Contents
dskysm - Skyline format triangular solve
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 (int transa, int m, int n, int unitd, double
*dv, double alpha, int *descra, double *val, int *pntr,
double *b, int ldb, double beta, double *c, int ldc);
void dskysm_64 (long transa, long m, long n, long unitd,
double *dv, double alpha, long *descra, double *val, long
*pntr, double *b, long ldb, double beta, double *c, long
ldc);
dskysm 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).
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.
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 routine. 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.