def test_define():
expr = sympy.exp(3*t)
yield assert_equal(str(expr), 'exp(3*t)')
newf = define('f', expr)
yield assert_equal(str(newf), 'f(t)')
f = lambdify_t(newf)
tval = np.random.standard_normal((3,))
yield assert_almost_equal(np.exp(3*tval), f(tval))
def _blankdrift():
""" Create the blank drift formula
Returns
-------
df a formula that contains a constant regressor
"""
t = formula.Term('t')
pt = [utils.define('constant', 1.0 + 0 * t)]
df = formula.Formula(pt)
return df
def _polydrift(order, tmax):
"""
Create a polynomial drift formula
Parameters
----------
order, int, number of polynomials in the drift model
tmax, float maximal time value used in the sequence
this is used to normalize porperly the columns
Returns
-------
pol a formula that contains all the polynomial drift
plus a constant regressor
"""
t = formula.Term("t")
pt = []
# fixme : ideally this should be orthonormalized
for k in range(order):
pt.append(utils.define("poly_drift_%d" % (k + 1), t ** (k + 1) / tmax ** (k + 1)))
pt.append(utils.define("constant", 1.0 + 0 * t))
pol = formula.Formula(pt)
return pol
def _cosinedrift(hfcut, tmax, tsteps):
"""
Create a cosine drift formula
Parameters
----------
hfcut, float , cut frequency of the low-pass filter
tmax, float maximal time value used in the sequence
tsteps, int, number of TRs in the sequence
Returns
-------
cos a formula that contains all the polynomial drift
plus a constant regressor
"""
t = formula.Term("t")
pt = []
order = int(np.floor(2 * float(tmax) / float(hfcut)) + 1)
for k in range(1, order):
u = np.sqrt(2.0 / tmax) * sympy.cos(np.pi * (t / tmax + 0.5 / tsteps) * k)
pt.append(utils.define("cosine_drift_%d" % (k + 1), u))
pt.append(utils.define("constant", 1.0 + 0 * t))
cos = formula.Formula(pt)
return cos
"""
import numpy as np
import sympy
from nipy.algorithms.statistics.api import Formula, make_recarray
from nipy.modalities.fmri import utils, hrf
# Inter-stimulus intervals (time between events)
dt = np.random.uniform(low=0, high=2.5, size=(50,))
# Onset times from the ISIs
t = np.cumsum(dt)
# We're going to model the amplitudes ('a') by dt (the time between events)
a = sympy.Symbol('a')
linear = utils.define('linear', utils.events(t, dt, f=hrf.glover))
quadratic = utils.define('quad', utils.events(t, dt, f=hrf.glover, g=a**2))
cubic = utils.define('cubic', utils.events(t, dt, f=hrf.glover, g=a**3))
f1 = Formula([linear, quadratic, cubic])
# Evaluate this time-based formula at specific times to make the design matrix
tval = make_recarray(np.linspace(0,100, 1001), 't')
X1 = f1.design(tval, return_float=True)
# Now we make a model where the relationship of time between events and signal
# is an exponential with a time constant tau
l = sympy.Symbol('l')
exponential = utils.events(t, dt, f=hrf.glover, g=sympy.exp(-l*a))
f3 = Formula([exponential])
def convolve_regressors(paradigm, hrf_model, names=None, fir_delays=[0], fir_duration=1.0):
"""
Creation of a formula that represents
the convolution of the conditions onset witha certain hrf model
Parameters
----------
paradigm: paradigm instance
hrf_model, string that can be 'Canonical',
'Canonical With Derivative' or 'FIR'
that specifies the hemodynamic reponse function
names=None, list of strings corresponding to the condition names
if names==None, these are create as 'c1',..,'cn'
meaning 'condition 1'.. 'condition n'
fir_delays=[0], optional, array of shape(nb_onsets) or list
in case of FIR design, yields the array of delays
used in the FIR model
fir_duration=1., float, duration of the FIR block;
in general it should eb equal to the tr
Returns
-------
f a formula object that contains the convolved regressors
as functions of time
names list of strings corresponding to the condition names
the output names depend on teh hrf model used
if 'Canonical' then this is identical to the input names
if 'Canonical With Derivative', then two names are produced for
input name 'name': 'name' and 'name_derivative'
fixme:
normalization of the columns of the design matrix ?
