direction

Returns a process pool object

Deprecate a renamed or removed function argument.

The decorator assumes that the argument with the old_name was removed from the function signature and the new_name replaced it at the same position in the signature. If the old_name argument is given when calling the decorated function the decorator will catch it and issue a deprecation warning and pass it on as new_name argument.

Parameters

old_namestr or list/tuple thereof

The old name of the argument.

new_namestr or list/tuple thereof or None, optional

The new name of the argument. Set this to None to remove the argument old_name instead of renaming it.

sincestr or number or list/tuple thereof, optional

The release at which the old argument became deprecated.

untilstr or number or list/tuple thereof, optional

Last released version at which this function will still raise a deprecation warning. Versions higher than this will raise an error.

version_comparatorcallable

Callable accepting string as argument, and return 1 if string represents a higher version than encoded in the version_comparator, 0 if the version is equal, and -1 if the version is lower. For example, the version_comparator may compare the input version string to the current package version string.

arg_in_kwargsbool or list/tuple thereof, optional

If the argument is not a named argument (for example it was meant to be consumed by **kwargs) set this to True. Otherwise the decorator will throw an Exception if the new_name cannot be found in the signature of the decorated function. Default is False.

warn_classwarning, optional

Warning to be issued.

error_classException, optional

Error to be issued

alternativestr, optional

An alternative function or class name that the user may use in place of the deprecated object if new_name is None. The deprecation warning will tell the user about this alternative if provided.

Raises

TypeError

If the new argument name cannot be found in the function signature and arg_in_kwargs was False or if it is used to deprecate the name of the *args-, **kwargs-like arguments. At runtime such an Error is raised if both the new_name and old_name were specified when calling the function and “relax=False”.

Notes

This function is based on the Astropy (major modification). https://github.com/astropy/astropy. See COPYING file distributed along with the astropy package for the copyright and license terms.

Examples

The deprecation warnings are not shown in the following examples. To deprecate a positional or keyword argument:: >>> from dipy.utils.deprecator import deprecated_params >>> @deprecated_params(‘sig’, ‘sigma’, ‘0.3’) … def test(sigma): … return sigma >>> test(2) 2 >>> test(sigma=2) 2 >>> test(sig=2) # doctest: +SKIP 2

It is also possible to replace multiple arguments. The old_name, new_name and since have to be tuple or list and contain the same number of entries:: >>> @deprecated_params([‘a’, ‘b’], [‘alpha’, ‘beta’], … [‘0.2’, 0.4]) … def test(alpha, beta): … return alpha, beta >>> test(a=2, b=3) # doctest: +SKIP (2, 3)

Determine the effective number of processes for parallelization.

• For num_processes = None` return the maximum number of cores retrieved

by cpu_count().

• For num_processes > 0, return this value.

• For num_processes < 0, return the maximal number of cores minus

num_processes + 1. In particular num_processes = -1 will use as many cores as possible.

• For num_processes = 0 a ValueError is raised.

Parameters

num_processesint or None

Desired number of processes to be used.

The general fractional anisotropy of a function evaluated on the unit sphere

Parameters

samplesndarray

Values of data on the unit sphere.

Returns

gfandarray

GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain all-zeros in samples.

Notes

The GFA is defined as [1]

\sqrt{\frac{n \sum_i{(\Psi_i - <\Psi>)^2}}{(n-1) \sum{\Psi_i ^ 2}}}

Where \(\Psi\) is an orientation distribution function sampled discretely on the unit sphere and angle brackets denote average over the samples on the sphere.

1

Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Q-ball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 1194-1208.

Local maxima of a function evaluated on a discrete set of points.

If a function is evaluated on some set of points where each pair of neighboring points is an edge in edges, find the local maxima.

Parameters

odfarray, 1d, dtype=double

The function evaluated on a set of discrete points.

edgesarray (N, 2)

The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.

Returns

peak_valuesndarray

Value of odf at a maximum point. Peak values is sorted in descending order.

peak_indicesndarray

Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].

Notes

A point is a local maximum if it is > at least one neighbor and >= all neighbors. If no points meet the above criteria, 1 maximum is returned such that odf[maximum] == max(odf).

An N-dimensional iterator object to index arrays.

Given the shape of an array, an ndindex instance iterates over the N-dimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.

