zptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiag- onal, provide error bounds and backward error estimates for the solu- tion
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, doublecomplex *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);
Oracle Solaris Studio Performance Library zptrfs(3P)
NAME
zptrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and tridiag-
onal, provide error bounds and backward error estimates for the solu-
tion
SYNOPSIS
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, doublecomplex *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);
PURPOSE
zptrfs 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 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 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
7 Nov 2015 zptrfs(3P)