"""
ncond = int(paradigm.index.max() + 1)
if names == None:
names = ["c%d" % k for k in range(ncond)]
else:
if len(names) < ncond:
raise ValueError, "the number of names is less than the \
number of conditions"
else:
ncond = len(names)
listc = []
hnames = []
typep = paradigm.type
for nc in range(ncond):
onsets = paradigm.onset[paradigm.index == nc]
nos = np.size(onsets)
if paradigm.amplitude is not None:
values = paradigm.amplitude[paradigm.index == nc]
else:
values = np.ones(nos)
if nos > 0:
if typep == "event":
if hrf_model == "Canonical":
c = utils.define(names[nc], utils.events(onsets, values, f=hrf.glover))
listc.append(c)
hnames.append(names[nc])
elif hrf_model == "Canonical With Derivative":
c1 = utils.define(names[nc], utils.events(onsets, values, f=hrf.glover))
c2 = utils.define(names[nc] + "_derivative", utils.events(onsets, values, f=hrf.dglover))
listc.append(c1)
listc.append(c2)
hnames.append(names[nc])
hnames.append(names[nc] + "_derivative")
elif hrf_model == "FIR":
for i, ft in enumerate(fir_delays):
lnames = names[nc] + "_delay_%d" % i
changes = np.hstack((onsets + ft, onsets + ft + fir_duration))
ochanges = np.argsort(changes)
lvalues = np.hstack((values, np.zeros(nos)))
changes = changes[ochanges]
lvalues = lvalues[ochanges]
c = utils.define(lnames, utils.step_function(changes, lvalues))
listc.append(c)
hnames.append(lnames)
else:
raise NotImplementedError, "unknown hrf model"
elif typep == "block":
offsets = onsets + paradigm.duration[paradigm.type == nc]
changes = np.hstack((onsets, offsets))
values = np.hstack((values, -values))
if hrf_model == "Canonical":
c = utils.events(changes, values, f=hrf.iglover)
listc.append(c)
hnames.append(names[nc])
elif hrf_model == "Canonical With Derivative":
c1 = utils.events(changes, values, f=hrf.iglover)
c2 = utils.events(changes, values, f=hrf.glover)
listc.append(c1)
listc.append(c2)
hnames.append(names[nc])
hnames.append(names[nc] + "_derivative")
elif hrf_model == "FIR":
raise NotImplementedError, "block design are not compatible with FIR at the moment"
else:
raise NotImplementedError, "unknown hrf model"
# create the formula
p = formula.Formula(listc)
return p, hnames
def protocol(recarr, design_type, *hrfs):
""" Create an object that can evaluate the FIAC
Subclass of formula.Formula, but not necessary.
Parameters
----------
recarr : (N,) structured array
with fields 'time' and 'event'
design_type : str
one of ['event', 'block']. Handles how the 'begin' term is
handled. For 'block', the first event of each block is put in
this group. For the 'event', only the first event is put in this
group. The 'begin' events are convolved with hrf.glover.
hrfs: symoblic HRFs
Each event type ('SSt_SSp','SSt_DSp','DSt_SSp','DSt_DSp') is
convolved with each of these HRFs in order.
Returns
-------
f: Formula
Formula for constructing design matrices.
contrasts : dict
Dictionary of the contrasts of the experiment.
"""
event_types = np.unique(recarr['event'])
N = recarr.size
if design_type == 'block':
keep = np.not_equal((np.arange(N)) % 6, 0)
else:
keep = np.greater(np.arange(N), 0)
# This first frame was used to model out a potentially
# 'bad' first frame....
_begin = recarr['time'][~keep]
termdict = {}
termdict['begin'] = utils.define('begin', utils.events(_begin, f=hrf.glover))
drift = formula.natural_spline(utils.T,
knots=[N_ROWS/2.+1.25],
intercept=True)
for i, t in enumerate(drift.terms):
termdict['drift%d' % i] = t
# After removing the first frame, keep the remaining
# events and times
times = recarr['time'][keep]
events = recarr['event'][keep]