Parameters

shapetuple of ints

The dimensions of the array.

Examples

>>> from dipy.core.ndindex import ndindex
>>> shape = (3, 2, 1)
>>> for index in ndindex(shape):
...     print(index)
(0, 0, 0)
(0, 1, 0)
(1, 0, 0)
(1, 1, 0)
(2, 0, 0)
(2, 1, 0)

Get the directions of odf peaks.

Peaks are defined as points on the odf that are greater than at least one neighbor and greater than or equal to all neighbors. Peaks are sorted in descending order by their values then filtered based on their relative size and spacing on the sphere. An odf may have 0 peaks, for example if the odf is perfectly isotropic.

Parameters

odf1d ndarray

The odf function evaluated on the vertices of sphere

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat in [0., 1.]

Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray

N vertices for sphere, one for each peak

values(N,) ndarray

peak values

indices(N,) ndarray

peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.

Non Linear Direction Finder.

Parameters

sphere_evalcallable

A function which can be evaluated on a sphere.

relative_peak_thresholdfloat

Only return peaks greater than relative_peak_threshold * m where m is the largest peak.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

sphereSphere

A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.

xtolfloat

Relative tolerance for optimization.

Returns

directionsarray (N, 3)

Points on the sphere corresponding to N local maxima on the sphere.

valuesarray (N,)

Value of sphere_eval at each point on directions.

Fit the model to data and computes peaks and metrics

Parameters

modela model instance

model will be used to fit the data.

datandarray

Diffusion data.

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat

Only return peaks greater than relative_peak_threshold * m where m is the largest peak.

min_separation_anglefloat in [0, 90] The minimum distance between

directions. If two peaks are too close only the larger of the two is returned.

maskarray, optional

If mask is provided, voxels that are False in mask are skipped and no peaks are returned.

return_odfbool

If True, the odfs are returned.

return_shbool

If True, the odf as spherical harmonics coefficients is returned

gfa_thrfloat

Voxels with gfa less than gfa_thr are skipped, no peaks are returned.

normalize_peaksbool

If true, all peak values are calculated relative to max(odf).

sh_orderint, optional

Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients (default 8).

sh_basis_type{None, ‘tournier07’, ‘descoteaux07’}

None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).

npeaksint

Maximum number of peaks found (default 5 peaks).

Bndarray, optional

Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).

invBndarray, optional

Inverse of B.

parallel: bool

If True, use multiprocessing to compute peaks and metric (default False). Temporary files are saved in the default temporary directory of the system. It can be changed using import tempfile and tempfile.tempdir = '/path/to/tempdir'.

num_processes: int, optional

If parallel is True, the number of subprocesses to use (default multiprocessing.cpu_count()). If < 0 the maximal number of cores minus num_processes + 1 is used (enter -1 to use as many cores as possible). 0 raises an error.

Returns

pamPeaksAndMetrics

An object with gfa, peak_directions, peak_values, peak_indices, odf, shm_coeffs as attributes

References

1

Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.

2

Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

Remove vertices that are less than theta degrees from any other

Returns vertices that are at least theta degrees from any other vertex. Vertex v and -v are considered the same so if v and -v are both in vertices only one is kept. Also if v and w are both in vertices, w must be separated by theta degrees from both v and -v to be unique.

Parameters

vertices(N, 3) ndarray

N unit vectors.

thetafloat

The minimum separation between vertices in degrees.

return_mapping{False, True}, optional

If True, return mapping as well as vertices and maybe indices (see below).

return_indices{False, True}, optional

If True, return indices as well as vertices and maybe mapping (see below).

Returns

unique_vertices(M, 3) ndarray

Vertices sufficiently separated from one another.

mapping(N,) ndarray

For each element vertices[i] (\(i \in 0..N-1\)), the index \(j\) to a vertex in unique_vertices that is less than theta degrees from vertices[i]. Only returned if return_mapping is True.

indices(N,) ndarray

indices gives the reverse of mapping. For each element unique_vertices[j] (\(j \in 0..M-1\)), the index \(i\) to a vertex in vertices that is less than theta degrees from unique_vertices[j]. If there is more than one element of vertices that is less than theta degrees from unique_vertices[j], return the first (lowest index) matching value. Only return if return_indices is True.

