zgtrfs.f(3)

NAME
zgtrfs.f -

SYNOPSIS

  Functions/Subroutines
subroutine zgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZGTRFS

Function/Subroutine Documentation

  subroutine zgtrfs (characterTRANS, integerN, integerNRHS, complex*16, dimension( * )DL, complex*16, dimension( * )D, complex*16, dimension( * )DU, complex*16, dimension( * )DLF, complex*16, dimension( * )DF, complex*16, dimension( * )DUF, complex*16, dimension( * )DU2, integer, dimension( * )IPIV, 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)

ZGTRFS

Purpose:

     ZGTRFS improves the computed solution to a system of linear
     equations when the coefficient matrix is tridiagonal, and provides
     error bounds and backward error estimates for the solution.

Parameters:
    TRANS

              TRANS is CHARACTER*1
              Specifies the form of the system of equations:
              = 'N':  A * X = B     (No transpose)
              = 'T':  A**T * X = B  (Transpose)
              = 'C':  A**H * X = B  (Conjugate transpose)

    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.

    DL

              DL is COMPLEX*16 array, dimension (N-1)
              The (n-1) subdiagonal elements of A.

    D

              D is COMPLEX*16 array, dimension (N)
              The diagonal elements of A.

    DU

              DU is COMPLEX*16 array, dimension (N-1)
              The (n-1) superdiagonal elements of A.

    DLF

              DLF is COMPLEX*16 array, dimension (N-1)
              The (n-1) multipliers that define the matrix L from the
              LU factorization of A as computed by ZGTTRF.

    DF

              DF is COMPLEX*16 array, dimension (N)
              The n diagonal elements of the upper triangular matrix U from
              the LU factorization of A.

    DUF

              DUF is COMPLEX*16 array, dimension (N-1)
              The (n-1) elements of the first superdiagonal of U.

    DU2

              DU2 is COMPLEX*16 array, dimension (N-2)
              The (n-2) elements of the second superdiagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, row i of the matrix was
              interchanged with row IPIV(i).  IPIV(i) will always be either
              i or i+1; IPIV(i) = i indicates a row interchange was not
              required.

    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 ZGTTRS.
              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 estimated 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).  The estimate is as reliable as
              the estimate for RCOND, and is almost always a slight
              overestimate of the true error.

    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 (2*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 209 of file zgtrfs.f.

Author

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