rsa_analysis_9x9.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9x9 RSA (crossvalidated and not crossvalidated)\n",
    "\n",
    "(Crossvalidated) RSA analysis on 9x9 RDMs using these models:\n",
    "\n",
    "- identity\n",
    "- numberline\n",
    "- extremity\n",
    "- subject and task specific sample frequency\n",
    "\n",
    "--> and the orthogonalized version of each of those\n",
    "\n",
    "\n",
    "For crossvalidation we split each epoch into:\n",
    "\n",
    "- even trials --> average --> array `A` (9 x n_channels x n_timepoints)\n",
    "- odd trials --> average --> array `B` (9 x n_channels x n_timepoints)\n",
    "\n",
    "the empirical RDM, array `C` (9 x 9 x n_timepoints) is then calculated:\n",
    "\n",
    "```\n",
    "for t in timepoints:\n",
    "    - C[0, 0, t] = euclidean_distance(A[0, :, t], B[0, :, t]\n",
    "    - C[1, 0, t] = euclidean_distance(A[1, :, t], B[0, :, t]\n",
    "    - C[0, 1, t] = euclidean_distance(A[0, :, t], B[1, :, t]\n",
    "    - C[1, 1, t] = euclidean_distance(A[1, :, t], B[1, :, t]\n",
    "    - C[2, 1, t] = euclidean_distance(A[2, :, t], B[1, :, t]\n",
    "    - etc.\n",
    "    \n",
    "```\n",
    "\n",
    "or in Python code:\n",
    "\n",
    "```Python\n",
    "\"\"\"example code for cross validated RDM based on two vectors.\"\"\"\n",
    "import itertools\n",
    "\n",
    "import numpy as np\n",
    "import scipy.spatial\n",
    "\n",
    "\n",
    "# Pretend we are working at a single timepoint\n",
    "ndims = 9\n",
    "nchs = 64\n",
    "\n",
    "# `a` and `b` are ERPs based on even and uneven trials respectively\n",
    "a = np.random.random((ndims, nchs))\n",
    "b = np.random.random((ndims, nchs))\n",
    "\n",
    "# create the cross validated RDM: `c`\n",
    "idxs = list(itertools.product(np.arange(ndims), np.arange(ndims)))\n",
    "c = np.nan * np.zeros((ndims, ndims))\n",
    "for idx in idxs:\n",
    "    u = a[idx[0], ...]\n",
    "    v = b[idx[1], ...]\n",
    "    c[idx] = scipy.spatial.distance.euclidean(u, v)\n",
    "    \n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:34.120869Z",
     "start_time": "2020-09-02T12:27:33.869554Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:35.732445Z",
     "start_time": "2020-09-02T12:27:34.122692Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import os.path as op\n",
    "from warnings import warn\n",
    "import itertools\n",
    "import json\n",
    "import multiprocessing\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.lines import Line2D\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import scipy.spatial\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import mne\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "import scipy.stats\n",
    "\n",
    "from utils import (\n",
    "    _rdm2vec,\n",
    "    BIDS_ROOT,\n",
    "    _kendall_tau_a,\n",
    "    extract_sample_frequencies,\n",
    "    get_model_rdm_dict,\n",
    "    orth_model_rdms,\n",
    "    prep_epochs,\n",
    "    get_mahalanobis_rdm_times,\n",
    "    calc_sigma,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:35.736671Z",
     "start_time": "2020-09-02T12:27:35.733946Z"
    }
   },
   "outputs": [],
   "source": [
    "# do not warn about too many figures open\n",
    "plt.rcParams.update({'figure.max_open_warning': 0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot model RDMs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:35.942281Z",
     "start_time": "2020-09-02T12:27:35.738511Z"
    }
   },
   "outputs": [],
   "source": [
    "# Get overall histogram of number samples\n",
    "beh_fname = \"behavioral_data.csv\"\n",
    "beh_fpath = op.join(BIDS_ROOT, \"code\", beh_fname)\n",
    "df = pd.read_csv(beh_fpath)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:36.021709Z",
     "start_time": "2020-09-02T12:27:35.944310Z"
    }
   },
   "outputs": [],
   "source": [
    "# settings\n",
    "double = False  # work on 9x9\n",
    "with_sides = False\n",
    "lower_tri = False  # in cross-validated, we work on full RDMs\n",
    "mean_center = True  \n",
    "\n",
    "\n",
    "# Get all model RDMs\n",
    "sample_frequencies = extract_sample_frequencies(df, with_sides=with_sides)\n",
    "model_rdms = get_model_rdm_dict(\n",
    "    sample_frequencies, double=double, lower_tri=lower_tri, mean_center=mean_center\n",
    ")\n",
    "model_rdms = orth_model_rdms(model_rdms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:37.660294Z",
     "start_time": "2020-09-02T12:27:36.023683Z"
    }
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot all RDMs\n",
    "fig, axs = plt.subplots(2, int(np.ceil(len(model_rdms) / 2)), constrained_layout=True, figsize=(12,5))\n",
    "for i, (name, model) in enumerate(model_rdms.items()):\n",
    "    if not lower_tri:\n",
    "        tmpsquare = model\n",
    "    else:\n",
    "        tmpsquare = np.zeros((18, 18)) * np.nan\n",
    "        idx = np.tril_indices(tmpsquare.shape[0], k=-1)\n",
    "        tmpsquare[idx] = model    \n",
    "    \n",
    "    ax = axs.flat[i]\n",
    "    im = ax.imshow(tmpsquare)\n",
    "    \n",
    "    divider = make_axes_locatable(ax)\n",
    "    cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05)    \n",
    "    plt.colorbar(im, cax=cax)\n",
    "    \n",
    "    ax.set_title(name, fontsize=15)\n",
    "    ax.set_xticklabels([])\n",
    "    ax.set_yticklabels([])\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:37.663800Z",
     "start_time": "2020-09-02T12:27:37.661371Z"
    }
   },
   "outputs": [],
   "source": [
    "# colors for plots\n",
    "colors = {\n",
    "    name: f\"C{i}\"\n",
    "    for i, name in enumerate(\n",
    "        [\n",
    "            \"side\",\n",
    "            \"identity\",\n",
    "            \"numberline\",\n",
    "            \"extremity\",\n",
    "            \"sample_frequency\",\n",
    "            \"mean_number_extrem\",\n",
    "        ]\n",
    "    )\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:37.681843Z",