Reshape peaks for visualization.

Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.

Parameters

peaks: nd array (…, N, 3) or PeaksAndMetrics object

The peaks to be reshaped and converted to float32.

Returns

peaksnd array (…, 3*N)

i in descending array a so a[i] < a[0] * relative_threshold

Call T = a[0] * relative_threshold. Return value i will be the smallest index in the descending array a such that a[i] < T. Equivalently, i will be the largest index such that all(a[:i] >= T). If all values in a are >= T, return the length of array a.

Parameters

andarray, ndim=1, c-contiguous

Array to be searched. We assume a is in descending order.

relative_thresholdfloat

Applied threshold will be T with T = a[0] * relative_threshold.

Returns

inp.intp

If T = a[0] * relative_threshold then i will be the largest index such that all(a[:i] >= T). If all values in a are >= T then i will be len(a).

Examples

>>> a = np.arange(10, 0, -1, dtype=float)
>>> a
array([ 10.,   9.,   8.,   7.,   6.,   5.,   4.,   3.,   2.,   1.])
>>> search_descending(a, 0.5)
6
>>> a < 10 * 0.5
array([False, False, False, False, False, False,  True,  True,  True,  True], dtype=bool)
>>> search_descending(a, 1)
1
>>> search_descending(a, 2)
0
>>> search_descending(a, 0)
10

Matrix that transforms Spherical harmonics (SH) to spherical function (SF).

Parameters

sphereSphere

The points on which to sample the spherical function.

sh_orderint, optional

Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients for a symmetric basis and (sh_order + 1) * (sh_order + 1) coefficients for a full SH basis.

basis_type{None, ‘tournier07’, ‘descoteaux07’}, optional

None for the default DIPY basis, tournier07 for the Tournier 2007 [R0296267dba6e-2]_[R0296267dba6e-3]_ basis, descoteaux07 for the Descoteaux 2007 [1] basis, (None defaults to descoteaux07).

full_basis: bool, optional

If True, uses a SH basis containing even and odd order SH functions. Else, uses a SH basis consisting only of even order SH functions.

legacy: bool, optional

True to use a legacy basis definition for backward compatibility with previous tournier07 and descoteaux07 implementations.

return_invbool, optional

If True then the inverse of the matrix is also returned.

smoothfloat, optional

Lambda-regularization in the SH fit.

Returns

Bndarray

Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).

invBndarray

Inverse of B.

References

1

Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.

2

Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

3

Tournier J-D, Smith R, Raffelt D, Tabbara R, Dhollander T, Pietsch M, et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage. 2019 Nov 15;202:116-137.

Get the directions of odf peaks.

Peaks are defined as points on the odf that are greater than at least one neighbor and greater than or equal to all neighbors. Peaks are sorted in descending order by their values then filtered based on their relative size and spacing on the sphere. An odf may have 0 peaks, for example if the odf is perfectly isotropic.

Parameters

odf1d ndarray

The odf function evaluated on the vertices of sphere

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat in [0., 1.]

Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray

N vertices for sphere, one for each peak

values(N,) ndarray

peak values

indices(N,) ndarray

peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.

Returns a process pool object

Deprecate a renamed or removed function argument.

The decorator assumes that the argument with the old_name was removed from the function signature and the new_name replaced it at the same position in the signature. If the old_name argument is given when calling the decorated function the decorator will catch it and issue a deprecation warning and pass it on as new_name argument.

Parameters

old_namestr or list/tuple thereof

The old name of the argument.

new_namestr or list/tuple thereof or None, optional

The new name of the argument. Set this to None to remove the argument old_name instead of renaming it.

sincestr or number or list/tuple thereof, optional

The release at which the old argument became deprecated.

untilstr or number or list/tuple thereof, optional

Last released version at which this function will still raise a deprecation warning. Versions higher than this will raise an error.

version_comparatorcallable

Callable accepting string as argument, and return 1 if string represents a higher version than encoded in the version_comparator, 0 if the version is equal, and -1 if the version is lower. For example, the version_comparator may compare the input version string to the current package version string.

arg_in_kwargsbool or list/tuple thereof, optional

If the argument is not a named argument (for example it was meant to be consumed by **kwargs) set this to True. Otherwise the decorator will throw an Exception if the new_name cannot be found in the signature of the decorated function. Default is False.

warn_classwarning, optional

Warning to be issued.

error_classException, optional

Error to be issued

alternativestr, optional

An alternative function or class name that the user may use in place of the deprecated object if new_name is None. The deprecation warning will tell the user about this alternative if provided.

