Contents
cellsm - Ellpack format triangular solve
SUBROUTINE CELLSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, LDA, MAXNZ,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, M, N, UNITD, DESCRA(5), LDA, MAXNZ,
* LDB, LDC, LWORK
INTEGER INDX(LDA,MAXNZ)
COMPLEX ALPHA, BETA
COMPLEX DV(M), VAL(LDA,MAXNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CELLSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, LDA, MAXNZ,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), LDA, MAXNZ,
* LDB, LDC, LWORK
INTEGER*8 INDX(LDA,MAXNZ)
COMPLEX ALPHA, BETA
COMPLEX DV(M), VAL(LDA,MAXNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE ELLSM( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* INDX, [LDA], MAXNZ, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, M, MAXNZ
INTEGER, DIMENSION(:) :: DESCRA
INTEGER, DIMENSION(:, :) :: INDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: DV
COMPLEX, DIMENSION(:, :) :: VAL, B, C
SUBROUTINE ELLSM_64( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* INDX, [LDA], MAXNZ, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, M, MAXNZ
INTEGER*8, DIMENSION(:) :: DESCRA
INTEGER*8, DIMENSION(:, :) :: INDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: DV
COMPLEX, DIMENSION(:, :) :: VAL, B, C
C INTERFACE
#include <sunperf.h>
void cellsm (int transa, int m, int n, int unitd, complex
*dv, complex *alpha, int *descra, complex *val, int *indx,
int lda, int maxnz, complex *b, int ldb, complex *beta,
complex *c, int ldc);
void cellsm_64 (long transa, long m, long n, long unitd,
complex *dv, complex *alpha, long *descra, complex *val,
long *indx, long lda, long maxnz, complex *b, long ldb,
complex *beta, complex *c, long ldc);
zellsm 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 ellpack/itpack 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, 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 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 two-dimensional LDA-by-MAXNZ array
such that VAL(I,:) consists of non-zero elements
in row I of A, padded by zero values if the row
contains less than MAXNZ. If UNITD is 4, VAL contains
the scaled matrix D*A (see section NOTES for further
details). Otherwise, unchanged on exit.
INDX(input) On entry, INDX is an integer two-dimensional
LDA-by-MAXNZ array such that INDX(I,:) consists
of the column indices of the nonzero elements
in row I, padded by the integer value I if the
number of nonzeros is less than MAXNZ.
The column indices MUST be sorted in increasing order
for each row. Unchanged on exit.
LDA(input) On entry, LDA specifies the leading dimension of VAL
and INDX. Unchanged on exit.
MAXNZ(input) On entry, MAXNZ specifies the max number of
nonzeros elements per row. 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 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 ELL 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 ELL
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