o 8Va\@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.matrices 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||std|t||S)Nr Permutationz({} must be a SymPy Permutation instance.) sympy.combinatorics.permutationsr r isinstance ValueErrorformatsuper__new__)clspermr  __class__H/usr/lib/python3/dist-packages/sympy/matrices/expressions/permutation.pyr;s  zPermutationMatrix.__new__cCs|jdj}||fSNr)argssize)selfrrrrshapeEs zPermutationMatrix.shapecC |jdjSr)r is_IdentityrrrrrJ zPermutationMatrix.is_IdentitycCs|jrt|jS|S)N)rrZrowsr rrrdoitNs zPermutationMatrix.doitcKs|jd}t|||Sr)rrapply)rijkwargsrrrr_entrySs zPermutationMatrix._entrycCst|jd|Sr)r rr")rZexprrr _eval_powerWszPermutationMatrix._eval_powercCst|jddS)Nr)r rr rrr _eval_inverseZszPermutationMatrix._eval_inversecCs.|jd}|dkrtjS|dkrtjSt)Nrrr))rZ signaturerOneZ NegativeOneNotImplementedError)rsignrrr_eval_determinant_s z#PermutationMatrix._eval_determinantcsddlm}ddlm}|jd}|j}g}d\}} } d} |D]x} t| } t| }| sH|d|| kr=d} | g}|} | } q|| g|| 7}q|| krs|d|| | krg|| ||d} |d}q|} || | | 7} q| d|| | kr|| ||d} | d}q|| | | 7} qdg}|D]0}g}d} |D]} fdd | D}||| t| 7} q| 7||}t |}||q||S) Nrr r)BlockDiagMatrix)rrrFTcsg|]}|qSrr).0r$prr szFPermutationMatrix._eval_rewrite_as_BlockDiagMatrix..) r r Z blockmatrixr/rfull_cyclic_formlenmaxappendr )rrr&r r/rr4Z cycles_picksabcflagcyclelmZtempZpickZ new_cyclesZ new_cyclematrr1r _eval_rewrite_as_BlockDiagMatrixgs`                  z2PermutationMatrix._eval_rewrite_as_BlockDiagMatrix)__name__ __module__ __qualname____doc__rpropertyrrr"r'r(r*Z_eval_transposeZ _eval_adjointr.r@ __classcell__rrrrr s 1  r csLeZdZdZejffdd Zd ddZeddZ d d Z d d Z Z S) MatrixPermuteaSymbolic 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.common.MatrixCommon.permute`. Examples ======== >>> from sympy.matrices 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.common.MatrixCommon.permute c sddlm}t|}|jstd|t|}t|tr"|jd}t||s.td|t|}|dvr:td|j |}||j kr\z| |}Wnty[td|||wt ||||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 rrrZresizerr)rr?raxisr Zmat_sizerrrrs8        zMatrixPermute.__new__TcCs|j\}}}|r|j|d}|j|d}|jr|S|jr0|tjur%t|S|tjur0t|dSt|tt fr9|St|t rS|jd|krSt |jd||jd|S|S)N)deepr)rr) rr"rrZeror r+rrr rG)rrIr?rrHrrrr"s      zMatrixPermute.doitcCrr)rrr rrrrr!zMatrixPermute.shapecKsD|j\}}}|dkr||||fS|dkr ||||fSdS)Nrr)rr#)rr$r%r&r?rrHrrrr's zMatrixPermute._entrycOsfddlm}|j\}}}|dd}|r||}|dkr$|t||S|dkr1||t|dSdS)Nr)MatMulrITrr))matmulrLrgetZrewriter )rrr&rLr?rrHrIrrr_eval_rewrite_as_MatMul"s    z%MatrixPermute._eval_rewrite_as_MatMul)T) rArBrCrDrrKrr"rErr'rOrFrrrrrGs3 " rGN)Z sympy.corerZsympy.core.sympifyrZsympy.functionsrZmatexprrZspecialrrr r rGrrrrs