zcscsm - compressed sparse column format triangular solve
SUBROUTINE ZCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER INDX(NNZ), PNTRB(M), PNTRE(M) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE ZCSCSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, PNTRB, PNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5), * LDB, LDC, LWORK INTEGER*8 INDX(NNZ), PNTRB(M), PNTRE(M) DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ = PNTRE(M)-PNTRB(1) F95 INTERFACE SUBROUTINE CSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTRB, PNTRE, B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER TRANSA, M, UNITD INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C SUBROUTINE CSCSM_64(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX, * PNTRB, PNTRE, B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*8 TRANSA, M, UNITD INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE DOUBLE COMPLEX ALPHA, BETA DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV DOUBLE COMPLEX, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void zcscsm (const int transa, const int m, const int n, const int unitd, const doublecomplex* dv, const doublecomplex* alpha, const int* descra, const doublecomplex* val, const int* indx, const int* pntrb, const int* pntre, const doublecomplex* b, const int ldb, const doublecomplex* beta, doublecomplex* c, const int ldc); void zcscsm_64 (const long transa, const long m, const long n, const long unitd, const doublecomplex* dv, const doublecomplex* alpha, const long* descra, const doublecomplex* val, const long* indx, const long* pntrb, const long* pntre, const dou- blecomplex* b, const long ldb, const doublecomplex* beta, doublecomplex* c, const long ldc);
Oracle Solaris Studio Performance Library zcscsm(3P)
NAME
zcscsm - compressed sparse column format triangular solve
SYNOPSIS
SUBROUTINE ZCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZCSCSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, PNTRB, PNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK)
INTEGER*8 TRANSA, M, N, UNITD, DESCRA(5),
* LDB, LDC, LWORK
INTEGER*8 INDX(NNZ), PNTRB(M), PNTRE(M)
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(1)
F95 INTERFACE
SUBROUTINE CSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, M, UNITD
INTEGER, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE CSCSM_64(TRANSA, M, N, UNITD, DV, ALPHA, DESCRA, VAL, INDX,
* PNTRB, PNTRE, B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, M, UNITD
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, PNTRB, PNTRE
DOUBLE COMPLEX ALPHA, BETA
DOUBLE COMPLEX, DIMENSION(:) :: VAL, DV
DOUBLE COMPLEX, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void zcscsm (const int transa, const int m, const int n, const int
unitd, const doublecomplex* dv, const doublecomplex* alpha,
const int* descra, const doublecomplex* val, const int* indx,
const int* pntrb, const int* pntre, const doublecomplex* b,
const int ldb, const doublecomplex* beta, doublecomplex* c,
const int ldc);
void zcscsm_64 (const long transa, const long m, const long n, const
long unitd, const doublecomplex* dv, const doublecomplex*
alpha, const long* descra, const doublecomplex* val, const
long* indx, const long* pntrb, const long* pntre, const dou-
blecomplex* b, const long ldb, const doublecomplex* beta,
doublecomplex* c, const long ldc);
DESCRIPTION
zcscsm performs one of the matrix-matrix operations
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 scalars, C and B are m by n dense matrices,
D is a diagonal scaling matrix, A is a sparse m by m unit, or non-unit,
upper or lower triangular matrix represented in the compressed sparse
column 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).
ARGUMENTS
TRANSA(input) On entry, integer 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.
Unchanged on exit.
M(input) On entry, M specifies the number of rows in
the matrix A. Unchanged on exit.
N(input) On entry, N specifies the number of columns in
the matrix C. Unchanged on exit.
UNITD(input) On entry, UNITD specifies the type of scaling:
1 : Identity matrix (argument DV[] is ignored)
2 : Scale on left (row scaling)
3 : Scale on right (column scaling)
4 : Automatic column scaling (see section NOTES for
further details)
Unchanged on exit.
DV(input) On entry, DV is an array of length M consisting of the
diagonal entries of the diagonal scaling matrix D.
If UNITD is 4, DV contains diagonal matrix by which
the columns of A have been scaled (see section NOTES for
further details). Otherwise, unchanged on exit.
