1.000    0.1346    0.9532    0.2706   0.00000000000000022
+     E21      90.000      26.400       1.000    0.0000    0.8957    0.4446   0.00000000000000000
+     E22      98.640      36.400       1.000   -0.1209    0.7958    0.5934   0.00000000000000022
+     E23     109.200      45.500       1.000   -0.2305    0.6619    0.7133   0.00000000000000000
+     E24     127.200      54.200       1.000   -0.3537    0.4659    0.8111   0.00000000000000000
+     E25      82.540      -3.260       1.000    0.1296    0.9899   -0.0569   0.00000000000000000
+     E26      90.000       5.370       1.000    0.0000    0.9956    0.0936   0.00000000000000000
+     E27      98.040      15.700       1.000   -0.1346    0.9532    0.2706   0.00000000000000022
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mne/channels/data/montages/GSN-HydroCel-32.sfp

@@ -0,0 +1,36 @@
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mne/channels/data/montages/GSN-HydroCel-64_1.0.sfp

@@ -0,0 +1,67 @@
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mne/channels/data/montages/GSN-HydroCel-65_1.0.sfp

@@ -0,0 +1,68 @@
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mne/channels/data/montages/artinis-brite23.elc

@@ -0,0 +1,48 @@
+# ASA optode file
+ReferenceLabel	avg
+UnitPosition	mm
+NumberPositions=	21
+Positions
+-4.62 82.33 -45.74
+79.66 -18.72 -45.89
+-81.41 -17.18 -45.56
+65.18 27.28 35.31
+48.62 59.71 22.68
+18.95 72.41 38.32
+-3.97 79.74 30.28
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+-52.51 60.53 14.54
+-66.37 32.04 31.08
+76.10 -0.29 31.24
+65.61 -0.26 56.15
+64.93 42.43 8.29
+43.32 46.36 50.77
+21.58 82.45 1.06
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+-29.62 79.35 2.38
+-48.13 44.76 49.15
+-67.68 43.26 -3.18
+-65.37 4.89 56.36
+-77.24 5.88 27.58
+Labels
+Nz
+RPA
+LPA
+D1
+D2
+D3
+D4
+D5
+D6
+D7
+S1
+S2
+S3
+S4
+S5
+S6
+S7
+S8
+S9
+S10
+S11

mne/channels/data/montages/artinis-octamon.elc

@@ -0,0 +1,32 @@
+# ASA optode file
+ReferenceLabel	avg
+UnitPosition	mm
+NumberPositions=	13
+Positions
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+17.84 84.96 -10.84
+-10.81 77.96 32.10
+-15.96 85.24 -7.41
+-61.78 40.78 29.92
+-65.28 48.14 -10.73
+Labels
+Nz
+RPA
+LPA
+D1
+D2
+S1
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+S7
+S8

mne/channels/data/montages/biosemi128.txt

@@ -0,0 +1,132 @@
+Site	 Theta	Phi
+A1	0	0
+A2	11.5	-90
+A3	23	-90
+A4	34.5	-90
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+C1	11.5	54
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+C24	-34.5	-60
+C25	-46	-67.5
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+C27	-69	-72
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+D29	-69	36
+D30	-80.5	36
+D31	-92	36
+D32	-103.5	36
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/biosemi16.txt

@@ -0,0 +1,20 @@
+Site	 Theta	Phi
+Fp1	 -92	-72
+Fp2	  92	 72
+F4	  60	 51
+Fz	  46	 90
+F3	 -60	-51
+T7	 -92	  0
+C3	 -46	  0
+Cz	   0	  0
+C4	  46	  0
+T8	  92	  0
+P4	  60	-51
+Pz	  46	-90
+P3	 -60	 51
+O1	 -92	 72
+Oz	  92	-90
+O2	  92	-72
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/biosemi160.txt

