Contents
sdiasm - 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 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
* LDB, LDC, LWORK
INTEGER IDIAG(NDIAG)
REAL ALPHA, BETA
REAL DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE SDIASM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, LDA, IDIAG, NDIAG,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
* LDB, LDC, LWORK
INTEGER*8 IDIAG(NDIAG)
REAL ALPHA, BETA
REAL DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE DIASM(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* [LDA], IDIAG, NDIAG, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, M, NDIAG
INTEGER, DIMENSION(:) :: DESCRA, IDIAG
REAL ALPHA, BETA
REAL, DIMENSION(:) :: DV
REAL, DIMENSION(:, :) :: VAL, B, C
SUBROUTINE DIASM_64(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* [LDA], IDIAG, NDIAG, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, M, NDIAG
INTEGER*8, DIMENSION(:) :: DESCRA, IDIAG
REAL ALPHA, BETA
REAL, DIMENSION(:) :: DV
REAL, DIMENSION(:, :) :: VAL, 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 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)
4 : Automatic row 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, 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/
"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 rows 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
rows have been scaled. UNITD=2 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 row
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 DIA 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 DIA 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.