csrsm, scsrsm, dcsrsm, ccsrsm, zcsrsm - compressed sparse row format triangular solve
SUBROUTINE SCSRSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) REAL*4 ALPHA, BETA REAL*4 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DCSRSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) REAL*8 ALPHA, BETA REAL*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CCSRSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZCSRSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTRB(M), PNTRE(M) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(1)
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 row 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)
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, only DESCRA(1)=3 is 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 column
indices of nonzero entries of A (column indices MUST be
sorted in increasing order for each row)
PNTRB() integer array of length M such that PNTRB(J)-PNTRB(1)+1
points to location in VAL of the first nonzero element
in row J.
PNTRE() integer array of length M such that PNTRE(J)-PNTRB(1)
points to location in VAL of the last nonzero element
in row 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/
1. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
2. It is known that there exits another representation of the compressed sparse row 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 row in the arrays VAL and INDX is used instead of two arrays PNTRB and PNTRE. To use the routine with this kind of compressed sparse row format the following calling sequence should be used SUBROUTINE SCSRSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, IA, IA(2), B, LDB, BETA, C, * LDC, WORK, LWORK )