Contents
zskysm - Skyline format triangular solve
SUBROUTINE ZSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, PNTR,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER PNTR(*),
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZSKYSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, PNTR,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER*8 PNTR(*),
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTR(M+1)-PNTR(1) (upper triangular)
NNZ = PNTR(K+1)-PNTR(1) (lower triangular)
PNTR() size = (M+1) (upper triangular)
PNTR() size = (K+1) (lower triangular)
F95 INTERFACE
SUBROUTINE SKYSM( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
* PNTR, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, M, UNITD
INTEGER, DIMENSION(:) :: DESCRA, PNTR
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE SKYSM_64( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA,
* VAL, PNTR, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, M, UNITD
INTEGER*8, DIMENSION(:) :: DESCRA, PNTR
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 skyline 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 or 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() array contain the nonzeros of A in skyline profile form.
Row-oriented if DESCRA(2) = 1 (lower triangular),
column oriented if DESCRA(2) = 2 (upper triangular).
PNTR() integer array of length M+1 (lower triangular) or
K+1 (upper triangular) such that PNTR(I)-PNTR(1)+1
points to the location in VAL of the first element of
the skyline profile in row (column) I.
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. Also not supported:
a. lower triangular matrix A of size m by n where m > n
b. upper triangular matrix A of size m by n where m < n
2. No test for singularity or near-singularity is included
in this routine. Such tests must be performed before calling
this routine.
3. If UNITD =4, the routine scales the rows of A if
DESCRA(2)=1 and the columns of A if DESCRA(2)=2 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 this particular case. On return DV matrix
stored as a vector contains the diagonal matrix by which the
rows (columns) have been scaled. UNITD=2 if DESCRA(2)=1 and
UNITD=3 if DESCRA(2)=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
(column) number which 2-norm is exactly zero.
4. If DESCRA(3)=1 and UNITD < 4, the unit diagonal elements
might or might not be referenced in the SKY 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 SKY representation.
5. 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.