@@ -0,0 +1,164 @@
+Site	 Theta	Phi
+A1	0	0
+A2	11.5	-90
+A3	23	-90
+A4	34.5	-90
+A5	-46	72
+A6	-46	54
+A7	-57.5	54
+A8	-69	60
+A9	-80.5	60
+A10	-92	60
+A11	-103.5	60
+A12	-115	60
+A13	-115	75
+A14	-103.5	75
+A15	-92	75
+A16	-80.5	75
+A17	-69	75
+A18	-57.5	72
+A19	46	-90
+A20	57.5	-90
+A21	69	-90
+A22	80.5	-90
+A23	92	-90
+A24	103.5	-90
+A25	115	-90
+A26	115	-75
+A27	103.5	-75
+A28	92	-75
+A29	80.5	-75
+A30	69	-75
+A31	57.5	-72
+A32	46	-72
+B1	11.5	-18
+B2	23	-60
+B3	46	-54
+B4	57.5	-54
+B5	69	-60
+B6	80.5	-60
+B7	92	-60
+B8	103.5	-60
+B9	115	-60
+B10	115	-45
+B11	103.5	-45
+B12	92	-45
+B13	80.5	-45
+B14	69	-45
+B15	69	-30
+B16	80.5	-30
+B17	92	-30
+B18	103.5	-30
+B19	92	-15
+B20	80.5	-15
+B21	69	-15
+B22	57.5	-36
+B23	46	-36
+B24	34.5	-45
+B25	23	-30
+B26	34.5	-22.5
+B27	46	-18
+B28	57.5	-18
+B29	57.5	0
+B30	69	0
+B31	80.5	0
+B32	92	0
+C1	11.5	54
+C2	23	30
+C3	23	0
+C4	34.5	0
+C5	34.5	22.5
+C6	46	18
+C7	46	0
+C8	57.5	18
+C9	69	15
+C10	80.5	15
+C11	92	15
+C12	92	30
+C13	80.5	30
+C14	69	30
+C15	69	45
+C16	80.5	45
+C17	92	45
+C18	92	60
+C19	80.5	60
+C20	69	60
+C21	57.5	54
+C22	57.5	36
+C23	46	36
+C24	34.5	45
+C25	23	60
+C26	34.5	67.5
+C27	46	54
+C28	46	72
+C29	57.5	72
+C30	69	75
+C31	80.5	75
+C32	92	75
+D1	-11.5	-54
+D2	23	90
+D3	34.5	90
+D4	46	90
+D5	57.5	90
+D6	69	90
+D7	80.5	90
+D8	92	90
+D9	-92	-75
+D10	-80.5	-75
+D11	-69	-75
+D12	-57.5	-72
+D13	-46	-72
+D14	-34.5	-67.5
+D15	-23	-60
+D16	-23	-30
+D17	-34.5	-45
+D18	-46	-54
+D19	-57.5	-54
+D20	-69	-60
+D21	-80.5	-60
+D22	-92	-60
+D23	-92	-45
+D24	-80.5	-45
+D25	-69	-45
+D26	-57.5	-36
+D27	-46	-36
+D28	-34.5	-22.5
+D29	-46	-18
+D30	-69	-30
+D31	-80.5	-30
+D32	-92	-30
+E1	-11.5	18
+E2	-23	0
+E3	-34.5	0
+E4	-46	0
+E5	-57.5	-18
+E6	-69	-15
+E7	-80.5	-15
+E8	-92	-15
+E9	-92	0
+E10	-80.5	0
+E11	-69	0
+E12	-57.5	0
+E13	-57.5	18
+E14	-69	15
+E15	-80.5	15
+E16	-92	15
+E17	-103.5	30
+E18	-92	30
+E19	-80.5	30
+E20	-69	30
+E21	-46	18
+E22	-34.5	22.5
+E23	-23	30
+E24	-23	60
+E25	-34.5	45
+E26	-46	36
+E27	-57.5	36
+E28	-69	45
+E29	-80.5	45
+E30	-92	45
+E31	-103.5	45
+E32	-115	45
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/biosemi256.txt

