def ols(self):
"""
Compute the design matrices the matrices for OLS fitting and the OLS
solution. Cache them for reuse in each direction over all voxels.
"""
ols_weights = np.empty((len(self.rot_idx), self.n_canonicals + 1,
self._flat_signal.shape[0]))
iso_regressor, tensor_regressor, fit_to = self.regressors
where_are_we = 0
for row, idx in enumerate(self.rot_idx):
# 'row' refers to where we are in ols_weights
if self.verbose:
if idx[0] == where_are_we:
s = "Starting MultiCanonicalTensorModel fit"
s += " for %sth set of basis functions" % (where_are_we)
print(s)
where_are_we += 1
# The 'design matrix':
d = np.vstack([[tensor_regressor[i] for i in idx],
iso_regressor]).T
# This is $(X' X)^{-1} X':
ols_mat = ozu.ols_matrix(d)
# Multiply to find the OLS solution:
ols_weights[row] = np.array(np.dot(ols_mat, fit_to)).squeeze()
return ols_weights
def ls_fit_b(log_prop, unique_b):
"""
Does calculations for fitting a first order least squares solution to the
properties
Parameters
----------
log_prop: list
List of all the log of the desired property values
unique_b: 1 dimensional array
Array of all the unique b values found
Returns
-------
ls_fit: 1 dimensional array
An array with the results from the least squares fit
"""
if 0 in unique_b:
unique_b = unique_b[1:]
log_prop_matrix = np.matrix(log_prop)
b_matrix = np.matrix([unique_b, np.ones(len(unique_b))]).T
b_inv = utils.ols_matrix(b_matrix)
ls_fit = np.dot(b_inv, log_prop_matrix)
return ls_fit
def ols(self):
"""
Compute the design matrices the matrices for OLS fitting and the OLS
solution. Cache them for reuse in each direction over all voxels.
"""
ols_weights = np.empty((len(self.rot_idx),
self.n_canonicals + 1,
self._flat_signal.shape[0]))
iso_regressor, tensor_regressor, fit_to = self.regressors
where_are_we = 0
for row, idx in enumerate(self.rot_idx):
# 'row' refers to where we are in ols_weights
if self.verbose:
if idx[0]==where_are_we:
s = "Starting MultiCanonicalTensorModel fit"
s += " for %sth set of basis functions"%(where_are_we)
print (s)
where_are_we += 1
# The 'design matrix':
d = np.vstack([[tensor_regressor[i] for i in idx],
iso_regressor]).T
# This is $(X' X)^{-1} X':
ols_mat = ozu.ols_matrix(d)
# Multiply to find the OLS solution:
ols_weights[row] = np.array(np.dot(ols_mat, fit_to)).squeeze()
return ols_weights
def test_ls_fit_b():
log_prop_t = test_log_prop_vals()
b_matrix_t = np.matrix([[1,2], [1,1]]).T
b_inv = ols_matrix(b_matrix_t)
ls_fit_FA_t = np.dot(b_inv, np.matrix(log_prop_t))
npt.assert_equal(ls_fit_FA_t, mf.ls_fit_b(log_prop_t, unique_b_t))
return ls_fit_FA_t
def test_ols_matrix():
"""
Test that this really does OLS regression.
"""
# Parameters
beta = np.random.rand(10)
# Inputs
x = np.random.rand(100, 10)
# Outputs (noise-less!)
y = np.dot(x, beta)
# Estimate back:
ols_matrix = ozu.ols_matrix(x)
beta_hat = np.array(np.dot(ols_matrix, y)).squeeze()
# This should have recovered the original:
npt.assert_almost_equal(beta, beta_hat)
# Make sure that you can normalize and it gives you the same shape matrix:
npt.assert_almost_equal(ols_matrix.shape,
ozu.ols_matrix(x, norm_func=ozu.l2_norm).shape)
def test_ols_matrix():
"""
Test that this really does OLS regression.
"""
# Parameters
beta = np.random.rand(10)
# Inputs
x = np.random.rand(100,10)
# Outputs (noise-less!)
y = np.dot(x, beta)
# Estimate back:
ols_matrix = ozu.ols_matrix(x)
beta_hat = np.array(np.dot(ols_matrix, y)).squeeze()
# This should have recovered the original:
npt.assert_almost_equal(beta, beta_hat)
# Make sure that you can normalize and it gives you the same shape matrix:
npt.assert_almost_equal(ols_matrix.shape,
ozu.ols_matrix(x, norm_func=ozu.l2_norm).shape)
def test_ls_fit_b():
log_prop_t = test_log_prop_vals()
b_matrix_t = np.matrix([[1,2], [1,1]]).T
b_inv = ols_matrix(b_matrix_t)
ls_fit_FA_t = np.dot(b_inv, np.matrix(log_prop_t))
for idx in np.arange(len(ls_fit_FA_t)):
npt.assert_equal(abs(ls_fit_FA_t[idx]-mf.ls_fit_b(log_prop_t,
unique_b_t)[idx])<0.001, 1)
return ls_fit_FA_t
def ols(self):
"""
Compute the OLS solution.
"""
# Preallocate:
ols_weights = np.empty((self.rotations.shape[0], 2,
self._flat_signal.shape[0]))
iso_regressor, tensor_regressor, fit_to = self.regressors
for idx in xrange(ols_weights.shape[0]):
# The 'design matrix':
d = np.vstack([tensor_regressor[idx], iso_regressor]).T
# This is $(X' X)^{-1} X':
ols_mat = ozu.ols_matrix(d)
# Multiply to find the OLS solution (fitting to all the voxels in
# one fell swoop):
ols_weights[idx] = np.dot(ols_mat, fit_to)
# ols_weights[idx] = npla.lstsq(d, fit_to)[0]
return ols_weights
def ols(self):
"""
Compute the OLS solution.
"""
# Preallocate:
ols_weights = np.empty(
(self.rotations.shape[0], 2, self._flat_signal.shape[0]))
iso_regressor, tensor_regressor, fit_to = self.regressors
for idx in xrange(ols_weights.shape[0]):
# The 'design matrix':
d = np.vstack([tensor_regressor[idx], iso_regressor]).T
# This is $(X' X)^{-1} X':
ols_mat = ozu.ols_matrix(d)
# Multiply to find the OLS solution (fitting to all the voxels in
# one fell swoop):
ols_weights[idx] = np.dot(ols_mat, fit_to)
# ols_weights[idx] = npla.lstsq(d, fit_to)[0]
return ols_weights
