Contents
cbelsm - block Ellpack format triangular solve
SUBROUTINE CBELSM( 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)
COMPLEX ALPHA, BETA
COMPLEX DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
* WORK(LWORK)
SUBROUTINE CBELSM_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)
COMPLEX ALPHA, BETA
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
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
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
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
COMPLEX, DIMENSION(:, :) :: B, C
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 scalar, C and B are m by n dense matrices,
D is a block diagonal matrix, A is a unit, or non-unit, upper or
lower triangular matrix represented in 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)
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.
MB Number of block rows in matrix A
N Number of columns in matrix C
UNITD Type of scaling:
1 : Identity matrix (argument DV[] is ignored)
2 : Scale on left (row scaling)
3 : Scale on right (column scaling)
DV() Array of the length MB*LB*LB consisting of the block
entries of block diagonal matrix D where each
block is stored in standard column-major form.
ALPHA Scalar parameter
DESCRA() 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() scalar array of length LB*LB*BLDA*MAXBNZ containing
matrix entries, stored column-major within each dense
block.
BINDX() two-dimensional integer BLDA-by-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.
BLDA leading dimension of BINDX(:,:).
MAXBNZ max number of nonzeros blocks per row.
LB row and column dimension of the dense blocks composing A.
B() rectangular array with first dimension LDB.
LDB leading dimension of B
BETA Scalar parameter
C() rectangular array with first dimension LDC.
LDC leading dimension of C
WORK() scratch array of length LWORK.
On exit, if LWORK= -1, WORK(1) returns the minimum
size of LWORK.
LWORK 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.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
"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 unit diagonal blocks might or might
not be referenced in the BEL representation of a sparse
matrix. They are not used anyway.
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 can be applied for solving triangular systems
when the upper or lower triangle of the general sparse
matrix A is used. Howerver DESCRA(1) must be equal to 3 in
this case.