dporfs(l) [redhat man page]

DPORFS(l)								 )								 DPORFS(l)

NAME

       DPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

SYNOPSIS

       SUBROUTINE DPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LDAF, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

       DPORFS  improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and pro-
       vides error bounds and backward error estimates for the solution.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       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.

       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
	       The symmetric matrix A.	If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper  triangular  part  of  the
	       matrix  A,  and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part
	       of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

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

       AF      (input) DOUBLE PRECISION array, dimension (LDAF,N)
	       The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF.

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

       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/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by DPOTRS.	On exit, the improved 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 vector X(j) (i.e., the smallest relative change in any element of A or B
	       that makes X(j) an exact solution).

       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

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 DPORFS(l)

ZHERFS(l)								 )								 ZHERFS(l)

NAME

       ZHERFS  -  improve  the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides
       error bounds and backward error estimates for the solution

SYNOPSIS

       SUBROUTINE ZHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LDAF, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX*16	  A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is  Hermitian	indefinite,  and  provides
       error bounds and backward error estimates for the solution.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       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.

       A       (input) COMPLEX*16 array, dimension (LDA,N)
	       The  Hermitian  matrix  A.   If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the
	       matrix A, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower  triangular  part
	       of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

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

       AF      (input) COMPLEX*16 array, dimension (LDAF,N)
	       The  factored  form  of the matrix A.  AF contains the block diagonal matrix D and the multipliers used to obtain the factor U or L
	       from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHETRF.

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

       IPIV    (input) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D as determined by ZHETRF.

       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/output) COMPLEX*16 array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by ZHETRS.	On exit, the improved 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 vector 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

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 ZHERFS(l)