'jtgRUddlmZddlmZmZmZmZmZmZm Z ddl m Z ddl Z ddl mZddlmZddlZddlZddlZddlmZddlmZgdZdDd ZeeeZd ed <eeedfZd ed<eeefZ d ed<ej!ej"Z!d ed<dEdZ#eddFdZ$GddZ%Gdde j&Z'dGdHd#Z(dId%Z)dJd)Z*dKd,Z+Gd-d.e'Z,dLd/Z-dJd0Z.dMd2Z/dNdOd5Z0dNdPd7Z1dQd:Z2Gd;dZ4dSdCZ5dS)T) annotations)IterableTupleListSequenceAnycastOptional) TypeAliasN) lru_cache)repeat) USE_C_EXT)MatrixSolvernumpy_vector_solvernumpy_matrix_solver NumpySolvertridiagonal_vector_solvertridiagonal_matrix_solverdetect_banded_matrixcompact_banded_matrixBandedMatrixLU banded_matrixquadratic_equationcubic_equationbinomial_coefficientreturnIterable[list]c'DKt|D]}t|VdSN)ziplist)argses K/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/linalg.py zip_to_listr&,s4 $Z1gg r MatrixData.FrozenMatrixDataShapeNDArraycRt|tr|j}d|DS)Nc&g|]}d|DS)c,g|]}t|Sfloat.0vs r% z0copy_float_matrix...:s # # #!U1XX # # #r'r/r3rows r%r5z%copy_float_matrix..:s' 1 1 1 # #s # # # 1 1 1r') isinstancermatrix)As r%copy_float_matrixr;7s/!V H 1 1q 1 1 11r')maxsizekintir1c||krtdStj|}tj|}tj||z }t|||zz S)a Computes the binomial coefficient (denoted by `k choose i`). Please see the following website for details: http://mathworld.wolfram.com/BinomialCoefficient.html Args: k: size of the set of distinct elements i: size of the subsets r)r1math factorial)r>r@k_facti_factk_i_facts r%rr=sa 1uuQxx.##F.##FN1q5))H 8f,- . ..r'cxeZdZdZdZ d@dAd ZdBd ZdCdZdDdZdDdZ e dEdZ e dFdZ e dFdZe dGdZdHdZdHdZdHdZdId ZdId!ZdJdKd%ZdJdKd&ZdLdKd(ZedMd)ZdNd+ZdNd,ZdOd-ZdPd1ZdQd3ZdRd7ZdRd8Z dSd:Z!e!Z"dSd;Z#e#Z$dSd<Z%e%Z&dOd=Z'dOd>Z(dTd?Z)dS)UraBasic matrix implementation based :class:`numpy.ndarray`. Matrix data is stored in row major order, this means in a list of rows, where each row is a list of floats. 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An `index` of ``0`` specifies the main diagonal, negative values specifies diagonals below the main diagonal and positive values specifies diagonals above the main diagonal. e.g. given a 4x4 matrix: index ``0`` is [00, 11, 22, 33], index ``-1`` is [10, 21, 32] and index ``+1`` is [01, 12, 23] rN) r8r1r?r maxabsminr!rrsrwr9 IndexError)rZryrI col_offset row_offsetvalues r%set_diagzMatrix.set_diags eeS\ * * )5<<((EeQ-- c%mm,, c$*dj&A&A B BEJJ  LE5 FK EJ. 0BBCC      s!B44 CCcRt|}|dd|S)z6Returns the identity matrix for configuration `shape`.)rJrr)rr)clsrJrds r%identityzMatrix.identitys-     1cr'Sequence[float]c|jjdkr(tj|gtj|_dSt ||jkr tj|j|f|_dStd)zAppend a row to the matrix.rrOInvalid item count.N) r9sizerSrTrUrrwr_rrZrIs r% append_rowzMatrix.append_rowsk ; q (E7"*===DKKK ZZ4: % %% U 23DKKK233 3r'c|jjdkr1tjd|Dtj|_dSt ||jkr tj|j|f|_dStd)zAppend a column to the matrix.rcg|]}|gSr/r/)r3items r%r5z%Matrix.append_col..s#=#=#=tTF#=#=#=r'rOrN) r9rrSrTrUrrsc_rrs r% append_colzMatrix.append_colsx ; q (#=#=u#=#=#=RZPPPDKKK ZZ4: % %% U 23DKKK233 3r'cP|}d|jj_|S)z@Returns a frozen matrix, all data is stored in immutable tuples.F)rer9flags writeablercs r%freezez Matrix.freeze s MMOO#( r'rtuple[int, int]r1c6t|j|S)zjGet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. )r1r9)rZrs r% __getitem__zMatrix.__getitem__s T[&'''r'rc||j|<dS)zjSet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. Nrb)rZrrs r% __setitem__zMatrix.