def fourier_basis(t, freq):
"""
Create a design matrix with columns given by the Fourier
basis with a given set of frequencies.
Parameters
----------
t : np.ndarray
An array of np.float values at which to evaluate
the design. Common examples would be the acquisition
times of an fMRI image.
freq : [float]
Frequencies for the terms in the Fourier basis.
Returns
-------
X : np.ndarray
Examples
--------
>>> t = np.linspace(0,50,101)
>>> drift = fourier_basis(t, np.array([4,6,8]))
>>> drift.shape
(101, 6)
>>>
"""
tval = formula.make_recarray(t, ['t'])
f = fourier_basis_sym(freq)
return f.design(tval, return_float=True)
def natural_spline(t, knots=None, order=3, intercept=True):
"""
Create a design matrix with columns given by a
natural spline of a given order and a specified set of knots.
Parameters
----------
t : np.array
knots : None or sequence, optional
Sequence of float. Default None (same as empty list)
order : int, optional
Order of the spline. Defaults to a cubic (==3)
intercept : bool, optional
If True, include a constant function in the natural
spline. Default is False
Returns
-------
X : np.ndarray
Examples
--------
>>> t = np.linspace(0,50,101)
>>> drift = natural_spline(t, knots=[10,20,30,40])
>>> drift.shape
(101, 8)
>>>
"""
tval = formula.make_recarray(t, ['t'])
t = formula.Term('t')
f = formula.natural_spline(t, knots=knots, order=order,
intercept=intercept)
return f.design(tval, return_float=True)
def event_design(event_spec, t, order=2, hrfs=[glover]):
"""
Create a design matrix for a GLM analysis based
on an event specification, evaluating
it a sequence of time values. Each column
in the design matrix will be convolved with each HRF in hrfs.
Parameters
----------
event_spec : np.recarray
A recarray having at least a field named 'time' signifying
the event time, and all other fields will be treated as factors
in an ANOVA-type model.
t : np.ndarray
An array of np.float values at which to evaluate
the design. Common examples would be the acquisition
times of an fMRI image.
order : int
The highest order interaction to be considered in
constructing the contrast matrices.
hrfs : seq
A sequence of (symbolic) HRF that will be convolved
with each event. If empty, glover is used.
Outputs
-------
X : np.ndarray
The design matrix with X.shape[0] == t.shape[0]. The number
of columns will depend on the other fields of event_spec.
contrasts : dict
Dictionary of contrasts that is expected to be of interest
from the event specification. For each interaction / effect
up to a given order will be returned. Also, a contrast
is generated for each interaction / effect for each HRF
specified in hrfs.
"""
fields = list(event_spec.dtype.names)
if 'time' not in fields:
raise ValueError('expecting a field called "time"')
fields.pop(fields.index('time'))
e_factors = [formula.Factor(n, np.unique(event_spec[n])) for n in fields]
e_formula = np.product(e_factors)
e_contrasts = {}
if len(e_factors) > 1:
for i in range(1, order+1):
for comb in combinations(zip(fields, e_factors), i):
names = [c[0] for c in comb]
fs = [c[1].main_effect for c in comb]
e_contrasts[sjoin(names, ':')] = np.product(fs).design(event_spec)
e_contrasts['constant'] = formula.I.design(event_spec)
# Design and contrasts in event space
# TODO: make it so I don't have to call design twice here
# to get both the contrasts and the e_X matrix as a recarray
e_X = e_formula.design(event_spec)
e_dtype = e_formula.dtype
# Now construct the design in time space
t_terms = []
t_contrasts = {}
for l, h in enumerate(hrfs):
t_terms += [events(event_spec['time'], \
amplitudes=e_X[n], f=h) for i, n in enumerate(e_dtype.names)]
for n, c in e_contrasts.items():
t_contrasts["%s_%d" % (n, l)] = formula.Formula([ \
events(event_spec['time'], amplitudes=c[nn], f=h) for i, nn in enumerate(c.dtype.names)])
t_formula = formula.Formula(t_terms)
tval = formula.make_recarray(t, ['t'])
X_t, c_t = t_formula.design(tval, contrasts=t_contrasts)
return X_t, c_t