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

CTPRFS(l)					)					CTPRFS(l)

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

       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

LAPACK version 3.0			   15 June 2000 				CTPRFS(l)


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