     "start_time": "2020-09-02T12:27:37.665038Z"
    }
   },
   "outputs": [],
   "source": [
    "# IO: Where to find the data\n",
    "# Where to find epochs\n",
    "fname_epo_template = op.join(\n",
    "    BIDS_ROOT, \"derivatives\", \"sub-{0:02}\", \"sub-{0:02}_epochs-epo.fif.gz\"\n",
    ")\n",
    "\n",
    "# Where to save RSA results\n",
    "rsa_9x9 = op.join(BIDS_ROOT, \"derivatives\", \"rsa_9x9\")\n",
    "fname_rsa_results = op.join(rsa_9x9, \"{}\", \"rsa_results.csv\")\n",
    "\n",
    "# Where to save rsa single subj plots\n",
    "fname_rsa_subj_plots_template = op.join(\n",
    "    rsa_9x9, \"{}\", \"single_subj_plots\", \"sub-{:02}_task-{}_{}\"\n",
    ")\n",
    "\n",
    "# RSA overall plots\n",
    "fname_rsa_overall_plots_template = op.join(rsa_9x9, \"{}\", \"rsa_{}.pdf\")\n",
    "\n",
    "# Pack all names in a dict\n",
    "name_templates = dict()\n",
    "name_templates[\"epochs\"] = fname_epo_template\n",
    "name_templates[\"rsa_subj_plots\"] = fname_rsa_subj_plots_template\n",
    "name_templates[\"rsa_results\"] = fname_rsa_results\n",
    "name_templates[\"rsa_overall_plots\"] = fname_rsa_overall_plots_template"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:37.696168Z",
     "start_time": "2020-09-02T12:27:37.683145Z"
    }
   },
   "outputs": [],
   "source": [
    "def _build_empirical_rdms(\n",
    "    epochs,\n",
    "    preproc_settings,\n",
    "    crossvalidate,\n",
    "    distance_metric,\n",
    "    subj,\n",
    "    numbers,\n",
    "    nchs,\n",
    "    ntimes,\n",
    "    samp,\n",
    "    stop,\n",
    "    half,\n",
    "    warni=20,\n",
    "    mnn=False,\n",
    "    mnn_separate_epoch_types=True,\n",
    "    mnn_average_over_time=True,\n",
    "):\n",
    "    \"\"\"Build an RDM per timepoint.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    epochs : mne.Epochs\n",
    "        The epochs data associated with subj.\n",
    "    preproc_settings : dict\n",
    "        The dictionary of preprocessing settings passed to `prep_epochs`.\n",
    "        Must not contain a key called \"crossvalidate\".\n",
    "    crossvalidate : bool\n",
    "        Whether or not to work on crossvalidated RDMs.        \n",
    "    distance_metric : str, one of [\"euclidean\", \"correlation\"]\n",
    "        Distance metric to use for calculating RDMs.\n",
    "    subj : int\n",
    "        The subject ID.\n",
    "    numbers : array_like of str\n",
    "        The sample outcomes (=numbers) to work on. Can also be\n",
    "        \"bins\" or \"orthogonalized bins\". But here referred to as\n",
    "        \"numbers\".\n",
    "    nchs : int\n",
    "        Number of channels in the data.\n",
    "    ntimes : int\n",
    "        Number of timepoints in the data.\n",
    "    samp : str, one of [\"active\", \"yoked\"]\n",
    "        The type of sampling task to work on.\n",
    "    stop : str, one of [\"fixed\", \"variable\"]\n",
    "        The type of stopping task to work on.\n",
    "    half : str, one of [\"both\", \"first_half\", \"second_half\"]\n",
    "        Which part of the data to work on.\n",
    "    warni : int\n",
    "        If number of trials in any epochs object is below `warni`, trigger\n",
    "        a warning. Defaults to 20\n",
    "    mnn : bool\n",
    "        Whether or not to perform multivariate noise normalization.\n",
    "        Defaults to False.\n",
    "    mnn_separate_epoch_types : bool\n",
    "        If True, perform MNN for each epoch selection separately. That is,\n",
    "        for an epoch from the active/variable condition in the first half,\n",
    "        calculate a covariance matrix over numbers 1-9 ... and then another\n",
    "        one for active/variable second half, etc.\n",
    "        If False, calculate a single covariance matrix to be used for each\n",
    "        epoch selection. The calculation of that covariance matrix is done\n",
    "        over sampling and numbers active/1-9, yoked/1-9, because stopping \n",
    "        is a between subjects factor. Defaults to True.\n",
    "    mnn_average_over_time : bool\n",
    "        If True, the covariance matrix is averaged over timepoints and\n",
    "        the data is corrected once over all timepoints.\n",
    "        If False, perform MNN over time. That is, calculate a covariance \n",
    "        matrix for each timepoint, and correct the data per timepoint.\n",
    "        Defaults to True.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    rdm_times : ndarray, shape(len(numbers), len(numbers), ntimes)\n",
    "        The RDMs per timepoint.\n",
    "    \n",
    "    \"\"\"\n",
    "    # settings for MNN\n",
    "    preproc_settings_noAverage = {**preproc_settings}\n",
    "    preproc_settings_noAverage['average'] = False\n",
    "\n",
    "    # Make sure only EEG channels have been picked\n",
    "    epochs = epochs.pick_types(meg=False, eeg=True)\n",
    "\n",
    "    # Collect number ERPs for this subj and task\n",
    "    if crossvalidate:\n",
    "        # one for even trials, and one for odd trials (=2)\n",
    "        data_uV = np.nan * np.zeros((2, len(numbers), nchs, ntimes))\n",
    "    else:\n",
    "        data_uV = np.nan * np.zeros((len(numbers), nchs, ntimes))\n",
    "    \n",
    "\n",
    "    # If we do multivariate noise normalization, get normalization arrays\n",
    "    if mnn:\n",
    "\n",
    "        if mnn_separate_epoch_types:\n",
    "            # do mnn for each \"epoch\" selection separately,\n",
    "            # i.e., calculate a new covariance matrix for each\n",
    "            # condition like epochs[\"active\"/\"variable\"/\"first_half]\n",
    "            mnn_conditions = [f\"out{i}\" for i in range(1, 10)]\n",
    "\n",
    "            if half == 'both':\n",
    "                sel_str = f\"{samp}/{stop}\"\n",
    "            else:\n",
    "                sel_str = f\"{half}/{samp}/{stop}\"\n",
    "\n",
