sjadsm - diagonal format triangular solve
SUBROUTINE SJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SJADSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*8 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ=PNTR(MAXNZ+1)-PNTR(1)+1 is the number of non-zero elements F95 INTERFACE SUBROUTINE JADSM(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTR, MAXNZ, IPERM, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, M, MAXNZ INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTR, IPERM REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C SUBROUTINE JADSM_64(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTR, MAXNZ, IPERM, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, M, MAXNZ INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTR, IPERM REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sjadsm (const int transa, const int m, const int n, const int unitd, const float* dv, const float alpha, const int* descra, const float* val, const int* indx, const int* pntr, const int maxnz, const int* iperm, const float* b, const int ldb, const float beta, float* c, const int ldc); void sjadsm_64 (const long transa, const long m, const long n, const long unitd, const float* dv, const float alpha, const long* descra, const float* val, const long* indx, const long* pntr, const long maxnz, const long* iperm, const float* b, const long ldb, const float beta, float* c, const long ldc);
Oracle Solaris Studio Performance Library sjadsm(3P) NAME sjadsm - Jagged-diagonal format triangular solve SYNOPSIS SUBROUTINE SJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SJADSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*8 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ=PNTR(MAXNZ+1)-PNTR(1)+1 is the number of non-zero elements F95 INTERFACE SUBROUTINE JADSM(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTR, MAXNZ, IPERM, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, M, MAXNZ INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTR, IPERM REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C SUBROUTINE JADSM_64(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTR, MAXNZ, IPERM, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, M, MAXNZ INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTR, IPERM REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sjadsm (const int transa, const int m, const int n, const int unitd, const float* dv, const float alpha, const int* descra, const float* val, const int* indx, const int* pntr, const int maxnz, const int* iperm, const float* b, const int ldb, const float beta, float* c, const int ldc); void sjadsm_64 (const long transa, const long m, const long n, const long unitd, const float* dv, const float alpha, const long* descra, const float* val, const long* indx, const long* pntr, const long maxnz, const long* iperm, const float* b, const long ldb, const float beta, float* c, const long ldc); DESCRIPTION sjadsm 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 diagonal scaling matrix, A is a sparse m by m unit, or non-unit, upper or lower triangular matrix represented in jagged-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. M(input) On entry, M specifies the number of 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. 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) 4 : Automatic row scaling (see section NOTES for further details) Unchanged on exit. DV(input) On entry, DV is an array of length M consisting of the diagonal entries of the diagonal scaling matrix D. If UNITD is 4, DV contains diagonal matrix by which the rows have been scaled (see section NOTES for further details). Otherwise, 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-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 NNZ=PNTR(MAXNZ+1)-PNTR(1)+1 consisting of entries of A. VAL can be viewed as a column major ordering of a row permutation of the Ellpack representation of A, where the Ellpack representation is permuted so that the rows are non-increasing in the number of nonzero entries. Values added for padding in Ellpack are not included in the Jagged-Diagonal format. Unchanged on exit if UNITD is not equal to 4. INDX(input) On entry, INDX is an integer array of length NNZ=PNTR(MAXNZ+1)-PNTR(1)+1 consisting of the column indices of the corresponding entries in VAL. Unchanged on exit. PNTR(input) On entry, PNTR is an integer array of length MAXNZ+1, where PNTR(I)-PNTR(1)+1 points to the location in VAL of the first element in the row-permuted Ellpack represenation of A. Unchanged on exit. MAXNZ(input) On entry, MAXNZ specifies the max number of nonzeros elements per row. Unchanged on exit. IPERM(input) On entry, IPERM is an integer array of length M such that I = IPERM(I'), where row I in the original Ellpack representation corresponds to row I' in the permuted representation. If IPERM(1) = 0, it is assumed by convention that IPERM(I) = I. IPERM is used to determine the order in which rows of C are updated. Unchanged on exit. B (input) Array of DIMENSION ( LDB, N ). On entry, 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 ). On entry, the leading m 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 2*M. For good performance, LWORK should generally be larger. For optimum performance on multiple processors, LWORK >=2*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 UNITD =4, the routine scales the rows of the sparse matrix A such that their 2-norms are one. The scaling may improve the accuracy of the computed solution. Corresponding entries of VAL are changed only in the particular case. On return DV matrix stored as a vector contains the diagonal matrix by which the rows have been scaled. UNITD=2 should be used for the next calls to the routine with overwritten VAL and DV. WORK(1)=0 on return if the scaling has been completed successfully, otherwise WORK(1) = - i where i is the row number which 2-norm is exactly zero. 3. If DESCRA(3)=1 and UNITD < 4, the diagonal entries are each used with the mathematical value 1. The entries of the main diagonal in the JAD representation of a sparse matrix do not need to be 1.0 in this usage. They are not used by the routine in these cases. But if UNITD=4, the unit diagonal elements MUST be referenced in the JAD representa- tion. 4. The routine is designed so that it checks the validity of each sparse entry given in the sparse blas representation. 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 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 lower triangle of A, U is the strictly upper triangle of A, D is the 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 sjadsm(3P)