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CSYRFS(3F)							    CSYRFS(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	CSYRFS(	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( *	)

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

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

PURPOSE    [Toc]    [Back]

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

ARGUMENTS    [Toc]    [Back]

     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 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) COMPLEX 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



									Page 1






CSYRFS(3F)							    CSYRFS(3F)



	     or	L from the factorization A = U*D*U**T or A = L*D*L**T as
	     computed by CSYTRF.

     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 CSYTRF.

     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 CSYTRS.  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 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) 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 solution).

     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

PARAMETERS    [Toc]    [Back]

     ITMAX is the maximum number of steps of iterative refinement.
CSYRFS(3F)							    CSYRFS(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	CSYRFS(	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( *	)

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

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

PURPOSE    [Toc]    [Back]

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

ARGUMENTS    [Toc]    [Back]

     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 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) COMPLEX 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



									Page 1






CSYRFS(3F)							    CSYRFS(3F)



	     or	L from the factorization A = U*D*U**T or A = L*D*L**T as
	     computed by CSYTRF.

     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 CSYTRF.

     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 CSYTRS.  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 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) 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 solution).

     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

PARAMETERS    [Toc]    [Back]

     ITMAX is the maximum number of steps of iterative refinement.


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