@@ -0,0 +1,260 @@
+Site	 Theta	Phi
+A1	0	0
+A2	9.2	-90
+A3	18.4	-90
+A4	27.6	-90
+A5	36.8	-90
+A6	46	-90
+A7	-46	75
+A8	-55.2	75
+A9	-64.4	78
+A10	-73.6	78
+A11	-82.8	78.75
+A12	-92	78.75
+A13	-101.2	78.75
+A14	-110.4	78
+A15	-119.6	78
+A16	119.6	-90
+A17	110.4	-90
+A18	101.2	-90
+A19	92	-90
+A20	82.8	-90
+A21	73.6	-90
+A22	64.4	-90
+A23	55.2	-90
+A24	46	-75
+A25	55.2	-75
+A26	64.4	-78
+A27	73.6	-78
+A28	82.8	-78.75
+A29	92	-78.75
+A30	101.2	-78.75
+A31	110.4	-78
+A32	119.6	-78
+B1	18.4	-54
+B2	27.6	-66
+B3	36.8	-54
+B4	46	-60
+B5	55.2	-60
+B6	64.4	-66
+B7	73.6	-66
+B8	82.8	-67.5
+B9	92	-67.5
+B10	101.2	-67.5
+B11	110.4	-66
+B12	119.6	-66
+B13	110.4	-54
+B14	101.2	-56.25
+B15	92	-56.25
+B16	82.8	-56.25
+B17	73.6	-54
+B18	64.4	-54
+B19	55.2	-45
+B20	46	-45
+B21	27.6	-42
+B22	36.8	-36
+B23	46	-30
+B24	55.2	-30
+B25	64.4	-42
+B26	73.6	-42
+B27	82.8	-45
+B28	92	-45
+B29	101.2	-45
+B30	110.4	-42
+B31	110.4	-30
+B32	101.2	-33.75
+C1	9.2	-18
+C2	18.4	-18
+C3	27.6	-18
+C4	36.8	-18
+C5	46	-15
+C6	55.2	-15
+C7	64.4	-18
+C8	64.4	-30
+C9	73.6	-30
+C10	82.8	-33.75
+C11	92	-33.75
+C12	101.2	-22.5
+C13	92	-22.5
+C14	82.8	-22.5
+C15	73.6	-18
+C16	82.8	-11.25
+C17	92	-11.25
+C18	92	0
+C19	82.8	0
+C20	73.6	-6
+C21	64.4	-6
+C22	55.2	0
+C23	46	0
+C24	36.8	0
+C25	27.6	6
+C26	36.8	18
+C27	46	15
+C28	55.2	15
+C29	64.4	6
+C30	73.6	6
+C31	82.8	11.25
+C32	92	11.25
+D1	9.2	54
+D2	18.4	18
+D3	27.6	30
+D4	36.8	36
+D5	46	30
+D6	64.4	18
+D7	73.6	18
+D8	82.8	22.5
+D9	92	22.5
+D10	101.2	22.5
+D11	101.2	33.75
+D12	92	33.75
+D13	82.8	33.75
+D14	73.6	30
+D15	64.4	30
+D16	55.2	30
+D17	46	45
+D18	55.2	45
+D19	64.4	42
+D20	73.6	42
+D21	82.8	45
+D22	92	45
+D23	101.2	45
+D24	92	56.25
+D25	82.8	56.25
+D26	73.6	54
+D27	64.4	54
+D28	55.2	60
+D29	64.4	66
+D30	73.6	66
+D31	82.8	67.5
+D32	92	67.5
+E1	18.4	90
+E2	18.4	54
+E3	27.6	54
+E4	36.8	54
+E5	46	60
+E6	46	75
+E7	55.2	75
+E8	64.4	78
+E9	73.6	78
+E10	82.8	78.75
+E11	92	78.75
+E12	92	90
+E13	82.8	90
+E14	73.6	90
+E15	64.4	90
+E16	55.2	90
+E17	46	90
+E18	36.8	90
+E19	36.8	72
+E20	27.6	78
+E21	-27.6	-78
+E22	-36.8	-72
+E23	-46	-75
+E24	-55.2	-75
+E25	-64.4	-78
+E26	-73.6	-78
+E27	-82.8	-78.75
+E28	-92	-78.75
+E29	-92	-67.5
+E30	-82.8	-67.5
+E31	-73.6	-66
+E32	-64.4	-66
+F1	-9.2	-54
+F2	-18.4	-54
+F3	-27.6	-54
+F4	-36.8	-54
+F5	-46	-60
+F6	-55.2	-60
+F7	-64.4	-54
+F8	-73.6	-54
+F9	-82.8	-56.25
+F10	-92	-56.25
+F11	-101.2	-45
+F12	-92	-45
+F13	-82.8	-45
+F14	-73.6	-42
+F15	-64.4	-42
+F16	-55.2	-45
+F17	-46	-45
+F18	-36.8	-36
+F19	-27.6	-30
+F20	-18.4	-18
+F21	-27.6	-6
+F22	-36.8	-18
+F23	-46	-30
+F24	-55.2	-30
+F25	-64.4	-30
+F26	-73.6	-30
+F27	-82.8	-33.75
+F28	-92	-33.75
+F29	-101.2	-33.75
+F30	-101.2	-22.5
+F31	-92	-22.5
+F32	-82.8	-22.5
+G1	-9.2	18
+G2	-18.4	18
+G3	-27.6	18
+G4	-36.8	0
+G5	-46	-15
+G6	-55.2	-15
+G7	-64.4	-18
+G8	-73.6	-18
+G9	-82.8	-11.25
+G10	-92	-11.25
+G11	-92	0
+G12	-82.8	0
+G13	-73.6	-6
+G14	-64.4	-6
+G15	-55.2	0
+G16	-46	0
+G17	-55.2	15
+G18	-64.4	6
+G19	-73.6	6
+G20	-82.8	11.25
+G21	-92	11.25
+G22	-101.2	22.5
+G23	-92	22.5
+G24	-82.8	22.5
+G25	-73.6	18
+G26	-64.4	18
+G27	-64.4	30
+G28	-73.6	30
+G29	-82.8	33.75
+G30	-92	33.75
+G31	-101.2	33.75
+G32	-110.4	30
+H1	-18.4	54
+H2	-27.6	42
+H3	-36.8	36
+H4	-36.8	18
+H5	-46	15
+H6	-46	30
+H7	-55.2	30
+H8	-64.4	42
+H9	-73.6	42
+H10	-82.8	45
+H11	-92	45
+H12	-101.2	45
+H13	-110.4	42
+H14	-110.4	54
+H15	-101.2	56.25
+H16	-92	56.25
+H17	-82.8	56.25
+H18	-73.6	54
+H19	-64.4	54
+H20	-55.2	45
+H21	-46	45
+H22	-36.8	54
+H23	-27.6	66
+H24	-46	60
+H25	-55.2	60
+H26	-64.4	66
+H27	-73.6	66
+H28	-82.8	67.5
+H29	-92	67.5
+H30	-101.2	67.5
+H31	-110.4	66
+H32	-119.6	66
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/biosemi32.txt

