'j1ddlmZddlmZmZddlmZddlZddlm Z m Z m Z m Z gdZ dd ZddZddZddZd dZd!dZd"dZGdde ZdS)#) annotations)Iterablecast)repeatN)Matrix MatrixDataNDArraySolver)gauss_vector_solvergauss_matrix_solvergauss_jordan_solvergauss_jordan_inverseLUDecompositionreturnr cRt|tr|j}d|DS)Nc&g|]}d|DS)c,g|]}t|Sfloat.0vs K/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/legacy.py z0copy_float_matrix...s # # #!U1XX # # #rrrows rrz%copy_float_matrix..s' 1 1 1 # #s # # # 1 1 1r) isinstancermatrix)As rcopy_float_matrixr#s/!V H 1 1q 1 1 11rr"MatrixData | NDArrayBIterable[float] list[float]c0t|}t|}t|}t|d|krtdt||krtdt ||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.)r#listlen ValueError_build_upper_triangle_backsubstitution)r"r%nums rr r s, !A QA a&&C 1Q4yyC=>>> 1vv}} K   !Q Q " ""rrct|}t|}t|}t|d|krtdt||krtdt||t |}t }|D]%}|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!)r#r+r,r-rcols append_colr.)r"r%matrix_amatrix_br/columnsresultcols rr r ?s(!##H ##H h--C 8A;3=>>> 8}}FGGG(H---H%%%**,,G XXF<<+Hc::;;;; Mrr*Nonec Vt|} t|d}n#t$rd}YnwxYwtd|D]^}t|||}|}t|dz|D]'}t|||}||kr|}|}(||||c||<||<||||c||<||<t|dz|D]}||| |||z } t||D]9} || kr d||| <||| xx| ||| zz cc<:|dkr||xx| ||zz cc<t|D]'} ||| xx| ||| zz cc<(`dS)zBuild upper triangle for backsubstitution. Modifies A and B inplace! Args: A: row major matrix B: vector of floats or row major matrix rrN)r+ TypeErrorrangeabs) r"r%r/ b_col_counti max_elementmax_rowrvaluecr9s rr-r-fs  a&&C!A$ii  1c]]11!A$q'll Q$$  C#q NNE{""# Q47' AaDQ47' AaDQ$$ 1 1C3 QqT!W$AQ}} 1 188"#AcF3KKcF3KKK1qtCy=0KKKKa#!ad(" --11CcF3KKK1qtCy=0KKKK1 111s ' 66c t|}dg|z}t|dz ddD]X}|||||z ||<t|dz ddD]'}||xx|||||zzcc<(Y|S)zSolve equation A . x = B for an upper triangular matrix A by backsubstitution. Args: A: row major matrix B: vector of floats r)r+r=)r"r%r/xr@rs rr.r.s a&&C  A 37B # #''tad1g~!QB'' ' 'C cFFFafQi!A$& &FFFF ' Hrtuple[Matrix, Matrix]ct|}t|}t|}t|d}t|d|krtdt||krtdd}d}dg|z}dg|z} dg|z} t|D]} d} t|D]j} | | dkr\t|D]L}| |dkr>t || || krt || |} | }|}Mk| |xxdz cc<||kr.||||c||<||<||||c||<||<|| | <||| <d|||z d|||<fd||D||<fd||D||<t|D]}||kr |||}d|||<t|D]'}|||xx||||zzcc<(t|D]'}|||xx||||zzcc<(t|dz d d D]4} | | }|| }||kr|D]}||||c||<||<5t | t | fS) 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 rr)r1rFr?cg|]}|zSrrrrpivinvs rrz'gauss_jordan_solver..===!f*===rcg|]}|zSrrrMs rrz'gauss_jordan_solver..rOrrGr2)r#r+r,r=r>r)r"r%r5r6nmicolirow col_indices row_indicesipivr@bigjkrdumr9_rowrNs @rrrs}.!##H ##H H A HQKA 8A;1=>>> 8}}FGGG D D#'K#'K 37D 1XX@@q % %AAw!||q%%AAw!||x{1~..#55"%hqk!n"5"5C#$D#$D T a 4<<-5d^Xd^ *HTNHTN-5d^Xd^ *HTNHTN A Ax~d++"t====htn=======htn===88 @ @Cd{{3-%C"%HSM$ Qxx @ @ c"""htnS&9C&??""""Qxx @ @ c"""htnS&9C&??"""" @ @1q5"b ! !@@1~1~ 4<<  @ @)-dT$Z&T DJJ  " " "F($;$;$; ;;rc t|tr|j}nt|}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 rFr)r rr!r*r+rr)r"r5nrowss rrrs^!V877 MME xfcUE.B.B)C)C D DQ GGrcfeZdZdZdZddZddZdd Zedd Z ddZ ddZ ddZ ddZ dS)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 )r!index_detr"r$c t|}t|}d}g}d|D}t|D],}d}|} t||D]0} || t|| |z} | |kr| }| } 1|| krPt|D]2} || | } ||| || | <| ||| <3| }|||| <|| t|dz|D]e} || ||||z } | || |<t|dz|D]'} || | xx| ||| zzcc<(f.||_||_||_dS)NrKcFg|]}dtd|Dz S)rKc34K|]}t|VdSN)r>rs r z6LUDecomposition.__init__...'s()>)>Q#a&&)>)>)>)>)>)>r)maxrs rrz,LUDecomposition.__init__..'s4MMM3c)>)>#)>)>)>&>&> >MMMrrFr)r#r+r=r>appendr`r!ra)selfr"lurQdetr`scalingrZrXimaxr@tempr9rYs r__init__zLUDecomposition.__init__ s*1--R NM"MMMq 0 0ACD1a[[  %aj3r!uQx==8#::CDDyy 88&&Cd8C=D$&qE#JBtHSM!%BqE#JJd '  LL   1q5!__ 0 0!uQx"Q%(*1aq1ua00AqE!HHHr!uQx/HHHH0 0 !& "$  rrstrc*t|jSre)rpr!ris r__str__zLUDecomposition.__str__Fs4;rcH|jdtj|jS)N ) __class__reprlibreprr!rrs r__repr__zLUDecomposition.__repr__Is$.>>7< #<#<>>>rintc*t|jS)z Count of matrix rows (and cols).)r+r!rrs rr^zLUDecomposition.nrowsLs4;rr%r&r'c>d|D}|j}|j}|j}d}t||krt dt |D]d}||}||} ||||<|dkr1t |dz |D]} | ||| || zz} n | dkr|dz}| ||<et |dz ddD]N} || } t | dz|D]} | || | || zz} | || | z || <O|S)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 c,g|]}t|Srrrs rrz0LUDecomposition.solve_vector..\s...q%((...rrz;Item count of vector B has to be equal to matrix row count.rrFrG)r!r`r^r+r,r=) rir%Xrjr`rQiir@ipsum_rYrr9s r solve_vectorzLUDecomposition.solve_vectorQsn/.A...: q66Q;;M q  AAhBB%DaDAbEQwwrAvq)),,ABqE!HqtO+DD,UAaDDQB'' ) )CS6DS1Wa(( . .3 qv--BsGCL(AcFFrrcLt|tstd|D}ntt|}|jjkrt dtfd|DS)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 c,g|]}t|Sr)r*rs rrz0LUDecomposition.solve_matrix..s%=%=%=Cd3ii%=%=%=rr2z,Row count of self and matrix B has to match.c:g|]}|Sr)r)rr9ris rrz0LUDecomposition.solve_matrix..s'FFFsD%%c**FFFr)r rrr^r,r3 transpose)rir%r6s` r solve_matrixzLUDecomposition.solve_matrixys!V$$ '%=%=1%=%=%=>>>HHFAH >TZ ' 'KLL LFFFFhmmooFFF   )++ rct|tj|j|jfjS)zReturns the inverse of matrix as :class:`Matrix` object, raise :class:`ZeroDivisionError` for a singular matrix. )shape)rridentityr^r!rrs rinversezLUDecomposition.inverses1    DJ7O!P!P!P!WXXXrrcr|j}|j}t|jD]}||||z}|S)zmReturns the determinant of matrix, raises :class:`ZeroDivisionError` if matrix is singular. )rar!r=r^)rirkrjr@s r determinantzLUDecomposition.determinantsC Ytz""  A 2a58OCC rN)r"r$)rrp)rrz)r%r&rr')r%r$rr)rr)rr)__name__ __module__ __qualname____doc__ __slots__rorsrypropertyr^rrrrrrrrr s&,I$$$$L    ????   X &&&&P0YYYY      rr)rr )r"r$r%r&rr')r"r$r%r$rr)r"r r%r*rr:)r"r r%r'rr')r"r$r%r$rrI)r"r rr) __future__rtypingrr itertoolsrrwlinalgrr r r __all__r#r r r-r.rrrrrrrsW#"""""!!!!!!!!777777777777   2222 "#"#"#"#J$$$$N(1(1(1(1V    $O<O<O<O