dbscsm(3P) Sun Performance Library dbscsm(3P)NAMEdbscsm - block sparse column format triangular solve
SYNOPSIS
SUBROUTINE DBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, MB, N, UNITD, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DBSCSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER*8 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where: BNNZ = BPNTRE(MB)- BPNTRB(1)
F95 INTERFACE
SUBROUTINE BSCSM(TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, N, UNITD, LB
INTEGER, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, DIMENSION(:, :) :: B, C
SUBROUTINE BSCSM_64(TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, N, UNITD, LB
INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void dbscsm (const int transa, const int mb, const int n, const int
unitd, const double* dv, const double alpha, const int*
descra, const double* val, const int* bindx, const int* bpn‐
trb, const int* bpntre, const int lb, const double* b, const
int ldb, const double beta, double* c, const int ldc);
void dbscsm_64 (const long transa, const long mb, const long n, const
long unitd, const double* dv, const double alpha, const long*
descra, const double* val, const long* bindx, const long*
bpntrb, const long* bpntre, const long lb, const double* b,
const long ldb, const double beta, double* c, const long
ldc);
DESCRIPTIONdbscsm 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
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).
ARGUMENTSTRANSA(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.
MB(input) On entry, MB specifies the number of block columns
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, 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)
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 scalar array of length LB*LB*BNNZ
consisting of the non-zero block entries stored
column-major within each dense block where
BNNZ = BPNTRE(MB)-BPNTRB(1). Unchanged on exit.
BINDX(input) On entry, BINDX is an integer array of length BNNZ consisting
of the block row indices of the block entries of A where
BNNZ = BPNTRE(MB)-BPNTRB(1). The block row indices MUST
be sorted in increasing order for each block column.
Unchanged on exit.
BPNTRB(input) On entry,BPNTRB is an integer array of length MB such
that BPNTRB(J)-BPNTRB(1)+1 points to location in BINDX
of the first block entry of the J-th block column
of A. Unchanged on exit.
BPNTRE(input) On entry, BPNTRE is an integer array of length MB such
that BPNTRE(J)-BPNTRB(1) points to location in BINDX
of the last block entry of the J-th block column
of A. 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.
SEE ALSO
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 rou‐
tine. 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 sparse column rep‐
resentation 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 , the diagonal blocks are considered as dense matri‐
ces and the LU factorization with partial pivoting is used by the rou‐
tine. 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 repre‐
sentation 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
6. It is known that there exists another representation of the block
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 block column in the arrays VAL and BINDX is
used instead of two arrays BPNTRB and BPNTRE. To use the routine with
this kind of block sparse column format the following calling sequence
should be used
CALL DBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, IA, IA(2), LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
3rd Berkeley Distribution 6 Mar 2009 dbscsm(3P)
