# Copyright 2016 Intel Corporation, Princeton University

#

# Licensed under the Apache License, Version 2.0 (the "License");

# you may not use this file except in compliance with the License.

# You may obtain a copy of the License at

#

# http://www.apache.org/licenses/LICENSE-2.0

#

# Unless required by applicable law or agreed to in writing, software

# distributed under the License is distributed on an "AS IS" BASIS,

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

# See the License for the specific language governing permissions and

# limitations under the License.

import numpy as np

import re

import warnings

import os.path

import psutil

from .fmrisim import generate_stimfunction, _double_gamma_hrf, convolve_hrf

from scipy.fftpack import fft, ifft

import logging

logger = logging.getLogger(__name__)

"""

Some utility functions that can be used by different algorithms

"""

__all__ = [

"array_correlation",

"center_mass_exp",

"concatenate_not_none",

"cov2corr",

"from_tri_2_sym",

"from_sym_2_tri",

"gen_design",

"phase_randomize",

"p_from_null",

"ReadDesign",

"sumexp_stable",

"usable_cpu_count",

]

def from_tri_2_sym(tri, dim):

"""convert a upper triangular matrix in 1D format

to 2D symmetric matrix

Parameters

----------

tri: 1D array

Contains elements of upper triangular matrix

dim : int

The dimension of target matrix.

Returns

-------

symm : 2D array

Symmetric matrix in shape=[dim, dim]

"""

symm = np.zeros((dim, dim))

symm[np.triu_indices(dim)] = tri

return symm

def from_sym_2_tri(symm):

"""convert a 2D symmetric matrix to an upper

triangular matrix in 1D format

Parameters

----------

symm : 2D array

Symmetric matrix

Returns

-------

tri: 1D array

Contains elements of upper triangular matrix

"""

inds = np.triu_indices_from(symm)

tri = symm[inds]

return tri

def sumexp_stable(data):

"""Compute the sum of exponents for a list of samples

Parameters

----------

data : array, shape=[features, samples]

A data array containing samples.

Returns

-------

result_sum : array, shape=[samples,]

The sum of exponents for each sample divided by the exponent

of the maximum feature value in the sample.

max_value : array, shape=[samples,]

The maximum feature value for each sample.

result_exp : array, shape=[features, samples]

The exponent of each element in each sample divided by the exponent

of the maximum feature value in the sample.

Note

----

This function is more stable than computing the sum(exp(v)).

It useful for computing the softmax_i(v)=exp(v_i)/sum(exp(v)) function.

"""

max_value = data.max(axis=0)

result_exp = np.exp(data - max_value)

result_sum = np.sum(result_exp, axis=0)

return result_sum, max_value, result_exp

def concatenate_not_none(l, axis=0):

"""Construct a numpy array by stacking not-None arrays in a list

Parameters

----------

data : list of arrays

The list of arrays to be concatenated. Arrays have same shape in all

but one dimension or are None, in which case they are ignored.

axis : int, default = 0

Axis for the concatenation

Returns

-------

data_stacked : array

The resulting concatenated array.

"""

# Get the indexes of the arrays in the list

mask = []

for i in range(len(l)):

if l[i] is not None:

mask.append(i)

# Concatenate them

l_stacked = np.concatenate([l[i] for i in mask], axis=axis)

return l_stacked

def cov2corr(cov):

"""Calculate the correlation matrix based on a

covariance matrix

Parameters

----------

cov: 2D array

Returns

-------

corr: 2D array

correlation converted from the covarince matrix

"""

assert cov.ndim == 2, 'covariance matrix should be 2D array'

inv_sd = 1 / np.sqrt(np.diag(cov))

corr = cov * inv_sd[None, :] * inv_sd[:, None]

return corr

class ReadDesign:

"""A class which has the ability of reading in design matrix in .1D file,

generated by AFNI's 3dDeconvolve.

Parameters

----------

fname: string, the address of the file to read.

include_orth: Boollean, whether to include "orthogonal" regressors in

the nuisance regressors which are usually head motion parameters.

All the columns of design matrix are still going to be read in,

but the attribute cols_used will reflect whether these orthogonal

regressors are to be included for furhter analysis.

Note that these are not entered into design_task attribute which

include only regressors related to task conditions.

include_pols: Boollean, whether to include polynomial regressors in

the nuisance regressors which are used to capture slow drift of

signals.

