zbdism - block diagonal format triangular solve
SUBROUTINE ZBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER IBDIAG(NBDIAG) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK) SUBROUTINE ZBDISM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*8 IBDIAG(NBDIAG) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK) F95 INTERFACE SUBROUTINE BDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BLDA, * IBDIAG, NBDIAG, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB INTEGER, DIMENSION(:) :: DESCRA, IBDIAG DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE BDISM_64(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BLDA, * IBDIAG, NBDIAG, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB INTEGER*8, DIMENSION(:) :: DESCRA, IBDIAG DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void zbdism (const int transa, const int mb, const int n, const int unitd, const doublecomplex* dv, const doublecomplex* alpha, const int* descra, const doublecomplex* val, const int blda, const int* ibdiag, const int nbdiag, const int lb, const dou- blecomplex* b, const int ldb, const doublecomplex* beta, dou- blecomplex* c, const int ldc); void zbdism_64 (const long transa, const long mb, const long n, const long unitd, const doublecomplex* dv, const doublecomplex* alpha, const long* descra, const doublecomplex* val, const long blda, const long* ibdiag, const long nbdiag, const long lb, const doublecomplex* b, const long ldb, const doublecom- plex* beta, doublecomplex* c, const long ldc);
Oracle Solaris Studio Performance Library zbdism(3P) NAME zbdism - block diagonal format triangular solve SYNOPSIS SUBROUTINE ZBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER IBDIAG(NBDIAG) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK) SUBROUTINE ZBDISM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*8 IBDIAG(NBDIAG) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK) F95 INTERFACE SUBROUTINE BDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BLDA, * IBDIAG, NBDIAG, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB INTEGER, DIMENSION(:) :: DESCRA, IBDIAG DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE BDISM_64(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BLDA, * IBDIAG, NBDIAG, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB INTEGER*8, DIMENSION(:) :: DESCRA, IBDIAG DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void zbdism (const int transa, const int mb, const int n, const int unitd, const doublecomplex* dv, const doublecomplex* alpha, const int* descra, const doublecomplex* val, const int blda, const int* ibdiag, const int nbdiag, const int lb, const dou- blecomplex* b, const int ldb, const doublecomplex* beta, dou- blecomplex* c, const int ldc); void zbdism_64 (const long transa, const long mb, const long n, const long unitd, const doublecomplex* dv, const doublecomplex* alpha, const long* descra, const doublecomplex* val, const long blda, const long* ibdiag, const long nbdiag, const long lb, const doublecomplex* b, const long ldb, const doublecom- plex* beta, doublecomplex* c, const long ldc); DESCRIPTION zbdism 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 mb*lb by n dense matrices, D is a block diagonal matrix, A is a sparse mb*lb by mb*lb unit, or non-unit, upper or lower triangular matrix represented in the block diagonal 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) ARGUMENTS TRANSA(input) TRANSA specifies the form of op( A ) to be used in the sparse matrix inverse as follows: 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, MB specifies the number of block rows in the matrix A. Unchanged on exit. N(input) On entry, N specifies the number of columns in in the matrix A. Unchanged on exit. UNITD(input) On entry, UNITD specifies the type of scaling: 1 : Identity matrix (argument DV[] is ignored) 2 : Scale on left (row scaling) 3 : Scale on right (column scaling) Unchanged on exit. DV(input) On entry, DV is an array of length MB*LB*LB consisting of the elements of the diagonal blocks of the matrix D. The size of each square block is LB-by-LB and each block is stored in standard column-major form. 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, VAL is a two-dimensional LB*LB*BLDA-by-NBDIAG array consisting of the NBDIAG non-zero block diagonal. Each dense block is stored in standard column-major form. Unchanged on exit. BLDA(input) On entry, BLDA*LB*LB specifies the leading block dimension of VAL(). Unchanged on exit. IBDIAG(input) On entry, IBDIAG is an integer array of length NBDIAG consisting of corresponding diagonal offsets of the non-zero block diagonals of A in VAL. Lower triangular block diagonals have negative offsets, the main block diagonal has offset 0, and upper triangular block diagonals have positive offset. Elements of IBDIAG MUST be sorted in increasing order. Unchanged on exit. LB (input) On entry, LB specifies the dimension of dense blocks composing A. Unchanged on exit. B (input) Array of DIMENSION ( LDB, N ). On entry, the leading mb*lb 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 ). On entry, the leading mb*lb by n part of the array C must contain the matrix C. On exit, the array C is overwritten. 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 MB*LB. For good performance, LWORK should generally be larger. For optimum performance on multiple processors, LWORK >=MB*LB*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 block diagonal represen- tation of 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 3rd Berkeley Distribution 7 Nov 2015 zbdism(3P)