hjbUddlmZddlmZmZmZmZmZmZm Z ddl m Z ddl Z ddl mZddlmZddlZddlZddlZddlmZddlmZgdZd(d ZeeeZd ed <eeed fZd ed <eeefZ d ed<ejBejDZ!d ed<d)dZ#edd*dZ$GddZ%Gdde jLZ'd+d,dZ(d-dZ)d.dZ*d/dZ+Gdde'Z,d0dZ- d.dZ. d1d Z/d2d3d!Z0d2d4d"Z1d5d#Z2Gd$d%e'Z3d6d&Z4 d7d'Z5y)8) 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_coefficientc'@Kt|D]}t|ywN)ziplist)argses 1lib/python3.12/site-packages/ezdxf/math/linalg.py zip_to_listr$,s $Z1g sr MatrixData.FrozenMatrixDataShapeNDArrayc t|tr |j}|Dcgc]}|Dcgc] }t|c}c}}Scc}wcc}}wr isinstancermatrixfloat)Arowvs r#copy_float_matrixr17sC!V HH/0 1qs #s!U1Xs #q 11 # 1s A A A A )maxsizec||kDr tdStj|}tj|}tj||z }t|||zz S)a Computes the binomial coefficient (denoted by `k choose i`). Please see the following website for details: http://mathworld.wolfram.com/BinomialCoefficient.html Args: k: size of the set of distinct elements i: size of the subsets r)r-math factorial)kik_facti_factk_i_facts r#rr=sW 1uQx..#F..#FNN1q5)H 8f,- ..cbeZdZdZdZ d# d$dZd%dZd&dZd'dZd'dZ e d(d Z e d)d Z e d)d Ze d*d Zd+d Zd+dZd+dZd,dZd,dZd-d.dZd-d.dZd/d.dZed0dZd1dZd1dZd2dZd3dZd4dZd5dZd5dZ d6dZ!e!Z"d6dZ#e#Z$d6dZ%e%Z&d2d Z'd2d!Z(d7d"Z)y)8raBasic matrix implementation based :class:`numpy.ndarray`. Matrix data is stored in row major order, this means in a list of rows, where each row is a list of floats. Initialization: - Matrix(shape=(rows, cols)) ... new matrix filled with zeros - Matrix(matrix[, shape=(rows, cols)]) ... from copy of matrix and optional reshape - Matrix([[row_0], [row_1], ..., [row_n]]) ... from Iterable[Iterable[float]] - Matrix([a1, a2, ..., an], shape=(rows, cols)) ... from Iterable[float] and shape .. versionchanged:: 1.2 Implementation based on :class:`numpy.ndarray`. Attributes: matrix: matrix data as :class:`numpy.ndarray` )r,abs_tolNcd|_tjdtj|_|+tj|tj|_y||tj ||_yyt |tr=| |j}|jj|j|_yt|} tj|Dcgc] }t|c}tj|_ycc}w#t$rI|Dtjt|tjj||_YyYywxYw)N-q=dtype) r>nparrayfloat64r,zerosr+rshapereshapecopyr TypeError)selfitemsrHr,r/s r#__init__zMatrix.__init__is $ !xx"**=  ((6rLms r#__copy__zMatrix.__copy__s) $++**, -LL r<c,t|jSr)strr,rQs r#__str__zMatrix.__str__s4;;r<cHdtj|jdS)NzMatrix())reprlibreprr,rQs r#__repr__zMatrix.__repr__sdkk23155r<cttjt|tjj |S)z[Returns a new matrix for iterable `items` in the configuration of `shape`. rBrT)rrDrEr rFrI)rMrHs r#rIzMatrix.reshapes- RXXd5kDLLUSTTr<c4|jjdSzCount of matrix rows.rr,rHrQs r#nrowsz Matrix.nrows{{  ##r<c4|jjdS)zCount of matrix columns.rcrQs r#ncolsz Matrix.ncolsrer<c.|jjS)z9Shape of matrix as (n, m) tuple for n rows and m columns.rcrQs r#rHz Matrix.shapes{{   r<c2t|j|S)z&Returns row `index` as list of floats.r r,rLindexs r#r/z Matrix.rowsDKK&''r<c:t|jdd|fS)z(Return column `index` as list of floats.Nrkrls r#colz Matrix.colsDKK5)**r<cJt|jj|S)aReturns diagonal `index` as list of floats. 