Attributes

----------

design: 2d array. The design matrix read in from the csv file.

design_task: 2d array. The part of design matrix corresponding to

task conditions.

n_col: number of total columns in the design matrix.

column_types: 1d array. the types of each column in the design matrix.

0 for orthogonal regressors (usually head motion parameters),

-1 for polynomial basis (capturing slow drift of signals),

values > 0 for stimulus conditions

n_basis: scalar. The number of polynomial bases in the designn matrix.

n_stim: scalar. The number of stimulus conditions.

n_orth: scalar. The number of orthogoanal regressors (usually head

motions)

StimLabels: list. The names of each column in the design matrix.

"""

def __init__(self, fname=None, include_orth=True, include_pols=True):

if fname is None:

# fname is the name of the file to read in the design matrix

self.design = np.zeros([0, 0])

self.n_col = 0

# number of columns (conditions) in the design matrix

self.column_types = np.ones(0)

self.n_basis = 0

self.n_stim = 0

self.n_orth = 0

self.StimLabels = []

else:

# isAFNI = re.match(r'.+[.](1D|1d|txt)$', fname)

filename, ext = os.path.splitext(fname)

# We assume all AFNI 1D files have extension of 1D or 1d or txt

if ext in ['.1D', '.1d', '.txt']:

self.read_afni(fname=fname)

self.include_orth = include_orth

self.include_pols = include_pols

# The two flags above dictates whether columns corresponding to

# baseline drift modeled by polynomial functions of time and

# columns corresponding to other orthogonal signals (usually motion)

# are included in nuisance regressors.

self.cols_task = np.where(self.column_types == 1)[0]

self.design_task = self.design[:, self.cols_task]

if np.ndim(self.design_task) == 1:

self.design_task = self.design_task[:, None]

# part of the design matrix related to task conditions.

self.n_TR = np.size(self.design_task, axis=0)

self.cols_nuisance = np.array([])

if self.include_orth:

self.cols_nuisance = np.int0(

np.sort(np.append(self.cols_nuisance,

np.where(self.column_types == 0)[0])))

if self.include_pols:

self.cols_nuisance = np.int0(

np.sort(np.append(self.cols_nuisance,

np.where(self.column_types == -1)[0])))

if np.size(self.cols_nuisance) > 0:

self.reg_nuisance = self.design[:, self.cols_nuisance]

if np.ndim(self.reg_nuisance) == 1:

self.reg_nuisance = self.reg_nuisance[:, None]

else:

self.reg_nuisance = None

# Nuisance regressors for motion, baseline, etc.

def read_afni(self, fname):

# Read design file written by AFNI

self.n_basis = 0

self.n_stim = 0

self.n_orth = 0

self.StimLabels = []

self.design = np.loadtxt(fname, ndmin=2)

with open(fname) as f:

all_text = f.read()

find_n_column = re.compile(

r'^#[ ]+ni_type[ ]+=[ ]+"(?P<n_col>\d+)[*]', re.MULTILINE)

n_col_found = find_n_column.search(all_text)

if n_col_found:

self.n_col = int(n_col_found.group('n_col'))

if self.n_col != np.size(self.design, axis=1):

warnings.warn(

'The number of columns in the design matrix'

+ 'does not match the header information')

self.n_col = np.size(self.design, axis=1)

else:

self.n_col = np.size(self.design, axis=1)

self.column_types = np.ones(self.n_col)

# default that all columns are conditions of interest

find_ColumnGroups = re.compile(

r'^#[ ]+ColumnGroups[ ]+=[ ]+"(?P<CGtext>.+)"', re.MULTILINE)

CG_found = find_ColumnGroups.search(all_text)

if CG_found:

CG_text = re.split(',', CG_found.group('CGtext'))

curr_idx = 0

for CG in CG_text:

split_by_at = re.split('@', CG)

if len(split_by_at) == 2:

# the first tells the number of columns in this condition

# the second tells the condition type

n_this_cond = int(split_by_at[0])

self.column_types[curr_idx:curr_idx + n_this_cond] = \

int(split_by_at[1])

curr_idx += n_this_cond

elif len(split_by_at) == 1 and \

not re.search(r'\..', split_by_at[0]):

