Contents
sbdism - block diagonal format triangular solve
SUBROUTINE SBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BLDA, IBDIAG, NBDIAG, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB,
* LDB, LDC, LWORK
INTEGER IBDIAG(NBDIAG)
REAL ALPHA, BETA
REAL DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*),
* WORK(LWORK)
SUBROUTINE SBDISM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BLDA, IBDIAG, NBDIAG, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB,
* LDB, LDC, LWORK
INTEGER*8 IBDIAG(NBDIAG)
REAL ALPHA, BETA
REAL DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*),
* WORK(LWORK)
F95 INTERFACE
SUBROUTINE BDISM( TRANSA, MB,[N], UNITD, DV, ALPHA, DESCRA, VAL, BLDA,
* IBDIAG, NBDIAG, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB
INTEGER, DIMENSION(:) :: DESCRA, IBDIAG
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, DIMENSION(:, :) :: B, C
SUBROUTINE BDISM_64(TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA, VAL, BLDA,
* IBDIAG, NBDIAG, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, N, UNITD, BLDA, NBDIAG, LB
INTEGER*8, DIMENSION(:) :: DESCRA, IBDIAG
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void sbdism (int transa, int mb, int n, int unitd, float
*dv, float alpha, int *descra, float *val, int blda, int
*ibdiag, int nbdiag, int lb, float *b, int ldb, float beta,
float *c, int ldc);
void sbdism_64(long transa, long mb, long n, long unitd,
float *dv, float alpha, long *descra, float *val, long blda,
long *ibdiag, long nbdiag, long lb, float *b, long ldb,
float beta, float *c, long ldc);
sbdism 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 mb*lb by n dense matrices,
D is a block diagonal matrix, A is a sparse mb*lb by mb*lb unit, or non-unit,
upper or lower triangular matrix represented in the block 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) 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.
MB(input) On entry, MB specifies the number of block rows
in matrix the 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)
Unchanged on exit.
DV(input) On entry, DV is an array of length MB*LB*LB consisting
of the elements of the diagonal blocks of the matrix D.
The size of each square block is LB-by-LB and each
block is stored in standard column-major form.
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-identity blocks on the main diagonal
1 : identity diagonal blocks
2 : diagonal blocks are dense matrices
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 LB*LB*BLDA-by-NBDIAG
array consisting of the NBDIAG non-zero block diagonal.
Each dense block is stored in standard column-major
form. Unchanged on exit.
BLDA(input) On entry, BLDA*LB*LB specifies the leading block dimension
of VAL(). Unchanged on exit.
IBDIAG(input) On entry, IBDIAG is an integer array of length NBDIAG
consisting of corresponding diagonal offsets of the
non-zero block diagonals of A in VAL. Lower triangular
block diagonals have negative offsets, the main block
diagonal has offset 0, and upper triangular block
diagonals have positive offset. Elements of IBDIAG
MUST be sorted in increasing order. Unchanged on exit.
LB (input) On entry, LB specifies the dimension of dense blocks
composing A. Unchanged on exit.
B (input) Array of DIMENSION ( LDB, N ).
On entry, the leading mb*lb 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 mb*lb 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 MB*LB.
For good performance, LWORK should generally be larger.
For optimum performance on multiple processors, LWORK
>=MB*LB*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 DESCRA(3)=0 , the lower or upper triangular part of
each diagonal block is used by the routine depending on
DESCRA(2) .
3. If DESCRA(3)=1 , the diagonal blocks in the block
diagonal representation of A don't need to be the identity
matrices because these block entries are not used by the
routine in this case.
4. If DESCRA(3)=2 , diagonal blocks are considered as dense
matrices and the LU factorization with partial pivoting is
used by the routine.
WORK(1)=0 on return if the factorization for all diagonal
blocks has been completed successfully, otherwise WORK(1) =
- i where i is the block number for which the LU
factorization could not be computed.
5. The routine is designed so that it checks the validity of
each sparse block entry given in the sparse blas
representation. Block 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 block 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 block lower triangle of A, U is the
strictly block upper triangle of A, D is the block 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