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CTPRFS(3F)							    CTPRFS(3F)

NAME
     CTPRFS - 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

									Page 1

CTPRFS(3F)							    CTPRFS(3F)

	     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

									Page 2

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