    "            epochs_sel = epochs[sel_str]\n",
    "        else:\n",
    "            # do mnn over all epochs,\n",
    "            # i.e., calculate a single covariance matrix for all\n",
    "            # conditions like epochs\n",
    "            sampling = (\"active\", \"yoked\")                                          \n",
    "            # stopping is a between subj factor, so pre-determined by subject ID\n",
    "            number = tuple(f\"out{i}\" for i in range(1, 10)) \n",
    "            # we do not enter \"half\" into the list, because \"both\" and \"first\",\n",
    "            # and \"both\" and \"second\" are confounded\n",
    "\n",
    "            combinations = itertools.product(sampling, number)\n",
    "\n",
    "            mnn_conditions = [\"/\".join(combi) for combi in combinations]\n",
    "            epochs_sel = epochs.copy()  # working on the full epochs, no selection\n",
    "\n",
    "        sigmas = calc_sigma(\n",
    "            epochs=epochs_sel,\n",
    "            preproc_settings=preproc_settings_noAverage,\n",
    "            crossvalidate=crossvalidate,\n",
    "            scaletomu=False,\n",
    "            conditions=mnn_conditions,\n",
    "            average_over_time=mnn_average_over_time,\n",
    "        )\n",
    "\n",
    "    for inumber, number in enumerate(numbers):\n",
    "\n",
    "        if half == 'both':\n",
    "            sel_str = f\"{samp}/{stop}/{number}\"\n",
    "        else:\n",
    "            sel_str = f\"{half}/{samp}/{stop}/{number}\"        \n",
    "            \n",
    "        epochs_sel = epochs[sel_str]\n",
    "\n",
    "        nepos = len(epochs_sel)\n",
    "        warni = 20\n",
    "        if nepos < warni:\n",
    "            warn(f\"Less than {warni} epos in {subj}/{sel_str} --> {nepos}\")\n",
    "\n",
    "        if crossvalidate:\n",
    "            if mnn:\n",
    "                epo_even, epo_uneven = prep_epochs(\n",
    "                    epochs_sel, **preproc_settings_noAverage, crossvalidate=True\n",
    "                )\n",
    "\n",
    "                sigma_even = sigmas[0]\n",
    "                sigma_uneven = sigmas[1]\n",
    "\n",
    "                if mnn_average_over_time:\n",
    "                    # need to swap axes to multiply \"ntrls x nchs x ntimes\" with \"nchs x nchs\"\n",
    "                    # swap, multiply, swap back - as in code accompanying guggenmos 2018\n",
    "                    epo_even._data[:] = (epo_even.get_data().swapaxes(1, 2) @ sigma_even).swapaxes(1, 2)\n",
    "                    epo_uneven._data[:] = (epo_uneven.get_data().swapaxes(1, 2) @ sigma_uneven).swapaxes(1, 2)\n",
    "                else:\n",
    "                    # no need to swap axes anymore --> \"ntrls x nchs x ntimes\", pick times: \"ntrls x nchs\"\n",
    "                    # multiply with --> \"nchs x nchs x ntimes\", pick times: \"nchs x nchs\"\n",
    "                    for t in range(ntimes):\n",
    "                        epo_even._data[..., t] = (epo_even.get_data()[..., t] @ sigma_even[..., t])\n",
    "                        epo_uneven._data[..., t] = (epo_uneven.get_data()[..., t] @ sigma_uneven[..., t])\n",
    "\n",
    "                erp_even = epo_even.average()\n",
    "                erp_uneven = epo_uneven.average()\n",
    "            else:\n",
    "                erp_even, erp_uneven = prep_epochs(\n",
    "                    epochs_sel, **preproc_settings, crossvalidate=True\n",
    "                )\n",
    "\n",
    "            # scale MNE internal representation (V) to micro Volts\n",
    "            data_uV[0, inumber, ...] = erp_even.data * 1e6\n",
    "            data_uV[1, inumber, ...] = erp_uneven.data * 1e6\n",
    "        else:\n",
    "            if mnn:\n",
    "                epo = prep_epochs(epochs_sel, **preproc_settings_noAverage, crossvalidate=False)\n",
    "                \n",
    "                sigma = sigmas[0]\n",
    "\n",
    "                if mnn_average_over_time:\n",
    "                    epo._data[:] = (epo.get_data().swapaxes(1, 2) @ sigma).swapaxes(1, 2)\n",
    "                else:\n",
    "                    for t in range(ntimes):\n",
    "                        epo._data[..., t] = (epo.get_data()[..., t] @ sigma[..., t])\n",
    "\n",
    "                erp = epo.average()\n",
    "            else:\n",
    "                erp = prep_epochs(epochs_sel, **preproc_settings, crossvalidate=False)\n",
    "\n",
    "            data_uV[inumber, ...] = erp.data * 1e6\n",
    "\n",
    "    # Form RDM out of collected data\n",
    "    if crossvalidate:\n",
    "        nparities, nkeys, nchs, ntimes = data_uV.shape\n",
    "        rdm_times = np.nan * np.zeros((nkeys, nkeys, ntimes))\n",
    "\n",
    "        for itime in range(ntimes):\n",
    "            # get the 9x64 data: once for even, once for uneven\n",
    "            timepoint_data_even = data_uV[0, ..., itime]\n",
    "            timepoint_data_uneven = data_uV[1, ..., itime]\n",
    "\n",
    "            # idxs is a list of (x,y) coordinates into the cells of the RDM\n",
    "            idxs = list(itertools.product(np.arange(nkeys), np.arange(nkeys)))\n",
    "            rdm = np.nan * np.zeros((nkeys, nkeys))\n",
    "            for idx in idxs:\n",
    "                # vectors to calculate a distance between\n",
    "                u = timepoint_data_even[idx[0], ...]\n",
    "                v = timepoint_data_uneven[idx[1], ...]\n",
    "\n",
    "                if distance_metric == \"euclidean\":\n",
    "                    rdm[idx] = scipy.spatial.distance.euclidean(u, v)\n",
    "                elif distance_metric == \"correlation\":\n",
    "                    rdm[idx] = scipy.spatial.distance.correlation(u, v)\n",
    "\n",
    "            rdm_times[..., itime] = rdm\n",
    "    else:\n",
    "        nkeys, nchs, ntimes = data_uV.shape\n",
    "        rdm_times = np.nan * np.zeros((nkeys, nkeys, ntimes))\n",