Raises

TypeError

If the new argument name cannot be found in the function signature and arg_in_kwargs was False or if it is used to deprecate the name of the *args-, **kwargs-like arguments. At runtime such an Error is raised if both the new_name and old_name were specified when calling the function and “relax=False”.

Notes

This function is based on the Astropy (major modification). https://github.com/astropy/astropy. See COPYING file distributed along with the astropy package for the copyright and license terms.

Examples

The deprecation warnings are not shown in the following examples. To deprecate a positional or keyword argument:: >>> from dipy.utils.deprecator import deprecated_params >>> @deprecated_params(‘sig’, ‘sigma’, ‘0.3’) … def test(sigma): … return sigma >>> test(2) 2 >>> test(sigma=2) 2 >>> test(sig=2) # doctest: +SKIP 2

It is also possible to replace multiple arguments. The old_name, new_name and since have to be tuple or list and contain the same number of entries:: >>> @deprecated_params([‘a’, ‘b’], [‘alpha’, ‘beta’], … [‘0.2’, 0.4]) … def test(alpha, beta): … return alpha, beta >>> test(a=2, b=3) # doctest: +SKIP (2, 3)

Determine the effective number of processes for parallelization.

• For num_processes = None` return the maximum number of cores retrieved

by cpu_count().

• For num_processes > 0, return this value.

• For num_processes < 0, return the maximal number of cores minus

num_processes + 1. In particular num_processes = -1 will use as many cores as possible.

• For num_processes = 0 a ValueError is raised.

Parameters

num_processesint or None

Desired number of processes to be used.

The general fractional anisotropy of a function evaluated on the unit sphere

Parameters

samplesndarray

Values of data on the unit sphere.

Returns

gfandarray

GFA evaluated in each entry of the array, along the last dimension. An np.nan is returned for coordinates that contain all-zeros in samples.

Notes

The GFA is defined as [1]

\sqrt{\frac{n \sum_i{(\Psi_i - <\Psi>)^2}}{(n-1) \sum{\Psi_i ^ 2}}}

Where \(\Psi\) is an orientation distribution function sampled discretely on the unit sphere and angle brackets denote average over the samples on the sphere.

1

Quality assessment of High Angular Resolution Diffusion Imaging data using bootstrap on Q-ball reconstruction. J. Cohen Adad, M. Descoteaux, L.L. Wald. JMRI 33: 1194-1208.

Local maxima of a function evaluated on a discrete set of points.

If a function is evaluated on some set of points where each pair of neighboring points is an edge in edges, find the local maxima.

Parameters

odfarray, 1d, dtype=double

The function evaluated on a set of discrete points.

edgesarray (N, 2)

The set of neighbor relations between the points. Every edge, ie edges[i, :], is a pair of neighboring points.

Returns

peak_valuesndarray

Value of odf at a maximum point. Peak values is sorted in descending order.

peak_indicesndarray

Indices of maximum points. Sorted in the same order as peak_values so odf[peak_indices[i]] == peak_values[i].

Notes

A point is a local maximum if it is > at least one neighbor and >= all neighbors. If no points meet the above criteria, 1 maximum is returned such that odf[maximum] == max(odf).

An N-dimensional iterator object to index arrays.

Given the shape of an array, an ndindex instance iterates over the N-dimensional index of the array. At each iteration a tuple of indices is returned; the last dimension is iterated over first.

Parameters

shapetuple of ints

The dimensions of the array.

Examples

>>> from dipy.core.ndindex import ndindex
>>> shape = (3, 2, 1)
>>> for index in ndindex(shape):
...     print(index)
(0, 0, 0)
(0, 1, 0)
(1, 0, 0)
(1, 1, 0)
(2, 0, 0)
(2, 1, 0)

Get the directions of odf peaks.

Peaks are defined as points on the odf that are greater than at least one neighbor and greater than or equal to all neighbors. Peaks are sorted in descending order by their values then filtered based on their relative size and spacing on the sphere. An odf may have 0 peaks, for example if the odf is perfectly isotropic.

