_-Ph:|dZddlmZddlZddlmZmZmZm Z m Z ddl m Z ddl mZdd Zdd Zd ZddZ ddZdS)z$Classical AMG Interpolation methods.)warnN) csr_matrix bsr_matrixisspmatrix_csrisspmatrix_bsrSparseEfficiencyWarning)amg_core) classical_strength_of_connectionminc :t|stdt|std|t|||}n|}|d|jdd<||}tj|j }tj |j d|j |j |||d}tj||j}tj||j}tj|j d|j |j |j|j |j |j|||| tj|} |j d} t%|||f| | g S) aCreate prolongator using direct interpolation. Parameters ---------- A : csr_matrix NxN matrix in CSR format C : csr_matrix Strength-of-Connection matrix Must have zero diagonal theta : float in [0, 1), default None theta value defining strong connections in a classical AMG sense. Provide if a different SOC is used for P than for CF-splitting; otherwise, theta = None. norm : string, default 'abs' Norm used in redefining classical SOC. Options are 'min' and 'abs' for CSR matrices. See strength.py for more information. splitting : array C/F splitting stored in an array of length N Returns ------- P : csr_matrix Prolongator using direct interpolation Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.interpolate import direct_interpolation >>> import numpy as np >>> A = poisson((5,),format='csr') >>> splitting = np.array([1,0,1,0,1], dtype='intc') >>> P = direct_interpolation(A, A, splitting) >>> print(P.toarray()) [[1. 0. 0. ] [0.5 0.5 0. ] [0. 1. 0. ] [0. 0.5 0.5] [0. 0. 1. ]] expected csr_matrix for Azexpected csr_matrix for CNthetanorm?rdtypeshape)r TypeErrorr copyeliminate_zerosdatamultiplynp empty_likeindptrr rs_direct_interpolation_pass1rindicesemptyrrs_direct_interpolation_pass2sumr) AC splittingrrP_indptrnnz P_indicesP_datancns [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/classical/interpolate.pydirect_interpolationr/ sP !  53444 !  53444  ,Qe$ G G G FFHHAF111I 1 A}QX&&H *171:qx+4h@@@ 2,CHN333I Xc ) ) )F *171:qxAF+,8QY+4h 6SSS   B  A vy(3Ar7 C C CCTct|stdt|stdtj|}|jd}|t |||}n|}|r2tj|jd|j |j |j || d|j dd<| |}tj|j }tj|jd|j |j |||d} tj| |j} tj| |j} tj|jd|j |j |j |j |j |j ||| | | t'| | |f||g S) a8Create prolongator using distance-1 classical interpolation. Parameters ---------- A : csr_matrix NxN matrix in CSR format C : csr_matrix Strength-of-Connection matrix Must have zero diagonal splitting : array C/F splitting stored in an array of length N theta : float in [0,1), default None theta value defining strong connections in a classical AMG sense. Provide if a different SOC is used for P than for CF-splitting; otherwise, theta = None. norm : string, default 'abs' Norm used in redefining classical SOC. Options are 'min' and 'abs' for CSR matrices. See strength.py for more information. modified : bool, default True Use modified classical interpolation. More robust if RS coarsening with second pass is not used for CF splitting. Ignores interpolating from strong F-connections without a common C-neighbor. Returns ------- P : csr_matrix Prolongator using classical interpolation; see Sec. 3 Eq. (8) of [0] for modified=False and Eq. (9) for modified=True. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.interpolate import classical_interpolation >>> import numpy as np >>> A = poisson((5,),format='csr') >>> splitting = np.array([1,0,1,0,1], dtype='intc') >>> P = classical_interpolation(A, A, splitting, 0.25) >>> print(P.todense()) [[ 1. 0. 0. ] [ 0.5 0.5 0. ] [ 0. 1. 0. ] [ 0. 0.5 0.5] [ 0. 0. 1. ]] rz"Expected csr_matrix SOC matrix, C.rNrrrrr)rrrr$rr rr remove_strong_FF_connectionsrr!rrrr rs_classical_interpolation_pass1r"r rs_classical_interpolation_pass2r) r%r&r'rrmodifiedr,r-r(r)r*r+s r.classical_interpolationr6VsZ !  53444 !  ><===   B  A  ,Qe$ G G G FFHHA-agaj!(AI./fi A A A AF111I 1 A}QX&&H -agaj!(./iHNNN 2,CHN333I Xc ) ) )F -agaj!(AI./fah ./fi.7KKK vy(3Ar7 C C CCr0cjt|r|jd}|jd|z }n{t|r|jd}d}n\ |}t dt |jd}d}n"#t$r}td|d}~wwxYwtj tj dg|j j tj||j j }|d}tjd|d|j j }|dkr1t!tj|f|j ||f||g }nWtj |tj||j gz|j } t'| ||f||g||z||zg }|S) aCreate interpolation operator by injection. Parameters ---------- A : {csr_matrix} NxN matrix in CSR format or BSR format splitting : array C/F splitting stored in an array of length N Returns ------- NxNc interpolation operator, P Notes ----- C-points are interpolated by value and F-points are not interpolated. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.interpolate import injection_interpolation >>> import numpy as np >>> A = poisson((5,),format='csr') >>> splitting = np.array([1,0,1,0,1], dtype='intc') >>> P = injection_interpolation(A, splitting) >>> print(P.todense()) [[1. 