zbelsm - block Ellpack format triangular solve
SUBROUTINE ZBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BLDA, MAXBNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB, * LDB, LDC, LWORK INTEGER BINDX(BLDA,MAXBNZ) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*), * WORK(LWORK) SUBROUTINE ZBELSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BLDA, MAXBNZ, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB, * LDB, LDC, LWORK INTEGER*8 BINDX(BLDA,MAXBNZ) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*), * WORK(LWORK) F95 INTERFACE SUBROUTINE BELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX, * BLDA, MAXBNZ, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, MB, UNITD, BLDA, MAXBNZ, LB INTEGER, DIMENSION(:) :: DESCRA, BINDX DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE BELSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX, * BLDA, MAXBNZ, LB, B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, MB, UNITD, BLDA, MAXBNZ, LB INTEGER*8, DIMENSION(:) :: DESCRA, BINDX DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void zbelsm (const int transa, const int mb, const int n, const int unitd, const doublecomplex* dv, const doublecomplex* alpha, const int* descra, const doublecomplex* val, const int* bindx, const int blda, const int maxbnz, const int lb, const doublecomplex* b, const int ldb, const doublecomplex* beta, doublecomplex* c, const int ldc); void zbelsm_64 (const long transa, const long mb, const long n, const long unitd, const doublecomplex* dv, const doublecomplex* alpha, const long* descra, const doublecomplex* val, const long* bindx, const long blda, const long maxbnz, const long lb, const doublecomplex* b, const long ldb, const doublecom- plex* beta, doublecomplex* c, const long ldc);
Oracle Solaris Studio Performance Library zbelsm(3P)
NAME
zbelsm - block Ellpack format triangular solve
SYNOPSIS
SUBROUTINE ZBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BLDA, MAXBNZ, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
* LDB, LDC, LWORK
INTEGER BINDX(BLDA,MAXBNZ)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
* WORK(LWORK)
SUBROUTINE ZBELSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BLDA, MAXBNZ, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
* LDB, LDC, LWORK
INTEGER*8 BINDX(BLDA,MAXBNZ)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
* WORK(LWORK)
F95 INTERFACE
SUBROUTINE BELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BLDA, MAXBNZ, LB, B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, MB, UNITD, BLDA, MAXBNZ, LB
INTEGER, DIMENSION(:) :: DESCRA, BINDX
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE BELSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BLDA, MAXBNZ, LB, B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, MB, UNITD, BLDA, MAXBNZ, LB
INTEGER*8, DIMENSION(:) :: DESCRA, BINDX
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void zbelsm (const int transa, const int mb, const int n, const int
unitd, const doublecomplex* dv, const doublecomplex* alpha,
const int* descra, const doublecomplex* val, const int*
bindx, const int blda, const int maxbnz, const int lb, const
doublecomplex* b, const int ldb, const doublecomplex* beta,
doublecomplex* c, const int ldc);
void zbelsm_64 (const long transa, const long mb, const long n, const
long unitd, const doublecomplex* dv, const doublecomplex*
alpha, const long* descra, const doublecomplex* val, const
long* bindx, const long blda, const long maxbnz, const long
lb, const doublecomplex* b, const long ldb, const doublecom-
plex* beta, doublecomplex* c, const long ldc);
DESCRIPTION
zbelsm 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 ellpack
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).
ARGUMENTS
TRANSA(input) 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 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, 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 two-dimensional LB*LB*BLDA-by-MAXBNZ
array consisting of the non-zero blocks, stored
column-major within each dense block. Unchanged on exit.
BINDX(input) On entry, BINDX is an integer two-dimensional BLDA-MAXBNZ
array such BINDX(i,:) consists of the block column indices
of the nonzero blocks in block row i, padded by the integer
value i if the number of nonzero blocks is less than MAXBNZ.
The block column indices MUST be sorted in increasing order
for each block row. Unchanged on exit.
BLDA(input) On entry, BLDA specifies the leading dimension of BINDX(:,:).
Unchanged on exit.
MAXBNZ (input) On entry, MAXBNZ specifies the max number of nonzeros
blocks per row. 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 ellpack represen-
tation 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 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
3rd Berkeley Distribution 7 Nov 2015 zbelsm(3P)