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] )r r,diagonalrls r#diagz Matrix.diagsDKK((/00r<c:td|jDS)zReturn a list of all rows.c32K|]}t|ywr)r ).0rs r# zMatrix.rows..s1[DG[srkrQs r#rowsz Matrix.rowss1T[[111r<ct|jDcgc]}t|j|c}Scc}w)zReturn a list of all columns.)rangerhr ro)rLr8s r#colsz Matrix.colss2+0+<=+Set row values to a fixed value or from an iterable of floats.zInvalid item countN)r+r-intrhr len ValueErrorr,rLrmrMs r#set_rowzMatrix.set_rowsW eeS\ *5\NTZZ/EU  u: #12 2" Er<ct|ttfrt|g|jz}t ||j dd|f<y)zASet column values to a fixed value or from an iterable of floats.N)r+r-r}rdr r,rs r#set_colzMatrix.set_cols: eeS\ *5\NTZZ/E $U  AuHr<c`t|ttfrtt|}t |d}t t |d}ttt |j|j|D]\}} ||j||z||zf<y#t$rYywxYw)aSet diagonal values to a fixed value or from an iterable of floats. 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) r+r-r}r maxabsminrrzrdrhr, IndexError)rLrmrM col_offset row_offsetvalues r#set_diagzMatrix.set_diags eeS\ *5<(EeQ- c%m, c$**djj&A BEJLE5 FK EJ. 0BBCK  sB  B-,B-cBt|}|jdd|S)z6Returns the identity matrix for configuration `shape`.)rHr?)rr)clsrHrVs r#identityzMatrix.identitys!   1cr<c|jjdk(r,tj|gtj|_yt ||j k(r%tj|j|f|_ytd)zAppend a row to the matrix.rrBInvalid item count.N) r,sizerDrErFr~rhr_r)rLrMs r# append_rowzMatrix.append_rowsa ;;  q ((E7"**=DK Z4:: %%% U 23DK23 3r<cB|jjdk(r:tj|Dcgc]}|gc}tj|_yt ||j k(r%tj|j|f|_ytdcc}w)zAppend a column to the matrix.rrBrN) r,rrDrErFr~rdc_r)rLrMitems r# append_colzMatrix.append_colsu ;;  q ((u#=utTFu#=RZZPDK Z4:: %%% U 23DK23 3 $>s Bc\|j}d|jj_|S)z@Returns a frozen matrix, all data is stored in immutable tuples.F)rWr,flags writeablerUs r#freezez Matrix.freeze s" MMO#( r<c2t|j|S)zjGet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. )r-r,)rLrs r# __getitem__zMatrix.__getitem__s T[[&''r<c"||j|<y)zjSet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. NrT)rLrrs r# __setitem__zMatrix.__setitem__s " Dr<ct|ts td|j|jk7r tdt t j |j|jk(S)z'Returns ``True`` if matrices are equal.Matrix class required.Matrices have different shapes.)r+rrKrHboolrDallr,rLothers r#__eq__z Matrix.__eq__sU%(45 5 :: $=> >BFF4;;%,,6788r<c $t|ts td|j|jk7r tdt t j t j|j|j|jS)zReturns ``True`` if matrices are close to equal, tolerance value for comparison is adjustable by the attribute :attr:`Matrix.abs_tol`. rr)atol) r+rrKrHrrDriscloser,r>rs r#rzMatrix.isclose'sc %(45 5 :: $=> >BFF2::dkk5<F r<ct|tr#t|j|jzSt|jt|zS)zCMatrix addition by another matrix or a float, returns a new matrix.rTr*rs r#__add__zMatrix.