zcposv - computes the solution to system of linear equations A * X = B for PO matrices
SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO ) CHARACTER*1 UPLO INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RWORK(*) COMPLEX SWORK(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*) SUBROUTINE ZCPOSV_64( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO ) CHARACTER*1 UPLO INTEGER*8 INFO, ITER, LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RWORK(*) COMPLEX SWORK(*) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*) F95 INTERFACE SUBROUTINE CPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO ) INTEGER :: N, NRHS, LDA, LDB, LDX, ITER, INFO CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: RWORK COMPLEX, DIMENSION(:) :: SWORK COMPLEX(8), DIMENSION(:,:) :: A, B, X SUBROUTINE CPOSV_64( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO ) INTEGER(8) :: N, NRHS, LDA, LDB, LDX, ITER, INFO CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: RWORK COMPLEX, DIMENSION(:) :: SWORK COMPLEX(8), DIMENSION(:,:) :: A, B, X C INTERFACE #include <sunperf.h> void zcposv (char uplo, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, doublecomplex *x, int ldx, int *iter, int *info); void zcposv_64 (char uplo, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *x, long ldx, long *iter, long *info);
Oracle Solaris Studio Performance Library zcposv(3P)
NAME
zcposv - computes the solution to system of linear equations A * X = B
for PO matrices
SYNOPSIS
SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK,
RWORK, ITER, INFO )
CHARACTER*1 UPLO
INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
DOUBLE PRECISION RWORK(*)
COMPLEX SWORK(*)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*)
SUBROUTINE ZCPOSV_64( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
SWORK, RWORK, ITER, INFO )
CHARACTER*1 UPLO
INTEGER*8 INFO, ITER, LDA, LDB, LDX, N, NRHS
DOUBLE PRECISION RWORK(*)
COMPLEX SWORK(*)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*)
F95 INTERFACE
SUBROUTINE CPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK,
RWORK, ITER, INFO )
INTEGER :: N, NRHS, LDA, LDB, LDX, ITER, INFO
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: RWORK
COMPLEX, DIMENSION(:) :: SWORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
SUBROUTINE CPOSV_64( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
SWORK, RWORK, ITER, INFO )
INTEGER(8) :: N, NRHS, LDA, LDB, LDX, ITER, INFO
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: RWORK
COMPLEX, DIMENSION(:) :: SWORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
C INTERFACE
#include <sunperf.h>
void zcposv (char uplo, int n, int nrhs, doublecomplex *a, int lda,
doublecomplex *b, int ldb, doublecomplex *x, int ldx, int
*iter, int *info);
void zcposv_64 (char uplo, long n, long nrhs, doublecomplex *a, long
lda, doublecomplex *b, long ldb, doublecomplex *x, long ldx,
long *iter, long *info);
PURPOSE
zcposv computes the solution to a complex system of linear equations A
* X = B, where A is an N-by-N Hermitian positive definite matrix and X
and B are N-by-NRHS matrices.
ZCPOSV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16 factorization
and solve.
The iterative refinement is not going to be a winning strategy if the
ratio COMPLEX performance over COMPLEX*16 performance is too small. A
reasonable strategy should take the number of right-hand sides and the
size of the matrix into account. This might be done with a call to
ILAENV in the future. Up to now, we always try iterative refinement.
The iterative refinement process is stopped if ITER > ITERMAX or for
all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER
is the number of the current iteration in the iterative refinement
process o RNRM is the infinity-norm of the residual o XNRM is the
infinity-norm of the solution o ANRM is the infinity-operator-norm of
the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
ARGUMENTS
UPLO (input)
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input)
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input)
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output)
A is COMPLEX*16 array,
dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
Note that the imaginary parts of the diagonal
elements need not be set and are assumed to be zero.
On exit, if iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array A contains the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.
LDA (input)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input)
B is COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
LDB (input)
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (output)
X is COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.
LDX (input)
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
WORK (output)
WORK is COMPLEX*16 array, dimension (N*NRHS)
This array is used to hold the residual vectors.
SWORK (output)
SWORK is COMPLEX array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
right-hand sides or solutions in single precision.
RWORK (output)
RWORK is DOUBLE PRECISION array, dimension (N)
ITER (output)
ITER is INTEGER
< 0: iterative refinement has failed, COMPLEX*16
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of CPOTRF
-31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been sucessfully used.
Returns the number of iterations
INFO (output)
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i of
(COMPLEX*16) A is not positive definite, so the
factorization could not be completed, and the solution
has not been computed.
7 Nov 2015 zcposv(3P)