@@ -0,0 +1,36 @@
+Site	 Theta	Phi
+Fp1	 -92	-72
+AF3	 -74	-65
+F7	 -92	-36
+F3	 -60	-51
+FC1	 -32	-45
+FC5	 -72	-21
+T7	 -92	  0
+C3	 -46	  0
+CP1	 -32	 45
+CP5	 -72	 21
+P7	 -92	 36
+P3	 -60	 51
+Pz	  46	-90
+PO3	 -74	 65
+O1	 -92	 72
+Oz	  92	-90
+O2	  92	-72
+PO4	  74	-65
+P4	  60	-51
+P8	  92	-36
+CP6	  72	-21
+CP2	  32	-45
+C4	  46	  0
+T8 	  92	  0
+FC6	  72	 21
+FC2	  32	 45
+F4	  60	 51
+F8	  92	 36
+AF4	  74	 65
+Fp2	  92	 72
+Fz	  46	 90
+Cz	   0	  0
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/biosemi64.txt

@@ -0,0 +1,68 @@
+Site	 Theta	Phi
+Fp1	-92	-72
+AF7	-92	-54
+AF3	-74	-65
+F1	-50	-68
+F3	-60	-51
+F5	-75	-41
+F7	-92	-36
+FT7	-92	-18
+FC5	-72	-21
+FC3	-50	-28
+FC1	-32	-45
+C1	-23	0
+C3	-46	0
+C5	-69	0
+T7	-92	0
+TP7	-92	18
+CP5	-72	21
+CP3	-50	28
+CP1	-32	45
+P1	-50	68
+P3	-60	51
+P5	-75	41
+P7	-92	36
+P9	-115	36
+PO7	-92	54
+PO3	-74	65
+O1	-92	72
+Iz	115	-90
+Oz	92	-90
+POz	69	-90
+Pz	46	-90
+CPz	23	-90
+Fpz	92	90
+Fp2	92	72
+AF8	92	54
+AF4	74	65
+AFz	69	90
+Fz	46	90
+F2	50	68
+F4	60	51
+F6	75	41
+F8	92	36
+FT8	92	18
+FC6	72	21
+FC4	50	28
+FC2	32	45
+FCz	23	90
+Cz	0	0
+C2	23	0
+C4	46	0
+C6	69	0
+T8	92	0
+TP8	92	-18
+CP6	72	-21
+CP4	50	-28
+CP2	32	-45
+P2	50	-68
+P4	60	-51
+P6	75	-41
+P8	92	-36
+P10	115	-36
+PO8	92	-54
+PO4	74	-65
+O2	92	-72
+Nz	 115	 90
+LPA	-115	  0
+RPA	 115	  0