# Just a number, and not the type like '1..4'

self.column_types[curr_idx] = int(split_by_at[0])

curr_idx += 1

else: # must be a single stimulus condition

split_by_dots = re.split(r'\..', CG)

n_this_cond = int(split_by_dots[1])

self.column_types[curr_idx:curr_idx + n_this_cond] = 1

curr_idx += n_this_cond

self.n_basis = np.sum(self.column_types == -1)

self.n_stim = np.sum(self.column_types > 0)

self.n_orth = np.sum(self.column_types == 0)

find_StimLabels = re.compile(

r'^#[ ]+StimLabels[ ]+=[ ]+"(?P<SLtext>.+)"', re.MULTILINE)

StimLabels_found = find_StimLabels.search(all_text)

if StimLabels_found:

self.StimLabels = \

re.split(r'[ ;]+', StimLabels_found.group('SLtext'))

else:

self.StimLabels = []

def gen_design(stimtime_files, scan_duration, TR, style='FSL',

temp_res=0.01,

hrf_para={'response_delay': 6, 'undershoot_delay': 12,

'response_dispersion': 0.9,

'undershoot_dispersion': 0.9,

'undershoot_scale': 0.035}):

""" Generate design matrix based on a list of names of stimulus

timing files. The function will read each file, and generate

a numpy array of size [time_points \\* condition], where

time_points equals duration / TR, and condition is the size of

stimtime_filenames. Each column is the hypothetical fMRI response

based on the stimulus timing in the corresponding file

of stimtime_files.

This function uses generate_stimfunction and double_gamma_hrf

of brainiak.utils.fmrisim.

Parameters

----------

stimtime_files: a string or a list of string.

Each string is the name of the file storing

the stimulus timing information of one task condition.

The contents in the files will be interpretated

based on the style parameter.

Details are explained under the style parameter.

scan_duration: float or a list (or a 1D numpy array) of numbers.

Total duration of each fMRI scan, in unit of seconds.

If there are multiple runs, the duration should be

a list (or 1-d numpy array) of numbers.

If it is a list, then each number in the list

represents the duration of the corresponding scan

in the stimtime_files.

If only a number is provided, it is assumed that

there is only one fMRI scan lasting for scan_duration.

TR: float.

The sampling period of fMRI, in unit of seconds.

style: string, default: 'FSL'

Acceptable inputs: 'FSL', 'AFNI'

The formating style of the stimtime_files.

'FSL' style has one line for each event of the same condition.

Each line contains three numbers. The first number is the onset

of the event relative to the onset of the first scan,

in units of seconds.

(Multiple scans should be treated as a concatenated long scan

for the purpose of calculating onsets.

However, the design matrix from one scan won't leak into the next).

The second number is the duration of the event,

in unit of seconds.

The third number is the amplitude modulation (or weight)

of the response.

It is acceptable to not provide the weight,

or not provide both duration and weight.

In such cases, these parameters will default to 1.0.

This code will accept timing files with only 1 or 2 columns for

convenience but please note that the FSL package does not allow this

'AFNI' style has one line for each scan (run).

Each line has a few triplets in the format of

stim_onsets*weight:duration

(or simpler, see below), separated by spaces.

For example, 3.2\\*2.0:1.5 means that one event starts at 3.2s,

modulated by weight of 2.0 and lasts for 1.5s.

If some run does not include a single event

of a condition (stimulus type), then you can put \\*,

or a negative number, or a very large number in that line.

Either duration or weight can be neglected. In such

cases, they will default to 1.0.

For example, 3.0, 3.0\\*1.0, 3.0:1.0 and 3.0\\*1.0:1.0 all

means an event starting at 3.0s, lasting for 1.0s, with

amplitude modulation of 1.0.

temp_res: float, default: 0.01

Temporal resolution of fMRI, in second.

hrf_para: dictionary

The parameters of the double-Gamma hemodynamic response function.

To set different parameters, supply a dictionary with

the same set of keys as the default, and replace the corresponding

values with the new values.

