pyjacket.graphtools

Submodules

pyjacket.graphtools.absorbing_markov module

pyjacket.graphtools.absorbing_markov.absorb_probabilities(m)

What is the probability to end in a particular absorbing state, starting from any transient state i

pyjacket.graphtools.absorbing_markov.classify_states(m)

Classify each state in a transition matrix as either absorbing or transient

pyjacket.graphtools.absorbing_markov.expected_visits(A: ndarray)

Expected number of visits to <j> - starting from <i> - before being absorbed.

pyjacket.graphtools.absorbing_markov.is_absorbing(m: ndarray)

Is this matrix an absorbing matrix?

pyjacket.graphtools.absorbing_markov.slice_absorbing(m: ndarray)

Spit matrix in components based on absorbing/transient

pyjacket.graphtools.grid module

Grids are graphs represented as a binary image

pyjacket.graphtools.grid.convolve(input, weights, output=None, mode='reflect', cval=0.0, origin=0, *, axes=None)

Multidimensional convolution.

The array is convolved with the given kernel.

Parameters:

• input (array_like) – The input array.

• weights (array_like) – Array of weights, same number of dimensions as input

• output (array or dtype, optional) – The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.

• mode ({'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional) –

  The mode parameter determines how the input array is extended beyond its boundaries. Default is ‘reflect’. Behavior for each valid value is as follows:

  ’reflect’ (d c b a | a b c d | d c b a)

  The input is extended by reflecting about the edge of the last pixel. This mode is also sometimes referred to as half-sample symmetric.

  ’constant’ (k k k k | a b c d | k k k k)

  The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.

  ’nearest’ (a a a a | a b c d | d d d d)

  The input is extended by replicating the last pixel.

  ’mirror’ (d c b | a b c d | c b a)

  The input is extended by reflecting about the center of the last pixel. This mode is also sometimes referred to as whole-sample symmetric.

  ’wrap’ (a b c d | a b c d | a b c d)

  The input is extended by wrapping around to the opposite edge.

  For consistency with the interpolation functions, the following mode names can also be used:

  ’grid-mirror’

  This is a synonym for ‘reflect’.

  ’grid-constant’

  This is a synonym for ‘constant’.

  ’grid-wrap’

  This is a synonym for ‘wrap’.

• cval (scalar, optional) – Value to fill past edges of input if mode is ‘constant’. Default is 0.0

• origin (int or sequence, optional) – Controls the placement of the filter on the input array’s pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the right, and negative ones to the left. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

• axes (tuple of int or None, optional) – If None, input is filtered along all axes. Otherwise, input is filtered along the specified axes. When axes is specified, any tuples used for mode or origin must match the length of axes. The ith entry in any of these tuples corresponds to the ith entry in axes.

Returns:

result – The result of convolution of input with weights.

Return type:

ndarray

See also

correlate()

Correlate an image with a kernel.

Notes

Each value in result is \(C_i = \sum_j{I_{i+k-j} W_j}\), where W is the weights kernel, j is the N-D spatial index over \(W\), I is the input and k is the coordinate of the center of W, specified by origin in the input parameters.

Array API Standard Support

convolve has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	⚠️ computes graph	n/a

See dev-arrayapi for more information.

Examples

Perhaps the simplest case to understand is mode='constant', cval=0.0, because in this case borders (i.e., where the weights kernel, centered on any one value, extends beyond an edge of input) are treated as zeros.

>>> import numpy as np
>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> k = np.array([[1,1,1],[1,1,0],[1,0,0]])
>>> from scipy import ndimage
>>> ndimage.convolve(a, k, mode='constant', cval=0.0)
array([[11, 10,  7,  4],
       [10,  3, 11, 11],
       [15, 12, 14,  7],
       [12,  3,  7,  0]])

Setting cval=1.0 is equivalent to padding the outer edge of input with 1.0’s (and then extracting only the original region of the result).

>>> ndimage.convolve(a, k, mode='constant', cval=1.0)
array([[13, 11,  8,  7],
       [11,  3, 11, 14],
       [16, 12, 14, 10],
       [15,  6, 10,  5]])

With mode='reflect' (the default), outer values are reflected at the edge of input to fill in missing values.

>>> b = np.array([[2, 0, 0],
...               [1, 0, 0],
...               [0, 0, 0]])
>>> k = np.array([[0,1,0], [0,1,0], [0,1,0]])
>>> ndimage.convolve(b, k, mode='reflect')
array([[5, 0, 0],
       [3, 0, 0],
       [1, 0, 0]])

This includes diagonally at the corners.

>>> k = np.array([[1,0,0],[0,1,0],[0,0,1]])
>>> ndimage.convolve(b, k)
array([[4, 2, 0],
       [3, 2, 0],
       [1, 1, 0]])

With mode='nearest', the single nearest value in to an edge in input is repeated as many times as needed to match the overlapping weights.

