cvbrsm - variable block sparse row format triangular solve
SUBROUTINE CVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX ALPHA, BETA COMPLEX DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE CVBRSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*8 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX ALPHA, BETA COMPLEX DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK) F95 INTERFACE SUBROUTINE VBRSM(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, UNITD INTEGER, DIMENSION(:) :: DESCRA, INDX, BINDX INTEGER, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE COMPLEX ALPHA, BETA COMPLEX, DIMENSION(:) :: VAL, DV COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE VBRSM_64(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, UNITD INTEGER*8, DIMENSION(:) :: DESCRA, INDX, BINDX INTEGER*8, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE COMPLEX ALPHA, BETA COMPLEX, DIMENSION(:) :: VAL, DV COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void cvbrsm (const int transa, const int mb, const int n, const int unitd, const floatcomplex* dv, const floatcomplex* alpha, const int* descra, const floatcomplex* val, const int* indx, const int* bindx, const int* rpntr, const int* cpntr, const int* bpntrb, const int* bpntre, const floatcomplex* b, const int ldb, const floatcomplex* beta, floatcomplex* c, const int ldc); void cvbrsm_64 (const long transa, const long mb, const long n, const long unitd, const floatcomplex* dv, const floatcomplex* alpha, const long* descra, const floatcomplex* val, const long* indx, const long* bindx, const long* rpntr, const long* cpntr, const long* bpntrb, const long* bpntre, const float- complex* b, const long ldb, const floatcomplex* beta, float- complex* c, const long ldc);
Oracle Solaris Studio Performance Library cvbrsm(3P) NAME cvbrsm - variable block sparse row format triangular solve SYNOPSIS SUBROUTINE CVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX ALPHA, BETA COMPLEX DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE CVBRSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*8 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX ALPHA, BETA COMPLEX DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK) F95 INTERFACE SUBROUTINE VBRSM(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, UNITD INTEGER, DIMENSION(:) :: DESCRA, INDX, BINDX INTEGER, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE COMPLEX ALPHA, BETA COMPLEX, DIMENSION(:) :: VAL, DV COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE VBRSM_64(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, UNITD INTEGER*8, DIMENSION(:) :: DESCRA, INDX, BINDX INTEGER*8, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE COMPLEX ALPHA, BETA COMPLEX, DIMENSION(:) :: VAL, DV COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void cvbrsm (const int transa, const int mb, const int n, const int unitd, const floatcomplex* dv, const floatcomplex* alpha, const int* descra, const floatcomplex* val, const int* indx, const int* bindx, const int* rpntr, const int* cpntr, const int* bpntrb, const int* bpntre, const floatcomplex* b, const int ldb, const floatcomplex* beta, floatcomplex* c, const int ldc); void cvbrsm_64 (const long transa, const long mb, const long n, const long unitd, const floatcomplex* dv, const floatcomplex* alpha, const long* descra, const floatcomplex* val, const long* indx, const long* bindx, const long* rpntr, const long* cpntr, const long* bpntrb, const long* bpntre, const float- complex* b, const long ldb, const floatcomplex* beta, float- complex* c, const long ldc); DESCRIPTION cvbrsm performs one of the matrix-matrix operations C <- alpha op(A) B + beta C, C <-alpha D op(A) B + beta C, C <- alpha op(A) D B + beta C, where alpha and beta are scalars, C and B are m by n dense matrices, D is a block diagonal matrix, A is a sparse m by m unit, or non-unit, upper or lower triangular matrix represented in the variable block sparse row format and op( A ) is one of op( A ) = inv(A) or op( A ) = inv(A') or op( A ) =inv(conjg( A' )) (inv denotes matrix inverse, ' indicates matrix transpose). The number of rows in A is determined as follows m=RPNTR(MB+1)-RPNTR(1). ARGUMENTS TRANSA(input) On entry, TRANSA indicates how to operate with the sparse matrix: 0 : operate with matrix 1 : operate with transpose matrix 2 : operate with the conjugate transpose of matrix. 