sskysm - Skyline format triangular solve
SUBROUTINE SSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER PNTR(*), REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SSKYSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*8 PNTR(*), REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ = PNTR(M+1)-PNTR(1) PNTR() size = (M+1) F95 INTERFACE SUBROUTINE SKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, * PNTR, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, M, UNITD INTEGER, DIMENSION(:) :: DESCRA, PNTR REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C SUBROUTINE SKYSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, M, UNITD INTEGER*8, DIMENSION(:) :: DESCRA, PNTR REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sskysm (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* pntr, const float* b, const int ldb, const float beta, float* c, const int ldc); void sskysm_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* pntr, const float* b, const long ldb, const float beta, float* c, const long ldc);
Oracle Solaris Studio Performance Library sskysm(3P) NAME sskysm - Skyline format triangular solve SYNOPSIS SUBROUTINE SSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER PNTR(*), REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SSKYSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*8 PNTR(*), REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ = PNTR(M+1)-PNTR(1) PNTR() size = (M+1) F95 INTERFACE SUBROUTINE SKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, * PNTR, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, M, UNITD INTEGER, DIMENSION(:) :: DESCRA, PNTR REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C SUBROUTINE SKYSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, PNTR, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, M, UNITD INTEGER*8, DIMENSION(:) :: DESCRA, PNTR REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void sskysm (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* pntr, const float* b, const int ldb, const float beta, float* c, const int ldc); void sskysm_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* pntr, const float* b, const long ldb, const float beta, float* c, const long ldc); DESCRIPTION sskysm 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 the skyline 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) On entry, integer 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, integer M specifies the number of 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. UNITD(input) On entry, integer 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 or column 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 scaling matrix D. If UNITD is 4, DV contains diagonal matrix by which the rows (columns) have been scaled (see section NOTES for further details). Otherwise, unchanged on exit. DESCRA (input) Descriptor argument. Five element integer array. DESCRA(1) matrix structure 0 : general (NOT SUPPORTED) 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 contains the nonzeros of A in skyline profile form. Row-oriented if DESCRA(2) = 1 (lower triangular), column oriented if DESCRA(2) = 2 (upper triangular). Unchanged on exit if UNITD is not 4. Otherwise, VAL contains entries of D*A or A*D (see section NOTES for further details). PNTR (input) On entry, INDX is an integer array of length M+1 such that PNTR(I)-PNTR(1)+1 points to the location in VAL of the first element of the skyline profile in row (column) I. 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 M. 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 UNITD =4, the routine scales the rows of A if DESCRA(2)=1 (lower triangular), and the columns of A if DESCRA(2)=2 (upper triangular)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 this particular case. On exit, DV matrix stored as a vector contains the diagonal matrix by which the rows (columns) have been scaled. UNITD=2 if DESCRA(2)=1 and UNITD=3 if DESCRA(2)=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 (column) 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 skyline representation of a sparse matrix don't need to be referenced in this usage but they need to be 1.0 if they are referenced. However if UNITD=4, the unit diagonal elements with the mathematical value 1 MUST be referenced in the skyline representation. 3rd Berkeley Distribution 7 Nov 2015 sskysm(3P)