mne/channels/data/montages/brainproducts-RNP-BA-128.txt

@@ -0,0 +1,131 @@
+Name   Theta  Phi
+Fp1      -90  -72
+Fz        45   90
+F3       -60  -51
+F7       -90  -36
+F9      -113  -36
+FC5      -69  -21
+FC1      -31  -46
+C3       -45    0
+T7       -90    0
+CP5      -69   21
+CP1      -31   46
+Pz        45  -90
+P3       -60   51
+P7       -90   36
+P9      -113   36
+O1       -90   72
+Oz        90  -90
+O2        90  -72
+P10      113  -36
+P8        90  -36
+P4        60  -51
+CP2       31  -46
+CP6       69  -21
+T8        90    0
+C4        45    0
+Cz         0    0
+FC2       31   46
+FC6       69   21
+F10      113   36
+F8        90   36
+F4        60   51
+Fp2       90   72
+AF7      -90  -54
+AF3      -74  -68
+AFz       67   90
+F1       -49  -68
+F5       -74  -41
+FT7      -90  -18
+FC3      -49  -29
+C1       -23    0
+C5       -68    0
+TP7      -90   18
+CP3      -49   29
+P1       -49   68
+P5       -74   41
+PO7      -90   54
+PO3      -74   68
+Iz       112  -90
+POz       67  -90
+PO4       74  -68
+PO8       90  -54
+P6        74  -41
+P2        49  -68
+CPz       22  -90
+CP4       49  -29
+TP8       90  -18
+C6        68    0
+C2        23    0
+FC4       49   29
+FT8       90   18
+F6        74   41
+F2        49   68
+AF4       74   68
+AF8       90   54
+AFF3h    -62  -67
+FFC1h    -35  -73
+FFC5h    -62  -35
+FT9     -113  -18
+FTT7h    -79  -10
+FCC3h    -35  -19
+CCP1h    -16   45
+CCP5h    -57   12
+TP9     -113   18
+TPP7h    -81   29
+CPP3h    -46   48
+PPO3h    -62   67
+PPO9h   -101   45
+POO1     -79   82
+PO9     -113   54
+I1      -112   72
+I2       112  -72
+PO10     113  -54
+POO2      79  -82
+PPO10h   101  -45
+PPO4h     62  -67
+CPP4h     46  -48
+TPP8h     81  -29
+TP10     113  -18
+CCP6h     57  -12
+CCP2h     16  -45
+FCC4h     35   19
+FTT8h     79   10
+FT10     113   18
+FFC6h     62   35
+FFC2h     35   73
+AFF4h     62   67
+AFp1     -79  -82
+AFF1h    -57  -82
+AFF5h    -72  -55
+FFT7h    -81  -29
+FFC3h    -46  -48
+FCC1h    -16  -45
+FCC5h    -57  -12
+TTP7h    -79   10
+CCP3h    -35   19
+CPP1h    -35   73
+CPP5h    -62   35
+TPP9h   -101   27
+PPO5h    -72   55
+PPO1h    -57   82
+POO9h   -101   63
+OI1h    -101   81
+OI2h     101  -81
+POO10h   101  -63
+PPO2h     57  -82
+PPO6h     72  -55
+TPP10h   101  -27
+CPP6h     62  -35
+CPP2h     35  -73
+CCP4h     35  -19
+TTP8h     79  -10
+FCC6h     57   12
+FCC2h     16   45
+FFC4h     46   48
+FFT8h     81   29
+AFF6h     72   55
+AFF2h     57   82
+AFp2      79   82
+FCz       23   90
+Fpz       90   90

mne/channels/data/montages/easycap-M1.txt

@@ -0,0 +1,75 @@
+Site	 Theta	Phi
+Fp1	 -92	-72
+Fp2	  92	 72
+F3	 -60	-51
+F4	  60	 51
+C3	 -46	  0
+C4	  46	  0
+P3	 -60	 51
+P4	  60	-51
+O1	 -92	 72
+O2	  92	-72
+F7	 -92	-36
+F8	  92	 36
+T7	 -92	  0
+T8	  92	  0
+P7	 -92	 36
+P8	  92	-36
+Fz	  46	 90
+Cz	   0	  0
+Pz	  46	-90
+F1	 -50	-68
+F2	  50	 68
+FC1	 -32	-45
+FC2	  32	 45
+C1	 -23	  0
+C2	  23	  0
+CP1	 -32	 45
+CP2	  32	-45
+P1	 -50	 68
+P2	  50	-68
+AF3	 -74	-65
+AF4	  74	 65
+FC3	 -53	-33
+FC4	  53	 33
+CP3	 -52	 33
+CP4	  52	-33
+PO3	 -74	 65
+PO4	  74	-65
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