cptrfs.f man page

cptrfs.f —

Synopsis

Functions/Subroutines

subroutine cptrfs (UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CPTRFS

Function/Subroutine Documentation

subroutine cptrfs (characterUPLO, integerN, integerNRHS, real, dimension( * )D, complex, dimension( * )E, real, dimension( * )DF, complex, dimension( * )EF, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CPTRFS

Purpose:

CPTRFS 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.

Parameters:

UPLO

UPLO is CHARACTER*1
Specifies whether the superdiagonal or the subdiagonal 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

N is INTEGER
The order of the matrix A.  N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

D

D is REAL array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A.

E

E is COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO).

DF

DF is REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from
the factorization computed by CPTTRF.

EF

EF is COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal
factor U or L from the factorization computed by CPTTRF
(see UPLO).

B

B is COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

X

X is COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPTTRS.
On exit, the improved solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X.  LDX >= max(1,N).

FERR

FERR is REAL array, dimension (NRHS)
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

BERR is REAL array, dimension (NRHS)
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

WORK is COMPLEX array, dimension (N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 183 of file cptrfs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

cptrfs(3) is an alias of cptrfs.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK