Contents
cdiasm - diagonal format triangular solve
SUBROUTINE CDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, LDA, IDIAG, NDIAG,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
* LDB, LDC, LWORK
INTEGER IDIAG(NDIAG)
COMPLEX ALPHA, BETA
COMPLEX DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CDIASM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, LDA, IDIAG, NDIAG,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
* LDB, LDC, LWORK
INTEGER*8 IDIAG(NDIAG)
COMPLEX ALPHA, BETA
COMPLEX DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE DIASM(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* [LDA], IDIAG, NDIAG, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, M, NDIAG
INTEGER, DIMENSION(:) :: DESCRA, IDIAG
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: DV
COMPLEX, DIMENSION(:, :) :: VAL, B, C
SUBROUTINE DIASM_64(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* [LDA], IDIAG, NDIAG, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, M, NDIAG
INTEGER*8, DIMENSION(:) :: DESCRA, IDIAG
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: DV
COMPLEX, DIMENSION(:, :) :: VAL, B, C
C INTERFACE
#include <sunperf.h>
void cdiasm (int transa, int m, int n, int unitd,
complex *dv, complex *alpha, int *descra, complex *val, int
lda,
int *idiag, int ndiag, complex *b, int ldb, complex *beta,
complex *c, int ldc);
void cdiasm_64 (long transa, long m, long n, long unitd,
complex *dv, complex *alpha, long *descra, complex *val,
long lda,
long *idiag, long ndiag, complex *b, long ldb,
complex *beta, complex *c, long ldc);
cdiasm 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 diagonal 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-NDIAG array
such that VAL(:,I) consists of non-zero elements on
diagonal IDIAG(I) of A. Diagonals in the lower triangular
part of A are padded from the top, and those in the upper
triangular part are padded from the bottom. If UNITD is 4,
VAL contains the scaled matrix D*A (see section NOTES for
further details). Otherwise, unchanged on exit.
LDA(input) On entry, LDA specifies the leading dimension of VAL
and INDX. LDA must be > MIN(M,K). Unchanged on exit.
IDIAG() On entry, IDIAG is an integer array of length NDIAG
consisting of the corresponding diagonal offsets of
the non-zero diagonals of A in VAL. Lower triangular
diagonals have negative offsets, the main diagonal
has offset 0, and upper triangular diagonals have
positive offset. Elements of IDIAG of MUST be sorted
in increasing order. Unchanged on exit.
NDIAG(input) On entry, NDIAG specifies the number of non-zero diagonals
in A. 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 DIA 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 DIA
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