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ZTPRFS(1)		 LAPACK routine (version 3.2)		     ZTPRFS(1)

NAME
       ZTPRFS  -  provides  error  bounds and backward error estimates for the
       solution to a system of linear equations with a triangular packed coef‐
       ficient 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 solu‐
       tion  to	 a system of linear equations with a triangular packed coeffi‐
       cient 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 vec‐
	       tor  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

 LAPACK routine (version 3.2)	 November 2008			     ZTPRFS(1)
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