__setitem__s " Dr'otherobjectboolct|tstd|j|jkrtdt t j|j|jkS)z'Returns ``True`` if matrices are equal.Matrix class required.Matrices have different shapes.)r8rrYrJrrSallr9rZrs r%__eq__z Matrix.__eq__sb%(( 6455 5 : $ $=>> >BF4;%,677888r'c t|tstd|j|jkrtdt t jt j|j|j|j S)zReturns ``True`` if matrices are close to equal, tolerance value for comparison is adjustable by the attribute :attr:`Matrix.abs_tol`. rr)atol) r8rrYrJrrSriscloser9rHrs r%rzMatrix.isclose'sr %(( 6455 5 : $ $=>> >BF2:dk5>>F r'ct|trt|j|jzSt|jt|zS)zCMatrix addition by another matrix or a float, returns a new matrix.rbr8rr9r1rs r%__add__zMatrix.__add__?sL eV $ $ =u|!;<<< <uU||!;<<< >>>#####,,,,, 2[ 44444444 ((((""""9999 V V V V    H====H====H,,,,$$$$111111r'rcReZdZejd dZejd dZd S) rBMatrixData | NDArrayrrcdSr r/rZrs r% solve_matrixzSolver.solve_matrixj r'rnrzcdSr r/rs r% solve_vectorzSolver.solve_vectornrr'Nrrrrrrnrrz)rrrabcabstractmethodrrr/r'r%rrisZ           r'rrNabcrct||krt||kr| fS| |z fS tj|dzd|z|zz }n#t$rt cYSwxYw| |zd|zz | |z d|zz fS)z~Returns the solution for the quadratic equation ``a*x^2 + b*x + c = 0``. Returns 0-2 solutions as a tuple of floats. @)rrBsqrtrtuple)rrrrH discriminants r%rrss  1vv q66G  B5LQyyAA !122 wwR, 37 +\0AcAg/N OOs AA/.A/dct|dkr0 t|||S#t$rtcYSwxYw||z }||z }||z }||z}|dz }d|z|z dz } d|z|zd|zz d||zzz dz } | | z| z} | | | zz} | dkrt j| } d}t jd | | zt jt| | z|z}t jd | | z t jt| | z |z}||z}||z r| |zfS|dz }| |z| |z | |z fSt j| t j| z }t j| dz}|t j |dz z|z |t j |dtj zzdz z|z |t j |d tj zzdz z|z fS) zReturns the solution for the cubic equation ``a*x^3 + b*x^2 + c*x + d = 0``. Returns 0-3 solutions as a tuple of floats. rNg@g"@g;@rgK@gUUUUUU?rg@) rrArithmeticErrorrrBrcopysignpowacoscospi)rrrrr:rCAAA3QRQQQDsqrtDexpSrSTST_2thsqrtQ2s r%rrsF  1vv~~ %aA.. .   77NNN  AA AA AA QB SB q2A q1tax #a. 0D8A a%!)C q1u ACxx !  M#q5y ) )DHSU^^S,I,I I M#q5y ) )DHSU^^S,I,I I U q5 C"H; 8Dbd d   1ty#& ' 'B Yr]]S F"s(###b(2dg -4555:2dg -4555: s&AAr:rrctj|tj}tj|tj}ttj||S)amSolves the linear equation system given by a nxn Matrix A . x = B by the numpy.linalg.solve() function. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Raises: numpy.linalg.LinAlgError: singular matrix rOrb)rSrTrUrrsolver:rmat_Amat_Bs r%rrsQ HQbj ) ) )E HQbj ) ) )E 66 7 7 77r'rnrzctj|tj}tjd|Dtj}ttjtj||S)atSolves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as vector B with n elements by the numpy.linalg.solve() function. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: vector [b1, b2, ..., bn] Raises: numpy.linalg.LinAlgError: singular matrix rOc.g|]}t|gSr/r0r2s r%r5z'numpy_vector_solver..s ,,,QuQxxj,,,r')rSrTrUr"r]rrrs r%rrsg HQbj ) ) )E H,,!,,,BJ ? ? ?E 6677 8 88r'c*eZdZdZddZdd Zdd Zd S)rz5Replaces in v1.2 the :class:`LUDecomposition` solver.r:rrrcPtj|tj|_dS)NrO)rSrTrUr)rZr:s r%r[zNumpySolver.__init__sXarz222 r'rrctj|tj}ttj|j|S)aN 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]] Raises: numpy.linalg.LinAlgError: singular matrix rOrb)rSrTrUrrrrrZrrs r%rzNumpySolver.solve_matrixs="*---RY__TZ??@@@@r'rnrzctjd|Dtj}ttjtj|j|S)a Solves 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] Raises: numpy.linalg.LinAlgError: singular matrix c.g|]}t|gSr/r0r2s r%r5z,NumpySolver.solve_vector..s 000588*000r'rO)rSrTrUr"r]rrrrs r%rzNumpySolver.solve_vectorsS00a000 CCCBHRY__TZ??@@AAAr'N)r:rrrrr)rrrrr[rrr/r'r%rrs`??3333AAAA B B B B B Br'rc`d|D\}}}t|||t|S)a%Solves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as vector B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)]. Note: a0 is not used but has to be present, cn-1 is also not used and must not be present. If an :class:`ZeroDivisionError` exception occurs, the equation system can possibly be solved by :code:`BandedMatrixLU(A, 1, 1).solve_vector(B)` Args: A: diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]] :: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] B: iterable of floats [[b1, b1, ..., bn] Returns: list of floats Raises: ZeroDivisionError: singular matrix c,g|]}t|Sr/rRr2s r%r5z-tridiagonal_vector_solver.."""1tAww"""r')_solve_tridiagonal_matrixr")r:rrrrs r%rrs78#""""GAq! $Q1d1gg 6 66r'cd|D\t|tstd|D}ntt|}|jt krt dtfd|DS)aSolves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)]. Note: a0 is not used but has to be present, cn-1 is also not used and must not be present. If an :class:`ZeroDivisionError` exception occurs, the equation system can possibly be solved by :code:`BandedMatrixLU(A, 1, 1).solve_vector(B)` Args: A: diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]] :: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: matrix as :class:`Matrix` object Raises: ZeroDivisionError: singular matrix c,g|]}t|Sr/rRr2s r%r5z-tridiagonal_matrix_solver..;r"r'c,g|]}t|Sr/rRr6s r%r5z-tridiagonal_matrix_solver..=s!9!9!9$s))!9!9!9r'rbz+Row count of matrices A and B has to match.c4g|]}t|Sr/)r#)r3rrrrs r%r5z-tridiagonal_matrix_solver..Ds(SSSC)!Q377SSSr')r8rr rsrrrr)r:rmatrix_brrrs @@@r%rrsB#""""GAq! a #!9!9q!9!9!9:::??~QFGGG SSSSSS8==??SSS   ikkr'rct|}dg|z}dg|z}|d}|d|z |d<td|D]P}||dz |z ||<||||||zz }||||||dz zz |z ||<Qt|dz ddD]'}||xx||dz||dzzzcc<(|S)aBSolves the linear equation system given by a tri-diagonal Matrix(a, b, c) . x = r. Matrix configuration:: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] Args: a: lower diagonal [a0 .. an-1], a0 is not used but has to be present b: central diagonal [b0 .. bn-1] c: upper diagonal [c0 .. cn-1], cn-1 is not used and must not be present r: right-hand side quantities Returns: vector x as list of floats Raises: ZeroDivisionError: singular matrix rrrvr)rr) rrrrnugambetjs r%r#r#Hs4VVAUQYAuqyC1C Q4#:AaD 1a[[..1q5CAdQqTCF]"!qtaAh&#-! AEB # #&& !AE Qq1uX%% Hr'Ttuple[Matrix, int, int]cTt||\}}t|||}|||fS)aYTransform matrix A into a compact banded matrix representation. Returns compact representation as :class:`Matrix` object and lower- and upper band count m1 and m2. Args: A: input :class:`Matrix` check_all: check all diagonals if ``True`` or abort testing after first all zero diagonal if ``False``. )rr)r: check_allm1m2rds r%rrqs4"!Y / /FBaR((A b"9r'rcJdfd }dfd }||fS)zReturns lower- and upper band count m1 and m2. Args: A: input :class:`Matrix` check_all: check all diagonals if ``True`` or abort testing after first all zero diagonal if ``False``. rr?cd}tdjD]+}t|r|}'sn,|SNrrv)rrwanyr)r4rr:r2s r% detect_m2z'detect_banded_matrix..detect_m2sYq!'""  A166!99~~    r'cd}tdjD],}t| r|}(sn-|Sr7)rrsr8r)r3rr:r2s r% detect_m1z'detect_banded_matrix..detect_m1s[q!'""  