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alkaline-ml / scipy python
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Éþÿ,ÉþÿNÉþÿ cÿÿbÿÿ¨bÿÿÀbÿÿbÿÿaÿÿaÿÿxaÿÿ÷cÿÿîcÿÿåcÿÿÜcÿÿÓcÿÿÊcÿÿÁcÿÿ¸cÿÿbÿÿ dÿÿ0dÿÿ`dÿÿdÿÿÀdÿÿìdÿÿTïÿÿ ïÿÿ$ïÿÿïÿÿðîÿÿìîÿÿ8ðÿÿ0ðÿÿ'ðÿÿ ðÿÿðÿÿ ðÿÿüîÿÿLðÿÿrðÿÿðÿÿ¶ðÿÿ Format string allocated too short. unable to allocate shape and strides. scipy.sparse.csgraph._validation scipy.sparse.csgraph._shortest_path numpy.core.umath failed to import no default __reduce__ due to non-trivial __cinit__ ndarray is not Fortran contiguous got differing extents in dimension %d (got %d and %d) Unable to convert item to object Out of bounds on buffer access (axis %d) Non-native byte order not supported Invalid mode, expected 'c' or 'fortran', got %s Indirect dimensions not supported Incompatible checksums (%s vs 0xb068931 = (name)) Graph has negative weights: dijkstra will give inaccurate results if the graph contains negative cycles. Consider johnson or bellman_ford. Format string allocated too short, see comment in numpy.pxd Empty shape tuple for cython.array Cannot specify indices with method == 'FW'. Cannot create writable memory view from read-only memoryview Cannot assign to read-only memoryview Can only create a buffer that is contiguous in memory. Buffer view does not expose strides unknown dtype code in numpy.pxd (%d)
shortest_path(csgraph, method='auto', directed=True, return_predecessors=False,
unweighted=False, overwrite=False, indices=None)
Perform a shortest-path graph search on a positive directed or
undirected graph.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
method : string ['auto'|'FW'|'D'], optional
Algorithm to use for shortest paths. Options are:
'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
based on the input data.
'FW' -- Floyd-Warshall algorithm. Computational cost is
approximately ``O[N^3]``. The input csgraph will be
converted to a dense representation.
'D' -- Dijkstra's algorithm with Fibonacci heaps. Computational
cost is approximately ``O[N(N*k + N*log(N))]``, where
``k`` is the average number of connected edges per node.
The input csgraph will be converted to a csr
representation.
'BF' -- Bellman-Ford algorithm. This algorithm can be used when
weights are negative. If a negative cycle is encountered,
an error will be raised. Computational cost is
approximately ``O[N(N^2 k)]``, where ``k`` is the average
number of connected edges per node. The input csgraph will
be converted to a csr representation.
'J' -- Johnson's algorithm. Like the Bellman-Ford algorithm,
Johnson's algorithm is designed for use when the weights
are negative. It combines the Bellman-Ford algorithm
with Dijkstra's algorithm for faster computation.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
overwrite : bool, optional
If True, overwrite csgraph with the result. This applies only if
method == 'FW' and csgraph is a dense, c-ordered array with
dtype=float64.
indices : array_like or int, optional
If specified, only compute the paths for the points at the given
indices. Incompatible with method == 'FW'.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
As currently implemented, Dijkstra's algorithm and Johnson's algorithm
do not work for graphs with direction-dependent distances when
directed == False. i.e., if csgraph[i,j] and csgraph[j,i] are non-equal
edges, method='D' may yield an incorrect result.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import shortest_path
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = shortest_path(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
numpy.core.multiarray failed to import
johnson(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False)
Compute the shortest path lengths using Johnson's algorithm.
Johnson's algorithm combines the Bellman-Ford algorithm and Dijkstra's
algorithm to quickly find shortest paths in a way that is robust to
the presence of negative cycles. If a negative cycle is detected,
an error is raised. For graphs without negative edge weights,
dijkstra() may be faster.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
This routine is specially designed for graphs with negative edge weights.
