Contents
dbdism - block diagonal format triangular solve
SUBROUTINE DBDISM( 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)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*),
* WORK(LWORK)
SUBROUTINE DBDISM_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)
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION 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
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, 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
DOUBLE PRECISION ALPHA, BETA
DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
DOUBLE PRECISION, 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 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 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 length MB*LB*LB containing 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.
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() Two-dimensional LB*LB*BLDA-by-NBDIAG scalar array
consisting of the NBDIAG non-zero block diagonal.
Each dense block is stored in standard column-major form.
BLDA Leading block dimension of VAL(). Should be greater
than or equal to MB.
IBDIAG() integer array of length NBDIAG consisting of the
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.
NBDIAG The number of non-zero block diagonals in A.
LB Dimension of 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 optimum 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 BDI 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.