Parameters

odf1d ndarray

The odf function evaluated on the vertices of sphere

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat in [0., 1.]

Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray

N vertices for sphere, one for each peak

values(N,) ndarray

peak values

indices(N,) ndarray

peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.

Non Linear Direction Finder.

Parameters

sphere_evalcallable

A function which can be evaluated on a sphere.

relative_peak_thresholdfloat

Only return peaks greater than relative_peak_threshold * m where m is the largest peak.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

sphereSphere

A discrete Sphere. The points on the sphere will be used for initial estimate of maximums.

xtolfloat

Relative tolerance for optimization.

Returns

directionsarray (N, 3)

Points on the sphere corresponding to N local maxima on the sphere.

valuesarray (N,)

Value of sphere_eval at each point on directions.

Fit the model to data and computes peaks and metrics

Parameters

modela model instance

model will be used to fit the data.

datandarray

Diffusion data.

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat

Only return peaks greater than relative_peak_threshold * m where m is the largest peak.

min_separation_anglefloat in [0, 90] The minimum distance between

directions. If two peaks are too close only the larger of the two is returned.

maskarray, optional

If mask is provided, voxels that are False in mask are skipped and no peaks are returned.

return_odfbool

If True, the odfs are returned.

return_shbool

If True, the odf as spherical harmonics coefficients is returned

gfa_thrfloat

Voxels with gfa less than gfa_thr are skipped, no peaks are returned.

normalize_peaksbool

If true, all peak values are calculated relative to max(odf).

sh_orderint, optional

Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients (default 8).

sh_basis_type{None, ‘tournier07’, ‘descoteaux07’}

None for the default DIPY basis, tournier07 for the Tournier 2007 [2] basis, and descoteaux07 for the Descoteaux 2007 [1] basis (None defaults to descoteaux07).

npeaksint

Maximum number of peaks found (default 5 peaks).

Bndarray, optional

Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).

invBndarray, optional

Inverse of B.

parallel: bool

If True, use multiprocessing to compute peaks and metric (default False). Temporary files are saved in the default temporary directory of the system. It can be changed using import tempfile and tempfile.tempdir = '/path/to/tempdir'.

num_processes: int, optional

If parallel is True, the number of subprocesses to use (default multiprocessing.cpu_count()). If < 0 the maximal number of cores minus num_processes + 1 is used (enter -1 to use as many cores as possible). 0 raises an error.

Returns

pamPeaksAndMetrics

An object with gfa, peak_directions, peak_values, peak_indices, odf, shm_coeffs as attributes

References

1

Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.

2

Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

Remove vertices that are less than theta degrees from any other

Returns vertices that are at least theta degrees from any other vertex. Vertex v and -v are considered the same so if v and -v are both in vertices only one is kept. Also if v and w are both in vertices, w must be separated by theta degrees from both v and -v to be unique.

Parameters

vertices(N, 3) ndarray

N unit vectors.

thetafloat

The minimum separation between vertices in degrees.

return_mapping{False, True}, optional

If True, return mapping as well as vertices and maybe indices (see below).

return_indices{False, True}, optional

If True, return indices as well as vertices and maybe mapping (see below).

Returns

unique_vertices(M, 3) ndarray

Vertices sufficiently separated from one another.

mapping(N,) ndarray

For each element vertices[i] (\(i \in 0..N-1\)), the index \(j\) to a vertex in unique_vertices that is less than theta degrees from vertices[i]. Only returned if return_mapping is True.

indices(N,) ndarray

indices gives the reverse of mapping. For each element unique_vertices[j] (\(j \in 0..M-1\)), the index \(i\) to a vertex in vertices that is less than theta degrees from unique_vertices[j]. If there is more than one element of vertices that is less than theta degrees from unique_vertices[j], return the first (lowest index) matching value. Only return if return_indices is True.

Reshape peaks for visualization.

Reshape and convert to float32 a set of peaks for visualisation with mrtrix or the fibernavigator.

Parameters

peaks: nd array (…, N, 3) or PeaksAndMetrics object

The peaks to be reshaped and converted to float32.