If all edge weights are positive, then Dijkstra's algorithm is a better
choice.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import johnson
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = johnson(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
floyd_warshall(csgraph, directed=True, return_predecessors=False,
unweighted=False, overwrite=False)
Compute the shortest path lengths using the Floyd-Warshall algorithm
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
overwrite : bool, optional
If True, overwrite csgraph with the result. This applies only if
csgraph is a dense, c-ordered array with dtype=float64.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import floyd_warshall
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
>>> dist_matrix
array([[ 0., 1., 2., 2.],
[ 1., 0., 3., 1.],
[ 2., 3., 0., 3.],
[ 2., 1., 3., 0.]])
>>> predecessors
array([[-9999, 0, 0, 1],
[ 1, -9999, 0, 1],
[ 2, 0, -9999, 2],
[ 1, 3, 3, -9999]], dtype=int32)
bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False)
Compute the shortest path lengths using the Bellman-Ford algorithm.
The Bellman-ford algorithm can robustly deal with graphs with negative
weights. If a negative cycle is detected, an error is raised. For
graphs without negative edge weights, dijkstra's algorithm may be faster.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
This routine is specially designed for graphs with negative edge weights.
If all edge weights are positive, then Dijkstra's algorithm is a better
choice.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import bellman_ford
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
Routines for performing shortest-path graph searches
The main interface is in the function :func:`shortest_path`. This
calls cython routines that compute the shortest path using
the Floyd-Warshall algorithm, Dijkstra's algorithm with Fibonacci Heaps,
the Bellman-Ford algorithm, or Johnson's Algorithm.
Negative cycle detected on node %i <strided and direct or indirect>
dijkstra(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False, limit=np.inf)
Dijkstra algorithm using Fibonacci Heaps
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of non-negative distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j] and from
point j to i along paths csgraph[j, i].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j or j to i along either
csgraph[i, j] or csgraph[j, i].
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
limit : float, optional
The maximum distance to calculate, must be >= 0. Using a smaller limit
will decrease computation time by aborting calculations between pairs
that are separated by a distance > limit. For such pairs, the distance
will be equal to np.inf (i.e., not connected).
.. versionadded:: 0.14.0
min_only : bool, optional
If False (default), for every node in the graph, find the shortest path
to every node in indices.
If True, for every node in the graph, find the shortest path to any of
the nodes in indices (which can be substantially faster).
.. versionadded:: 1.3.0
Returns
-------
dist_matrix : ndarray, shape ([n_indices, ]n_nodes,)
The matrix of distances between graph nodes. If min_only=False,
dist_matrix has shape (n_indices, n_nodes) and dist_matrix[i, j]
gives the shortest distance from point i to point j along the graph.
If min_only=True, dist_matrix has shape (n_nodes,) and contains the
shortest path from each node to any of the nodes in indices.
predecessors : ndarray, shape ([n_indices, ]n_nodes,)
If min_only=False, this has shape (n_indices, n_nodes),
otherwise it has shape (n_nodes,).
Returned only if return_predecessors == True.
The matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
sources : ndarray, shape (n_nodes,)
Returned only if min_only=True and return_predecessors=True.
Contains the index of the source which had the shortest path
to each target. If no path exists within the limit,
this will contain -9999. The value at the indices passed
will be equal to that index (i.e. the fastest way to reach
node i, is to start on node i).
Notes
-----
As currently implemented, Dijkstra's algorithm does not work for
graphs with direction-dependent distances when directed == False.
i.e., if csgraph[i,j] and csgraph[j,i] are not equal and
both are nonzero, setting directed=False will not yield the correct
result.
