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995 lines (807 loc) · 35.4 KB
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# 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",
"circ_dist",
"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 circ_dist(x, y):
"""
Computes the pairwise circular distance between two arrays of
points (in radians).
Parameters
----------
x: numpy vector of positions on a circle, in radians.
y: numpy vector of positions on a circle, in radians.
Returns
-------
r: numpy vector of distances between inputs.
"""
if x.size != y.size:
raise ValueError("Input sizes must match to compute pairwise "
"comparisons.")
r = np.angle(np.exp(x*1j) / np.exp(y*1j))
return r
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(data, 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(data)):
if data[i] is not None:
mask.append(i)
# Concatenate them
stacked = np.concatenate([data[i] for i in mask], axis=axis)
return 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(
<
8BD0
div>
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(
>
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