U Zʹjr@shddlmZddlmZddlmZddlmZddlm Z m Z m Z GdddeZ Gd d d eZ d S) )S)_sympify)KroneckerDelta) MatrixExpr) ZeroMatrixIdentity OneMatrixcspeZdZdZfddZeddZeddZdd Zd d Z d d Z ddZ e Z Z ddZddZZS)PermutationMatrixaA Permutation Matrix Parameters ========== perm : Permutation The permutation the matrix uses. The size of the permutation determines the matrix size. See the documentation of :class:`sympy.combinatorics.permutations.Permutation` for the further information of how to create a permutation object. Examples ======== >>> from sympy import Matrix, PermutationMatrix >>> from sympy.combinatorics import Permutation Creating a permutation matrix: >>> p = Permutation(1, 2, 0) >>> P = PermutationMatrix(p) >>> P = P.as_explicit() >>> P Matrix([ [0, 1, 0], [0, 0, 1], [1, 0, 0]]) Permuting a matrix row and column: >>> M = Matrix([0, 1, 2]) >>> Matrix(P*M) Matrix([ [1], [2], [0]]) >>> Matrix(M.T*P) Matrix([[2, 0, 1]]) See Also ======== sympy.combinatorics.permutations.Permutation cs:ddlm}t|}t||s,td|t||S)Nr Permutationz({} must be a SymPy Permutation instance.) sympy.combinatorics.permutationsr r isinstance ValueErrorformatsuper__new__)clspermr  __class__e/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/matrices/expressions/permutation.pyr;s  zPermutationMatrix.__new__cCs|jdj}||fSNr)argssize)selfrrrrshapeEs zPermutationMatrix.shapecCs |jdjSr)r is_IdentityrrrrrJszPermutationMatrix.is_IdentitycKs|jrt|jS|S)N)rrrows)rhintsrrrdoitNs zPermutationMatrix.doitcKs|jd}t|||Sr)rrapply)rijkwargsrrrr_entrySs zPermutationMatrix._entrycCst|jd|Sr)r rr")rexprrr _eval_powerWszPermutationMatrix._eval_powercCst|jddS)Nr)r rrrrr _eval_inverseZszPermutationMatrix._eval_inversecCs2|jd}|dkrtjS|dkr*tjStdS)Nrrr*)r signaturerOneZ NegativeOneNotImplementedError)rsignrrr_eval_determinant_s z#PermutationMatrix._eval_determinantcsddlm}ddlm}|jd}|j}g}d\}} } d} |D]} t| } t| }| s|d|| krzd} | g}|} | } n|| g|| 7}q>|| kr|d|| | kr|| ||d} |d}n|} || | | 7} q>| d|| | kr|| ||d} | d}q>|| | | 7} q>dg}|D]d}g}d} |D].} fdd | D}||| t| 7} qN| 7||}t |}||q>||S) Nrr r)BlockDiagMatrix)rrrFTcsg|] }|qSrr).0r$prr szFPermutationMatrix._eval_rewrite_as_BlockDiagMatrix..) r r Z blockmatrixr1rfull_cyclic_formlenmaxappendr )rrr&r r1rr6Z cycles_picksabcflagcyclelmtemppickZ new_cyclesZ new_cyclematrr3r _eval_rewrite_as_BlockDiagMatrixgs`                 z2PermutationMatrix._eval_rewrite_as_BlockDiagMatrix)__name__ __module__ __qualname____doc__rpropertyrrr"r'r)r+Z_eval_transposeZ _eval_adjointr0rD __classcell__rrrrr s1   r csLeZdZdZejffdd Zd ddZeddZ d d Z d d Z Z S) MatrixPermuteazSymbolic representation for permuting matrix rows or columns. Parameters ========== perm : Permutation, PermutationMatrix The permutation to use for permuting the matrix. The permutation can be resized to the suitable one, axis : 0 or 1 The axis to permute alongside. If `0`, it will permute the matrix rows. If `1`, it will permute the matrix columns. Notes ===== This follows the same notation used in :meth:`sympy.matrices.matrixbase.MatrixBase.permute`. Examples ======== >>> from sympy import Matrix, MatrixPermute >>> from sympy.combinatorics import Permutation Permuting the matrix rows: >>> p = Permutation(1, 2, 0) >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> B = MatrixPermute(A, p, axis=0) >>> B.as_explicit() Matrix([ [4, 5, 6], [7, 8, 9], [1, 2, 3]]) Permuting the matrix columns: >>> B = MatrixPermute(A, p, axis=1) >>> B.as_explicit() Matrix([ [2, 3, 1], [5, 6, 4], [8, 9, 7]]) See Also ======== sympy.matrices.matrixbase.MatrixBase.permute c sddlm}t|}|js(td|t|}t|trD|jd}t||s\td|t|}|dkrttd|j |}||j krz| |}Wn&tk rtd|||YnXt ||||S)Nrr z#{} must be a SymPy matrix instance.z>{} must be a SymPy Permutation or a PermutationMatrix instance)rrzThe axis must be 0 or 1.zsSize does not match between the permutation {} and the matrix {} threaded over the axis {} and cannot be converted.)r r rZ is_Matrixrrrr rrrresizerr)rrCraxisr Zmat_sizerrrrs>       zMatrixPermute.__new__TcKs|j\}}}|r8|jfd|i|}|jfd|i|}|jrB|S|jrp|tjkrZt|S|tjkrpt|dSt|tt fr|St|t r|jd|krt |jd||jd|S|S)Ndeepr*rr) rr"rrZeror r-rrr rK)rrNr!rCrrMrrrr"s     zMatrixPermute.doitcCs |jdjSr)rrrrrrrszMatrixPermute.shapecKsD|j\}}}|dkr&||||fS|dkr@||||fSdS)Nrr)rr#)rr$r%r&rCrrMrrrr's  zMatrixPermute._entrycOsfddlm}|j\}}}|dd}|r2||}|dkrH|t||S|dkrb||t|dSdS)Nr)MatMulrNTrr*)matmulrQrgetZrewriter )rrr&rQrCrrMrNrrr_eval_rewrite_as_MatMul"s    z%MatrixPermute._eval_rewrite_as_MatMul)T) rErFrGrHrrPrr"rIrr'rTrJrrrrrKs3"  rKN)Z sympy.corerZsympy.core.sympifyrZsympy.functionsrZmatexprrspecialrrr r rKrrrrs