Also, this routine does not work for graphs with negative
distances. Negative distances can lead to infinite cycles that must
be handled by specialized algorithms such as Bellman-Ford's algorithm
or Johnson's algorithm.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import dijkstra
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> dist_matrix, predecessors = dijkstra(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
unable to allocate array data. ndarray is not C contiguous itemsize <= 0 for cython.array Negative cycle in nodes %s NegativeCycleError.__init__ Invalid shape in axis %d: %d. indices out of range 0...N Cannot index with type '%s' floyd_warshall (line 208) <contiguous and indirect> <MemoryView of %r at 0x%x> <MemoryView of %r object> unrecognized method '%s' shortest_path (line 35) <contiguous and direct> bellman_ford (line 901) <strided and indirect> return_predecessors <strided and direct> predecessor_matrix cline_in_traceback NegativeCycleError _shortest_path.pyx __pyx_unpickle_Enum johnson (line 1133) dijkstra (line 394) __setstate_cython__ __pyx_PickleError limit must be >= 0 dtype_is_object allocate_buffer View.MemoryView validate_graph isspmatrix_csr isspmatrix_csc floyd_warshall copy_if_sparse source_matrix shortest_path __reduce_cython__ __pyx_getbuffer copy_if_dense stringsource scipy.sparse return_shape __pyx_checksum dense_output bellman_ford RuntimeError dist_matrix PickleError MemoryError ImportError unweighted __pyx_vtable__ __pyx_result isspmatrix dist_array csr_output csr_matrix atleast_1d ValueError IndexError __reduce_ex__ __pyx_state overwrite __metaclass__ enumerate csrT_data TypeError warnings __setstate__ __qualname__ __pyx_type min_only itemsize issparse __getstate__ directed dijkstra diagonal csr_data csgraphT Ellipsis reshape __prepare__ message memview johnson indices fortran float64 csgraph update unpack struct __reduce__ pickle __name__ __module__ method limitf indptr __import__ format encode arange zeros where tocsr start shape range order numpy limit isinf int32 flags error empty dtype __class__ array ITYPE DTYPE ASCII warn __test__ stop step size self pack ones ndim name mode __main__ __init__ full flat fill __dict__ data copy base auto sum ret obj nnz __new__ inf __doc__ any np id Nk FW BF c T O N J D C Buffer dtype mismatch, expected %s%s%s but got %s Buffer dtype mismatch, expected '%s' but got %s in '%s.%s' memviewslice is already initialized! %.200s() takes no arguments (%zd given) %.200s() takes exactly one argument (%zd given) Bad call flags in __Pyx_CyFunction_Call. METH_OLDARGS is no longer supported! %.200s() takes no keyword arguments %.200s.%.200s is not a type object %.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject %s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject Unable to initialize pickling for %s __annotations__ must be set to a dict object __kwdefaults__ must be set to a dict object __defaults__ must be set to a tuple object function's dictionary may not be deleted setting function's dictionary to a non-dict __qualname__ must be set to a string object __name__ must be set to a string object Does not understand character buffer dtype format string ('%c') scipy/sparse/csgraph/_shortest_path.c View.MemoryView.memoryview.__str__ View.MemoryView.memoryview.size.__get__ View.MemoryView.memoryview.nbytes.__get__ View.MemoryView.memoryview.itemsize.__get__ View.MemoryView.memoryview.ndim.__get__ View.MemoryView.memoryview.suboffsets.__get__ View.MemoryView.memoryview.shape.__get__ View.MemoryView.memoryview.setitem_indexed View.MemoryView.array.memview.__get__ View.MemoryView.array.__getattr__ View.MemoryView.array.__getitem__ View.MemoryView.array.__setitem__ Subscript deletion not supported by %.200s View.MemoryView.memoryview.assign_item_from_object View.MemoryView._memoryviewslice.assign_item_from_object %s() got multiple values for keyword argument '%U' %.200s() keywords must be strings %s() got an unexpected keyword argument '%U' %.200s() takes %.8s %zd positional argument%.1s (%zd given) scipy.sparse.csgraph._shortest_path.NegativeCycleError.__init__ calling %R should have returned an instance of BaseException, not %R raise: exception class must be a subclass of BaseException View.MemoryView.array.__reduce_cython__ View.MemoryView.array.__setstate_cython__ View.MemoryView.memoryview.__reduce_cython__ View.MemoryView.memoryview.__setstate_cython__ View.MemoryView.memoryview.strides.__get__ View.MemoryView._memoryviewslice.__reduce_cython__ View.MemoryView._memoryviewslice.__setstate_cython__ PyObject_GetBuffer: view==NULL argument is obsolete View.MemoryView.array.__getbuffer__ View.MemoryView.memoryview.