h3ddlmZddlmZmZddlmZddlZddlm Z m Z m Z m Z gdZ ddZdd Zdd Zdd Zdd Z dd ZddZGdde Zy)) annotations)Iterablecast)repeatN)Matrix MatrixDataNDArraySolver)gauss_vector_solvergauss_matrix_solvergauss_jordan_solvergauss_jordan_inverseLUDecompositionc t|tr |j}|Dcgc]}|Dcgc] }t|c}c}}Scc}wcc}}wN) isinstancermatrixfloat)Arowvs 1lib/python3.12/site-packages/ezdxf/math/legacy.pycopy_float_matrixrsC!V HH/0 1qs #s!U1Xs #q 11 # 1s A A A A ct|}t|}t|}t|d|k7r tdt||k7r tdt ||t ||S)aSolves 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 sp, !A QA a&C 1Q4yC=>> 1v} K  !Q Q ""cVt|}t|}t|}t|d|k7r tdt||k7r tdt||t |j }t }|D]}|j t|||S)aVSolves 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-H%**,G XF+Hc:; Mr$c t|} t|d}td|D]}t|||}|}t|dz|D]}t|||}||kDs|}|}||||c||<||<||||c||<||<t|dz|D]}||| |||z } t||D])} || k(r d||| <||| xx| ||| zz cc<+|dk(r||xx| ||zz cc<ft|D]} ||| xx| ||| zz cc< y#t$rd}Y&wxYw)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 fs a&C!A$i 1c]!A$q'l Q$C#q NE{"#  %Q47' AaDQ47' AaDQ$C3 QqT!W$AQ}8"#AcF3KcF3K1qtCy=0K % a#!ad(" -CcF3K1qtCy=0K.%  sD33 EEct|}dg|z}t|dz ddD]A}|||||z ||<t|dz ddD]}||xx|||||zzcc<C|S)zSolve equation A . x = B for an upper triangular matrix A by backsubstitution. Args: A: row major matrix B: vector of floats r)rr1)rr"r#xr4rs rr!r!s a&C  A 37B #tad1g~!QB'C cFafQi!A$& &F($ Hr$ct|}t|}t|}t|d}t|d|k7r tdt||k7r tdd}d}dg|z}dg|z} dg|z} t|D]\} d} t|D]N} | | dk7s t|D]5}| |dk(s t || || k\s!t || |} | }|}7P| |xxdz cc<||k7r"||||c||<||<||||c||<||<|| | <||| <d|||z }d|||<||Dcgc]}||z c}||<||Dcgc]}||z c}||<t|D]j}||k(r |||}d|||<t|D]}|||xx||||zzcc<t|D]}|||xx||||zzcc<l_t|dz ddD]*} | | }|| }||k7s|D]}||||c||<||<,t |t |fScc}wcc}w) aSolves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B by the `Gauss-Jordan`_ algorithm, which is the slowest of all, but it is very reliable. Returns a copy of the modified input matrix `A` and the result matrix `x`. Internally used for matrix inverse calculation. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: 2-tuple of :class:`Matrix` objects Raises: ZeroDivisionError: singular matrix rrr&r:r?r;r')rrrr1r2r)rr"r*r+nmicolirow col_indices row_indicesipivr4bigjkpivinvrrdumr._rows rrrs.!#H #H H A HQKA 8A;1=>> 8}FGG D D#'K#'K 37D 1XqAAw!|qAAw!|x{1~.#5"%hqk!n"5C#$D#$D " T a 4<-5d^Xd^ *HTNHTN-5d^Xd^ *HTNHTN A Ax~d++"t.6tn=n!f*n=.6tn=n!f*n=8Cd{3-%C"%HSM$ Qx c"htnS&9C&??" Qx c"htnS&9C&??" /B1q5"b !1~1~ 4< )-dT$Z&T DJ! "  "F($; ;;%>=s H; Ic t|tr |j}n t|}t |}t |tt dg|dS)a-Returns 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 rrrsI!V887 ME xfcUE.B)C DQ GGr$c^eZdZdZdZd dZd dZd dZeddZ ddZ ddZ dd Z dd Z y )raRepresents a `LU decomposition`_ matrix of A, raise :class:`ZeroDivisionError` for a singular matrix. This algorithm is a little bit faster than the `Gauss-Elimination`_ algorithm using CPython and much faster when using pypy. The :attr:`LUDecomposition.matrix` attribute gives access to the matrix data as list of rows like in the :class:`Matrix` class, and the :attr:`LUDecomposition.index` attribute gives access to the swapped row indices. