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dtprfs.f(3)				      LAPACK				      dtprfs.f(3)

NAME
       dtprfs.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dtprfs (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK,
	   IWORK, INFO)
	   DTPRFS

Function/Subroutine Documentation
   subroutine dtprfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerNRHS, double
       precision, dimension( * )AP, double precision, dimension( ldb, * )B, integerLDB, double
       precision, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double
       precision, dimension( * )BERR, double precision, dimension( * )WORK, integer, dimension( *
       )IWORK, integerINFO)
       DTPRFS

       Purpose:

	    DTPRFS 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 DTPTRS or some other
	    means before entering this routine.  DTPRFS does not do iterative
	    refinement because doing so cannot improve the backward error.

       Parameters:
	   UPLO

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

	   TRANS

		     TRANS is 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 = Transpose)

	   DIAG

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

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrices B and X.  NRHS >= 0.

	   AP

		     AP is DOUBLE PRECISION 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)*(2*n-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

		     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
		     The right hand side matrix B.

	   LDB

		     LDB is INTEGER
		     The leading dimension of the array B.  LDB >= max(1,N).

	   X

		     X is DOUBLE PRECISION array, dimension (LDX,NRHS)
		     The solution matrix X.

	   LDX

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

	   FERR

		     FERR is 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

		     BERR is 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

		     WORK is DOUBLE PRECISION array, dimension (3*N)

	   IWORK

		     IWORK is INTEGER array, dimension (N)

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 175 of file dtprfs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dtprfs.f(3)
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