B [a@sdZddlmZddlmZedddddd Zd d Zd d ZddZ ddZ ddZ ddZ ddZ ddZddZddZddZd d!Zd"S)#zZ Fundamental operations of dense matrices. The dense matrix is stored as a list of lists )range)SymPyDeprecationWarningZ densetoolsi1z1.1)ZfeatureZissueZdeprecated_since_versioncCs0|j}x$tt|D]}||||7}qW|S)aT Returns the trace of a matrix. Examples ======== >>> from sympy.matrices.densetools import trace, eye >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> b = eye(4, ZZ) >>> trace(a, ZZ) 10 >>> trace(b, ZZ) 4 )zerorlen)matlistKresultir 8lib/python3.7/site-packages/sympy/matrices/densetools.pytracesr cCsddt|DS)aG Returns the transpose of a matrix Examples ======== >>> from sympy.matrices.densetools import transpose >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> transpose(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] cSsg|] }t|qSr )list).0ar r r :sztranspose..)zip)rrr r r transpose)srcsfdd|DS)a~ Returns the conjugate of a matrix row-wise. Examples ======== >>> from sympy.matrices.densetools import conjugate >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(2), ZZ(6)], ... [ZZ(7), ZZ(4), ZZ(2)], ... [ZZ(4), ZZ(5), ZZ(3)]] >>> conjugate(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] See Also ======== conjugate_row csg|]}t|qSr ) conjugate_row)rrow)rr r rRszconjugate..r )rrr )rr conjugate=src CsHg}x>|D]6}y||Wq tk r>||Yq Xq W|S)z Returns the conjugate of a row element-wise Examples ======== >>> from sympy.matrices.densetools import conjugate_row >>> from sympy import ZZ >>> a = [ZZ(3), ZZ(2), ZZ(6)] >>> conjugate_row(a, ZZ) [3, 2, 6] )appendrAttributeError)rrrrr r r rUs  rcCstt|||S)ad Returns the conjugate-transpose of a matrix Examples ======== >>> from sympy import ZZ >>> from sympy.matrices.densetools import conjugate_transpose >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> conjugate_transpose(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] )rr)rrr r r conjugate_transposeksrcCsddt||DS)a Augments a matrix and a column. Examples ======== >>> from sympy.matrices.densetools import augment >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> b = [ ... [ZZ(4)], ... [ZZ(5)], ... [ZZ(6)]] >>> augment(a, b, ZZ) [[3, 7, 4, 4], [2, 4, 5, 5], [6, 2, 3, 6]] cSsg|]\}}||qSr r )rrelementr r r rszaugment..)r)rcolumnrr r r augment~srcCsbg}xXt|D]L}|gx>> from sympy.matrices.densetools import eye >>> from sympy import ZZ >>> eye(3, ZZ) [[1, 0, 0], [0, 1, 0], [0, 0, 1]] )rrr)nrrr jr r r eyes  r cCs||S)a Returns the ith row of a matrix Examples ======== >>> from sympy.matrices.densetools import row >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> row(a, 2) [6, 2, 3] r )rr r r r rsrcCs$ddt|D}dd||DS)aK Returns the ith column of a matrix Note: Currently very expensive Examples ======== >>> from sympy.matrices.densetools import col >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> col(a, 1) [[7], [4], [2]] cSsg|] }t|qSr )r )rlr r r rszcol..cSsg|] }|gqSr r )rr!r r r rs)r)rr Zmatcolr r r colsr"cCs||||||<||<|S)zC Returns the matrix with index1 row and index2 row swapped r )rindex1index2rr r r rowswapsr%cCs6x0tt||D]}|||||||<qW|S)z% Multiplies index row with k )rr)rindexkrr r r r rowmulsr(cCsFg}x>> from sympy.matrices.densetools import isHermitian >>> from sympy import QQ >>> a = [ ... [QQ(2,1), QQ(-1,1), QQ(-1,1)], ... [QQ(0,1), QQ(4,1), QQ(-1,1)], ... [QQ(0,1), QQ(0,1), QQ(3,1)]] >>> isHermitian(a, QQ) False )r)rrr r r isHermitiansr*N)__doc__Zsympy.core.compatibilityrZsympy.utilities.exceptionsrwarnr rrrrrr rr"r%r(r)r*r r r r s&