cptrfs-f(3)

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

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

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

 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 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 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

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