h1SSKJr SSKJrJr SSKJr SSKrSSKJ r J r J r J r /SQr SSjrSS jrSS jrSS jrSS jrSS jrSSjr"SS\ 5rg)) annotations)Iterablecast)repeatN)Matrix MatrixDataNDArraySolver)gauss_vector_solvergauss_matrix_solvergauss_jordan_solvergauss_jordan_inverseLUDecompositionc [U[5(a URnUVVs/sHoVs/sHn[U5PM snPM snn$s snfs snnfN) isinstancermatrixfloat)Arowvs C/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/legacy.pycopy_float_matrixrsF!V HH/0 1qs #s!U1Xs #q 11 # 1s AA AAc[U5n[U5n[U5n[US5U:wa [S5e[U5U:wa [S5e[ X5 [ X5$)abSolves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as vector B with n elements by the `Gauss-Elimination`_ algorithm, which is faster than the `Gauss-Jordan`_ algorithm. The speed improvement is more significant for solving multiple right-hand side quantities as matrix at once. Reference implementation for error checking. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: vector [b1, b2, ..., bn] Returns: vector as list of floats Raises: ZeroDivisionError: singular matrix r"A square nxn matrix A is required.z=Item count of vector B has to be equal to matrix A row count.)rlistlen ValueError_build_upper_triangle_backsubstitution)rBnums rr r sl, !A QA a&C 1Q4yC=>> 1v} K  ! Q ""cT[U5n[U5n[U5n[US5U:wa [S5e[U5U:wa [S5e[X#5 [ US9R 5n[ 5nUHnUR [X'55 M U$)a&Solves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B by the `Gauss-Elimination`_ algorithm, which is faster than the `Gauss-Jordan`_ algorithm. Reference implementation for error checking. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: matrix as :class:`Matrix` object Raises: ZeroDivisionError: singular matrix rr+Row count of matrices A and B has to match.r)rrrr rcols append_colr!)rr"matrix_amatrix_br#columnsresultcols rr r ?s(!#H #H h-C 8A;3=>> 8}FGG(-H%**,G XF+H:; Mr$c [U5n[US5n[SU5GHn[XU5nUn[US-U5Hn[XU5nX:dMUnUnM XXsX'X'XXsX'X'[US-U5HnXU*XU- n [XB5H(n XJ:Xa SXU 'MXU ==XUU -- ss'M* US:XaX==XU-- ss'Mc[U5Hn XU ==XUU -- ss'M M GM g![a SnGN!f=f)zBuild upper triangle for backsubstitution. Modifies A and B inplace! Args: A: row major matrix B: vector of floats or row major matrix rrN)r TypeErrorrangeabs) rr"r# b_col_counti max_elementmax_rowrvaluecr.s rr r fse a&C!A$i 1c]!$q'l Q$Cq NE"#  %4 AD4 ADQ$C QT!W$AQ}8"#AF3KF3K1tCy=0K % a!d(" -CF3K1tCy=0K.%  sD-- D=<D=c[U5nS/U-n[US- SS5H>nXXU- X4'[US- SS5HnX==XUX4--ss'M M@ U$)zSolve equation A . x = B for an upper triangular matrix A by backsubstitution. Args: A: row major matrix B: vector of floats r)rr1)rr"r#xr4rs rr!r!sy a&C  A 37B #tad1g~QB'C FafQi!$& &F($ Hr$c[U5n[U5n[U5n[US5n[US5U:wa [S5e[U5U:wa [S5eSnSnS/U-nS/U-n S/U-n [U5GH^n Sn [U5HSn XS:wdM [U5H7nXS:XdM [ X-U5U :dM#[ X-U5n U nUnM9 MU X==S- ss'Xv:waX&X'sX''X&'X6X7sX7'X6'XyU 'XhU 'SX&U- nSX&U'X&Vs/sHnUU-PM snX&'X6Vs/sHnUU-PM snX6'[U5HonUU:XaM UUUnSUUU'[U5HnUUU==X&UU--ss'M [U5HnUUU==X6UU--ss'M Mq GMa [US- SS5H,n XnXnXv:wdMUHnUUUUsUU'UU'M M. [ US9[ US94$s snfs snf) asSolves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B by the `Gauss-Jordan`_ algorithm, which is the slowest of all, but it is very reliable. Returns a copy of the modified input matrix `A` and the result matrix `x`. Internally used for matrix inverse calculation. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: 2-tuple of :class:`Matrix` objects Raises: ZeroDivisionError: singular matrix rrr&r:r?r;r')rrrr1r2r)rr"r*r+nmicolirow col_indices row_indicesipivr4bigjkpivinvrrdumr._rows rrrs.!#H #H H A HQKA 8A;1=>> 8}FGG D D#'K#'K 37D 1XqAw!|qAw!|x{1~.#5"%hk!n"5C#$D#$D " a <-5^X^ *HNHN-5^X^ *HNHNAAx~d++"t.6n=n!f*n=.6n=n!f*n=8Cd{3-%C"%HSM$ Qx c"hnS&9C&??" Qx c"hnS&9C&??" /B1q5"b !