B ˜‘[˜ใ@szdZddlmZddlmZedddd กdd „Zd d „Zd d „Zdd„Z dd„Z dd„Z dd„Z dd„Z dd„ZdS)z[ Fundamental arithmetic of dense matrices. The dense matrix is stored as a list of lists. ้)ฺrange)ฺSymPyDeprecationWarningZ densearithi—1z1.1)ZfeatureZissueZdeprecated_since_versioncs‡fdd„t||ƒDƒS)aำ 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||ˆƒ‘qSฉ)ฺaddrow)ฺ.0ฺrow1ฺrow2)ฺKr๚8lib/python3.7/site-packages/sympy/matrices/densearith.py๚ +szadd..)ฺzip)ฺmatlist1ฺmatlist2r r)r r ฺaddsrcCsdd„t||ƒDƒS)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 Aszaddrow..)r )rrr rrr r-srcCst|t||ƒ|ƒS)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 )rฺnegate)r rr rrr ฺsubDsrcs‡fdd„|DƒS)aข 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|ˆƒ‘qSr)ฺ negaterow)rฺrow)r rr r ~sznegate..r)ฺmatlistr r)r r resrcCsdd„|DƒS)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|] }| ‘qSrr)rฺelementrrr r ’sznegaterow..r)rr rrr rsrcsBdd„t|ŽDƒ}g}x&|D]‰| ‡‡fdd„|DƒกqW|S)aแ 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|ƒ‘qSr)ฺlist)rฺirrr r ดszmulmatmat..csg|]}tˆ|ˆƒ‘qSr)ฺ mulrowcol)rฺcol)r rrr r ทs)r ฺappend)r rr Zmatcolฺresultr)r rr ฺ mulmatmat•s  rcs‡‡fdd„|DƒS)aึ 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|ˆˆƒ‘qSr)ฺ mulrowscaler)rr)r ฺscalerrr r ัsz mulmatscaler..r)rrr r)r rr ฺ mulmatscalerปsrcs‡fdd„|DƒS)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|] }ˆ|‘qSrr)rr)rrr r โsz mulrowscaler..r)rrr r)rr rิsrcCs4|j}x(tt|ƒƒD]}|||||7}qW|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 )Zzerorฺlen)rrr rrrrr rๅsrN)ฺ__doc__Zsympy.core.compatibilityrZsympy.utilities.exceptionsrฺwarnrrrrrrrrrrrrr ฺs   !&