A1661"::    r'rr/)r:r2r9r;s`` r%rrsc 9;; ##r'r3r4c|j|jkrtdt}t |ddD]F}dg|z}||| ||G||dt d|dzD]E}||}|dg|z||F|S)zReturns compact banded matrix representation as :class:`Matrix` object. Args: A: matrix to transform m1: lower band count, excluding main matrix diagonal m2: upper band count, excluding main matrix diagonal zSquare matrix required.rr*rrv)rsrwrYrrextendrr)r:r3r4rdrrs r%rrs w!'1222A 2q"  eai 1661":: SLL 1b1f  ffQii C519 S Hr'cBeZdZdZddZedd Zdd ZddZdS)rz9Represents a LU decomposition of a compact banded matrix.r:rr3r?r4ct}trddlm}t ||_t ||_||j|j|j\|_|_ |_ dS)Nr) lu_decompose) _lu_decomposerezdxf.acc.np_supportr@r?r3r4r9upperlowerry)rZr:r3r4r@s r%r[zBandedMatrixLU.__init__se$  : 9 9 9 9 9 92ww2ww-9\!(DGTW-U-U* DJ r'rc&|jjdSrq)rCrJr^s r%rszBandedMatrixLU.nrowssz""r'rrnrzc $t}trddlm}t j|tj}t||jkrtdt|||j |j |j |j|jS)aSolves the linear equation system given by the banded 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 r)solve_vector_banded_matrixrO;Item count of vector B has to be equal to matrix row count.)_solve_vector_banded_matrixrrBrGrSrTrUrrsrr"rCrDryr3r4)rZrrGxs r%rzBandedMatrixLU.solve_vectors&A"  H G G G G G GXarz222 q66TZ  M  & &4:tz4:tw     r'rct|}|jjkrtdtfd|DS)aM Solves the linear equation system given by the banded 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 rbz,Row count of self and matrix B has to match.c:g|]}|Sr/)r)r3rrZs r%r5z/BandedMatrixLU.solve_matrix..s'FFFsD%%c**FFFr')rrsrrr)rZrr(s` r%rzBandedMatrixLU.solve_matrixsr### >TZ ' 'KLL LFFFFhmmooFFF   )++ r'N)r:rr3r?r4r?rrr) rrrrr[rrsrrr/r'r%rrszCCVVVV###X#    8r'r tuple[NDArray, NDArray, NDArray]ctj|tj}|jd}tj||ftj}tj|ftj}||zdz}|}t |D][} t || z |D]} || | || | |z <|dz}t ||z dz |D] } d|| | <\|}t |D]P} || d} | } ||kr|dz }t | dz|D]>} t|| dt| kr|| d} | } ?| dz|| <| | krAt |D]1} || | || | c|| | <|| | <2t | dz|D]}} || d|| dz } | || | | z dz <t d|D].} || | | || | zz || | dz </d|| |dz <~R|||fS)NrOrrvr)rSrTrUrJrVint64rr) r:r3r4rCr+rDrymmlr@r/r>dums r%rArAsXarz222E[^AXq"gRZ888EXqd"(333E2gkB A 2YYrAvr"" * *A#AhqkE!HQUOO QrAvz2&&  AE!HQKK  A 1XX##Ahqk  q55 FAq1ua  A58A;#c((**Ahqkq5a 662YY D D+08A;a (a U1Xa[[q1ua # #A(1+a +C"%E!HQUQY 1b\\ B B"'(1+eAhqk0A"AaQ"E!HR!V    # % r'rJrCrDrych|jd}|jd|krtd|}|}||zdz} |} t|D]v} || dz } | | kr|| || c|| <|| <| |kr| dz } t| dz| D]-} || xx|| | | z dz || zzcc<.wd} t|dz ddD]Y} || }td| D]} ||| | || | zzz} ||| dz || <| | kr| dz } Z|S)zSolves the linear equation system given by the banded 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 rrHrvr*)rJrr)rJrCrDryr3r4r+alaurPrQr>r/r@rRs r%rIrI*s$[^AwqzQVWWWBB2gkB A 1XX,, !HqL 661qtJAaD!A$ q55 FAq1ua , ,A aDDDBqE!a%!)$qt+ +DDDD , A 1q5"b ! !dq! ' 'A 2a58aAh& &CCRU1X~! r66 FA Hr')rr)rr()r>r?r@r?rr1)rN)rr1rr1rr1rr) rr1rr1rr1rr1rr)r:rrrrr)r:rrrnrrz)r:r(rrnrrz) rrzrrzrrzrrzrrz)T)r:rrr0)r:rrr)r:rr3r?r4r?rr)r:r+r3r?r4r?rrM)rJr+rCr+rDr+ryr+r3r?r4r?rr+)6 __future__rtypingrrrrrr r typing_extensionsr r functoolsr itertoolsr rBrknumpyrS numpy.typingnpt ezdxf.accr__all__r&r1r(__annotations__r)r?r*r+rUr;rrABCrrrrrrrrr#rrrrrArIr/r'r%rbs#""""""('''''     $ T%[) ))))#E%*$566666c?""""[,,,,,2222  3////,R1R1R1R1R1R1R1R1j     SW    P P P P P"++++\8888"9999$"B"B"B"B"B&"B"B"BJ7777@++++\& & & & R      $$$$$>    8AAAAAVAAAH''''T, , , , , , r'