__getbuffer__ Out of bounds on buffer access (axis %d) scipy.sparse.csgraph._shortest_path._johnson_add_weights Unexpected format string character: '%c' Expected a dimension of size %zu, got %zu Expected %d dimensions, got %d Python does not define a standard format string size for long double ('g').. Buffer dtype mismatch; next field is at offset %zd but %zd expected Big-endian buffer not supported on little-endian compiler Buffer acquisition: Expected '{' after 'T' Cannot handle repeated arrays in format string Expected a dimension of size %zu, got %d Expected a comma in format string, got '%c' Expected %d dimension(s), got %d Unexpected end of format string, expected ')' Buffer has wrong number of dimensions (expected %d, got %d) Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s) __int__ returned non-int (type %.200s). The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python. __%.4s__ returned non-%.4s (type %.200s) Acquisition count is %d (line %d) View.MemoryView.array.get_memview View.MemoryView.memoryview_cwrapper Item size of buffer (%zu byte%s) does not match size of '%s' (%zu byte%s) Buffer is not indirectly contiguous in dimension %d. Buffer and memoryview are not contiguous in the same dimension. C-contiguous buffer is not contiguous in dimension %d C-contiguous buffer is not indirect in dimension %d Buffer exposes suboffsets but no strides Buffer not compatible with direct access in dimension %d. Buffer is not indirectly accessible in dimension %d. View.MemoryView.memoryview.is_slice View.MemoryView.memoryview_fromslice View.MemoryView.memoryview_copy_from_slice value too large to convert to int scipy.sparse.csgraph._shortest_path._dijkstra_directed scipy.sparse.csgraph._shortest_path._dijkstra_undirected View.MemoryView.memoryview.__repr__ View.MemoryView.Enum.__reduce_cython__ View.MemoryView.memoryview.convert_item_to_object View.MemoryView._memoryviewslice.convert_item_to_object c-string too long to convert to Python Cannot convert %.200s to %.200s View.MemoryView.get_slice_from_memview View.MemoryView.assert_direct_dimensions View.MemoryView.memoryview.setitem_slice_assign_scalar 'NoneType' object is not subscriptable hasattr(): attribute name must be string View.MemoryView.__pyx_unpickle_Enum__set_state View.MemoryView.Enum.__setstate_cython__ Cannot transpose memoryview with indirect dimensions View.MemoryView.transpose_memslice View.MemoryView.memoryview_copy View.MemoryView.memoryview.T.__get__ View.MemoryView.copy_data_to_temp View.MemoryView.memoryview_copy_contents Cannot copy memoryview slice with indirect dimensions (axis %d) View.MemoryView.array_cwrapper View.MemoryView.memoryview.copy_fortran View.MemoryView.memoryview.copy View.MemoryView.__pyx_unpickle_Enum integer division or modulo by zero value too large to perform division View.MemoryView.pybuffer_index View.MemoryView.memoryview.get_item_pointer too many values to unpack (expected %zd) need more than %zd value%.1s to unpack 'NoneType' object is not iterable View.MemoryView.memoryview.__setitem__ View.MemoryView.array.__cinit__ Argument '%.200s' must not be None object of type 'NoneType' has no len() expected bytes, NoneType found Argument '%.200s' has incorrect type (expected %.200s, got %.200s) scipy.sparse.csgraph._shortest_path._floyd_warshall All dimensions preceding dimension %d must be indexed and not sliced View.MemoryView.slice_memviewslice Step may not be zero (axis %d) local variable '%s' referenced before assignment View.MemoryView.memoryview.__getitem__ View.MemoryView.memoryview.__cinit__ View.MemoryView.memoryview.setitem_slice_assignment scipy.sparse.csgraph._shortest_path.shortest_path scipy.sparse.csgraph._shortest_path._bellman_ford_directed scipy.sparse.csgraph._shortest_path._bellman_ford_undirected scipy.sparse.csgraph._shortest_path.bellman_ford scipy.sparse.csgraph._shortest_path.floyd_warshall scipy.sparse.csgraph._shortest_path._dijkstra_directed_multi scipy.sparse.csgraph._shortest_path._dijkstra_undirected_multi scipy.sparse.csgraph._shortest_path.dijkstra scipy.sparse.csgraph._shortest_path._johnson_directed scipy.sparse.csgraph._shortest_path._johnson_undirected scipy.sparse.csgraph._shortest_path.johnson scipy.sparse.csgraph._shortest_path compiletime version %s of module '%.100s' does not match runtime version %s Shared Cython type %.200s is not a type object Shared Cython type %.200s has the wrong size, try recompiling metaclass conflict: the metaclass of a derived class must be a (non-strict) subclass of the metaclasses of all its bases init scipy.sparse.csgraph._shortest_path scipy.sparse.csgraph._shortest_path._memoryviewslice Internal class for passing memoryview slices to Python scipy.sparse.csgraph._shortest_path.memoryview scipy.sparse.csgraph._shortest_path.Enum scipy.sparse.csgraph._shortest_path.array ÿÿÿÿÿÿï Ð?V瞯Ò< ð ð¿ ÿÿÿÿÿÿÿ ; ° °/üÿ¨ ð7üÿÐ 8üÿè [8üÿ G:üÿ@ :üÿ ;üÿà ÄLüÿà .Müÿ @PüÿX Püÿp \Qüÿ Qüÿ¸ Süÿ aTüÿP Wüÿh ÄZüÿÈ j[üÿ \üÿH ®\üÿ L]üÿ¸ ê]üÿð ^üÿ8! 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johnson(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False)
Compute the shortest path lengths using Johnson's algorithm.