0. 0.] [0. 0. 0.] [0. 1. 0.] [0. 0. 0.] [0. 0. 1.]] rImplicit conversion of A to csr(Invalid matrix type, must be CSR or BSR.Nrr)startstopsteprr blocksizer)rr?rrtocsrrr Exceptionrrappendarrayrrcumsumarangeronesidentityr) r%r'r?r-eP_rowptrr, P_colindsPr+s r.injection_interpolationrLsBa OKN GAJ "    O GAJ  O A 24K L L L AII O O OFGGQ N Oy1#QX^<<<9AHNCCCEEH "B !(.IIIIA~~ QW555 (,45r7 < < <"bk)17CCCDDAGTTT  84I@V k2i<8 : : : Hs8B B&B!!B&Fc t|r+|jd}t|jd|z }n{t |r|jd}d}n\ |}t dt|jd}d}n"#t$r}td|d}~wwxYwtj |}tj |dzf|j j}tj |f|j j} tj |f|j} |dkr|r@tj|| | |j |j|j|t'| | |f||g} ntj|| | |j |j|j|tj|f|j} t'| | |f||g} ntj|| | |j |j|j|tj|tj||jgz|j} t/| | |f||g||z||zg} | S) afCreate one-point interpolation operator. Parameters ---------- A : {csr_matrix} NxN matrix in CSR format C : {csr_matrix} Strength-of-Connection matrix (does not need zero diagonal) splitting : array C/F splitting stored in an array of length N by_val : bool For CSR matrices only right now, use values of -Afc in interp as an approximation to P_ideal. If false, F-points are interpolated by value with weight 1. Returns ------- NxNc interpolation operator, P Notes ----- C-points are interpolated by value and F-points are interpolated by value from their strongest-connected C-point neighbor. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.interpolate import one_point_interpolation >>> import numpy as np >>> A = poisson((5,),format='csr') >>> splitting = np.array([1,0,1,0,1], dtype='intc') >>> P = one_point_interpolation(A, A, splitting) >>> print(P.todense()) [[1. 0. 0.] [1. 0. 0.] [0. 1. 0.] [0. 1. 0.] [0. 0. 1.]] rr8r9r:Nrrr>)rr?intrrr@rrrArrr$r"rrr one_point_interpolationr!rrrFrCrGr) r%r&r'by_valr?r-rHr,rIrJr+rKs r.rOrOsPa OKN  Y& ' '    O GAJ  O A 24K L L L AII O O OFGGQ N O   Bx1ahn555H!QX^444I Xqd!' * * *FA~~  I  ,Xy&!(-.Y  K K KFIx8BHHHAA  ,Xy&!(-.Y  K K KWaT111FFIx8BHHHAA(9fah)*AFI G G G!R[!'BBBCC17SSS  84I@V'k9R<8 : : : Hs8B B3B..B3皙?absr8 ct|r!t||d|}|jd} nt|rd} t||d|}nb |}t dt t||d|}d} n"#t$r} td| d} ~ wwxYwtj tj |dkd|j j } | jd} tj| dz|j j } t!j| |j |j| ||| d }tj||j j }t|rtj|| z| z|j }t!j| |||j |j|j|j |j|j| || ||||t/||| | f|| f| | g| | z|jdg }n|tj||j }t!j| |||j |j|j|j |j|j| |||||t5||| f| |jdg }||S) aCompute approx ideal restriction by setting RA = 0, within sparsity pattern of R. Parameters ---------- A : {csr_matrix, bsr_matrix} NxN matrix in CSR or BSR format splitting : array C/F splitting stored in an array of length N theta : float, default 0.1 Solve local system for each row of R for all values |A_ij| >= 0.1 * max_{i!=k} |A_ik| degree : int, default 1 Expand sparsity pattern for R by considering strongly connected neighbors within 'degree' of a given node. Only supports degree 1 and 2. use_gmres : bool Solve local linear system for each row of R using GMRES. If False, use direct solve. maxiter : int Maximum number of GMRES iterations precondition : bool Diagonally precondition GMRES Returns ------- Approximate ideal restriction, R, in same sparse format as A. Notes ----- Supports BSR (block) matrices, in addition to CSR. Sparsity pattern of R for the ith row (i.e. ith C-point) is the set of all strongly connected F-points, or the max_row *most* strongly connected F-points Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.interpolate import local_air >>> import numpy as np >>> A = poisson((5,),format='csr') >>> splitting = np.array([1,0,1,0,1], dtype='intc') >>> R = local_air(A, splitting) >>> print(R.todense()) [[1. 0.5 0. 0. 0. ] [0. 0.5 1. 0.5 0. ] [0. 0. 0. 0.5 1. ]] T)r%rblockrrr8Fr9r:Nrrr>r)rr r?rr@rrrArrrCwhererrrr"r approx_ideal_restriction_pass1r!zeros$block_approx_ideal_restriction_pass2rravelrreshapeapprox_ideal_restriction_pass2rr)r%r'rrdegree use_gmresmaxiter preconditionr&r?rHCptsr,R_rowptrr) R_colindsR_dataRs r. local_airrf=sda O ,qTPT U U UKN    O ,qUQU V V V O A 24K L L L01EUYZZZAII O O OFGGQ N O 8BHY!^,,Q/qx~ F F FD ABx1AHN333H +Hah ,0)VEEE 2,CAHN333IaN#i- 1AAA5h 6STS[67iQRQY67iy6?T[6B  D D D Y 'BCCYPXY"+Y!79 agVWj?Y [ [ [#QW---/)VQX01 1618QY01iQZ07 G G G  84RB B5 B00B5)Nr )Nr T)F)rQrRr8FrST)__doc__warningsrnumpyr scipy.sparserrrrrr strengthr r/r6rLrOrfr0r.rns$**,,,,,,,,,,,,,,777777FDFDFDFDRTDTDTDTDn= = = @M M M M `;<8<` ` ` ` ` ` r0