zpprfs(3P) Sun Performance Library zpprfs(3P)NAMEzpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and packed,
and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZPPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR,
WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZPPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE PPRFS(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE PPRFS_64(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zpprfs(char uplo, int n, int nrhs, doublecomplex *a, doublecomplex
*af, doublecomplex *b, int ldb, doublecomplex *x, int ldx,
double *ferr, double *berr, int *info);
void zpprfs_64(char uplo, long n, long nrhs, doublecomplex *a, double‐
complex *af, doublecomplex *b, long ldb, doublecomplex *x,
long ldx, double *ferr, double *berr, long *info);
PURPOSEzpprfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and packed,
and provides error bounds and backward error estimates for the solu‐
tion.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) =
A(i,j) for j<=i<=n.
AF (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H, as computed by DPPTRF/ZPPTRF,
packed columnwise in a linear array in the same format as A
(see A).
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPPTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X). If XTRUE is
the true solution corresponding to X(j), FERR(j) is an esti‐
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele‐
ment in X(j). The estimate is as reliable as the estimate
for RCOND, and is almost always a slight overestimate of the
true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any ele‐
ment of A or B that makes X(j) an exact solution).
WORK (workspace)
COMPLEX*16 array, dimension(2*N)
WORK2 (workspace)
DOUBLE PRECISION array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zpprfs(3P)