# Now, specify the experimental conditions
# This creates expressions
# named SSt_SSp0, SSt_SSp1, etc.
# with one expression for each (eventtype, hrf) pair
for v in event_types:
for l, h in enumerate(hrfs):
k = np.array([events[i] == v for i in
range(times.shape[0])])
termdict['%s%d' % (v,l)] = utils.define("%s%d" % (v, l),
utils.events(times[k], f=h))
f = formula.Formula(termdict.values())
Tcontrasts = {}
Tcontrasts['average'] = (termdict['SSt_SSp0'] + termdict['SSt_DSp0'] +
termdict['DSt_SSp0'] + termdict['DSt_DSp0']) / 4.
Tcontrasts['speaker'] = (termdict['SSt_DSp0'] - termdict['SSt_SSp0'] +
termdict['DSt_DSp0'] - termdict['DSt_SSp0']) * 0.5
Tcontrasts['sentence'] = (termdict['DSt_DSp0'] + termdict['DSt_SSp0'] -
termdict['SSt_DSp0'] - termdict['SSt_SSp0']) * 0.5
Tcontrasts['interaction'] = (termdict['SSt_SSp0'] - termdict['SSt_DSp0'] -
termdict['DSt_SSp0'] + termdict['DSt_DSp0'])
# Ftest
Fcontrasts = {}
Fcontrasts['overall1'] = formula.Formula(Tcontrasts.values())
return f, Tcontrasts, Fcontrasts
def altprotocol(d, design_type, *hrfs):
""" Create an object that can evaluate the FIAC.
Subclass of formula.Formula, but not necessary.
Parameters
----------
d : np.recarray
recarray defining design in terms of time, sentence speaker
design_type : str in ['event', 'block']
Handles how the 'begin' term is handled.
For 'block', the first event of each block
is put in this group. For the 'event',
only the first event is put in this group.
The 'begin' events are convolved with hrf.glover.
hrfs: symoblic HRFs
Each event type ('SSt_SSp','SSt_DSp','DSt_SSp','DSt_DSp')
is convolved with each of these HRFs in order.
"""
if design_type == 'block':
keep = np.not_equal((np.arange(d.time.shape[0])) % 6, 0)
else:
keep = np.greater(np.arange(d.time.shape[0]), 0)
# This first frame was used to model out a potentially
# 'bad' first frame....
_begin = d.time[~keep]
d = d[keep]
termdict = {}
termdict['begin'] = utils.define('begin', utils.events(_begin, f=hrf.glover))
drift = formula.natural_spline(utils.T,
knots=[N_ROWS/2.+1.25],
intercept=True)
for i, t in enumerate(drift.terms):
termdict['drift%d' % i] = t
# Now, specify the experimental conditions
# The elements of termdict are DiracDeltas, rather than HRFs
st = formula.Factor('sentence', ['DSt', 'SSt'])
sp = formula.Factor('speaker', ['DSp', 'SSp'])
indic = {}
indic['sentence'] = st.main_effect
indic['speaker'] = sp.main_effect
indic['interaction'] = st.main_effect * sp.main_effect
indic['average'] = formula.I
for key in indic.keys():
# The matrix signs will be populated with +- 1's
# d is the recarray having fields ('time', 'sentence', 'speaker')
signs = indic[key].design(d, return_float=True)
for l, h in enumerate(hrfs):
# symb is a sympy expression representing a sum
# of [h(t-_t) for _t in d.time]
symb = utils.events(d.time, amplitudes=signs, f=h)
# the values of termdict will have keys like
# 'average0', 'speaker1'
# and values that are sympy expressions like average0(t),
# speaker1(t)
termdict['%s%d' % (key, l)] = utils.define("%s%d" % (key, l), symb)
f = formula.Formula(termdict.values())
Tcontrasts = {}
Tcontrasts['average'] = termdict['average0']
Tcontrasts['speaker'] = termdict['speaker0']
Tcontrasts['sentence'] = termdict['sentence0']
Tcontrasts['interaction'] = termdict['interaction0']
# F tests
Fcontrasts = {}
Fcontrasts['overall1'] = formula.Formula(Tcontrasts.values())
nhrf = len(hrfs)
Fcontrasts['averageF'] = formula.Formula([termdict['average%d' % j] for j in range(nhrf)])
