csprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
SUBROUTINE CSPRFS( 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 CSPRFS_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(*)
SUBROUTINE SPRFS( 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 SPRFS_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
#include <sunperf.h>
void csprfs(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 csprfs_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);
csprfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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.
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 estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
X(j)
(i.e., the smallest relative change in
any element of A or B that makes X(j)
an exact solution).
dimension(2*N)
dimension(N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value