jadsm, sjadsm, djadsm, cjadsm, zjadsm - Jagged-diagonal format triangular solve
SUBROUTINE SJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL*4 ALPHA, BETA REAL*4 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) REAL*8 ALPHA, BETA REAL*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZJADSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTR, MAXNZ, IPERM, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), MAXNZ, * LDB, LDC, LWORK INTEGER*4 INDX(NNZ), PNTR(MAXNZ+1), IPERM(M) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(M), VAL(NNZ), 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 diagonal scaling matrix, A is a unit, or non-unit, upper or lower triangular matrix represented in jagged-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.
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, 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() array of length NNZ consisting of entries of A.
VAL can be viewed as a column major ordering of a
row permutation of the Ellpack representation of A,
where the Ellpack representation is permuted so that
the rows are non-increasing in the number of nonzero
entries. Values added for padding in Ellpack are
not included in the Jagged-Diagonal format.
INDX() array of length NNZ consisting of the column indices
of the corresponding entries in VAL.
PNTR() array of length MAXNZ+1, where PNTR(I)-PNTR(1)+1
points to the location in VAL of the first element
in the row-permuted Ellpack represenation of A.
MAXNZ max number of nonzeros elements per row.
IPERM() integer array of length M such that I = IPERM(I'),
where row I in the original Ellpack representation
corresponds to row I' in the permuted representation.
If IPERM(1)=0, it's assumed by convention that
IPERM(I)=I. IPERM is used to determine the order
in which rows of C are updated.
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 2*M.
For good performance, LWORK should generally be larger.
For optimum performance on multiple processors, LWORK
>=2*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/
No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.