def kfold_xval_MD_mod(data, bvals, bvecs, mask, func, n, factor = 1000,
initial="preset", bounds = "preset", params_file='temp',
signal="relative_signal"):
"""
Finds the parameters of the given function to the given data
that minimizes the sum squared errors using kfold cross validation.
Parameters
----------
data: 4 dimensional array
Diffusion MRI data
bvals: 1 dimensional array
All b values
bvecs: 3 dimensional array
All the b vectors
mask: 3 dimensional array
Brain mask of the data
func: function handle
Mean model to perform kfold cross-validation on.
initial: tuple
Initial values for the parameters.
n: int
Integer indicating the percent of vertices that you want to predict
factor: int
Integer indicating the scaling factor for the b values
bounds: list
List containing tuples indicating the bounds for each parameter in
the mean model function.
Returns
-------
cod: 1 dimensional array
Coefficent of Determination between data and predicted values
predicted: 2 dimensional array
Predicted mean for the vertices left out of the fit
"""
if isinstance(func, str):
# Grab the function handle for the desired mean model
func = globals()[func]
# Get the initial values for the desired mean model
if (bounds == "preset") | (initial == "preset"):
all_params = initial_params(data, bvecs, bvals, func, mask=mask,
params_file=params_file)
if bounds == "preset":
bounds = all_params[0]
if initial == "preset":
func_initial = all_params[1]
else:
this_initial = initial
bval_list, b_inds, unique_b, rounded_bvals = ozu.separate_bvals(bvals)
all_b_idx, b0_inds = _diffusion_inds(bvals, b_inds, rounded_bvals)
b_scaled = bvals/factor
flat_data = data[np.where(mask)]
# Pre-allocate outputs
ss_err = np.zeros(int(np.sum(mask)))
predict_out = np.zeros((int(np.sum(mask)),len(all_b_idx)))
# Setting up for creating combinations of directions for kfold cross
# validation:
# Number of directions to leave out at a time.
num_choose = (n/100.)*len(all_b_idx)
# Find the indices to all the non-b = 0 directions and shuffle them.
vec_pool = np.arange(len(all_b_idx))
np.random.shuffle(vec_pool)
all_inc_0 = np.arange(len(rounded_bvals))
# Start cross-validation
for combo_num in np.arange(np.floor(100./n)):
(si, vec_combo, vec_combo_rm0,
vec_pool_inds, these_bvecs, these_bvals,
this_data, these_inc0) = ozu.create_combos(bvecs, bvals, data,
all_b_idx,
np.arange(len(all_b_idx)),
all_b_idx, vec_pool,
num_choose, combo_num)
this_flat_data = this_data[np.where(mask)]
for vox in np.arange(np.sum(mask)).astype(int):
s0 = np.mean(flat_data[vox, b0_inds], -1)
these_b = b_scaled[vec_combo] # b values to predict
if initial == "preset":
this_initial = func_initial[vox]
input_signal = flat_data[vox, these_inc0]/s0
if signal == "log":
input_signal = np.log(input_signal)
# Fit mean model to part of the data
params, _ = opt.leastsq(err_func, this_initial,
args=(b_scaled[these_inc0],
input_signal, func))
if bounds == None:
params, _ = opt.leastsq(err_func, this_initial,
args=(b_scaled[these_inc0],
input_signal, func))
else:
lsq_b_out = lsq.leastsqbound(err_func, this_initial,
args = (b_scaled[these_inc0],
input_signal, func),
bounds = bounds)
params = lsq_b_out[0]
# Predict the mean values of the left out b values using the
# parameters from fitting to part of the b values.
predict = func(these_b, *params)
predict_out[vox, vec_combo_rm0] = func(these_b, *params)
# Find the relative diffusion signal.
s0 = np.mean(flat_data[:, b0_inds], -1).astype(float)
input_signal = flat_data[:, all_b_idx]/s0[..., None]
if signal == "log":
input_signal = np.log(input_signal)
cod = ozu.coeff_of_determination(input_signal, predict_out, axis=-1)
return cod, predict_out
def kfold_xval_MD_mod(data,
bvals,
bvecs,
mask,
func,
n,
factor=1000,
initial="preset",
bounds="preset",
params_file='temp',
signal="relative_signal"):
"""
Finds the parameters of the given function to the given data
that minimizes the sum squared errors using kfold cross validation.
