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CentOS 7.0 - man page for dla_syrfsx_extended.f (centos section 3)

dla_syrfsx_extended.f(3)		      LAPACK			 dla_syrfsx_extended.f(3)

NAME
       dla_syrfsx_extended.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dla_syrfsx_extended (PREC_TYPE, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, COLEQU,
	   C, B, LDB, Y, LDY, BERR_OUT, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, RES, AYB, DY,
	   Y_TAIL, RCOND, ITHRESH, RTHRESH, DZ_UB, IGNORE_CWISE, INFO)
	   DLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for
	   symmetric indefinite matrices by performing extra-precise iterative refinement and
	   provides error bounds and backward error estimates for the solution.

Function/Subroutine Documentation
   subroutine dla_syrfsx_extended (integerPREC_TYPE, characterUPLO, integerN, integerNRHS, double
       precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldaf, * )AF,
       integerLDAF, integer, dimension( * )IPIV, logicalCOLEQU, double precision, dimension( *
       )C, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldy,
       * )Y, integerLDY, double precision, dimension( * )BERR_OUT, integerN_NORMS, double
       precision, dimension( nrhs, * )ERR_BNDS_NORM, double precision, dimension( nrhs, *
       )ERR_BNDS_COMP, double precision, dimension( * )RES, double precision, dimension( * )AYB,
       double precision, dimension( * )DY, double precision, dimension( * )Y_TAIL, double
       precisionRCOND, integerITHRESH, double precisionRTHRESH, double precisionDZ_UB,
       logicalIGNORE_CWISE, integerINFO)
       DLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for
       symmetric indefinite matrices by performing extra-precise iterative refinement and
       provides error bounds and backward error estimates for the solution.

       Purpose:

	    DLA_SYRFSX_EXTENDED improves the computed solution to a system of
	    linear equations by performing extra-precise iterative refinement
	    and provides error bounds and backward error estimates for the solution.
	    This subroutine is called by DSYRFSX to perform iterative refinement.
	    In addition to normwise error bound, the code provides maximum
	    componentwise error bound if possible. See comments for ERR_BNDS_NORM
	    and ERR_BNDS_COMP for details of the error bounds. Note that this
	    subroutine is only resonsible for setting the second fields of
	    ERR_BNDS_NORM and ERR_BNDS_COMP.

       Parameters:
	   PREC_TYPE

		     PREC_TYPE is INTEGER
		Specifies the intermediate precision to be used in refinement.
		The value is defined by ILAPREC(P) where P is a CHARACTER and
		P    = 'S':  Single
		     = 'D':  Double
		     = 'I':  Indigenous
		     = 'X', 'E':  Extra

	   UPLO

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

	   N

		     N is INTEGER
		The number of linear equations, i.e., the order of the
		matrix A.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		The number of right-hand-sides, i.e., the number of columns of the
		matrix B.

	   A

		     A is DOUBLE PRECISION array, dimension (LDA,N)
		On entry, the N-by-N matrix A.

	   LDA

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

	   AF

		     AF is DOUBLE PRECISION array, dimension (LDAF,N)
		The block diagonal matrix D and the multipliers used to
		obtain the factor U or L as computed by DSYTRF.

	   LDAF

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

	   IPIV

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

	   COLEQU

		     COLEQU is LOGICAL
		If .TRUE. then column equilibration was done to A before calling
		this routine. This is needed to compute the solution and error
		bounds correctly.

	   C

		     C is DOUBLE PRECISION array, dimension (N)
		The column scale factors for A. If COLEQU = .FALSE., C
		is not accessed. If C is input, each element of C should be a power
		of the radix to ensure a reliable solution and error estimates.
		Scaling by powers of the radix does not cause rounding errors unless
		the result underflows or overflows. Rounding errors during scaling
		lead to refining with a matrix that is not equivalent to the
		input matrix, producing error estimates that may not be
		reliable.

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
		The right-hand-side matrix B.

	   LDB

		     LDB is INTEGER
		The leading dimension of the array B.  LDB >= max(1,N).

	   Y

		     Y is DOUBLE PRECISION array, dimension
			       (LDY,NRHS)
		On entry, the solution matrix X, as computed by DSYTRS.
		On exit, the improved solution matrix Y.

	   LDY

		     LDY is INTEGER
		The leading dimension of the array Y.  LDY >= max(1,N).

	   BERR_OUT

		     BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
		On exit, BERR_OUT(j) contains the componentwise relative backward
		error for right-hand-side j from the formula
		    max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
		where abs(Z) is the componentwise absolute value of the matrix
		or vector Z. This is computed by DLA_LIN_BERR.

	   N_NORMS

		     N_NORMS is INTEGER
		Determines which error bounds to return (see ERR_BNDS_NORM
		and ERR_BNDS_COMP).
		If N_NORMS >= 1 return normwise error bounds.
		If N_NORMS >= 2 return componentwise error bounds.

	   ERR_BNDS_NORM

		     ERR_BNDS_NORM is DOUBLE PRECISION array, dimension
			       (NRHS, N_ERR_BNDS)
		For each right-hand side, this array contains information about
		various error bounds and condition numbers corresponding to the
		normwise relative error, which is defined as follows:

		Normwise relative error in the ith solution vector:
			max_j (abs(XTRUE(j,i) - X(j,i)))
		       ------------------------------
			     max_j abs(X(j,i))

		The array is indexed by the type of error information as described
		below. There currently are up to three pieces of information
		returned.

