cpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, provide error bounds and backward error estimates for the solution
SUBROUTINE CPPRFS(UPLO, N, NRHS, A, AF, 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 REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CPPRFS_64(UPLO, N, NRHS, A, AF, 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 REAL 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, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO REAL, 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, DIMENSION(:) :: A, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void cpprfs(char uplo, int n, int nrhs, complex *a, complex *af, com- plex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void cpprfs_64(char uplo, long n, long nrhs, complex *a, complex *af, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library cpprfs(3P)
NAME
cpprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and packed,
provide error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CPPRFS(UPLO, N, NRHS, A, AF, 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
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CPPRFS_64(UPLO, N, NRHS, A, AF, 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
REAL 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, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL, 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, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void cpprfs(char uplo, int n, int nrhs, complex *a, complex *af, com-
plex *b, int ldb, complex *x, int ldx, float *ferr, float
*berr, int *info);
void cpprfs_64(char uplo, long n, long nrhs, complex *a, complex *af,
complex *b, long ldb, complex *x, long ldx, float *ferr,
float *berr, long *info);
PURPOSE
cpprfs 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 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 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 SPPTRF/CPPTRF,
packed columnwise in a linear array in the same format as A
(see A).
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 CPPTRS. 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
7 Nov 2015 cpprfs(3P)