__add__?s< eV $u||!;< <uU|!;< eV $u||!;< <uU|!;< #, 2 44 ("9 V H=H=H,$1r<rcXeZdZejddZejddZy)rcyrrArLBs r# solve_matrixzSolver.solve_matrixj r<cyrrArs r# solve_vectorzSolver.solve_vectornrr<NrMatrixData | NDArrayrrrrrr)rrrabcabstractmethodrrrAr<r#rris4     r<rct||krt||kr| fS| |z fS tj|dzd|z|zz }| |zd|zz | |z d|zz fS#t$r t cYSwxYw)z~Returns the solution for the quadratic equation ``a*x^2 + b*x + c = 0``. Returns 0-2 solutions as a tuple of floats. @)rr5sqrtrtuple)abcr> discriminants r#rrss  1v q6G B5LQyyyAA !12 R, 37 +\0AcAg/N OO ws!A""A87A8c t|dkr t|||S||z }||z }||z }||z}|dz }d|z|z dz } d|z|zd|zz d||zzz dz } | | z| z} | | | zz} | dk\rt j | } d}t j d | | zt jt| | z|z}t j d | | 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|dtjzzdz z|z |t j|d tjzzdz z|z fS#t$r tcYSwxYw) 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. r@g@g"@g;@rgK@gUUUUUU?rg@) rrArithmeticErrorrr5rcopysignpowacoscospi)rrrdr.rCAAA3QRQQQDsqrtDexpSrSTST_2thsqrtQ2s r#rrs"  1v~ %aA. . AA AA AA QB SB q2A q1tax #a. 0D8A a%!)C q1u ACx !  MM#q5y )DHHSU^S,I I MM#q5y )DHHSU^S,I I U q5C"H; 8Dbd d   1tyy#& 'B YYr]S F"s(##b(2dgg -455:2dgg -455: ? 7N s G,,HHctj|tj}tj|tj}ttjj ||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 rBrT)rDrErFrrsolve)r.rmat_Amat_Bs r#rrsF HHQbjj )E HHQbjj )E 6 77r<cHtj|tj}tj|Dcgc]}t|gc}tj}t tj tj j||Scc}w)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 rB)rDrErFr-r rPrr)r.rrr0rs r#rrsi HHQbjj )E HH!,!QuQxj!,BJJ ?E 67 88-sBc(eZdZdZddZddZddZy) rz5Replaces in v1.2 the :class:`LUDecomposition` solver.cXtj|tj|_y)NrB)rDrErFr)rLr.s r#rNzNumpySolver.__init__sXXarzz2 r<ctj|tj}ttjj |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 rBrT)rDrErFrrrr)rLrrs r#rzNumpySolver.solve_matrixs6"**-RYY__TZZ?@@r<ctj|Dcgc]}t|gc}tj}t tj tj j|j|Scc}w)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 rB) rDrEr-rFr rPrrr)rLrr0rs r#rzNumpySolver.solve_vectorsYa0a58*a0 CBHHRYY__TZZ?@AA1sBN)r.rrrrr)rrrrrNrrrAr<r#rrs?3A Br<rct|Dcgc] }t|c}\}}}t|||t|Scc}w)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 )r _solve_tridiagonal_matrix)r.rr0rrrs r#rrs<8!""1tAw"GAq! $Q1d1g 66#s5c |Dcgc] }t|c}\}}}t|ts$t|Dcgc] }t|c}}ntt|}|jt |k7r t dt|jDcgc]}t||||c}jScc}wcc}wcc}w)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 rTz+Row count of matrices A and B has to match.) r r+rr rdr~rr{r r) r.rr0rrrr/matrix_bros r#rrsB!""1tAw"GAq! a q!9q$s)q!9:?~~QFGG CK==?S?C)!Q37?S ik#!9TsCC CcJt|}dg|z}dg|z}|d}|d|z |d<td|D];}||dz |z ||<||||||zz }||||||dz zz |z ||<=t|dz ddD]}||xx||dz||dzzzcc< |S)aBSolves the linear equation system given by a tri-diagonal Matrix(a, b, c) . x = r. Matrix configuration:: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] Args: a: lower diagonal [a0 .. an-1], a0 is not used but has to be present b: central diagonal [b0 .. bn-1] c: upper diagonal [c0 .. cn-1], cn-1 is not used and must not be present r: right-hand side quantities Returns: vector x as list of floats Raises: ZeroDivisionError: singular matrix rrrgr)r~rz) rrrrvnugambetjs r#r r Hs4VAUQYAuqyC1C Q4#:AaD 1a[1q5CAdQqTCF]"!qtaAh&#-! AEB # !AE Qq1uX%%$ Hr<cDt||\}}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_allm1m2rVs r#rrqs."