scsrsm - compressed sparse row format triangular solve
SUBROUTINE SCSRSM( 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) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) SUBROUTINE SCSRSM_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) REAL ALPHA, BETA REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK) where NNZ = PNTRE(M)-PNTRB(1) F95 INTERFACE SUBROUTINE CSRSM( 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 REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C SUBROUTINE CSRSM_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 REAL ALPHA, BETA REAL, DIMENSION(:) :: VAL, DV REAL, DIMENSION(:, :) :: B, C C INTERFACE #include <sunperf.h> void scsrsm (const int transa, const int m, const int n, const int unitd, const float* dv, const float alpha, const int* descra, const float* val, const int* indx, const int* pntrb, const int* pntre, const float* b, const int ldb, const float beta, float* c, const int ldc); void scsrsm_64 (const long transa, const long m, const long n, const long unitd, const float* dv, const float alpha, const long* descra, const float* val, const long* indx, const long* pntrb, const long* pntre, const float* b, const long ldb, const float beta, float* c, const long ldc);
Oracle Solaris Studio Performance Library scsrsm(3P)
NAME
scsrsm - compressed sparse row format triangular solve
SYNOPSIS
SUBROUTINE SCSRSM( 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)
REAL ALPHA, BETA
REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE SCSRSM_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)
REAL ALPHA, BETA
REAL DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where NNZ = PNTRE(M)-PNTRB(1)
F95 INTERFACE
SUBROUTINE CSRSM( 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
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, DIMENSION(:, :) :: B, C
SUBROUTINE CSRSM_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
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void scsrsm (const int transa, const int m, const int n, const int
unitd, const float* dv, const float alpha, const int* descra,
const float* val, const int* indx, const int* pntrb, const
int* pntre, const float* b, const int ldb, const float beta,
float* c, const int ldc);
void scsrsm_64 (const long transa, const long m, const long n, const
long unitd, const float* dv, const float alpha, const long*
descra, const float* val, const long* indx, const long*
pntrb, const long* pntre, const float* b, const long ldb,
const float beta, float* c, const long ldc);
DESCRIPTION
scsrsm 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
row 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, 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 row 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 rows 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
D*A (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 column
indices of nonzero entries of A. Column indices
MUST be sorted in increasing order for each
row. 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 row 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 row 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.
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 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 particu-
lar 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 diagonal entries are each used
with the mathematical value 1. The entries of the main diagonal in the
CSR 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 CSR 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 row format (see for example Y.Saad, "Iterative Methods
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 row in the arrays VAL and INDX is used instead
of two arrays PNTRB and PNTRE. To use the routine with this kind of
compressed sparse row format the following calling sequence should be
used
SUBROUTINE SCSRSM( 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 scsrsm(3P)