o 8Vam@sndZddlmZeddddddZd d Zd d Zd dZddZddZ ddZ ddZ ddZ dS)z[ Fundamental arithmetic of dense matrices. The dense matrix is stored as a list of lists. )SymPyDeprecationWarningZ densearithi1z1.1)ZfeatureZissueZdeprecated_since_versioncsfddt||DS)a Adds matrices row-wise. Examples ======== >>> from sympy.matrices.densearith import add >>> from sympy import ZZ >>> e = [ ... [ZZ(12), ZZ(78)], ... [ZZ(56), ZZ(79)]] >>> f = [ ... [ZZ(1), ZZ(2)], ... [ZZ(3), ZZ(4)]] >>> g = [ ... [ZZ.zero, ZZ.zero], ... [ZZ.zero, ZZ.zero]] >>> add(e, f, ZZ) [[13, 80], [59, 83]] >>> add(f, g, ZZ) [[1, 2], [3, 4]] See Also ======== addrow csg|] \}}t||qS)addrow).0row1row2Kr;/usr/lib/python3/dist-packages/sympy/matrices/densearith.py *szadd..zipmatlist1matlist2r rrr addsrcCsddt||DS)ac Adds two rows of a matrix element-wise. Examples ======== >>> from sympy.matrices.densearith import addrow >>> from sympy import ZZ >>> a = [ZZ(12), ZZ(34), ZZ(56)] >>> b = [ZZ(14), ZZ(56), ZZ(63)] >>> c = [ZZ(0), ZZ(0), ZZ(0)] >>> addrow(a, b, ZZ) [26, 90, 119] >>> addrow(b, c, ZZ) [14, 56, 63] cSsg|]\}}||qSrr)rZelement1Zelement2rrr r @zaddrow..r )rrr rrr r,srcCst|t|||S)a, Subtracts two matrices by first negating the second matrix and then adding it to first matrix. Examples ======== >>> from sympy.matrices.densearith import sub >>> from sympy import ZZ >>> e = [ ... [ZZ(12), ZZ(78)], ... [ZZ(56), ZZ(79)]] >>> f = [ ... [ZZ(1), ZZ(2)], ... [ZZ(3), ZZ(4)]] >>> g = [ ... [ZZ.zero, ZZ.zero], ... [ZZ.zero, ZZ.zero]] >>> sub(e, f, ZZ) [[11, 76], [53, 75]] >>> sub(f, g, ZZ) [[1, 2], [3, 4]] See Also ======== negate negaterow )rnegaterrrr subCsrcfdd|DS)a Negates the elements of a matrix row-wise. Examples ======== >>> from sympy.matrices.densearith import negate >>> from sympy import ZZ >>> a = [ ... [ZZ(2), ZZ(3)], ... [ZZ(4), ZZ(5)]] >>> b = [ ... [ZZ(0), ZZ(0)], ... [ZZ(0), ZZ(0)]] >>> negate(a, ZZ) [[-2, -3], [-4, -5]] >>> negate(b, ZZ) [[0, 0], [0, 0]] See Also ======== negaterow csg|]}t|qSr) negaterowrrowrrr r }sznegate..r)matlistr rrr rdsrcCsdd|DS)a, Negates a row element-wise. Examples ======== >>> from sympy.matrices.densearith import negaterow >>> from sympy import ZZ >>> a = [ZZ(2), ZZ(3), ZZ(4)] >>> b = [ZZ(0), ZZ(0), ZZ(0)] >>> negaterow(a, ZZ) [-2, -3, -4] >>> negaterow(b, ZZ) [0, 0, 0] cSsg|]}| qSrrrelementrrr r sznegaterow..r)rr rrr rsrcs>ddt|D}g}|D]|fdd|Dq |S)a Multiplies two matrices by multiplying each row with each column at a time. The multiplication of row and column is done with mulrowcol. Firstly, the second matrix is converted from a list of rows to a list of columns using zip and then multiplication is done. Examples ======== >>> from sympy.matrices.densearith import mulmatmat >>> from sympy import ZZ >>> from sympy.matrices.densetools import eye >>> a = [ ... [ZZ(3), ZZ(4)], ... [ZZ(5), ZZ(6)]] >>> b = [ ... [ZZ(1), ZZ(2)], ... [ZZ(7), ZZ(8)]] >>> c = eye(2, ZZ) >>> mulmatmat(a, b, ZZ) [[31, 38], [47, 58]] >>> mulmatmat(a, c, ZZ) [[3, 4], [5, 6]] See Also ======== mulrowcol cSsg|]}t|qSr)list)rirrr r zmulmatmat..csg|]}t|qSr) mulrowcol)rcolr rrr r r)r append)rrr Zmatcolresultrr!r mulmatmats r$csfdd|DS)a Performs scaler matrix multiplication one row at at time. The row-scaler multiplication is done using mulrowscaler. Examples ======== >>> from sympy import ZZ >>> from sympy.matrices.densearith import mulmatscaler >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> mulmatscaler(a, ZZ(1), ZZ) [[3, 7, 4], [2, 4, 5], [6, 2, 3]] See Also ======== mulscalerrow csg|]}t|qSr) mulrowscalerrr scalerrr r rz mulmatscaler..r)rr'r rr&r mulmatscalersr(cr)a Performs the scaler-row multiplication element-wise. Examples ======== >>> from sympy import ZZ >>> from sympy.matrices.densearith import mulrowscaler >>> a = [ZZ(3), ZZ(4), ZZ(5)] >>> mulrowscaler(a, 2, ZZ) [6, 8, 10] csg|]}|qSrrrr'rr r rz mulrowscaler..r)rr'r rr)r r%sr%cCs0|j}tt|D] }|||||7}q |S)aJ Multiplies two lists representing row and column element-wise. Gotcha: Here the column is represented as a list contrary to the norm where it is represented as a list of one element lists. The reason is that the theoretically correct approach is too expensive. This problem is expected to be removed later as we have a good data structure to facilitate column operations. Examples ======== >>> from sympy.matrices.densearith import mulrowcol >>> from sympy import ZZ >>> a = [ZZ(2), ZZ(4), ZZ(6)] >>> mulrowcol(a, a, ZZ) 56 )Zzerorangelen)rr r r#rrrr rsrN) __doc__Zsympy.utilities.exceptionsrwarnrrrrrr$r(r%rrrrr s" !&