!Y /FBaR(A b"9r<c>dfd }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``. cd}tdjD]$}tj|r|} r#|S|SNrrg)rzrhanyrr)rrr.rs r# detect_m2z'detect_banded_matrix..detect_m2sCq!''"A166!9~ #  r<cd}tdjD]%}tj| r|}!r$|S|Sr)rzrdrrr)rrr.rs r# detect_m1z'detect_banded_matrix..detect_m1sEq!''"A1661": #  r<rrA)r.rrrs`` r#rrs ; ##r<c|j|jk7r tdt}t |ddD]:}dg|z}|j |j | |j|<|j|j dt d|dzD]9}|j |}|j dg|z|j|;|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.rrrrg)rdrhrKrrzextendrrr)r.rrrVrros r#rrs ww!''122A 2q" eai 1661": S LL 1b1f ffQi C519 S Hr<c:eZdZdZddZeddZd dZd dZy) rz9Represents a LU decomposition of a compact banded matrix.ct}trddlm}t ||_t ||_||j|j |j \|_|_ |_ y)Nr) lu_decompose) _lu_decomposerezdxf.acc.np_supportr$r}rrr,upperlowerrm)rLr.rrr$s r#rNzBandedMatrixLU.__init__sJ$  92w2w-9!((DGGTWW-U* DJ r<c4|jjdSrb)r'rHrQs r#rdzBandedMatrixLU.nrowsszz""r<c Ft}trddlm}t j |tj }t||jk7r tdt|||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_matrixrB;Item count of vector B has to be equal to matrix row count.)_solve_vector_banded_matrixrr&r+rDrErFr~rdrr r'r(rmrr)rLrr+xs r#rzBandedMatrixLU.solve_vectors}&A"  GXXarzz2 q6TZZ M  &4::tzz4::tww   r<ct|}|j|jk7r tdt|jDcgc]}|j |c}j Scc}w)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 rTz,Row count of self and matrix B has to match.)rrdrr{rr)rLrr ros r#rzBandedMatrixLU.solve_matrixsd# >>TZZ 'KL L6>mmoFosD%%c*oF )+ FsA6N)r.rrr}rr}rrr) rrrrrNrrdrrrAr<r#rrs)CV## 8r<rctj|tj}|jd}tj||ftj}tj|ftj }||zdz}|}t |D]K} t || z |D]} || | || | |z <|dz}t ||z dz |D] } d|| | < M|}t |D]} || d} | } ||kr|dz }t | dz|D]*} t|| dt| kDs!|| d} | } ,| dz|| <| | k7r-t |D]} || | || | c|| | <|| | <!t | dz|D]Z} || d|| dz } | || | | z dz <t d|D]} || | | || | zz || | dz <!d|| |dz <\|||fS)NrBrrgr)rDrErFrHrGint64rzr) r.rrr'rr(rmmmlr8rr7dums r#r%r%s8XXarzz2E[[^AXXq"gRZZ8EXXqd"((3E2gkB A 2YrAvr"A#AhqkE!HQUO# QrAvz2&AE!HQK'  A 1XAhqk  q5 FAq1uaA58A;#c(*Ahqk!q5a 62Y+08A;a (a U1Xa[q1uaA(1+a +C"%E!HQUQY 1b\"'(1+eAhqk0A"AaQ""E!HR!V  !( % r<c|jd}|jd|k7r td|}|}||zdz} |} t|D]]} || dz } | | k7r|| || c|| <|| <| |kr| dz } t| dz| D]!} || xx|| | | z dz || zzcc<#_d} t|dz ddD]E} || }td| D]} ||| | || | zzz}||| dz || <| | ksA| dz } G|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 rr,rgr)rHrrz)r.r'r(rmrrralaur2r3r7rr8r4s r#r-r-*sS$[[^AwwqzQVWWBB2gkB A 1X !HqL 61qtJAaD!A$ q5 FAq1uaA aDBqE!a%!)$qt+ +D!  A 1q5"b !dq!A 2a58aAh& &CRU1X~! r6 FA " Hr<)rzIterable[list])rr%)r7r}r8r}rr-)r@)rr-rr-rr-rr) rr-rr-rr-rr-rr)r.rrrrr)r.rrrrr)r.r%rrrr) rrrrrrrvrrr)T)r.rrztuple[Matrix, int, int])r.rrr)r.rrr}rr}rr)r.r(rr}rr}rz tuple[NDArray, NDArray, NDArray])r.r(r'r(r(r(rmr(rr}rr}rr()6 __future__rtypingrrrrrr r typing_extensionsr r functoolsr itertoolsr r5r]numpyrD numpy.typingnpt ezdxf.accr__all__r$r-r%__annotations__r&r}r'r(rFr1rrABCrrrrrrrrr rrrrr%r-rAr<r#rDs#(   $ T%[) I)#E%*$56)6c?y"[[,,2  3//,R1R1j SWW  P"+\8"9$"B&"BJ7@++ 4+ +\& & "& '2& 7B& & R  $> 8AVAH'T, , ,  ,   , , ,  , r<