Parameters
----------
data: 4 dimensional array
Diffusion MRI data
bvals: 1 dimensional array
All b values
bvecs: 3 dimensional array
All the b vectors
mask: 3 dimensional array
Brain mask of the data
func: function handle
Mean model to perform kfold cross-validation on.
initial: tuple
Initial values for the parameters.
n: int
Integer indicating the percent of vertices that you want to predict
factor: int
Integer indicating the scaling factor for the b values
bounds: list
List containing tuples indicating the bounds for each parameter in
the mean model function.
Returns
-------
cod: 1 dimensional array
Coefficent of Determination between data and predicted values
predicted: 2 dimensional array
Predicted mean for the vertices left out of the fit
"""
if isinstance(func, str):
# Grab the function handle for the desired isotropic model
func = globals()[func]
# Get the initial values for the desired isotropic model
if (bounds == "preset") | (initial == "preset"):
all_params = initial_params(data,
bvecs,
bvals,
func,
mask=mask,
params_file=params_file)
if bounds == "preset":
bounds = all_params[0]
if initial == "preset":
func_initial = all_params[1]
else:
this_initial = initial
bval_list, b_inds, unique_b, rounded_bvals = ozu.separate_bvals(bvals)
all_b_idx, b0_inds = _diffusion_inds(bvals, b_inds, rounded_bvals)
b_scaled = bvals / factor
flat_data = data[np.where(mask)]
# Pre-allocate outputs
ss_err = np.zeros(int(np.sum(mask)))
predict_out = np.zeros((int(np.sum(mask)), len(all_b_idx)))
# Setting up for creating combinations of directions for kfold cross
# validation:
# Number of directions to leave out at a time.
num_choose = (n / 100.) * len(all_b_idx)
# Find the indices to all the non-b = 0 directions and shuffle them.
vec_pool = np.arange(len(all_b_idx))
np.random.shuffle(vec_pool)
all_inc_0 = np.arange(len(rounded_bvals))
# Start cross-validation
for combo_num in np.arange(np.floor(100. / n)):
(si, vec_combo, vec_combo_rm0, vec_pool_inds, these_bvecs, these_bvals,
this_data, these_inc0) = ozu.create_combos(bvecs, bvals, data,
all_b_idx,
np.arange(len(all_b_idx)),
all_b_idx, vec_pool,
num_choose, combo_num)
these_b = b_scaled[vec_combo] # b values to predict
for vox in np.arange(np.sum(mask)).astype(int):
s0 = np.mean(flat_data[vox, b0_inds], -1)
if initial == "preset":
this_initial = func_initial[vox]
input_signal = flat_data[vox, these_inc0] / s0
if signal == "log":
input_signal = np.log(input_signal)
# Fit mean model to part of the data
params, _ = opt.leastsq(err_func,
this_initial,
args=(b_scaled[these_inc0], input_signal,
func))
if bounds == None:
params, _ = opt.leastsq(err_func,
this_initial,
args=(b_scaled[these_inc0],
input_signal, func))
else:
lsq_b_out = lsq.leastsqbound(err_func,
this_initial,
args=(b_scaled[these_inc0],
input_signal, func),
bounds=bounds)
params = lsq_b_out[0]
predict_out[vox, vec_combo_rm0] = func(these_b, *params)
# Find the relative diffusion signal.
s0 = np.mean(flat_data[:, b0_inds], -1).astype(float)
input_signal = flat_data[:, all_b_idx] / s0[..., None]
if signal == "log":
input_signal = np.log(input_signal)
cod = ozu.coeff_of_determination(input_signal, predict_out, axis=-1)
return cod, predict_out
def isotropic_params(data, bvals, bvecs, mask, func, factor=1000,
initial="preset", bounds="preset", params_file='temp',
signal="relative_signal"):
"""
Finds the parameters of the given function to the given data
that minimizes the sum squared errors.
Parameters
----------
data: 4 dimensional array
Diffusion MRI data
bvals: 1 dimensional array
All b values
mask: 3 dimensional array
Brain mask of the data
func: str or callable
String indicating the mean model function to perform kfold
cross-validation on.
initial: tuple
Initial values for the parameters.
factor: int
Integer indicating the scaling factor for the b values
bounds: list
List containing tuples indicating the bounds for each parameter in
the mean model function.
