zptrfs (3)

Functions/Subroutines

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

ZPTRFS

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.

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