ALPHA(input) On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
DESCRA (input) 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(input) On entry, VAL is a scalar array of length
NNZ = PNTRE(M)-PNTRB(1) consisting of nonzero
entries of A. If UNITD is 4, VAL contains
the scaled matrix A*D (see section NOTES for
further details). Otherwise, unchanged on exit.
INDX(input) On entry, INDX is an integer array of length
NNZ = PNTRE(M)-PNTRB(1) consisting of the row
indices of nonzero entries of A.
Row indices MUST be sorted in increasing order
for each column. Unchanged on exit.
PNTRB(input) On entry, PNTRB is an integer array of length M
such that PNTRB(J)-PNTRB(1)+1 points to location
in VAL of the first nonzero element in column J.
Unchanged on exit.
PNTRE(input) On entry, PNTRE is an integer array of length M
such that PNTRE(J)-PNTRB(1) points to location
in VAL of the last nonzero element in column J.
Unchanged on exit.
B (input) Array of DIMENSION ( LDB, N ).
On entry, the leading m by n part of the array B
must contain the matrix B. Unchanged on exit.
LDB (input) On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. Unchanged on exit.
BETA (input) On entry, BETA specifies the scalar beta. Unchanged on exit.
C(input/output) Array of DIMENSION ( LDC, N ).
On entry, the leading m by n part of the array C
must contain the matrix C. On exit, the array C is
overwritten.
LDC (input) On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. Unchanged on exit.
WORK(workspace) Scratch array of length LWORK.
On exit, if LWORK= -1, WORK(1) returns the optimum size
of LWORK.
LWORK (input) On entry, LWORK specifies the 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.
SEE ALSO
Libsunperf SPARSE BLAS is fully parallel and compatible with NIST FOR-
TRAN Sparse Blas but the sources are different. Libsunperf SPARSE BLAS
is free of bugs found in NIST FORTRAN Sparse Blas. Besides several new
features and routines are implemented.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
Based on the standard proposed in
"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 rou-
tine. Such tests must be performed before calling this routine.
2. If UNITD =4, the routine scales the columns 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 particu-
lar case. On return DV matrix stored as a vector contains the diagonal
matrix by which the columns have been scaled. UNITD=3 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 column number which 2-norm is
exactly zero.
3. If DESCRA(3)=1 and UNITD < 4, the diagonal entries are each used
with the mathematical value 1. The entries of the main diagonal in the
CSC representation of a sparse matrix do not need to be 1.0 in this
usage. They are not used by the routine in these cases. But if UNITD=4,
the unit diagonal elements MUST be referenced in the CSC representa-
tion.
4. The routine is designed so that it checks the validity of each
sparse entry given in the sparse blas representation. Entries with
incorrect indices are not used and no error message related to the
entries is issued.
The feature also provides a possibility to use the sparse matrix repre-
sentation of a general matrix A for solving triangular systems with the
upper or lower triangle of A. But DESCRA(1) MUST be equal to 3 even in
this case.
Assume that there is the sparse matrix representation a general matrix
A decomposed in the form
A = L + D + U
where L is the strictly lower triangle of A, U is the strictly upper
triangle of A, D is the diagonal matrix. Let's I denotes the identity
matrix.
Then the correspondence between the first three values of DESCRA and
the result matrix for the sparse representation of A is
DESCRA(1) DESCRA(2) DESCRA(3) RESULT
3 1 1 alpha*op(L+I)*B+beta*C
3 1 0 alpha*op(L+D)*B+beta*C
3 2 1 alpha*op(U+I)*B+beta*C
3 2 0 alpha*op(U+D)*B+beta*C
5. It is known that there exists another representation of the com-
pressed sparse column format (see for example Y.Saad, "Iterative Meth-
ods 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 column in the arrays VAL and INDX is used
instead of two arrays PNTRB and PNTRE. To use the routine with this
kind of sparse column format the following calling sequence should be
used
SUBROUTINE ZCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, IA, IA(2), B, LDB, BETA,
* C, LDC, WORK, LWORK )
3rd Berkeley Distribution 7 Nov 2015 zcscsm(3P)