o 8Vaa@sdZddlmZeddddddZd d Zd d Zd dZddZddZ ddZ ddZ ddZ ddZ ddZddZdd Zd!S)"zZ Fundamental operations of dense matrices. The dense matrix is stored as a list of lists )SymPyDeprecationWarningZ densetoolsi1z1.1)ZfeatureZissueZdeprecated_since_versioncCs,|j}tt|D] }||||7}q |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 )zerorangelen)matlistKresultir ;/usr/lib/python3/dist-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]] cSg|]}t|qSr list).0ar r r 9ztranspose..ziprrr 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)rrowrr r rQszconjugate..r rr rr conjugate<srcCs<g}|D]}t|dd}|dur|}n|}||q|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] rN)getattrappend)rrrrZconjZconjrowr r r rTs   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]] )rrrr r r conjugate_transposemsrcCsddt||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 augmentsr"cCsZg}t|D]$}|gt|D]}||kr!|||dq|||jqq|S)z Returns an identity matrix of size n. Examples ======== >>> from sympy.matrices.densetools import eye >>> from sympy import ZZ >>> eye(3, ZZ) [[1, 0, 0], [0, 1, 0], [0, 0, 1]] )rrr)nrrr jr r r eyes   r&cCs||S)a Returns the ith row of a matrix Examples ======== >>> from sympy.matrices.densetools import row >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> row(a, 2) [6, 2, 3] r )rr r r r rsrcCs$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]] cSr r rrlr r r rrzcol..cSsg|]}|gqSr r r'r r r rsr)rr Zmatcolr r r colsr)cCs||||||<||<|S)zC Returns the matrix with index1 row and index2 row swapped r )rindex1index2rr r r rowswapsr,cCs2tt||D]}|||||||<q|S)z% Multiplies index row with k rr)rindexkrr r r r rowmulsr0cCs>tt||D]}||||||||||<q|S)zN Adds the index1 row with index2 row which in turn is multiplied by k r-)rr*r+r/rr r r r rowadds&r1cCst|||kS)aD Checks whether matrix is hermitian Examples ======== >>> 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 )rrr r r isHermitiansr2N)__doc__Zsympy.utilities.exceptionsrwarnr rrrrr"r&rr)r,r0r1r2r r r r s*