Contents
zcscsm - compressed sparse column format triangular solve
SUBROUTINE ZCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZCSCSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER*8 INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(1)
F95 INTERFACE
SUBROUTINE CSCSM( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, [LDB], BETA, C, [LDC], [WORK], [LWORK] )
INTEGER TRANSA, M, UNITD
INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE CSCSM_64(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, [LDB], BETA, C, [LDC], [WORK], [LWORK] )
INTEGER*8 TRANSA, M, UNITD
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE 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 diagonal scaling matrix, A is a unit, or non-unit, upper or
lower triangular matrix represented in compressed 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)
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.
M Number of 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)
4 : Automatic column scaling (see section NOTES for
further details)
DV() Array of length M containing the diagonal entries of the
scaling diagonal matrix D.
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-unit
1 : unit
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 NNZ consisting of nonzero entries
of A.
INDX() integer array of length NNZ consisting of the row indices
of nonzero entries of A. (Row indices MUST be sorted in
increasing order for each column).
PNTRB() integer array of length M such that PNTRB(J)-PNTRB(1)+1
points to location in VAL of the first nonzero element
in column J.
PNTRE() integer array of length M such that PNTRE(J)-PNTRB(1)
points to location in VAL of the last nonzero element
in column J.
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 LWORK.
LWORK length of WORK array. LWORK should be at least M.
For good performance, LWORK should generally be larger.
For optimum performance on multiple processors, LWORK
>=M*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 UNITD =4, the routine scales the columns of A such
that their 2-norms are one. The scaling may improve the
accuracy of the computed solution. Corresponding entries of
VAL are changed only in the particular case. On return DV
matrix stored as a vector contains the diagonal matrix by
which the columns have been scaled. UNITD=3 should be used
for the next calls to the routine with overwritten VAL and
DV.
WORK(1)=0 on return if the scaling has been completed
successfully, otherwise WORK(1) = -i where i is the column
number which 2-norm is exactly zero.
3. If DESCRA(3)=1 and UNITD < 4, the unit diagonal elements
might or might not be referenced in the CSC representation
of a sparse matrix. They are not used anyway in these cases.
But if UNITD=4, the unit diagonal elements MUST be
referenced in the CSC representation.
4. The routine can be applied for solving triangular systems
when the upper or lower triangle of the general sparse
matrix A is used. However DESCRA(1) must be equal to 3 in
this case.
5. It is known that there exists another representation of
the compressed 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 column in the arrays VAL
and INDX is used instead of two arrays PNTRB and PNTRE. To
use the routine with this kind of sparse column format the
following calling sequence should be used
SUBROUTINE SCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, IA, IA(2), B, LDB, BETA,
* C, LDC, WORK, LWORK )