>>> c = np.array([[2, 0, 1],
...               [1, 0, 0],
...               [0, 0, 0]])
>>> k = np.array([[0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0]])
>>> ndimage.convolve(c, k, mode='nearest')
array([[7, 0, 3],
       [5, 0, 2],
       [3, 0, 1]])

pyjacket.graphtools.grid.graph_from_grid(skeleton: ndarray)

Convert a binary image into a graph

pyjacket.graphtools.grid.neighbor_positions(r, c, filter=None)

Find all neighboring coordinates. Optionally, return only coordinates that are present in the filter

pyjacket.graphtools.markov module

pyjacket.graphtools.markov.is_connected(m, i, j)

Is there a path between the two states?

pyjacket.graphtools.markov.is_regular(m: ndarray) → bool

Test if a matrix reaches an equilibrium Maybe, testing if eigenvalue of 1 exists could be quicker

pyjacket.graphtools.markov.is_transition_matrix(m)

pyjacket.graphtools.markov.n_step_transitions(transition_matrix, n)

Probability to go from state i to state j in n steps:

matrix[i, j]

pyjacket.graphtools.markov.state_probabilities(m: ndarray) → ndarray

The probability to be in each state after moving along the graph for a long time.

m: transition matrix.

pyjacket.graphtools.shortest_path module

pyjacket.graphtools.shortest_path.max_shortest_path(graph: Graph, endpoints: list[tuple])

Find the pair of endpoints whose shortest path is maximal and return it as a binary image.

pyjacket.graphtools.skeleton module

A skeleton is a grid whose features are 1-pixel wide

pyjacket.graphtools.skeleton.convolve(input, weights, output=None, mode='reflect', cval=0.0, origin=0, *, axes=None)

Multidimensional convolution.

The array is convolved with the given kernel.

Parameters:

• input (array_like) – The input array.

• weights (array_like) – Array of weights, same number of dimensions as input

• output (array or dtype, optional) – The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.

• mode ({'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional) –

  The mode parameter determines how the input array is extended beyond its boundaries. Default is ‘reflect’. Behavior for each valid value is as follows:

  ’reflect’ (d c b a | a b c d | d c b a)

  The input is extended by reflecting about the edge of the last pixel. This mode is also sometimes referred to as half-sample symmetric.

  ’constant’ (k k k k | a b c d | k k k k)

  The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.

  ’nearest’ (a a a a | a b c d | d d d d)

  The input is extended by replicating the last pixel.

  ’mirror’ (d c b | a b c d | c b a)

  The input is extended by reflecting about the center of the last pixel. This mode is also sometimes referred to as whole-sample symmetric.

  ’wrap’ (a b c d | a b c d | a b c d)

  The input is extended by wrapping around to the opposite edge.

  For consistency with the interpolation functions, the following mode names can also be used:

  ’grid-mirror’

  This is a synonym for ‘reflect’.

  ’grid-constant’

  This is a synonym for ‘constant’.

  ’grid-wrap’

  This is a synonym for ‘wrap’.

• cval (scalar, optional) – Value to fill past edges of input if mode is ‘constant’. Default is 0.0

• origin (int or sequence, optional) – Controls the placement of the filter on the input array’s pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the right, and negative ones to the left. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

• axes (tuple of int or None, optional) – If None, input is filtered along all axes. Otherwise, input is filtered along the specified axes. When axes is specified, any tuples used for mode or origin must match the length of axes. The ith entry in any of these tuples corresponds to the ith entry in axes.

Returns:

result – The result of convolution of input with weights.

Return type:

ndarray

See also

correlate()

Correlate an image with a kernel.

Notes

Each value in result is \(C_i = \sum_j{I_{i+k-j} W_j}\), where W is the weights kernel, j is the N-D spatial index over \(W\), I is the input and k is the coordinate of the center of W, specified by origin in the input parameters.

Array API Standard Support

convolve has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	⚠️ computes graph	n/a

See dev-arrayapi for more information.

Examples

Perhaps the simplest case to understand is mode='constant', cval=0.0, because in this case borders (i.e., where the weights kernel, centered on any one value, extends beyond an edge of input) are treated as zeros.

>>> import numpy as np
>>> a = np.array([[1, 2, 0, 0],
...               [5, 3, 0, 4],
...               [0, 0, 0, 7],
...               [9, 3, 0, 0]])
>>> k = np.array([[1,1,1],[1,1,0],[1,0,0]])
>>> from scipy import ndimage
>>> ndimage.convolve(a, k, mode='constant', cval=0.0)
array([[11, 10,  7,  4],
       [10,  3, 11, 11],
       [15, 12, 14,  7],
       [12,  3,  7,  0]])

Setting cval=1.0 is equivalent to padding the outer edge of input with 1.0’s (and then extracting only the original region of the result).

>>> ndimage.convolve(a, k, mode='constant', cval=1.0)
array([[13, 11,  8,  7],
       [11,  3, 11, 14],
       [16, 12, 14, 10],
       [15,  6, 10,  5]])

With mode='reflect' (the default), outer values are reflected at the edge of input to fill in missing values.

>>> b = np.array([[2, 0, 0],
...               [1, 0, 0],
...               [0, 0, 0]])
>>> k = np.array([[0,1,0], [0,1,0], [0,1,0]])
>>> ndimage.convolve(b, k, mode='reflect')
array([[5, 0, 0],
       [3, 0, 0],
       [1, 0, 0]])

This includes diagonally at the corners.

>>> k = np.array([[1,0,0],[0,1,0],[0,0,1]])
>>> ndimage.convolve(b, k)
array([[4, 2, 0],
       [3, 2, 0],
       [1, 1, 0]])

With mode='nearest', the single nearest value in to an edge in input is repeated as many times as needed to match the overlapping weights.

>>> c = np.array([[2, 0, 1],
...               [1, 0, 0],
...               [0, 0, 0]])
>>> k = np.array([[0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0],
...               [0, 1, 0]])
>>> ndimage.convolve(c, k, mode='nearest')
array([[7, 0, 3],
       [5, 0, 2],
       [3, 0, 1]])

pyjacket.graphtools.skeleton.critical_points(skeleton: ndarray)

Finds end points and branch points for a skeleton image

pyjacket.graphtools.skeleton.is_branch_point(skeleton: ndarray, y, x)

Module contents