SPTRFS (3lapack)

improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK,
                     INFO )

      INTEGER        INFO, LDB, LDX, N, NRHS

      REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( *
                     ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

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

ARGUMENTS

  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.

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

  E       (input) REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.

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

  EF      (input) REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor L from
          the factorization computed by SPTTRF.

  B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SPTTRS.  On exit,
          the improved solution matrix X.

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

  FERR    (output) 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    (output) 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    (workspace) REAL array, dimension (2*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.