Returns

-------

design: 2D numpy array

design matrix. Each time row represents one TR

(fMRI sampling time point) and each column represents

one experiment condition, in the order in stimtime_files

"""

if np.ndim(scan_duration) == 0:

scan_duration = [scan_duration]

scan_duration = np.array(scan_duration)

assert np.all(scan_duration > TR), \

'scan duration should be longer than a TR'

if type(stimtime_files) is str:

stimtime_files = [stimtime_files]

assert TR > 0, 'TR should be positive'

assert style == 'FSL' or style == 'AFNI', 'style can only be FSL or AFNI'

n_C = len(stimtime_files) # number of conditions

n_S = np.size(scan_duration) # number of scans

if n_S > 1:

design = [np.empty([int(np.round(duration / TR)), n_C])

for duration in scan_duration]

else:

design = [np.empty([int(np.round(scan_duration / TR)), n_C])]

scan_onoff = np.insert(np.cumsum(scan_duration), 0, 0)

if style == 'FSL':

design_info = _read_stimtime_FSL(stimtime_files, n_C, n_S, scan_onoff)

elif style == 'AFNI':

design_info = _read_stimtime_AFNI(stimtime_files, n_C, n_S, scan_onoff)

response_delay = hrf_para['response_delay']

undershoot_delay = hrf_para['undershoot_delay']

response_disp = hrf_para['response_dispersion']

undershoot_disp = hrf_para['undershoot_dispersion']

undershoot_scale = hrf_para['undershoot_scale']

# generate design matrix

for i_s in range(n_S):

for i_c in range(n_C):

if len(design_info[i_s][i_c]['onset']) > 0:

stimfunction = generate_stimfunction(

onsets=design_info[i_s][i_c]['onset'],

event_durations=design_info[i_s][i_c]['duration'],

total_time=scan_duration[i_s],

weights=design_info[i_s][i_c]['weight'],

temporal_resolution=1.0/temp_res)

hrf = _double_gamma_hrf(response_delay=response_delay,

undershoot_delay=undershoot_delay,

response_dispersion=response_disp,

undershoot_dispersion=undershoot_disp,

undershoot_scale=undershoot_scale,

temporal_resolution=1.0/temp_res)

design[i_s][:, i_c] = convolve_hrf(

stimfunction, TR, hrf_type=hrf, scale_function=False,

temporal_resolution=1.0 / temp_res).transpose() * temp_res

else:

design[i_s][:, i_c] = 0.0

# We multiply the resulting design matrix with

# the temporal resolution to normalize it.

# We do not use the internal normalization

# in double_gamma_hrf because it does not guarantee

# normalizing with the same constant.

return np.concatenate(design, axis=0)

def _read_stimtime_FSL(stimtime_files, n_C, n_S, scan_onoff):

""" Utility called by gen_design. It reads in one or more

stimulus timing file comforming to FSL style,

and return a list (size of [#run \\* #condition])

of dictionary including onsets, durations and weights of each event.

Parameters

----------

stimtime_files: a string or a list of string.

Each string is the name of the file storing the stimulus

timing information of one task condition.

The contents in the files should follow the style of FSL

stimulus timing files, refer to gen_design.

n_C: integer, number of task conditions

n_S: integer, number of scans

scan_onoff: list of numbers.

The onset of each scan after concatenating all scans,

together with the offset of the last scan.

For example, if 3 scans of duration 100s, 150s, 120s are run,

scan_onoff is [0, 100, 250, 370]

Returns

-------

design_info: list of stimulus information

The first level of the list correspond to different scans.

The second level of the list correspond to different conditions.

Each item in the list is a dictiornary with keys "onset",

"duration" and "weight". If one condition includes no event

in a scan, the values of these keys in that scan of the condition

are empty lists.

See also

--------

gen_design

"""

design_info = [[{'onset': [], 'duration': [], 'weight': []}

for i_c in range(n_C)] for i_s in range(n_S)]

# Read stimulus timing files

for i_c in range(n_C):

with open(stimtime_files[i_c]) as f:

for line in f.readlines():

tmp = line.strip().split()

i_s = np.where(

np.logical_and(scan_onoff[:-1] <= float(tmp[0]),

scan_onoff[1:] > float(tmp[0])))[0]

if len(i_s) == 1:

i_s = i_s[0]

design_info[i_s][i_c]['onset'].append(float(tmp[0])

- scan_onoff[i_s])

if len(tmp) >= 2:

design_info[i_s][i_c]['duration'].append(float(tmp[1]))

else:

design_info[i_s][i_c]['duration'].append(1.0)

if len(tmp) >= 3:

design_info[i_s][i_c]['weight'].append(float(tmp[2]))

else:

design_info[i_s][i_c]['weight'].append(1.0)

return design_info

def _read_stimtime_AFNI(stimtime_files, n_C, n_S, scan_onoff):

""" Utility called by gen_design. It reads in one or more stimulus timing

file comforming to AFNI style, and return a list

(size of ``[number of runs \\* number of conditions]``)

of dictionary including onsets, durations and weights of each event.

