def _blankdrift():
"""
Create the blank drift formula
Returns
-------
df a formula that contains a constant regressor
"""
t = formula.Term('t')
pt = [formula.define('constant',1.0+0*t)]
df = formula.Formula(pt)
return df
def test_define():
t = F.Term('t')
expr = sympy.exp(3*t)
yield assert_equal, str(expr), 'exp(3*t)'
newf = F.define('f', expr)
yield assert_equal, str(newf), 'f(t)'
f = aliased.lambdify(t, newf)
tval = np.random.standard_normal((3,))
yield assert_almost_equal, np.exp(3*tval), f(tval)
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(formula.define('poly_drift_%d'%(k+1),t**(k+1)/tmax**(k+1)))
pt.append(formula.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) * utils.sympy_cos(np.pi*(t/tmax+ 0.5/tsteps)*k )
pt.append(formula.define('cosine_drift_%d'%(k+1),u))
pt.append(formula.define('constant',1.0+0*t))
cos = formula.Formula(pt)
return cos
the amount of time since the last stimulus
T[i-1]
"""
import numpy as np
import nipy.testing as niptest
import sympy
from nipy.modalities.fmri import utils, formula, hrf
dt = np.random.uniform(low=0, high=2.5, size=(50,))
t = np.cumsum(dt)
a = sympy.Symbol('a')
linear = formula.define('linear', utils.events(t, dt, f=hrf.glover))
quadratic = formula.define('quad', utils.events(t, dt, f=hrf.glover, g=a**2))
cubic = formula.define('cubic', utils.events(t, dt, f=hrf.glover, g=a**3))
f1 = formula.Formula([linear, quadratic, cubic])
# Evaluate them
tval = formula.make_recarray(np.linspace(0,100, 1001), 't')
X1 = f1.design(tval, return_float=True)
# Let's make it 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.Formula([exponential])
the amount of time since the last stimulus
T[i-1]
"""
import numpy as np
import nipy.testing as niptest
import sympy
from nipy.modalities.fmri import utils, formula, hrf
dt = np.random.uniform(low=0, high=2.5, size=(50,))
t = np.cumsum(dt)
a = sympy.Symbol("a")
linear = formula.define("linear", utils.events(t, dt, f=hrf.glover))
quadratic = formula.define("quad", utils.events(t, dt, f=hrf.glover, g=a ** 2))
cubic = formula.define("cubic", utils.events(t, dt, f=hrf.glover, g=a ** 3))
f1 = formula.Formula([linear, quadratic, cubic])
# Evaluate them
tval = formula.make_recarray(np.linspace(0, 100, 1001), "t")
X1 = f1.design(tval, return_float=True)
# Let's make it 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.Formula([exponential])
def convolve_regressors(paradigm, hrf_model, names=None, fir_delays=[0],
fir_duration = 1.):
"""
Creation of a formula that represents
the convolution of the conditions onset witha certain hrf model
Parameters
----------
paradigm array of shape (nevents,2) if the type is event-related design
or (nenvets,3) for a block design
that contains (condition id, onset) or
(condition id, onset, duration)
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 ?
"""
paradigm = np.asarray(paradigm)
if paradigm.ndim !=2:
raise ValueError('Paradigm should have 2 dimensions')
ncond = int(paradigm[:,0].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 = []
if paradigm.shape[1]>2:
typep = 'block'
else:
typep='event'
for nc in range(ncond):
onsets = paradigm[paradigm[:,0]==nc,1]
nos = np.size(onsets)
if nos>0:
if typep=='event':
if hrf_model=="Canonical":
c = formula.define(names[nc], utils.events(onsets, f=hrf.glover))
listc.append(c)
hnames.append(names[nc])
elif hrf_model=="Canonical With Derivative":
c1 = formula.define(names[nc],
utils.events(onsets, f=hrf.glover))
c2 = formula.define(names[nc]+"_derivative",
utils.events(onsets, 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)
values = np.hstack((np.ones(nos), np.zeros(nos)))
changes = changes[ochanges]
values = values[ochanges]
c = formula.define(lnames, utils.step_function(changes,values))
listc.append(c)
hnames.append(lnames)
else:
raise NotImplementedError,'unknown hrf model'
elif typep=='block':
offsets = onsets+paradigm[paradigm[:,0]==nc,2]
changes = np.hstack((onsets,offsets))
values = np.hstack((np.ones(nos), -np.ones(nos)))
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'
else:
raise NotImplementedError,'unknown type of paradigm'
# create the formula
p = formula.Formula(listc)
return p, hnames
def protocol(fh, design_type, *hrfs):
"""
Create an object that can evaluate the FIAC.
Subclass of formula.Formula, but not necessary.
Parameters:
-----------
fh : file handler
File-like object that reads in the FIAC design,
i.e. like file('subj1_evt_fonc3.txt')
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.
Outputs:
--------
f: Formula
Formula for constructing design matrices.
contrasts : dict
Dictionary of the contrasts of the experiment.
"""
eventdict = {1: "SSt_SSp", 2: "SSt_DSp", 3: "DSt_SSp", 4: "DSt_DSp"}
fh = fh.read().strip().splitlines()
times = []
events = []
for row in fh:
time, eventtype = map(float, row.split())
times.append(time)
events.append(eventdict[eventtype])
if design_type == "block":
keep = np.not_equal((np.arange(len(times))) % 6, 0)
else:
keep = np.greater(np.arange(len(times)), 0)
# This first frame was used to model out a potentially
# 'bad' first frame....
_begin = np.array(times)[~keep]
termdict = {}
termdict["begin"] = formula.define("begin", utils.events(_begin, f=hrf.glover))
drift = formula.natural_spline(hrf.t, knots=[191 / 2.0 + 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 = np.array(times)[keep]
events = np.array(events)[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 eventdict.values():
for l, h in enumerate(hrfs):
k = np.array([events[i] == v for i in range(times.shape[0])])
termdict["%s%d" % (v, l)] = formula.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"]
) / 4.0
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(fh, design_type, *hrfs):
"""
Create an object that can evaluate the FIAC.
Subclass of formula.Formula, but not necessary.
Parameters:
-----------
fh : file handler
File-like object that reads in the FIAC design,
but has a different format (test_FIACdata.altdescr)
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.
"""
d = csv2rec(fh)
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"] = formula.define("begin", utils.events(_begin, f=hrf.glover))
drift = formula.natural_spline(hrf.t, knots=[191 / 2.0 + 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)] = formula.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