    "\n",
    "        for itime in range(ntimes):\n",
    "            # get the 9x64 data\n",
    "            timepoint_data = data_uV[..., itime]\n",
    "\n",
    "            if distance_metric == \"euclidean\":\n",
    "                rdm = squareform(pdist(timepoint_data, metric=distance_metric))\n",
    "            elif distance_metric == \"correlation\":\n",
    "                rdm = squareform(pdist(timepoint_data, metric=distance_metric))\n",
    "\n",
    "            rdm_times[..., itime] = rdm\n",
    "\n",
    "    return rdm_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:38:57.630536Z",
     "start_time": "2020-09-02T12:38:57.492397Z"
    }
   },
   "outputs": [],
   "source": [
    "def rsa_timecourse_xval(\n",
    "    subj,\n",
    "    df,\n",
    "    name_templates,\n",
    "    crossvalidate,\n",
    "    distance_metric,\n",
    "    rsa_method,\n",
    "    preproc_settings,\n",
    "    exclude_models,\n",
    "    flip_sign_sample_frequency,\n",
    "    folder_name,\n",
    "    half,\n",
    "    mnn_tuple=(False, True, True),\n",
    "    equalize_counts=False,\n",
    "    outcome_column_name=\"outcome\",\n",
    "):\n",
    "    \"\"\"Run crossvalidated RSA for subject and task.\n",
    "\n",
    "    Also saves plots.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    subj : int\n",
    "        The subject ID.\n",
    "    df : pandas.DataFrame\n",
    "        The overall behavioral data frame.\n",
    "    name_templates : dict\n",
    "        Dictionary with paths to save data. Must have the following keys:\n",
    "        ['epochs', 'rsa_subj_plots', 'rsa_results', 'rsa_overall_plots'].\n",
    "    crossvalidate : bool\n",
    "        Whether of not to do a crossvalidated RSA.\n",
    "    distance_metric : str\n",
    "        Metric to use for calculating empirical RDMs. Must be one of\n",
    "        ['euclidean', 'correlation', 'mahalanobis'].\n",
    "    rsa_method : str\n",
    "        Method to correlated model RDMs with empirical RDMs. Must be one of\n",
    "        ['pearson', 'kendall_a'].\n",
    "    preproc_settings : dict\n",
    "        Preprocessing settings for epochs that are subjected to RSA. Must\n",
    "        contain the following keys: ['crop', 'tshift', 'smooth', 'baseline'].\n",
    "    exclude_models : list of str\n",
    "        Which models to exclude. Must be a key in model_rdms dict.\n",
    "    flip_sign_sample_frequency : bool\n",
    "        Whether or not to flip the sign of the sample_frequency model before\n",
    "        orthogonalization. See:\n",
    "        https://chat.mpib-berlin.mpg.de/arc/pl/6auntgum8fg8tgr3hktrej69ih\n",
    "    folder_name : str\n",
    "        Under which folder to save the RSA results.\n",
    "    half : 'first_half' | 'second_half' | 'both'\n",
    "        Which half of samples to take, or both halves.\n",
    "    mnn_tuple : tuple of bool, len 3\n",
    "        A tuple with three boolean settings: (1) Whether or not to perform\n",
    "        multivariate noise normalization. (2) and (3) apply only If (1) is\n",
    "        True: (2) Whether or not to calc a cov matrix for each epo selection\n",
    "        separately, (3) Whether or not to do mnn for all timepoints at once.\n",
    "        Defaults to (False, True, True), so no MNN.\n",
    "    equalize_counts : bool\n",
    "        If True, equalize the occurrences of numeric samples for `subj`\n",
    "        across both tasks (active, and yoked). Note that the \"across\n",
    "        both tasks\" addendum is only relevant for subjs that were \n",
    "        yoked to *another* subj (not to themselves).\n",
    "    outcome_column_name : str\n",
    "        The kind of condition to use for constructing the RDMs. Most often,\n",
    "        this is \"outcome\", referring to the numeric samples. But it can also\n",
    "        be \"outcome_bin\", or \"outcome_bin_orth\" to use binned outcomes after\n",
    "        normalizing them with their trial specific outcome mean, or to\n",
    "        use them after orthogonalization with the normal \"outcomes\".    \n",
    "\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    df_rsa : pandas.DataFrame\n",
    "        The RSA data for this subject\n",
    "    \"\"\"\n",
    "    # Stable settings\n",
    "    if outcome_column_name == \"outcome\":\n",
    "        numbers = tuple(f\"out{i}\" for i in range(1, 10))\n",
    "    elif outcome_column_name == \"outcome_bin\":\n",
    "        numbers = tuple(f\"bin{i}\" for i in range(1, 10))\n",
    "    elif outcome_column_name == \"outcome_bin_orth\":\n",
    "        numbers = tuple(f\"orthbin{i}\" for i in range(1, 10))\n",
    "    else:\n",
    "        raise ValueError(f\"Unsupported outcome_column_name: {outcome_column_name}\")\n",
    "\n",
    "    lower_tri = False if crossvalidate else True\n",
    "\n",
    "    # unpack other settings\n",
    "    mnn = mnn_tuple[0]  # if true, do mnn (either guggenmos method, or mahalanobis)\n",
    "    mnn_separate_epoch_types = mnn_tuple[1]  # if true, do mnn separately for data\n",
    "    mnn_average_over_time = mnn_tuple[2]  # if true, do mnn *once* for all time\n",
    "\n",
    "    # identity not possible in 9x9-non-cv\n",
    "    if (\"identity\" not in exclude_models) and (crossvalidate is False):\n",
    "        raise RuntimeError('need to exclude \"identity\" for no cv.')\n",
    "\n",
    "    # load epochs\n",
    "    fname = name_templates[\"epochs\"].format(subj)\n",
    "    epochs = mne.read_epochs(fname, preload=True, verbose=False)\n",
    "    epochs.pick_types(meg=False, eeg=True, verbose=False)\n",
    "\n",
    "    # XXX: If desired, make sure that all number samples have equal occurrences\n",
    "    #      for all further calculations\n",
    "    if equalize_counts:\n",
    "        method = \"mintime\"  # minimizes bias, is deterministic\n",
    "        epochs, _ = epochs.equalize_event_counts(event_ids=numbers,\n",