Returns
-------
param_out: 2 dimensional array
Parameters that minimize the residuals
fit_out: 2 dimensional array
Model fitted means
ss_err: 2 dimensional array
Sum squared error between the model fitted means and the actual means
"""
if isinstance(func, str):
# Grab the function handle for the desired mean model
func = globals()[func]
# Get the initial values for the desired mean model
if (bounds == "preset") | (initial == "preset"):
all_params = initial_params(data, bvecs, bvals, func, mask=mask,
params_file=params_file)
if bounds == "preset":
bounds = all_params[0]
if initial == "preset":
func_initial = all_params[1]
else:
this_initial = initial
# Separate b values and grab their indices
bval_list, b_inds, unique_b, rounded_bvals = ozu.separate_bvals(bvals)
all_b_idx, b0_inds = _diffusion_inds(bvals, b_inds, rounded_bvals)
# Divide the b values by a scaling factor first.
b = bvals[all_b_idx]/factor
flat_data = data[np.where(mask)]
# Get the number of inputs to the mean diffusivity function
param_num = len(inspect.getargspec(func)[0])
# Pre-allocate the outputs:
param_out = np.zeros((int(np.sum(mask)), param_num - 1))
cod = ozu.nans(np.sum(mask))
fit_out = ozu.nans(cod.shape + (len(all_b_idx),))
for vox in np.arange(np.sum(mask)).astype(int):
s0 = np.mean(flat_data[vox, b0_inds], -1)
if initial == "preset":
this_initial = func_initial[vox]
input_signal = flat_data[vox, all_b_idx]/s0
if signal == "log":
input_signal = np.log(input_signal)
if bounds == None:
params, _ = opt.leastsq(err_func, this_initial, args=(b,
input_signal, func))
else:
lsq_b_out = lsq.leastsqbound(err_func, this_initial,
args=(b, input_signal, func),
bounds = bounds)
params = lsq_b_out[0]
param_out[vox] = np.squeeze(params)
fit_out[vox] = func(b, *params)
cod[vox] = ozu.coeff_of_determination(input_signal, fit_out[vox])
return param_out, fit_out, cod
def isotropic_params(data,
bvals,
bvecs,
mask,
func,
factor=1000,
initial="preset",
bounds="preset",
params_file='temp',
signal="relative_signal"):
"""
Finds the parameters of the given function to the given data
that minimizes the sum squared errors.
Parameters
----------
data: 4 dimensional array
Diffusion MRI data
bvals: 1 dimensional array
All b values
mask: 3 dimensional array
Brain mask of the data
func: str or callable
String indicating the mean model function to perform kfold
cross-validation on.
initial: tuple
Initial values for the parameters.
factor: int
Integer indicating the scaling factor for the b values
bounds: list
List containing tuples indicating the bounds for each parameter in
the mean model function.
Returns
-------
param_out: 2 dimensional array
Parameters that minimize the residuals
fit_out: 2 dimensional array
Model fitted means
ss_err: 2 dimensional array
Sum squared error between the model fitted means and the actual means
"""
if isinstance(func, str):
# Grab the function handle for the desired mean model
func = globals()[func]
# Get the initial values for the desired mean model
if (bounds == "preset") | (initial == "preset"):
all_params = initial_params(data,
bvecs,
bvals,
func,
mask=mask,
params_file=params_file)
if bounds == "preset":
bounds = all_params[0]
if initial == "preset":
func_initial = all_params[1]
else:
this_initial = initial
# Separate b values and grab their indices
bval_list, b_inds, unique_b, rounded_bvals = ozu.separate_bvals(bvals)
all_b_idx, b0_inds = _diffusion_inds(bvals, b_inds, rounded_bvals)
# Divide the b values by a scaling factor first.
b = bvals[all_b_idx] / factor
flat_data = data[np.where(mask)]
# Get the number of inputs to the mean diffusivity function
param_num = len(inspect.getargspec(func)[0])
# Pre-allocate the outputs:
param_out = np.zeros((int(np.sum(mask)), param_num - 1))
cod = ozu.nans(np.sum(mask))
fit_out = ozu.nans(cod.shape + (len(all_b_idx), ))
prog_bar = ozu.ProgressBar(flat_data.shape[0])
for vox in np.arange(np.sum(mask)).astype(int):
prog_bar.animate(vox)
s0 = np.mean(flat_data[vox, b0_inds], -1)
if initial == "preset":
this_initial = func_initial[vox]
input_signal = flat_data[vox, all_b_idx] / s0
if signal == "log":
input_signal = np.log(input_signal)
if bounds == None:
params, _ = opt.leastsq(err_func,
this_initial,
args=(b, input_signal, func))
else:
lsq_b_out = lsq.leastsqbound(err_func,
this_initial,
args=(b, input_signal, func),
bounds=bounds)
params = lsq_b_out[0]
param_out[vox] = np.squeeze(params)
fit_out[vox] = func(b, *params)
cod[vox] = ozu.coeff_of_determination(input_signal, fit_out[vox])
return param_out, fit_out, cod