Contents
dcscsm - compressed sparse column format triangular solve
SUBROUTINE DCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DCSCSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER*8 INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(1)
F95 INTERFACE
SUBROUTINE CSCSM( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, [LDB], BETA, C, [LDC], [WORK], [LWORK] )
INTEGER TRANSA, M, UNITD
INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, DIMENSION(:, :) :: B, C
SUBROUTINE CSCSM_64(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, [LDB], BETA, C, [LDC], [WORK], [LWORK] )
INTEGER*8 TRANSA, M, UNITD
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void dcscsm(int transa, int m, int n, int unitd,
double *dv, double alpha, int *descra, double *val,
int *indx, int *pntrb, int *pntre, double *b,
int ldb, double beta, double* c, int ldc);
void dcscsm_64(long transa, long m, long n, long unitd,
double *dv, double alpha, long *descra, double *val, long
*indx, long *pntrb, long *pntre, double *b, long ldb, double
beta, double *c, long ldc);
dcscsm 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 compressed sparse
column 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 indicates how to operate
with the sparse matrix:
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 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 diagonal scaling matrix D.
If UNITD is 4, DV contains diagonal matrix by which
the columns of A 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 = PNTRE(M)-PNTRB(1) consisting of nonzero
entries of A. If UNITD is 4, VAL contains
the scaled matrix A*D (see section NOTES for
further details). Otherwise, unchanged on exit.
INDX(input) On entry, INDX is an integer array of length
NNZ = PNTRE(M)-PNTRB(1) consisting of the row
indices of nonzero entries of A.
Row indices MUST be sorted in increasing order
for each column. Unchanged on exit.
PNTRB(input) On entry, PNTRB is an integer array of length M
such that PNTRB(J)-PNTRB(1)+1 points to location
in VAL of the first nonzero element in column J.
Unchanged on exit.
PNTRE(input) On entry, PNTRE is an integer array of length M
such that PNTRE(J)-PNTRB(1) points to location
in VAL of the last nonzero element in column J.
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 fully parallel and 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 columns of 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 columns have been scaled. UNITD=3 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)= - k where k is the 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 CSC 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 CSC
representation.
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 representation 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
5. It is known that there exists another representation of
the compressed sparse column format (see for example Y.Saad,
"Iterative Methods for Sparse Linear Systems", WPS, 1996).
Its data structure consists of three array instead of the
four used in the current implementation. The main
difference is that only one array, IA, containing the
pointers to the beginning of each column in the arrays VAL
and INDX is used instead of two arrays PNTRB and PNTRE. To
use the routine with this kind of sparse column format the
following calling sequence should be used
SUBROUTINE DCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, IA, IA(2), B, LDB, BETA,
* C, LDC, WORK, LWORK )