    "                                                 method=method)\n",
    "\n",
    "    # figure out time dimension of the data.\n",
    "    # note that this can change depending on the crop and tshift parameters\n",
    "    if not isinstance(preproc_settings['crop'], bool):\n",
    "        if not isinstance(preproc_settings['tshift'], bool):\n",
    "            # if cropped and shifted\n",
    "            times = (\n",
    "                epochs.copy()\n",
    "                .crop(*preproc_settings['crop'])\n",
    "                .shift_time(preproc_settings['tshift'], relative=True)\n",
    "                .times\n",
    "                )\n",
    "        else:\n",
    "            # if only cropped\n",
    "            times = (\n",
    "                epochs.copy()\n",
    "                .crop(*preproc_settings['crop'])\n",
    "                .times\n",
    "                )\n",
    "    else:\n",
    "        if not isinstance(preproc_settings['tshift'], bool):\n",
    "            # if only shifted\n",
    "            times = (\n",
    "                epochs.copy()\n",
    "                .shift_time(preproc_settings['tshift'], relative=True)\n",
    "                .times\n",
    "                )\n",
    "        else:\n",
    "            # if neither cropped nor shifted\n",
    "            times = epochs.times\n",
    "    ntimes = len(times)\n",
    "    nchs = len(epochs.ch_names)\n",
    "    assert nchs == 64, \"Should be working with 64 channels.\"\n",
    "\n",
    "    # figure out whether this was variable or fixed stopping ...\n",
    "    # to get the sampling factor level: one of ['active', 'yoked'].\n",
    "    keys = np.unique(\n",
    "        [k for j in [i.split(\"/\") for i in epochs.event_id.keys()] for k in j]\n",
    "    )\n",
    "    if \"fixed\" in keys:\n",
    "        stop = \"fixed\"\n",
    "    elif \"variable\" in keys:\n",
    "        stop = \"variable\"\n",
    "    else:\n",
    "        raise RuntimeError(f\"Could not make sense out of keys: {keys}\")\n",
    "\n",
    "    # Repeat the following for \"samp\": ...\n",
    "    # The sampling factor level: One of ['active', 'yoked'].\n",
    "    # later concatenate the resulting DFs\n",
    "    all_dfs = []\n",
    "    for samp in (\"active\", \"yoked\"):\n",
    "\n",
    "        task = (samp[0] + stop[0]).upper()\n",
    "        \n",
    "        if distance_metric == \"mahalanobis\":\n",
    "            do_full_mnn = not mnn_separate_epoch_types\n",
    "\n",
    "            rdm_times, _ = get_mahalanobis_rdm_times(\n",
    "                subj,\n",
    "                df,\n",
    "                epochs,\n",
    "                preproc_settings,\n",
    "                samp,\n",
    "                half,\n",
    "                zscore_before_regress=True,  # default\n",
    "                add_constant=False,  # default\n",
    "                do_full_mnn=do_full_mnn,\n",
    "                outcome_column_name=outcome_column_name,\n",
    "                )\n",
    "        else:\n",
    "            rdm_times = _build_empirical_rdms(\n",
    "                epochs,\n",
    "                preproc_settings,\n",
    "                crossvalidate,\n",
    "                distance_metric,\n",
    "                subj,\n",
    "                numbers,\n",
    "                nchs,\n",
    "                ntimes,\n",
    "                samp,\n",
    "                stop,\n",
    "                half,\n",
    "                warni=20,\n",
    "                mnn=mnn,\n",
    "                mnn_separate_epoch_types=mnn_separate_epoch_types,\n",
    "                mnn_average_over_time=mnn_average_over_time,                \n",
    "            )\n",
    "\n",
    "        # Save the RDMs per timepoint\n",
    "        fname = name_templates[\"rsa_subj_plots\"].format(folder_name, subj, task, \"rdm_times.npy\")\n",
    "        os.makedirs(op.split(fname)[0], exist_ok=True)\n",
    "        np.save(fname, rdm_times)\n",
    "\n",
    "        # Build model RDMs for this subj\n",
    "        df_subj_task = df[(df[\"subject\"] == subj) & (df[\"task\"] == task)]\n",
    "        sample_frequencies = extract_sample_frequencies(df_subj_task, with_sides=False)\n",
    "        model_rdms = get_model_rdm_dict(\n",
    "            sample_frequencies, double=False, lower_tri=lower_tri, mean_center=True\n",
    "        )\n",
    "\n",
    "        # potentially exclude models from analysis\n",
    "        for model_to_exclude in exclude_models:\n",
    "            del model_rdms[model_to_exclude]\n",
    "\n",
    "        # potentially try a tweak to get baseline right\n",
    "        if flip_sign_sample_frequency:\n",
    "            model_rdms[\"sample_frequency\"] = model_rdms[\"sample_frequency\"] * -1\n",
    "            warn(\"flipping sign of sample_frequency due to settings.\")\n",
    "\n",
    "        # get orthogonalized models\n",
    "        model_rdms = orth_model_rdms(model_rdms)\n",
    "\n",
    "        # sanity check models are still mean centered\n",
    "        for name, model in model_rdms.items():\n",
    "            assert np.isclose(model.mean(), 0)\n",
    "\n",
    "        # Make and save plot to double check the RDMs\n",
    "        fig, axs = plt.subplots(\n",
    "            2,\n",
    "            int(np.ceil(len(model_rdms) / 2)),\n",
    "            constrained_layout=True,\n",
    "            figsize=(12, 5),\n",
    "        )\n",
    "\n",
    "        for i, name in enumerate(model_rdms):\n",
    "            if crossvalidate:\n",
    "                tmpsquare = model_rdms[name]\n",
    "            else:\n",
    "                tmpsquare = np.zeros((9, 9)) * np.nan\n",
    "                idx = np.tril_indices(tmpsquare.shape[0], k=-1)\n",
    "                tmpsquare[idx] = model_rdms[name]\n",
    "\n",
    "            ax = axs.flat[i]\n",
    "            ax.imshow(tmpsquare)\n",
    "\n",