~~ < )-dT$Z&T DJ! "  "F($; ;;%>=s :H=Ic [U[5(a URnO [U5n[ U5n[ U[[ S/U555S$)aReturns the inverse of matrix `A` as :class:`Matrix` object. .. hint:: For small matrices (n<10) is this function faster than LUDecomposition(m).inverse() and as fast even if the decomposition is already done. Raises: ZeroDivisionError: singular matrix r:r)rrrrrrr)rr*nrowss rrrsL!V887 ME xfcUE.B)C DQ GGr$cv\rSrSrSrSrSSjrSSjrSSjr\ SSj5r SSjr SS jr SS jr SS jrS rg )ri aiRepresents a `LU decomposition`_ matrix of A, raise :class:`ZeroDivisionError` for a singular matrix. This algorithm is a little bit faster than the `Gauss-Elimination`_ algorithm using CPython and much faster when using pypy. The :attr:`LUDecomposition.matrix` attribute gives access to the matrix data as list of rows like in the :class:`Matrix` class, and the :attr:`LUDecomposition.index` attribute gives access to the swapped row indices. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] raises: ZeroDivisionError: singular matrix )rindex_detc [U5n[U5nSn/nUVs/sHnS[SU55- PM nn[U5HnSn Un [X5H#n X{[ X+U5-n X:dMU n U n M% X:wa5[U5Hn X*U n X(U X*U 'XUU 'M U*nXxXz'UR U 5 [US-U5HFn X+UX(U- n XU U'[US-U5HnX+U==XUU--ss'M MH M XPlX lX@lgs snf)Nr>c38# UHn[U5v M g7fr)r2).0rs r +LUDecomposition.__init__..'s)>#Q#a&&#sr:r) rrmaxr1r2appendrOrrP)selfrlur?detrOrscalingrHrFimaxr4tempr.rGs r__init__LUDecomposition.__init__ sf*1-RKMM"3c)>#)>&> >"MqACD1[%j3ruQx=8:CD ! y 8C8C=D$&E#JBHSM!%qE#J$ d '  LL 1q5!_uQx"%(*1aq1uaAE!H!uQx/H)%'2!& "$  ; NsD?c,[UR5$r)strrrXs r__str__LUDecomposition.__str__Fs4;;r$c`URS[R"UR53$)N ) __class__reprlibreprrrbs r__repr__LUDecomposition.__repr__Is&..!7<< #<"=>>r$c,[UR5$)z Count of matrix rows (and cols).)rrrbs rrMLUDecomposition.nrowsLs4;;r$cUVs/sHn[U5PM nnURnURnURnSn[ U5U:wa [ S5e[ U5HLnXXn X9n X8X9'US:wa&[ US- U5Hn XUU X;--n M O U S:waUS-nXU'MN [ US- SS5H8n X<n [ U S-U5Hn XU U X=--n M XU U - X<'M: U$s snf)zSolves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as vector B with n elements. Args: B: vector [b1, b2, ..., bn] Returns: vector as list of floats rz;Item count of vector B has to be equal to matrix row count.rr:r;)rrrOrMrrr1)rXr"rXrYrOr?iir4ipsum_rGrr.s r solve_vectorLUDecomposition.solve_vectorQs1-..Aq%(A.:: q6Q;M qAhB%DDAEQwrAvq)AqE!HqtO+D*UaDQB'C6DS1Wa(3 qv--)sGCL(AF ( 7/sDcz[U[5(d$[UVs/sHn[U5PM snS9nO[[U5nURUR:wa [ S5e[UR 5Vs/sHo@RU5PM snS9R5$s snfs snf)aSolves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Args: B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: matrix as :class:`Matrix` object r'z,Row count of self and matrix B has to match.) rrrrrMrr(rs transpose)rXr"rr+r.s r solve_matrixLUDecomposition.solve_matrixys!V$$1%=1Cd3i1%=>HFAH >>TZZ 'KL L6>mmoFos%%c*oF )+ &>Gs B3B8cUR[R"URUR4S9R5$)zrReturns the inverse of matrix as :class:`Matrix` object, raise :class:`ZeroDivisionError` for a singular matrix. )shape)rwridentityrMrrbs rinverseLUDecomposition.inverses1    DJJ7O!P!W!WXXr$cURnURn[UR5H nXUU-nM U$)z]Returns the determinant of matrix, raises :class:`ZeroDivisionError` if matrix is singular. )rPrr1rM)rXrZrYr4s r determinantLUDecomposition.determinants= YYtzz"A a58OC# r$)rPrOrN)rMatrixData | NDArray)returnra)rint)r"Iterable[float]r list[float])r"rrr)rr)rr)__name__ __module__ __qualname____firstlineno____doc__ __slots__r^rcrjpropertyrMrsrwr|r__static_attributes__r$rrr sH&,I$L ?  &P0Y r$r)rr )rrr"rrr)rrr"rrr)rr r"rrNone)rr r"rrr)rrr"rrztuple[Matrix, Matrix])rr rr) __future__rtypingrr itertoolsrrhlinalgrr r r __all__rr r r r!rrrrr$rrsr#!77 2 "#J$N(1V $O<O< 4O<O