cptrfs(3P) Sun Performance Library cptrfs(3P)NAMEcptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and tridiag‐
onal, and provides error bounds and backward error estimates for the
solution
SYNOPSIS
SUBROUTINE CPTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)
SUBROUTINE CPTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
REAL D(*), DF(*), FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE PTRFS(UPLO, [N], [NRHS], D, E, DF, EF, B, [LDB],
X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: E, EF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2
SUBROUTINE PTRFS_64(UPLO, [N], [NRHS], D, E, DF, EF, B,
[LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: E, EF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: D, DF, FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void cptrfs(char uplo, int n, int nrhs, float *d, complex *e, float
*df, complex *ef, complex *b, int ldb, complex *x, int ldx,
float *ferr, float *berr, int *info);
void cptrfs_64(char uplo, long n, long nrhs, float *d, complex *e,
float *df, complex *ef, complex *b, long ldb, complex *x,
long ldx, float *ferr, float *berr, long *info);
PURPOSEcptrfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and tridiag‐
onal, and provides error bounds and backward error estimates for the
solution.
ARGUMENTS
UPLO (input)
Specifies whether the superdiagonal or the subdiagonal of the
tridiagonal matrix A is stored and the form of the factoriza‐
tion:
= 'U': E is the superdiagonal of A, and A = U**H*D*U;
= 'L': E is the subdiagonal of A, and A = L*D*L**H. (The
two forms are equivalent if A is real.)
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 matrix B. NRHS >= 0.
D (input) The n real diagonal elements of the tridiagonal matrix A.
E (input) The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO).
DF (input)
The n diagonal elements of the diagonal matrix D from the
factorization computed by CPTTRF.
EF (input)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization computed by CPTTRF (see UPLO).
B (input) The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output)
On entry, the solution matrix X, as computed by CPTTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
The 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 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).
BERR (output)
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)
dimension(N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 cptrfs(3P)