    "            divider = make_axes_locatable(ax)\n",
    "            cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "            plt.colorbar(im, cax=cax)\n",
    "\n",
    "            ax.set_title(name, fontsize=15)\n",
    "            ax.axis(\"off\")\n",
    "\n",
    "        fname = name_templates[\"rsa_subj_plots\"].format(folder_name, subj, task, \"rdms.pdf\")\n",
    "        os.makedirs(op.split(fname)[0], exist_ok=True)\n",
    "        fig.savefig(fname)\n",
    "\n",
    "        # Calculate RSA timecourses\n",
    "        corr_model_times = np.nan * np.zeros((len(model_rdms), ntimes))\n",
    "        for imodel, (name, model) in enumerate(model_rdms.items()):\n",
    "\n",
    "            # Go over timepoints\n",
    "            for itime in range(ntimes):\n",
    "\n",
    "                rdm = rdm_times[..., itime]\n",
    "                vec = _rdm2vec(rdm, lower_tri=lower_tri)\n",
    "                if crossvalidate:\n",
    "                    modelvec = _rdm2vec(model, lower_tri=lower_tri)\n",
    "                else:\n",
    "                    modelvec = model.copy()\n",
    "\n",
    "                if rsa_method == \"pearson\":\n",
    "                    corr = scipy.stats.pearsonr(vec, modelvec)[0]\n",
    "                elif rsa_method == \"kendall_a\":\n",
    "                    corr = _kendall_tau_a(vec, modelvec)\n",
    "\n",
    "                corr_model_times[imodel, itime] = corr\n",
    "\n",
    "        # Prepare as wide data frame, then melt\n",
    "        df_rsa = pd.DataFrame(corr_model_times.T, columns=model_rdms.keys())\n",
    "        df_rsa.insert(0, \"method\", rsa_method)\n",
    "        df_rsa.insert(0, \"time_s\", times)\n",
    "        df_rsa.insert(0, \"itime\", range(ntimes))\n",
    "        df_rsa.insert(0, \"task\", task)\n",
    "        df_rsa.insert(0, \"stopping\", stop)\n",
    "        df_rsa.insert(0, \"sampling\", samp)\n",
    "        df_rsa.insert(0, \"subject\", subj)\n",
    "\n",
    "        df_rsa = df_rsa.melt(\n",
    "            id_vars=[\n",
    "                \"subject\",\n",
    "                \"task\",\n",
    "                \"sampling\",\n",
    "                \"stopping\",\n",
    "                \"time_s\",\n",
    "                \"itime\",\n",
    "                \"method\",\n",
    "            ],\n",
    "            var_name=\"model\",\n",
    "            value_name=\"similarity\",\n",
    "        )\n",
    "\n",
    "        # add boolean column whether orthogonalized\n",
    "        orth_bools = df_rsa[\"model\"].str.startswith(\"o_\").to_numpy()\n",
    "        df_rsa.insert(7, \"orth\", orth_bools)\n",
    "\n",
    "        # encode orthogonality only in \"orth\" column, not in model name\n",
    "        df_rsa.loc[:, \"model\"] = df_rsa[\"model\"].str.lstrip(\"o_\").to_numpy()\n",
    "\n",
    "        # append to list of all DFs\n",
    "        all_dfs.append(df_rsa)\n",
    "\n",
    "        # Make and save plot to double check timecourses\n",
    "        fig, ax = plt.subplots()\n",
    "        sns.lineplot(\n",
    "            x=\"time_s\",\n",
    "            y=\"similarity\",\n",
    "            hue=\"model\",\n",
    "            style=\"orth\",\n",
    "            data=df_rsa,\n",
    "            palette=colors,\n",
    "            ax=ax,\n",
    "        )\n",
    "\n",
    "        fname = name_templates[\"rsa_subj_plots\"].format(\n",
    "            folder_name, subj, task, \"timecourses\"\n",
    "        )\n",
    "        fig.savefig(fname)\n",
    "\n",
    "    # Combine both DFs\n",
    "    df_rsa = pd.concat(all_dfs, ignore_index=True)\n",
    "\n",
    "    return df_rsa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:50:04.886592Z",
     "start_time": "2020-09-02T12:38:59.194170Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using folder_name: cv-False_flip-False_long-False_baseline-True_rsa-pearson_dist-euclidean_half-both_exclude-Identity_mnn-True\n"
     ]
    }
   ],
   "source": [
    "# settings\n",
    "run_parallel = False\n",
    "df = pd.read_csv(beh_fpath)\n",
    "distance_metric = \"euclidean\"\n",
    "equalize_counts = False\n",
    "outcome_column_name = \"outcome\"\n",
    "\n",
    "# mnn_tuple:\n",
    "# [0] if True, do mnn, else ignore rest of tuple\n",
    "# [1] if True, do mnn separately for active and yoked, else for active and yoked together\n",
    "# [2] if True, do mnn once for all timepoints, else per each timepoint\n",
    "mnn_tuple = (False, False, False)\n",
    "\n",
    "\n",
    "rsa_method = \"pearson\"\n",
    "preproc_settings = {\n",
    "    \"crop\": (0.6, 1.6),\n",
    "    \"tshift\": -0.8,\n",
    "    \"smooth\": 150,\n",
    "    \"baseline\": (None, 0),\n",
    "    \"smooth_before_baseline\": True,\n",
    "}\n",
    "subjects = tuple(range(1, 41))\n",
    "crossvalidate = False\n",
    "\n",
    "flip_sign_sample_frequency = False\n",
    "half = 'both'\n",
    "\n",
    "NJOBS = min(multiprocessing.cpu_count() - 2, len(subjects))\n",
    "\n",
    "# which models to exclude (pass empty list otherwise)\n",
    "exclude_models = ['identity']\n",
    "\n",
    "# Try to find settings that would overwrite the settings here\n",
    "configpath = op.join(BIDS_ROOT, 'code', 'rsa_analysis_config.json')\n",
    "if op.exists(configpath):\n",
    "    print(f'\\n\\nOVERWRITTING SETTINGS USING CONFIG:\\n{configpath}\\n\\n')\n",
    "    with open(configpath, 'r') as fin:\n",
    "        config = json.load(fin)\n",
    "    print(config)\n",
    "    distance_metric = config.get('distance_metric', distance_metric)\n",
    "    run_parallel = config.get('run_parallel', run_parallel)\n",
    "    crossvalidate = config.get('crossvalidate', crossvalidate)\n",
    "    half = config.get('half', half)\n",
    "    exclude_models = config.get('exclude_models', exclude_models)\n",
    "    rsa_method = config.get('rsa_method', rsa_method)\n",
    "    mnn_tuple = config.get('mnn_tuple', mnn_tuple)\n",
