sbcomm - matrix multiply
SUBROUTINE SBCOMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BJNDX, BNNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB, * LDB, LDC, LWORK INTEGER BINDX(BNNZ), BJNDX(BNNZ) REAL ALPHA, BETA REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SBCOMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BJNDX, BNNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB, * LDB, LDC, LWORK INTEGER*8 BINDX(BNNZ), BJNDX(BNNZ) REAL ALPHA, BETA REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK) F95 INTERFACE SUBROUTINE BCOMM(TRANSA,MB,N,KB,ALPHA,DESCRA,VAL,BINDX, BJNDX, * BNNZ, LB, B, LDB, BETA, C,LDC, WORK, LWORK) INTEGER TRANSA, MB, N, KB, BNNZ, LB INTEGER, DIMENSION(:) :: DESCRA, BINDX, BJNDX REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL REAL, DIMENSION(:, :) :: B, C SUBROUTINE BCOMM_64(TRANSA,MB,N,KB,ALPHA,DESCRA,VAL,BINDX, BJNDX, * BNNZ, LB, B, LDB, BETA, C,LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, KB, BNNZ, LB INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BJNDX REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sbcomm (const int transa, const int mb, const int n, const int kb, const float alpha, const int* descra, const float* val, const int* bindx, const int* bjndx, const int bnnz, const int lb, const float* b, const int ldb, const float beta, float* c, const int ldc); void sbcomm_64 (const long transa, const long mb, const long n, const long kb, const float alpha, const long* descra, const float* val, const long* bindx, const long* bjndx, const long bnnz, const long lb, const float* b, const long ldb, const float beta, float* c, const long ldc);
Oracle Solaris Studio Performance Library sbcomm(3P) NAME sbcomm - block coordinate matrix-matrix multiply SYNOPSIS SUBROUTINE SBCOMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BJNDX, BNNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB, * LDB, LDC, LWORK INTEGER BINDX(BNNZ), BJNDX(BNNZ) REAL ALPHA, BETA REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SBCOMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, BINDX, BJNDX, BNNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB, * LDB, LDC, LWORK INTEGER*8 BINDX(BNNZ), BJNDX(BNNZ) REAL ALPHA, BETA REAL VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK) F95 INTERFACE SUBROUTINE BCOMM(TRANSA,MB,N,KB,ALPHA,DESCRA,VAL,BINDX, BJNDX, * BNNZ, LB, B, LDB, BETA, C,LDC, WORK, LWORK) INTEGER TRANSA, MB, N, KB, BNNZ, LB INTEGER, DIMENSION(:) :: DESCRA, BINDX, BJNDX REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL REAL, DIMENSION(:, :) :: B, C SUBROUTINE BCOMM_64(TRANSA,MB,N,KB,ALPHA,DESCRA,VAL,BINDX, BJNDX, * BNNZ, LB, B, LDB, BETA, C,LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, KB, BNNZ, LB INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BJNDX REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sbcomm (const int transa, const int mb, const int n, const int kb, const float alpha, const int* descra, const float* val, const int* bindx, const int* bjndx, const int bnnz, const int lb, const float* b, const int ldb, const float beta, float* c, const int ldc); void sbcomm_64 (const long transa, const long mb, const long n, const long kb, const float alpha, const long* descra, const float* val, const long* bindx, const long* bjndx, const long bnnz, const long lb, const float* b, const long ldb, const float beta, float* c, const long ldc); DESCRIPTION sbcomm performs one of the matrix-matrix operations C <- alpha op(A) B + beta C where op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ) ( ' indicates matrix transpose), A is an (mb*lb) by (kb*lb) sparse matrix represented in the block coordinate format, alpha and beta are scalars, C and B are dense matrices. ARGUMENTS TRANSA(input) On entry, integer TRANSA specifies the form of op( A ) to be used in the matrix multiplication 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, integer 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 the matrix C. Unchanged on exit. KB(input) On entry, integer KB specifies the number of block columns in the matrix A. 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')) DESCRA(2) upper/lower triangular indicator 1 : lower 2 : upper DESCRA(3) main block diagonal type 0 : non-unit 1 : unit 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 scalar array of length LB*LB*BNNZ consisting of the non-zero block entries of A, in any order. Each block is stored in standard column-major form. Unchanged on exit. BINDX(input) On entry, BINDX is an integer array of length BNNZ consisting of the block row indices of the non-zero block entries of A. Unchanged on exit. BJNDX(input) On entry, BJNDX is an integer array of length BNNZ consisting of the block column indices of the non-zero block entries of A. Unchanged on exit. BNNZ (input) On entry, integer BNNZ specifies the number of nonzero block entries in A. Unchanged on exit. LB (input) On entry, integer LB specifies the dimension of dense blocks composing A. Unchanged on exit. B (input) Array of DIMENSION ( LDB, N ). Before entry with TRANSA = 0, the leading kb*lb by n part of the array B must contain the matrix B, otherwise 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 ). Before entry with TRANSA = 0, the leading mb*lb by n part of the array C must contain the matrix C, otherwise the leading kb*lb 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 (is not referenced in the current version) LWORK (is not referenced in the current version) SEE ALSO Libsunperf SPARSE BLAS is fully parallel and compatible with NIST FOR- TRAN 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 The all sparse blas matrix-matrix multiply routines for block entry formats are designed so that if DESCRA(1)> 0, the routines check the validity of each sparse block entry given in the sparse blas represen- tation. 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 just one sparse matrix representation of a general block matrix A for computing matrix-matrix multiply for another sparse matrix composed by block triangles and/or the main block diagonal of A . Assume that there is the sparse matrix representation of a general real 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 ___________________________________________________________________ 1 or 2 1 0 alpha*op(L+D+L')*B+beta*C 1 or 2 1 1 alpha*op(L+I+L')*B+beta*C 1 or 2 2 0 alpha*op(U'+D+U)*B+beta*C 1 or 2 2 1 alpha*op(U'+I+U)*B+beta*C 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 4 or 6 1 0 or 1 alpha*op(L+D-L')*B+beta*C 4 or 6 2 0 or 1 alpha*op(U+D-U')*B+beta*C 5 1 or 2 0 alpha*op(D)*B+beta*C 5 1 or 2 1 alpha*B+beta*C ___________________________________________________________________ Remarks to the table: 1. the value of DESCRA(3) is simply ignored , if DESCRA(1)= 4 or 6 but the diagonal blocks which are referenced in the sparse matrix represen- tation are used; 2. the diagonal blocks which are referenced in the sparse matrix rep- resentation are not used, if DESCRA(3)=1 and DESCRA(1)is one of 1, 2, 3 or 5; 3. if DESCRA(3) is not 1 and DESCRA(1) is one of 1,2, 4 or 6, the type of D should correspond to the choosen value of DESCRA(1) . 3rd Berkeley Distribution 7 Nov 2015 sbcomm(3P)