Contents
zptrfs - improve the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive
definite and tridiagonal, and provides error bounds and
backward error estimates for the solution
SUBROUTINE ZPTRFS(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION D(*), DF(*), FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZPTRFS_64(UPLO, N, NRHS, D, E, DF, EF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX E(*), EF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION 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(8), DIMENSION(:) :: E, EF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL(8), 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(8), DIMENSION(:) :: E, EF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: D, DF, FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zptrfs(char uplo, int n, int nrhs, double *d, doub-
lecomplex *e, double *df, doublecomplex *ef,
doublecomplex *b, int ldb, doublecomplex *x, int
ldx, double *ferr, double *berr, int *info);
void zptrfs_64(char uplo, long n, long nrhs, double *d,
doublecomplex *e, double *df, doublecomplex *ef,
doublecomplex *b, long ldb, doublecomplex *x, long
ldx, double *ferr, double *berr, long *info);
zptrfs improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive
definite and tridiagonal, and provides error bounds and
backward error estimates for the solution.
UPLO (input)
Specifies whether the superdiagonal or the subdi-
agonal of the tridiagonal matrix A is stored and
the form of the factorization:
= '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 ZPTTRF.
EF (input)
The (n-1) off-diagonal elements of the unit
bidiagonal factor U or L from the factorization
computed by ZPTTRF (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
ZPTTRS. 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 element 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 ille-
gal value