zptrfs.f(3)

NAME
zptrfs.f -

SYNOPSIS

  Functions/Subroutines
subroutine zptrfs (UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPTRFS

Function/Subroutine Documentation

  subroutine zptrfs (characterUPLO, integerN, integerNRHS, double precision, dimension( * )D, complex*16, dimension( * )E, double precision, dimension( * )DF, complex*16, dimension( * )EF, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZPTRFS

Purpose:

     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.

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

    E

              E is COMPLEX*16 array, dimension (N-1)
              The (n-1) off-diagonal elements of the tridiagonal matrix A
              (see UPLO).

    DF

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

    EF

              EF is COMPLEX*16 array, dimension (N-1)
              The (n-1) off-diagonal elements of the unit bidiagonal
              factor U or L from the factorization computed by ZPTTRF
              (see UPLO).

    B

              B is COMPLEX*16 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*16 array, dimension (LDX,NRHS)
              On entry, the solution matrix X, as computed by ZPTTRS.
              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 DOUBLE PRECISION 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 DOUBLE PRECISION 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*16 array, dimension (N)

    RWORK

              RWORK is DOUBLE PRECISION 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 zptrfs.f.

Author

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