Returns

peaksnd array (…, 3*N)

i in descending array a so a[i] < a[0] * relative_threshold

Call T = a[0] * relative_threshold. Return value i will be the smallest index in the descending array a such that a[i] < T. Equivalently, i will be the largest index such that all(a[:i] >= T). If all values in a are >= T, return the length of array a.

Parameters

andarray, ndim=1, c-contiguous

Array to be searched. We assume a is in descending order.

relative_thresholdfloat

Applied threshold will be T with T = a[0] * relative_threshold.

Returns

inp.intp

If T = a[0] * relative_threshold then i will be the largest index such that all(a[:i] >= T). If all values in a are >= T then i will be len(a).

Examples

>>> a = np.arange(10, 0, -1, dtype=float)
>>> a
array([ 10.,   9.,   8.,   7.,   6.,   5.,   4.,   3.,   2.,   1.])
>>> search_descending(a, 0.5)
6
>>> a < 10 * 0.5
array([False, False, False, False, False, False,  True,  True,  True,  True], dtype=bool)
>>> search_descending(a, 1)
1
>>> search_descending(a, 2)
0
>>> search_descending(a, 0)
10

Matrix that transforms Spherical harmonics (SH) to spherical function (SF).

Parameters

sphereSphere

The points on which to sample the spherical function.

sh_orderint, optional

Maximum SH order in the SH fit. For sh_order, there will be (sh_order + 1) * (sh_order + 2) / 2 SH coefficients for a symmetric basis and (sh_order + 1) * (sh_order + 1) coefficients for a full SH basis.

basis_type{None, ‘tournier07’, ‘descoteaux07’}, optional

None for the default DIPY basis, tournier07 for the Tournier 2007 [Rc855ec825848-2]_[Rc855ec825848-3]_ basis, descoteaux07 for the Descoteaux 2007 [1] basis, (None defaults to descoteaux07).

full_basis: bool, optional

If True, uses a SH basis containing even and odd order SH functions. Else, uses a SH basis consisting only of even order SH functions.

legacy: bool, optional

True to use a legacy basis definition for backward compatibility with previous tournier07 and descoteaux07 implementations.

return_invbool, optional

If True then the inverse of the matrix is also returned.

smoothfloat, optional

Lambda-regularization in the SH fit.

Returns

Bndarray

Matrix that transforms spherical harmonics to spherical function sf = np.dot(sh, B).

invBndarray

Inverse of B.

References

1

Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R. Regularized, Fast, and Robust Analytical Q-ball Imaging. Magn. Reson. Med. 2007;58:497-510.

2

Tournier J.D., Calamante F. and Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage. 2007;35(4):1459-1472.

3

Tournier J-D, Smith R, Raffelt D, Tabbara R, Dhollander T, Pietsch M, et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage. 2019 Nov 15;202:116-137.

Return angles for Cartesian 3D coordinates x, y, and z

See doc for sphere2cart for angle conventions and derivation of the formulae.

\(0\le\theta\mathrm{(theta)}\le\pi\) and \(-\pi\le\phi\mathrm{(phi)}\le\pi\)

Parameters

xarray_like

x coordinate in Cartesian space

yarray_like

y coordinate in Cartesian space

zarray_like

z coordinate

Returns

rarray

radius

thetaarray

inclination (polar) angle

phiarray

azimuth angle

Get the directions of odf peaks.

Peaks are defined as points on the odf that are greater than at least one neighbor and greater than or equal to all neighbors. Peaks are sorted in descending order by their values then filtered based on their relative size and spacing on the sphere. An odf may have 0 peaks, for example if the odf is perfectly isotropic.

Parameters

odf1d ndarray

The odf function evaluated on the vertices of sphere

sphereSphere

The Sphere providing discrete directions for evaluation.

relative_peak_thresholdfloat in [0., 1.]

Only peaks greater than min + relative_peak_threshold * scale are kept, where min = max(0, odf.min()) and scale = odf.max() - min.

min_separation_anglefloat in [0, 90]

The minimum distance between directions. If two peaks are too close only the larger of the two is returned.

Returns

directions(N, 3) ndarray

N vertices for sphere, one for each peak

values(N,) ndarray

peak values

indices(N,) ndarray

peak indices of the directions on the sphere

Notes

If the odf has any negative values, they will be clipped to zeros.