chprfs(3P) Sun Performance Library chprfs(3P)NAMEchprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite and packed, and
provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CHPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CHPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HPRFS(UPLO, [N], [NRHS], A, AF, IPIVOT, B, [LDB], X, [LDX],
FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE HPRFS_64(UPLO, [N], [NRHS], A, AF, IPIVOT, B, [LDB], X,
[LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void chprfs(char uplo, int n, int nrhs, complex *a, complex *af, int
*ipivot, complex *b, int ldb, complex *x, int ldx, float
*ferr, float *berr, int *info);
void chprfs_64(char uplo, long n, long nrhs, complex *a, complex *af,
long *ipivot, complex *b, long ldb, complex *x, long ldx,
float *ferr, float *berr, long *info);
PURPOSEchprfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite and packed, and
provides error bounds and backward error estimates for the solution.
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 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)*(2*n-j)/2) =
A(i,j) for j<=i<=n.
AF (input) COMPLEX array, dimension (N*(N+1)/2)
The factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the fac‐
tor U or L from the factorization A = U*D*U**H or A =
L*D*L**H as computed by CHPTRF, stored as a packed triangular
matrix.
IPIVOT (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as
determined by CHPTRF.
B (input) COMPLEX 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 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CHPTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL 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) REAL 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 array, dimension(2*N)
WORK2 (workspace)
REAL array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 chprfs(3P)
