ZTPRFS (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 ZTPRFS( 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

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

      COMPLEX*16     AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

  ZTPRFS 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 ZTPTRS or some other means before
  entering this routine.  ZTPRFS 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*16 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*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) COMPLEX*16 array, dimension (LDX,NRHS)
          The 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