Johnson's algorithm combines the Bellman-Ford algorithm and Dijkstra's
algorithm to quickly find shortest paths in a way that is robust to
the presence of negative cycles. If a negative cycle is detected,
an error is raised. For graphs without negative edge weights,
dijkstra() may be faster.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
This routine is specially designed for graphs with negative edge weights.
If all edge weights are positive, then Dijkstra's algorithm is a better
choice.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import johnson
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = johnson(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False)
Compute the shortest path lengths using the Bellman-Ford algorithm.
The Bellman-ford algorithm can robustly deal with graphs with negative
weights. If a negative cycle is detected, an error is raised. For
graphs without negative edge weights, dijkstra's algorithm may be faster.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
This routine is specially designed for graphs with negative edge weights.
If all edge weights are positive, then Dijkstra's algorithm is a better
choice.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import bellman_ford
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
dijkstra(csgraph, directed=True, indices=None, return_predecessors=False,
unweighted=False, limit=np.inf)
Dijkstra algorithm using Fibonacci Heaps
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of non-negative distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j] and from
point j to i along paths csgraph[j, i].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j or j to i along either
csgraph[i, j] or csgraph[j, i].
indices : array_like or int, optional
if specified, only compute the paths for the points at the given
indices.
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
limit : float, optional
The maximum distance to calculate, must be >= 0. Using a smaller limit
will decrease computation time by aborting calculations between pairs
that are separated by a distance > limit. For such pairs, the distance
will be equal to np.inf (i.e., not connected).
.. versionadded:: 0.14.0
min_only : bool, optional
If False (default), for every node in the graph, find the shortest path
to every node in indices.
If True, for every node in the graph, find the shortest path to any of
the nodes in indices (which can be substantially faster).
.. versionadded:: 1.3.0
Returns
-------
dist_matrix : ndarray, shape ([n_indices, ]n_nodes,)
The matrix of distances between graph nodes. If min_only=False,
dist_matrix has shape (n_indices, n_nodes) and dist_matrix[i, j]
gives the shortest distance from point i to point j along the graph.
If min_only=True, dist_matrix has shape (n_nodes,) and contains the
shortest path from each node to any of the nodes in indices.
predecessors : ndarray, shape ([n_indices, ]n_nodes,)
If min_only=False, this has shape (n_indices, n_nodes),
otherwise it has shape (n_nodes,).
Returned only if return_predecessors == True.
The matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
sources : ndarray, shape (n_nodes,)
Returned only if min_only=True and return_predecessors=True.
Contains the index of the source which had the shortest path
to each target. If no path exists within the limit,
this will contain -9999. The value at the indices passed
will be equal to that index (i.e. the fastest way to reach
node i, is to start on node i).
Notes
-----
As currently implemented, Dijkstra's algorithm does not work for
graphs with direction-dependent distances when directed == False.
i.e., if csgraph[i,j] and csgraph[j,i] are not equal and
both are nonzero, setting directed=False will not yield the correct
result.