Parameters

----------

stimtime_files: a string or a list of string.

Each string is the name of the file storing the stimulus

timing information of one task condition.

The contents in the files should follow the style of AFNI

stimulus timing files, refer to gen_design.

n_C: integer, number of task conditions

n_S: integer, number of scans

scan_onoff: list of numbers.

The onset of each scan after concatenating all scans,

together with the offset of the last scan.

For example, if 3 scans of duration 100s, 150s, 120s are run,

scan_onoff is [0, 100, 250, 370]

Returns

-------

design_info: list of stimulus information

The first level of the list correspond to different scans.

The second level of the list correspond to different conditions.

Each item in the list is a dictiornary with keys "onset",

"duration" and "weight". If one condition includes no event

in a scan, the values of these keys in that scan of the condition

are empty lists.

See also

--------

gen_design

"""

design_info = [[{'onset': [], 'duration': [], 'weight': []}

for i_c in range(n_C)] for i_s in range(n_S)]

# Read stimulus timing files

for i_c in range(n_C):

with open(stimtime_files[i_c]) as f:

text = f.readlines()

assert len(text) == n_S, \

'Number of lines does not match number of runs!'

for i_s, line in enumerate(text):

events = line.strip().split()

if events[0] == '*':

continue

for event in events:

assert event != '*'

tmp = str.split(event, ':')

if len(tmp) == 2:

duration = float(tmp[1])

else:

duration = 1.0

tmp = str.split(tmp[0], '*')

if len(tmp) == 2:

weight = float(tmp[1])

else:

weight = 1.0

if (float(tmp[0]) >= 0

and float(tmp[0])

< scan_onoff[i_s + 1] - scan_onoff[i_s]):

design_info[i_s][i_c]['onset'].append(float(tmp[0]))

design_info[i_s][i_c]['duration'].append(duration)

design_info[i_s][i_c]['weight'].append(weight)

return design_info

def center_mass_exp(interval, scale=1.0):

""" Calculate the center of mass of negative exponential distribution

p(x) = exp(-x / scale) / scale

in the interval of (interval_left, interval_right).

scale is the same scale parameter as scipy.stats.expon.pdf

Parameters

----------

interval: size 2 tuple, float

interval must be in the form of (interval_left, interval_right),

where interval_left/interval_right is the starting/end point of the

interval in which the center of mass is calculated for exponential

distribution.

Note that interval_left must be non-negative, since exponential is

not supported in the negative domain, and interval_right must be

bigger than interval_left (thus positive) to form a well-defined

interval.

scale: float, positive

The scale parameter of the exponential distribution. See above.

Returns

-------

m: float

The center of mass in the interval of (interval_left,

interval_right) for exponential distribution.

"""

assert isinstance(interval, tuple), 'interval must be a tuple'

assert len(interval) == 2, 'interval must be length two'

(interval_left, interval_right) = interval

assert interval_left >= 0, 'interval_left must be non-negative'

assert interval_right > interval_left, \

'interval_right must be bigger than interval_left'

assert scale > 0, 'scale must be positive'

if interval_right < np.inf:

return ((interval_left + scale) * np.exp(-interval_left / scale) - (

scale + interval_right) * np.exp(-interval_right / scale)) / (

np.exp(-interval_left / scale) - np.exp(-interval_right / scale))

else:

return interval_left + scale

def usable_cpu_count():

"""Get number of CPUs usable by the current process.

Takes into consideration cpusets restrictions.

