CXML
        	    
LAPACK version 3.0
ctprfs(3)

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

SYNTAX
  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, * )

DESCRIPTION
  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