ZGTRFS (3lapack)

improve 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

SYNOPSIS

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

      CHARACTER      TRANS

      INTEGER        INFO, LDB, LDX, N, NRHS

      INTEGER        IPIV( * )

      DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )

      COMPLEX*16     B( LDB, * ), D( * ), DF( * ), DL( * ), DLF( * ), DU( *
                     ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )

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.

ARGUMENTS

  TRANS   (input) 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       (input) INTEGER
          The order of the matrix A.  N >= 0.

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

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

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

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

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

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

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

  IPIV    (input) 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       (input) COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.

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

  X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZGTTRS.  On exit,
          the improved solution matrix X.

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

  FERR    (output) 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    (output) 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    (workspace) COMPLEX*16 array, dimension (2*N)

  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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

PARAMETERS

  ITMAX is the maximum number of steps of iterative refinement.