Also, this routine does not work for graphs with negative
distances. Negative distances can lead to infinite cycles that must
be handled by specialized algorithms such as Bellman-Ford's algorithm
or Johnson's algorithm.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import dijkstra
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> dist_matrix, predecessors = dijkstra(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
floyd_warshall(csgraph, directed=True, return_predecessors=False,
unweighted=False, overwrite=False)
Compute the shortest path lengths using the Floyd-Warshall algorithm
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
overwrite : bool, optional
If True, overwrite csgraph with the result. This applies only if
csgraph is a dense, c-ordered array with dtype=float64.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import floyd_warshall
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
>>> dist_matrix
array([[ 0., 1., 2., 2.],
[ 1., 0., 3., 1.],
[ 2., 3., 0., 3.],
[ 2., 1., 3., 0.]])
>>> predecessors
array([[-9999, 0, 0, 1],
[ 1, -9999, 0, 1],
[ 2, 0, -9999, 2],
[ 1, 3, 3, -9999]], dtype=int32)
shortest_path(csgraph, method='auto', directed=True, return_predecessors=False,
unweighted=False, overwrite=False, indices=None)
Perform a shortest-path graph search on a positive directed or
undirected graph.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array, matrix, or sparse matrix, 2 dimensions
The N x N array of distances representing the input graph.
method : string ['auto'|'FW'|'D'], optional
Algorithm to use for shortest paths. Options are:
'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
based on the input data.
'FW' -- Floyd-Warshall algorithm. Computational cost is
approximately ``O[N^3]``. The input csgraph will be
converted to a dense representation.
'D' -- Dijkstra's algorithm with Fibonacci heaps. Computational
cost is approximately ``O[N(N*k + N*log(N))]``, where
``k`` is the average number of connected edges per node.
The input csgraph will be converted to a csr
representation.
'BF' -- Bellman-Ford algorithm. This algorithm can be used when
weights are negative. If a negative cycle is encountered,
an error will be raised. Computational cost is
approximately ``O[N(N^2 k)]``, where ``k`` is the average
number of connected edges per node. The input csgraph will
be converted to a csr representation.
'J' -- Johnson's algorithm. Like the Bellman-Ford algorithm,
Johnson's algorithm is designed for use when the weights
are negative. It combines the Bellman-Ford algorithm
with Dijkstra's algorithm for faster computation.
directed : bool, optional
If True (default), then find the shortest path on a directed graph:
only move from point i to point j along paths csgraph[i, j].
If False, then find the shortest path on an undirected graph: the
algorithm can progress from point i to j along csgraph[i, j] or
csgraph[j, i]
return_predecessors : bool, optional
If True, return the size (N, N) predecesor matrix
unweighted : bool, optional
If True, then find unweighted distances. That is, rather than finding
the path between each point such that the sum of weights is minimized,
find the path such that the number of edges is minimized.
overwrite : bool, optional
If True, overwrite csgraph with the result. This applies only if
method == 'FW' and csgraph is a dense, c-ordered array with
dtype=float64.
indices : array_like or int, optional
If specified, only compute the paths for the points at the given
indices. Incompatible with method == 'FW'.
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between graph nodes. dist_matrix[i,j]
gives the shortest distance from point i to point j along the graph.
predecessors : ndarray
Returned only if return_predecessors == True.
The N x N matrix of predecessors, which can be used to reconstruct
the shortest paths. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the
path from point i to point j. If no path exists between point
i and j, then predecessors[i, j] = -9999
Raises
------
NegativeCycleError:
if there are negative cycles in the graph
Notes
-----
As currently implemented, Dijkstra's algorithm and Johnson's algorithm
do not work for graphs with direction-dependent distances when
directed == False. i.e., if csgraph[i,j] and csgraph[j,i] are non-equal
edges, method='D' may yield an incorrect result.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import shortest_path
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 0) 2
(2, 3) 3
>>> dist_matrix, predecessors = shortest_path(csgraph=graph, directed=False, indices=0, return_predecessors=True)
>>> dist_matrix
array([ 0., 1., 2., 2.])
>>> predecessors
array([-9999, 0, 0, 1], dtype=int32)
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