Returns

-------

int

"""

try:

result = len(os.sched_getaffinity(0))

except AttributeError:

try:

result = len(psutil.Process().cpu_affinity())

except AttributeError:

result = os.cpu_count()

return result

def phase_randomize(data, voxelwise=False, random_state=None):

"""Randomize phase of time series across subjects

For each subject, apply Fourier transform to voxel time series

and then randomly shift the phase of each frequency before inverting

back into the time domain. This yields time series with the same power

spectrum (and thus the same autocorrelation) as the original time series

but will remove any meaningful temporal relationships among time series

across subjects. By default (voxelwise=False), the same phase shift is

applied across all voxels; however if voxelwise=True, different random

phase shifts are applied to each voxel. The typical input is a time by

voxels by subjects ndarray. The first dimension is assumed to be the

time dimension and will be phase randomized. If a 2-dimensional ndarray

is provided, the last dimension is assumed to be subjects, and different

phase randomizations will be applied to each subject.

The implementation is based on the work in [Lerner2011]_ and

[Simony2016]_.

Parameters

----------

data : ndarray (n_TRs x n_voxels x n_subjects)

Data to be phase randomized (per subject)

voxelwise : bool, default: False

Apply same (False) or different (True) randomizations across voxels

random_state : RandomState or an int seed (0 by default)

A random number generator instance to define the state of the

random permutations generator.

Returns

----------

shifted_data : ndarray (n_TRs x n_voxels x n_subjects)

Phase-randomized time series

"""

# Check if input is 2-dimensional

data_ndim = data.ndim

# Get basic shape of data

data, n_TRs, n_voxels, n_subjects = _check_timeseries_input(data)

# Random seed to be deterministically re-randomized at each iteration

if isinstance(random_state, np.random.RandomState):

prng = random_state

else:

prng = np.random.RandomState(random_state)

# Get randomized phase shifts

if n_TRs % 2 == 0:

# Why are we indexing from 1 not zero here? n_TRs / -1 long?

pos_freq = np.arange(1, data.shape[0] // 2)

neg_freq = np.arange(data.shape[0] - 1, data.shape[0] // 2, -1)

else:

pos_freq = np.arange(1, (data.shape[0] - 1) // 2 + 1)

neg_freq = np.arange(data.shape[0] - 1,

(data.shape[0] - 1) // 2, -1)

if not voxelwise:

phase_shifts = (prng.rand(len(pos_freq), 1, n_subjects)

* 2 * np.math.pi)

else:

phase_shifts = (prng.rand(len(pos_freq), n_voxels, n_subjects)

* 2 * np.math.pi)

# Fast Fourier transform along time dimension of data

fft_data = fft(data, axis=0)

# Shift pos and neg frequencies symmetrically, to keep signal real

fft_data[pos_freq, :, :] *= np.exp(1j * phase_shifts)

fft_data[neg_freq, :, :] *= np.exp(-1j * phase_shifts)

# Inverse FFT to put data back in time domain

shifted_data = np.real(ifft(fft_data, axis=0))

# Go back to 2-dimensions if input was 2-dimensional

if data_ndim == 2:

shifted_data = shifted_data[:, 0, :]

return shifted_data

def p_from_null(observed, distribution,

side='two-sided', exact=False,

axis=None):

"""Compute p-value from null distribution

Returns the p-value for an observed test statistic given a null

distribution. Performs either a 'two-sided' (i.e., two-tailed)

test (default) or a one-sided (i.e., one-tailed) test for either the

'left' or 'right' side. For an exact test (exact=True), does not adjust

for the observed test statistic; otherwise, adjusts for observed

test statistic (prevents p-values of zero). If a multidimensional

distribution is provided, use axis argument to specify which axis indexes

resampling iterations.

The implementation is based on the work in [PhipsonSmyth2010]_.

.. [PhipsonSmyth2010] "Permutation p-values should never be zero:

calculating exact p-values when permutations are randomly drawn.",

B. Phipson, G. K., Smyth, 2010, Statistical Applications in Genetics

and Molecular Biology, 9, 1544-6115.

https://doi.org/10.2202/1544-6115.1585

Parameters

----------

observed : float

Observed test statistic

distribution : ndarray

Null distribution of test statistic

side : str, default:'two-sided'

Perform one-sided ('left' or 'right') or 'two-sided' test

axis: None or int, default:None

Axis indicating resampling iterations in input distribution

Returns

-------

p : float

p-value for observed test statistic based on null distribution

"""

if side not in ('two-sided', 'left', 'right'):

raise ValueError("The value for 'side' must be either "

"'two-sided', 'left', or 'right', got {0}".

format(side))

n_samples = len(distribution)

logger.info("Assuming {0} resampling iterations".format(n_samples))

if side == 'two-sided':