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] raises: ZeroDivisionError: singular matrix )rindex_detc t|}t|}d}g}|Dcgc]}dtd|Dz }}t|D]}d} |} t||D]#} || t || |z} | | kDs | } | } %|| k7r9t|D] } || | } ||| || | <| ||| <"| }|||| <|j | t|dz|D]H} || ||||z } | || |<t|dz|D]}|| |xx| |||zzcc<J||_||_||_ycc}w)Nr>c32K|]}t|ywr)r2).0rs r z+LUDecomposition.__init__..'s)>#Q#a&#sr:r) rrmaxr1r2appendrOrrP)selfrlur?detrOrscalingrHrFimaxr4tempr.rGs r__init__zLUDecomposition.__init__ s*1-RKMM"3c)>#)>&> >"MqACD1a[%aj3r!uQx=8#:CD ! Dy 8Cd8C=D$&qE#JBtHSM!%BqE#J$ d '  LL 1q5!_!uQx"Q%(*1aq1uaAqE!Hr!uQx/H)%'2!& "$  ; NsEc,t|jSr)strrrWs r__str__zLUDecomposition.__str__Fs4;;r$c^|jdtj|jS)N ) __class__reprlibreprrr`s r__repr__zLUDecomposition.__repr__Is&..!7<< #<"=>>r$c,t|jS)z Count of matrix rows (and cols).)rrr`s rrMzLUDecomposition.nrowsLs4;;r$c|Dcgc] }t|}}|j}|j}|j}d}t ||k7r t dt |D]N}||} || } |||| <|dk7r&t |dz |D]} | ||| || zz} n | dk7r|dz}| ||<Pt |dz ddD]:} || } t | dz|D]} | || | || zz} | || | z || <<|Scc}w)zSolves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as vector B with n elements. Args: B: vector [b1, b2, ..., bn] Returns: vector as list of floats rz;Item count of vector B has to be equal to matrix row count.rr:r;)rrrOrMrrr1)rWr"rXrXrOr?iir4ipsum_rGrr.s r solve_vectorzLUDecomposition.solve_vectorQsI-..Aq%(A.:: q6Q;M qAAhBB%DaDAbEQwrAvq)ABqE!HqtO+D*UAaDQB'CS6DS1Wa(3 qv--)BsGCL(AcF ( 7/sDcpt|ts$t|Dcgc] }t|c}}ntt|}|j|jk7r t dt|j Dcgc]}|j|c}jScc}wcc}w)a=Solves 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(rn transpose)rWr"rr+r.s r solve_matrixzLUDecomposition.solve_matrixys!V$1%=1Cd3i1%=>HFAH >>TZZ 'KL L6>mmoFosD%%c*oF )+ &>Gs B.B3c|jtj|j|jfjS)zReturns the inverse of matrix as :class:`Matrix` object, raise :class:`ZeroDivisionError` for a singular matrix. )shape)rqridentityrMrr`s rinversezLUDecomposition.inverses1    DJJ7O!P!W!WXXr$c|j}|j}t|jD] }||||z}|S)zmReturns the determinant of matrix, raises :class:`ZeroDivisionError` if matrix is singular. )rPrr1rM)rWrYrXr4s r determinantzLUDecomposition.determinants? YYtzz"A 2a58OC# r$N)rMatrixData | NDArray)returnr_)ryint)r"Iterable[float]ry list[float])r"rxryr)ryr)ryr)__name__ __module__ __qualname____doc__ __slots__r]rargpropertyrMrnrqrurwr$rrr sH&,I$L ?  &P0Y r$r)ryr )rrxr"r{ryr|)rrxr"rxryr)rr r"rryNone)rr r"r|ryr|)rrxr"rxryztuple[Matrix, Matrix])rr ryr) __future__rtypingrr itertoolsrrelinalgrr r r __all__rr r r r!rrrrr$rrsr#!77 2 "#J$N(1V $O<O< 4O<O