Fcontrasts['speakerF'] = formula.Formula([termdict['speaker%d' % j] for j in range(nhrf)])
Fcontrasts['sentenceF'] = formula.Formula([termdict['sentence%d' % j] for j in range(nhrf)])
Fcontrasts['interactionF'] = formula.Formula([termdict['interaction%d' % j] for j in range(nhrf)])
Fcontrasts['overall2'] = Fcontrasts['averageF'] + Fcontrasts['speakerF'] + Fcontrasts['sentenceF'] + Fcontrasts['interactionF']
return f, Tcontrasts, Fcontrasts
def convolve_regressors(paradigm, hrf_model, end_time, fir_delays=[0],
fir_duration=1.):
""" Creation of a formula that represents
the convolution of the conditions onset with a certain hrf model
Parameters
----------
paradigm: paradigm instance
hrf_model: string that can be 'Canonical',
'Canonical With Derivative' or 'FIR'
that specifies the hemodynamic reponse function
end_time: float,
end time of the paradigm (needed only for block designs)
fir_delays=[0], optional, array of shape(nb_onsets) or list
in case of FIR design, yields the array of delays
used in the FIR model
fir_duration=1., float, duration of the FIR block
in general it should eb equal to the tr
Returns
-------
f: formula instance,
contains the convolved regressors as functions of time
names: list of strings,
the condition names, that depend on the hrf model used
if 'Canonical' then this is identical to the input names
if 'Canonical With Derivative', then two names are produced for
input name 'name': 'name' and 'name_derivative'
fixme
-----
normalization of the columns of the design matrix ?
"""
listc = []
hnames = []
typep = paradigm.type
for nc in np.unique(paradigm.con_id):
onsets = paradigm.onset[paradigm.con_id == nc]
nos = np.size(onsets)
if paradigm.amplitude is not None:
values = paradigm.amplitude[paradigm.con_id == nc]
else:
values = np.ones(nos)
if nos < 1:
continue
if typep == 'event':
if hrf_model == "Canonical":
c = utils.define(
nc, utils.events(onsets, values, f=hrf.glover))
listc.append(c)
hnames.append(nc)
elif hrf_model == "Canonical With Derivative":
c1 = utils.define(
nc, utils.events(onsets, values, f=hrf.glover))
c2 = utils.define(nc + "_derivative",
utils.events(onsets, values, f=hrf.dglover))
listc.append(c1)
listc.append(c2)
hnames.append(nc)
hnames.append(nc + "_derivative")
elif hrf_model == "FIR":
for i, ft in enumerate(fir_delays):
lnames = nc + "_delay_%d" % i
changes = np.hstack((onsets + ft,
onsets + ft + fir_duration))
ochanges = np.argsort(changes)
lvalues = np.hstack((values, np.zeros(nos)))
changes = changes[ochanges]
lvalues = lvalues[ochanges]
c = utils.define(lnames,
utils.step_function(changes, lvalues))
listc.append(c)
hnames.append(lnames)
else:
raise NotImplementedError('unknown hrf model')
elif typep == 'block':
offsets = onsets + paradigm.duration[paradigm.con_id == nc]
intervals = [[on, off] for (on, off) in zip(onsets, offsets)]
blks = utils.blocks(intervals, values)
changes = np.hstack((onsets, offsets))
cvalues = np.hstack((values, - values))
if hrf_model == "Canonical":
c = utils.convolve_functions(blks, hrf.glover(hrf.T),
[0, end_time], 0.001)
listc.append(c)
hnames.append(nc)
elif hrf_model == "Canonical With Derivative":
c1 = utils.convolve_functions(blks, hrf.glover(hrf.T),
[0, end_time], 0.001)
c2 = utils.events(changes, cvalues, f=hrf.glover)
listc.append(c1)
listc.append(c2)
hnames.append(nc)
hnames.append(nc + "_derivative")
elif hrf_model == "FIR":
raise NotImplementedError(
'block design are not compatible with FIR')
else:
raise NotImplementedError('unknown hrf model')
# create the formula
p = formula.Formula(listc)
return p, hnames