2 is equivalent to 1 if matrix is real. Unchanged on exit. MB(input) On entry, integer MB specifies the number of block rows in the matrix A. Unchanged on exit. N(input) On entry, integer N specifies the number of columns in the matrix C. Unchanged on exit. DV(input) On entry, array DV contains the block entries of the block diagonal matrix D. The size of the J-th block is RPNTR(J+1)-RPNTR(J) and each block contains matrix entries stored column-major. The total length of array DV is given by the formula: sum over J from 1 to MB: ((RPNTR(J+1)-RPNTR(J))*(RPNTR(J+1)-RPNTR(J))) Unchanged on exit. ALPHA(input) On entry, ALPHA specifies the scalar alpha. Unchanged on exit. DESCRA (input) Descriptor argument. Five element integer array: DESCRA(1) matrix structure 0 : general 1 : symmetric (A=A') 2 : Hermitian (A= CONJG(A')) 3 : Triangular 4 : Skew(Anti)-Symmetric (A=-A') 5 : Diagonal 6 : Skew-Hermitian (A= -CONJG(A')) Note: For the routine, DESCRA(1)=3 is only supported. DESCRA(2) upper/lower triangular indicator 1 : lower 2 : upper DESCRA(3) main diagonal type 0 : non-identity blocks on the main diagonal 1 : identity diagonal blocks 2 : diagonal blocks are dense matrices DESCRA(4) Array base (NOT IMPLEMENTED) 0 : C/C++ compatible 1 : Fortran compatible DESCRA(5) repeated indices? (NOT IMPLEMENTED) 0 : unknown 1 : no repeated indices VAL(input) On entry, scalar array VAL of length NNZ consists of the block entries of A where each block entry is a dense rectangular matrix stored column by column where NNZ denotes the total number of point entries in all nonzero block entries of the matrix A. Unchanged on exit. INDX(input) On entry, INDX is an integer array of length BNNZ+1 where BNNZ is the number of block entries of the matrix A such that the I-th element of INDX[] points to the location in VAL of the (1,1) element of the I-th block entry. Unchanged on exit. BINDX(input) On entry, BINDX is an integer array of length BNNZ consisting of the block column indices of the block entries of A where BNNZ is the number block entries of the matrix A. Block column indices MUST be sorted in increasing order for each block row. Unchanged on exit. RPNTR(input) On entry, RPNTR is an integer array of length MB+1 such that RPNTR(I)-RPNTR(1)+1 is the row index of the first point row in the I-th block row. RPNTR(MB+1) is set to M+RPNTR(1) where M is the number of rows in the matrix A. Thus, the number of point rows in the I-th block row is RPNTR(I+1)-RPNTR(I). Unchanged on exit. NOTE: For the current version CPNTR must equal RPNTR and a single array can be passed for both arguments CPNTR(input) On entry, CPNTR is integer array of length KB+1 such that CPNTR(J)-CPNTR(1)+1 is the column index of the first point column in the J-th block column. CPNTR(KB+1) is set to K+CPNTR(1) where K is the number of columns in the matrix A. Thus, the number of point columns in the J-th block column is CPNTR(J+1)-CPNTR(J). Unchanged on exit. NOTE: For the current version CPNTR must equal RPNTR and a single array can be passed for both arguments BPNTRB(input) On entry, BPNTRB is an integer array of length MB such that BPNTRB(I)-BPNTRB(1)+1 points to location in BINDX of the first block entry of the I-th block row of A. Unchanged on exit. BPNTRE(input) On entry, BPNTRE is an integer array of length MB such that BPNTRE(I)-BPNTRB(1)points to location in BINDX of the last block entry of the I-th block row of A. Unchanged on exit. B (input) Array of DIMENSION ( LDB, N ). Before entry with TRANSA = 0, the leading k by n part of the array B must contain the matrix B, otherwise the leading m by n part of the array B must contain the matrix B. Unchanged on exit. LDB (input) On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. Unchanged on exit. BETA (input) On entry, BETA specifies the scalar beta. Unchanged on exit. C(input/output) Array