# Numerator for two-sided test

numerator = np.sum(np.abs(distribution) >= np.abs(observed), axis=axis)

elif side == 'left':

# Numerator for one-sided test in left tail

numerator = np.sum(distribution <= observed, axis=axis)

elif side == 'right':

# Numerator for one-sided test in right tail

numerator = np.sum(distribution >= observed, axis=axis)

# If exact test all possible permutations and do not adjust

if exact:

p = numerator / n_samples

# If not exact test, adjust number of samples to account for

# observed statistic; prevents p-value from being zero

else:

p = (numerator + 1) / (n_samples + 1)

return p

def _check_timeseries_input(data):

"""Checks response time series input data (e.g., for ISC analysis)

Input data should be a n_TRs by n_voxels by n_subjects ndarray

(e.g., brainiak.image.MaskedMultiSubjectData) or a list where each

item is a n_TRs by n_voxels ndarray for a given subject. Multiple

input ndarrays must be the same shape. If a 2D array is supplied,

the last dimension is assumed to correspond to subjects. This

function is generally intended to be used internally by other

functions module (e.g., isc, isfc in brainiak.isc).

Parameters

----------

data : ndarray or list

Time series data

Returns

-------

data : ndarray

Input time series data with standardized structure

n_TRs : int

Number of time points (TRs)

n_voxels : int

Number of voxels (or ROIs)

n_subjects : int

Number of subjects

"""

# Convert list input to 3d and check shapes

if type(data) == list:

data_shape = data[0].shape

for i, d in enumerate(data):

if d.shape != data_shape:

raise ValueError("All ndarrays in input list "

"must be the same shape!")

if d.ndim == 1:

data[i] = d[:, np.newaxis]

data = np.dstack(data)

# Convert input ndarray to 3d and check shape

elif isinstance(data, np.ndarray):

if data.ndim == 2:

data = data[:, np.newaxis, :]

elif data.ndim == 3:

pass

else:

raise ValueError("Input ndarray should have 2 "

"or 3 dimensions (got {0})!".format(data.ndim))

# Infer subjects, TRs, voxels and log for user to check

n_TRs, n_voxels, n_subjects = data.shape

logger.info("Assuming {0} subjects with {1} time points "

"and {2} voxel(s) or ROI(s) for ISC analysis.".format(

n_subjects, n_TRs, n_voxels))

return data, n_TRs, n_voxels, n_subjects

def array_correlation(x, y, axis=0):

"""Column- or row-wise Pearson correlation between two arrays

Computes sample Pearson correlation between two 1D or 2D arrays (e.g.,

two n_TRs by n_voxels arrays). For 2D arrays, computes correlation

between each corresponding column (axis=0) or row (axis=1) where axis

indexes observations. If axis=0 (default), each column is considered to

be a variable and each row is an observation; if axis=1, each row is a

variable and each column is an observation (equivalent to transposing

the input arrays). Input arrays must be the same shape with corresponding

variables and observations. This is intended to be an efficient method

for computing correlations between two corresponding arrays with many

variables (e.g., many voxels).

Parameters

----------

x : 1D or 2D ndarray

Array of observations for one or more variables

y : 1D or 2D ndarray

Array of observations for one or more variables (same shape as x)

axis : int (0 or 1), default: 0

Correlation between columns (axis=0) or rows (axis=1)

Returns

-------

r : float or 1D ndarray

Pearson correlation values for input variables

"""

# Accommodate array-like inputs

if not isinstance(x, np.ndarray):

x = np.asarray(x)

if not isinstance(y, np.ndarray):

y = np.asarray(y)

# Check that inputs are same shape

if x.shape != y.shape:

raise ValueError("Input arrays must be the same shape")

# Transpose if axis=1 requested (to avoid broadcasting

# issues introduced by switching axis in mean and sum)

if axis == 1:

x, y = x.T, y.T

# Center (de-mean) input variables

x_demean = x - np.mean(x, axis=0)

y_demean = y - np.mean(y, axis=0)

# Compute summed product of centered variables

numerator = np.sum(x_demean * y_demean, axis=0)

# Compute sum squared error

denominator = np.sqrt(np.sum(x_demean ** 2, axis=0) *

np.sum(y_demean ** 2, axis=0))

return numerator / denominator