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RedHat 9 (Linux i386) - man page for dtprfs (redhat section l)

DTPRFS(l)					)					DTPRFS(l)

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

SYNOPSIS
       SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B,  LDB,  X,	LDX,  FERR,  BERR,  WORK,
			  IWORK, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION  AP(  *  ),  B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X(
			  LDX, * )

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.

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 = 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) 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       (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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 esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate 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  solu-
	       tion).

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

       IWORK   (workspace) INTEGER array, dimension (N)

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

LAPACK version 3.0			   15 June 2000 				DTPRFS(l)


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