dskysm(3P) Sun Performance Library dskysm(3P)NAMEdskysm - Skyline format triangular solve
SYNOPSIS
SUBROUTINE DSKYSM( 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(*),
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DSKYSM_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(*),
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION 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
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, 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
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void dskysm (const int transa, const int m, const int n, const int
unitd, const double* dv, const double alpha, const int*
descra, const double* val, const int* pntr, const double* b,
const int ldb, const double beta, double* c, const int ldc);
void dskysm_64 (const long transa, const long m, const long n, const
long unitd, const double* dv, const double alpha, const long*
descra, const double* val, const long* pntr, const double* b,
const long ldb, const double beta, double* c, const long
ldc);
DESCRIPTIONdskysm 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).
ARGUMENTSTRANSA(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 6 Mar 2009 dskysm(3P)