    "    equalize_counts = config.get('equalize_counts', equalize_counts)\n",
    "    preproc_settings = config.get('preproc_settings', preproc_settings)\n",
    "    outcome_column_name = config.get('outcome_column_name', outcome_column_name)\n",
    "\n",
    "# NOTE: all \"tuples\" that were read from JSON are now \"lists\",\n",
    "# because there are no \"tuples\" in JSON.\n",
    "# Can also be bool.\n",
    "try: \n",
    "    preproc_settings[\"crop\"] = tuple(preproc_settings[\"crop\"])\n",
    "except TypeError:\n",
    "    assert isinstance(preproc_settings[\"crop\"], bool)\n",
    "try:\n",
    "    preproc_settings[\"baseline\"] = tuple(preproc_settings[\"baseline\"])\n",
    "except TypeError:\n",
    "    assert isinstance(preproc_settings[\"baseline\"], (bool, type(None)))\n",
    "\n",
    "# NOTE: \"identity\" MUST be excluded in non-crossval 9x9 RSA\n",
    "if crossvalidate is False:\n",
    "    assert 'identity' in exclude_models\n",
    "\n",
    "# NOTE: \"mnn\" is automatically done if \"mahalanobis\" is used\n",
    "# so mnn_tuple[0] should be True\n",
    "if distance_metric == \"mahalanobis\":\n",
    "    assert mnn_tuple[0] is True, \"mahalanobis automatically means MNN\"\n",
    "    \n",
    "# NOTE: \"mahalanobis\" currently only supports MNN done per timepoint\n",
    "# so mnn_tuple[2] should be False\n",
    "if distance_metric == \"mahalanobis\":\n",
    "    assert mnn_tuple[2] is False, \"mahalanobis currently only supports MNN per timepoint\"\n",
    "\n",
    "# Construct a string for preproc_settings parameters\n",
    "preproc_str = \"\"\n",
    "for key, val in preproc_settings.items():\n",
    "    preproc_str += str(key)[0] + \"-\" + str(val)\n",
    "\n",
    "# Folder name for saving results\n",
    "folder_name = (\n",
    "    f\"cv-{crossvalidate}_flip-{flip_sign_sample_frequency}\"\n",
    "    f\"_rsa-{rsa_method}\"\n",
    "    f\"_dist-{distance_metric}_half-{half.split('_')[0]}\"\n",
    "    f\"_exclude-{''.join([i.capitalize() for i in exclude_models])}\"\n",
    "    f\"_mnn-{''.join([str(i) for i in mnn_tuple])}\"\n",
    "    f\"_ec-{equalize_counts}\"\n",
    "    f\"_{preproc_str}\"\n",
    "    f\"_{outcome_column_name}\"\n",
    "    )\n",
    "\n",
    "print(f\"using folder_name: {folder_name}\")\n",
    "    \n",
    "# parallelize\n",
    "pool_inputs = list(\n",
    "    itertools.product(\n",
    "        subjects,\n",
    "        [df],\n",
    "        [name_templates],\n",
    "        [crossvalidate],\n",
    "        [distance_metric],\n",
    "        [rsa_method],\n",
    "        [preproc_settings],\n",
    "        [exclude_models],\n",
    "        [flip_sign_sample_frequency],\n",
    "        [folder_name],\n",
    "        [half],\n",
    "        [mnn_tuple],\n",
    "        [equalize_counts],\n",
    "        [outcome_column_name],\n",
    "    )\n",
    ")\n",
    "\n",
    "# serial vs parallel version of code\n",
    "if run_parallel:\n",
    "    with multiprocessing.Pool(NJOBS) as pool:\n",
    "        results = pool.starmap(rsa_timecourse_xval, pool_inputs)\n",
    "else:\n",
    "    results = []\n",
    "    for inp in pool_inputs:\n",
    "        results.append(rsa_timecourse_xval(*inp))\n",
    "\n",
    "# concatenate results\n",
    "df_rsa = pd.concat(results, ignore_index=True)\n",
    "\n",
    "# add some metadata\n",
    "df_rsa['crossvalidated'] = crossvalidate\n",
    "df_rsa['baseline_corrected'] = True if isinstance(preproc_settings[\"baseline\"], tuple) else False\n",
    "df_rsa['distance_metric'] = distance_metric\n",
    "df_rsa['mnn'] = mnn_tuple[0]\n",
    "df_rsa['mnn_separate_epoch_types'] = mnn_tuple[1]\n",
    "df_rsa['mnn_average_over_time'] = mnn_tuple[2]\n",
    "df_rsa['equalized_counts'] = equalize_counts\n",
    "df_rsa[\"outcome_column_name\"] = outcome_column_name\n",
    "\n",
    "# Take mean of numberline and extremity model -> \"artificial model\"\n",
    "tmpa = df_rsa[df_rsa['model'] == 'numberline']\n",
    "tmpb = df_rsa[df_rsa['model'] == 'extremity']\n",
    "\n",
    "merge_on = list(df_rsa.columns)\n",
    "merge_on.remove('model')\n",
    "merge_on.remove('similarity')\n",
    "\n",
    "tmpc = tmpa.merge(tmpb, on=merge_on)\n",
    "tmpc['similarity'] = tmpc[['similarity_x', 'similarity_y']].to_numpy().mean(axis=1)\n",
    "tmpc['model'] = 'mean_number_extrem'\n",
    "tmpc = tmpc[list(df_rsa.columns)]\n",
    "\n",
    "df_rsa = pd.concat([df_rsa, tmpc], ignore_index=True)\n",
    "\n",
    "# save\n",
    "fname = name_templates[\"rsa_results\"].format(folder_name)\n",
    "df_rsa.to_csv(fname, index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-04T11:32:54.377151Z",
     "start_time": "2020-08-04T11:32:54.370416Z"
    }
   },
   "source": [
    "# Plot each model (all tasks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:42.982813Z",
     "start_time": "2020-09-02T12:27:33.897Z"
    }
   },
   "outputs": [],
   "source": [
    "# Make plots by models and save\n",
    "for meta, grp in df_rsa.groupby(['model', 'orth']):\n",
    "    \n",
    "    model = 'o_' + meta[0] if meta[1] else meta[0]\n",
    "    \n",
    "    with sns.plotting_context('talk'):\n",
    "        # Plot this group\n",
    "        fig, ax = plt.subplots(sharex=True, sharey=True)\n",
    "\n",
    "        sns.lineplot(x='time_s', y='similarity', ci=68,\n",
    "                     hue='stopping', style='sampling',\n",
    "                     hue_order=['fixed', 'variable'],\n",
    "                     style_order=['active', 'yoked'], legend=False,\n",
    "                     data=grp, ax=ax)\n",
    "        ax.set_title(model)\n",
    "        ax.axhline(0, color='black')\n",
    "        ax.axvline(0., color='black', linestyle='--')    \n",
    "        ax.set_xlabel('time (s)')\n",
    "        ax.set_ylabel(f'similarity ({rsa_method})')\n",
    "\n",
    "        # add legend\n",
    "        # https://matplotlib.org/3.1.1/gallery/text_labels_and_annotations/custom_legends.html\n",
