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

CPTRFS(l)					)					CPTRFS(l)

NAME
       CPTRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and
       backward error estimates for the solution

SYNOPSIS
       SUBROUTINE CPTRFS( UPLO,  N,  NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
			  INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   REAL 	  BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )

	   COMPLEX	  B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE
       CPTRFS improves the computed solution to a system of linear equations when the coefficient
       matrix is Hermitian positive definite and tridiagonal, and provides error bounds and back-
       ward error estimates for the solution.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A
	       is stored and the form of the factorization:
	       = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
	       =  'L':	 E is the subdiagonal of A, and A = L*D*L**H.  (The two forms are equiva-
	       lent if A is real.)

       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 matrix B.  NRHS
	       >= 0.

       D       (input) REAL array, dimension (N)
	       The n real diagonal elements of the tridiagonal matrix A.

       E       (input) COMPLEX array, dimension (N-1)
	       The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

       DF      (input) REAL array, dimension (N)
	       The  n  diagonal elements of the diagonal matrix D from the factorization computed
	       by CPTTRF.

       EF      (input) COMPLEX array, dimension (N-1)
	       The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the fac-
	       torization computed by CPTTRF (see UPLO).

       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/output) COMPLEX array, dimension (LDX,NRHS)
	       On  entry,  the	solution  matrix X, as computed by CPTTRS.  On exit, the improved
	       solution matrix X.

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

       FERR    (output) REAL array, dimension (NRHS)
	       The 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).

       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 (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

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0			   15 June 2000 				CPTRFS(l)


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