bdism, sbdism, dbdism, cbdism, zbdism - 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*4 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*4 IBDIAG(NBDIAG) REAL*4 ALPHA, BETA REAL*4 DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK)
SUBROUTINE DBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*4 IBDIAG(NBDIAG) REAL*8 ALPHA, BETA REAL*8 DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK)
SUBROUTINE CBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*4 IBDIAG(NBDIAG) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK)
SUBROUTINE ZBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BLDA, IBDIAG, NBDIAG, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB, * LDB, LDC, LWORK INTEGER*4 IBDIAG(NBDIAG) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(MB*LB*LB), VAL(LB*LB*BLDA, NBDIAG), B(LDB,*), C(LDC,*), * WORK(LWORK)
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)
All blocks of A on the main diagonal MUST be triangular matrices.
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 block
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/
No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.