    "        legend_elements = [\n",
    "            Line2D([0], [0], color=sns.color_palette()[1], linestyle='-', label='active/variable'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[1], linestyle='--', label='yoked/variable'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[0], linestyle='-', label='active/fixed'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[0], linestyle='--', label='yoked/fixed'),\n",
    "            \n",
    "        ]\n",
    "\n",
    "        ax.legend(\n",
    "            handles=legend_elements, loc='best',\n",
    "            prop={'size': 10}, framealpha=1,\n",
    "        )\n",
    "\n",
    "        fig.tight_layout()\n",
    "        \n",
    "        # save\n",
    "        fname = name_templates[\"rsa_overall_plots\"].format(folder_name, model)\n",
    "        fig.savefig(fname)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot each task (all models)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:42.983598Z",
     "start_time": "2020-09-02T12:27:33.900Z"
    }
   },
   "outputs": [],
   "source": [
    "# Make plots by task and save\n",
    "for task, grp in df_rsa.groupby(\"task\"):\n",
    "\n",
    "    with sns.plotting_context(\"talk\"):\n",
    "        # Plot this group\n",
    "        fig, ax = plt.subplots(sharex=True, sharey=True)\n",
    "\n",
    "        sns.lineplot(\n",
    "            x=\"time_s\",\n",
    "            y=\"similarity\",\n",
    "            ci=68,\n",
    "            hue=\"model\",\n",
    "            style='orth',            \n",
    "            legend=\"brief\",\n",
    "            data=grp,\n",
    "            palette=colors,\n",
    "            ax=ax,\n",
    "        )\n",
    "        ax.set_title(task)\n",
    "        ax.axhline(0, color=\"black\")\n",
    "        ax.axvline(0.0, color=\"black\", linestyle=\"--\")\n",
    "        ax.set_xlabel(\"time (s)\")\n",
    "        ax.set_ylabel(f\"similarity ({rsa_method})\")\n",
    "\n",
    "        ax.legend(bbox_to_anchor=(1, 0.5))\n",
    "\n",
    "        # save\n",
    "        fname = name_templates[\"rsa_overall_plots\"].format(folder_name, task)\n",
    "        fig.savefig(fname, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot mean across tasks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:42.984629Z",
     "start_time": "2020-09-02T12:27:33.904Z"
    }
   },
   "outputs": [],
   "source": [
    "# Plots of means across tasks\n",
    "\n",
    "with sns.plotting_context(\"talk\"):\n",
    "    # Plot this group\n",
    "    fig, ax = plt.subplots(sharex=True, sharey=True)\n",
    "\n",
    "    sns.lineplot(\n",
    "        x=\"time_s\",\n",
    "        y=\"similarity\",\n",
    "        ci=68,\n",
    "        hue=\"model\",\n",
    "        style='orth',        \n",
    "        legend=\"brief\",\n",
    "        data=df_rsa,\n",
    "        palette=colors,        \n",
    "        ax=ax,\n",
    "    )\n",
    "    ax.set_title('average over tasks')\n",
    "    ax.axhline(0, color=\"black\")\n",
    "    ax.axvline(0.0, color=\"black\", linestyle=\"--\")\n",
    "    ax.set_xlabel(\"time (s)\")\n",
    "    ax.set_ylabel(f\"similarity ({rsa_method})\")\n",
    "\n",
    "    ax.legend(bbox_to_anchor=(1, 0.5))\n",
    "\n",
    "    # save\n",
    "    fname = name_templates[\"rsa_overall_plots\"].format(folder_name, 'overall')\n",
    "    fig.savefig(fname, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot numberline + extremity averaged"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-02T12:27:42.985612Z",
     "start_time": "2020-09-02T12:27:33.907Z"
    }
   },
   "outputs": [],
   "source": [
    "# which models to average\n",
    "models_to_average = ['numberline', 'extremity']\n",
    "df_rsa_selection = df_rsa[df_rsa['model'].isin(models_to_average)]\n",
    "\n",
    "for meta, grp in df_rsa_selection.groupby('orth'):\n",
    "\n",
    "    pltsavelabel = 'orth' if meta else ''\n",
    "    \n",
    "    with sns.plotting_context(\"talk\"):\n",
    "        # Plot this group\n",
    "        fig, ax = plt.subplots(sharex=True, sharey=True)\n",
    "\n",
    "        sns.lineplot(\n",
    "            x=\"time_s\",\n",
    "            y=\"similarity\",\n",
    "            ci=68,\n",
    "            hue=\"stopping\",\n",
    "            hue_order=['fixed', 'variable'],\n",
    "            style='sampling',\n",
    "            style_order=['active', 'yoked'],\n",
    "            legend=False,\n",
    "            data=grp,\n",
    "            ax=ax,\n",
    "        )\n",
    "        ax.set_title(f'averaged models: {models_to_average}' + pltsavelabel)\n",
    "        ax.axhline(0, color=\"black\")\n",
    "        ax.axvline(0.0, color=\"black\", linestyle=\"--\")\n",
    "        ax.set_xlabel(\"time (s)\")\n",
    "        ax.set_ylabel(f\"similarity ({rsa_method})\")\n",
    "\n",
    "        # add legend\n",
    "        # https://matplotlib.org/3.1.1/gallery/text_labels_and_annotations/custom_legends.html\n",
    "        legend_elements = [\n",
    "            Line2D([0], [0], color=sns.color_palette()[1], linestyle='-', label='active/variable'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[1], linestyle='--', label='yoked/variable'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[0], linestyle='-', label='active/fixed'),\n",
    "            Line2D([0], [0], color=sns.color_palette()[0], linestyle='--', label='yoked/fixed'),\n",
    "            \n",
    "        ]\n",
    "\n",
    "        ax.legend(\n",
    "            handles=legend_elements,\n",
    "            prop={'size': 10}, framealpha=1,\n",
    "            bbox_to_anchor=(1, 0.5)\n",
    "        )        \n",
    "\n",
    "        # save\n",
    "        fname = name_templates[\"rsa_overall_plots\"].format(folder_name, 'averaged_models' + pltsavelabel)\n",
    "        fig.savefig(fname, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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