diasm, sdiasm, ddiasm, cdiasm, zdiasm - diagonal format triangular solve
SUBROUTINE SDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, LDA, IDIAG, NDIAG, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG, * LDB, LDC, LWORK INTEGER*4 IDIAG(NDIAG) REAL*4 ALPHA, BETA REAL*4 DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, LDA, IDIAG, NDIAG, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG, * LDB, LDC, LWORK INTEGER*4 IDIAG(NDIAG) REAL*8 ALPHA, BETA REAL*8 DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, LDA, IDIAG, NDIAG, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG, * LDB, LDC, LWORK INTEGER*4 IDIAG(NDIAG) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, LDA, IDIAG, NDIAG, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG, * LDB, LDC, LWORK INTEGER*4 IDIAG(NDIAG) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(M), VAL(LDA,NDIAG), 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 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, 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() two-dimensional LDA-by-NDIAG array such that VAL(:,I) consists of non-zero elements on diagonal IDIAG(I) of A. Diagonals in the lower triangular part of A are padded from the top, and those in the upper triangular part are padded from the bottom.
LDA leading dimension of VAL, must be .GE. MIN(M,K)
IDIAG() integer array of length NDIAG consisting of the corresponding diagonal offsets of the non-zero diagonals of A in VAL. Lower triangular diagonals have negative offsets, the main diagonal has offset 0, and upper triangular diagonals have positive offset. Elements of IDIAG of MUST be sorted in increasing order.
NDIAG number of non-zero diagonals in 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 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/
No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.