of DIMENSION ( LDC, N ). Before entry with TRANSA = 0, the leading m by n part of the array C must contain the matrix C, otherwise the leading k by n part of the array C must contain the matrix C. On exit, the array C is overwritten by the matrix ( alpha*op( A )* B + beta*C ). LDC (input) On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. Unchanged on exit. WORK(workspace) Scratch array of length LWORK. On exit, if LWORK= -1, WORK(1) returns the optimum size of LWORK. LWORK (input) On entry, LWORK specifies the length of WORK array. LWORK should be at least M = RPNTR(MB+1)-RPNTR(1). For good performance, LWORK should generally be larger. For optimum performance on multiple processors, LWORK >=M*N_CPUS where N_CPUS is the maximum number of processors available to the program. If LWORK=0, the routine is to allocate workspace needed. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimum size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. SEE ALSO Libsunperf SPARSE BLAS is parallelized with the help of OPENMP and it is fully compatible with NIST FORTRAN Sparse Blas but the sources are different. Libsunperf SPARSE BLAS is free of bugs found in NIST FORTRAN Sparse Blas. Besides several new features and routines are implemented. NIST FORTRAN Sparse Blas User's Guide available at: http://math.nist.gov/mcsd/Staff/KRemington/fspblas/ Based on the standard proposed in "Document for the Basic Linear Algebra Subprograms (BLAS) Standard", University of Tennessee, Knoxville, Tennessee, 1996: http://www.netlib.org/utk/papers/sparse.ps NOTES/BUGS 1. No test for singularity or near-singularity is included in this rou- tine. Such tests must be performed before calling this routine. 2. If DESCRA(3)=0 , the lower or upper triangular part of each diagonal block is used by the routine depending on DESCRA(2). 3. If DESCRA(3)=1 , the diagonal blocks in the variable block row rep- resentationof A don't need to be the identity matrices because these block entries are not used by the routine in this case. 4. If DESCRA(3)=2 , diagonal blocks are considered as dense matrices and the LU factorization with partial pivoting is used by the routine. WORK(1)=0 on return if the factorization for all diagonal blocks has been completed successfully, otherwise WORK(1) = - i where i is the block number for which the LU factorization could not be computed. 5. The routine is designed so that it checks the validity of each sparse block entry given in the sparse blas representation. Block entries with incorrect indices are not used and no error message related to the entries is issued. The feature also provides a possibility to use the sparse matrix repre- sentation of a general matrix A for solving triangular systems with the upper or lower block triangle of A. But DESCRA(1) MUST be equal to 3 even in this case. Assume that there is the sparse matrix representation a general matrix A decomposed in the form A = L + D + U where L is the strictly block lower triangle of A, U is the strictly block upper triangle of A, D is the block diagonal matrix. Let's I denotes the identity matrix. Then the correspondence between the first three values of DESCRA and the result matrix for the sparse representation of A is DESCRA(1) DESCRA(2) DESCRA(3) RESULT 3 1 1 alpha*op(L+I)*B+beta*C 3 1 0 alpha*op(L+D)*B+beta*C 3 2 1 alpha*op(U+I)*B+beta*C 3 2 0 alpha*op(U+D)*B+beta*C 6. It is known that there exists another representation of the variable block sparse row format (see for example Y.Saad, "Iterative Methods for Sparse Linear Systems", WPS, 1996). Its data structure consists of six array instead of the seven used in the current implementation. The main difference is that only one array, IA, containing the pointers to the beginning of each block row in the array BINDX is used instead of two arrays BPNTRB and BPNTRE. To use the routine with this kind of variable block sparse row format the following calling sequence should be used SUBROUTINE CVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2), * B, LDB, BETA, C, LDC, WORK, LWORK ) 3rd Berkeley Distribution 7 Nov 2015 cvbrsm(3P)