CTPRFS (3lapack)

provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

SYNOPSIS

  SUBROUTINE CTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR,
                     BERR, WORK, RWORK, INFO )

      CHARACTER      DIAG, TRANS, UPLO

      INTEGER        INFO, LDB, LDX, N, NRHS

      REAL           BERR( * ), FERR( * ), RWORK( * )

      COMPLEX        AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

  CTPRFS provides error bounds and backward error estimates for the solution
  to a system of linear equations with a triangular packed coefficient
  matrix.

  The solution matrix X must be computed by CTPTRS or some other means before
  entering this routine.  CTPRFS does not do iterative refinement because
  doing so cannot improve the backward error.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

  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)

  DIAG    (input) CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

  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
          matrices B and X.  NRHS >= 0.

  AP      (input) COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in a
          linear array.  The j-th column of A is stored in the array AP as
          follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
          UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  If DIAG =
          'U', the diagonal elements of A are not referenced and are assumed
          to be 1.

  B       (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
          The solution matrix X.

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

  FERR    (output) REAL 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) 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) COMPLEX array, dimension (2*N)

  RWORK   (workspace) REAL array, dimension (N)

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