		The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
		right-hand side.

		The second index in ERR_BNDS_NORM(:,err) contains the following
		three fields:
		err = 1 "Trust/don't trust" boolean. Trust the answer if the
			 reciprocal condition number is less than the threshold
			 sqrt(n) * slamch('Epsilon').

		err = 2 "Guaranteed" error bound: The estimated forward error,
			 almost certainly within a factor of 10 of the true error
			 so long as the next entry is greater than the threshold
			 sqrt(n) * slamch('Epsilon'). This error bound should only
			 be trusted if the previous boolean is true.

		err = 3  Reciprocal condition number: Estimated normwise
			 reciprocal condition number.  Compared with the threshold
			 sqrt(n) * slamch('Epsilon') to determine if the error
			 estimate is "guaranteed". These reciprocal condition
			 numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
			 appropriately scaled matrix Z.
			 Let Z = S*A, where S scales each row by a power of the
			 radix so all absolute row sums of Z are approximately 1.

		This subroutine is only responsible for setting the second field
		above.
		See Lapack Working Note 165 for further details and extra
		cautions.

	   ERR_BNDS_COMP

		     ERR_BNDS_COMP is DOUBLE PRECISION array, dimension
			       (NRHS, N_ERR_BNDS)
		For each right-hand side, this array contains information about
		various error bounds and condition numbers corresponding to the
		componentwise relative error, which is defined as follows:

		Componentwise relative error in the ith solution vector:
			       abs(XTRUE(j,i) - X(j,i))
			max_j ----------------------
				    abs(X(j,i))

		The array is indexed by the right-hand side i (on which the
		componentwise relative error depends), and the type of error
		information as described below. There currently are up to three
		pieces of information returned for each right-hand side. If
		componentwise accuracy is not requested (PARAMS(3) = 0.0), then
		ERR_BNDS_COMP is not accessed.	If N_ERR_BNDS .LT. 3, then at most
		the first (:,N_ERR_BNDS) entries are returned.

		The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
		right-hand side.

		The second index in ERR_BNDS_COMP(:,err) contains the following
		three fields:
		err = 1 "Trust/don't trust" boolean. Trust the answer if the
			 reciprocal condition number is less than the threshold
			 sqrt(n) * slamch('Epsilon').

		err = 2 "Guaranteed" error bound: The estimated forward error,
			 almost certainly within a factor of 10 of the true error
			 so long as the next entry is greater than the threshold
			 sqrt(n) * slamch('Epsilon'). This error bound should only
			 be trusted if the previous boolean is true.

		err = 3  Reciprocal condition number: Estimated componentwise
			 reciprocal condition number.  Compared with the threshold
			 sqrt(n) * slamch('Epsilon') to determine if the error
			 estimate is "guaranteed". These reciprocal condition
			 numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
			 appropriately scaled matrix Z.
			 Let Z = S*(A*diag(x)), where x is the solution for the
			 current right-hand side and S scales each row of
			 A*diag(x) by a power of the radix so all absolute row
			 sums of Z are approximately 1.

		This subroutine is only responsible for setting the second field
		above.
		See Lapack Working Note 165 for further details and extra
		cautions.

	   RES

		     RES is DOUBLE PRECISION array, dimension (N)
		Workspace to hold the intermediate residual.

	   AYB

		     AYB is DOUBLE PRECISION array, dimension (N)
		Workspace. This can be the same workspace passed for Y_TAIL.

	   DY

		     DY is DOUBLE PRECISION array, dimension (N)
		Workspace to hold the intermediate solution.

	   Y_TAIL

		     Y_TAIL is DOUBLE PRECISION array, dimension (N)
		Workspace to hold the trailing bits of the intermediate solution.

	   RCOND

		     RCOND is DOUBLE PRECISION
		Reciprocal scaled condition number.  This is an estimate of the
		reciprocal Skeel condition number of the matrix A after
		equilibration (if done).  If this is less than the machine
		precision (in particular, if it is zero), the matrix is singular
		to working precision.  Note that the error may still be small even
		if this number is very small and the matrix appears ill-
		conditioned.

	   ITHRESH

		     ITHRESH is INTEGER
		The maximum number of residual computations allowed for
		refinement. The default is 10. For 'aggressive' set to 100 to
		permit convergence using approximate factorizations or
		factorizations other than LU. If the factorization uses a
		technique other than Gaussian elimination, the guarantees in
		ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.

	   RTHRESH

		     RTHRESH is DOUBLE PRECISION
		Determines when to stop refinement if the error estimate stops
		decreasing. Refinement will stop when the next solution no longer
		satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
		the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
		default value is 0.5. For 'aggressive' set to 0.9 to permit
		convergence on extremely ill-conditioned matrices. See LAWN 165
		for more details.

	   DZ_UB

		     DZ_UB is DOUBLE PRECISION
		Determines when to start considering componentwise convergence.
		Componentwise convergence is only considered after each component
		of the solution Y is stable, which we definte as the relative
		change in each component being less than DZ_UB. The default value
		is 0.25, requiring the first bit to be stable. See LAWN 165 for
		more details.

	   IGNORE_CWISE

		     IGNORE_CWISE is LOGICAL
		If .TRUE. then ignore componentwise convergence. Default value
		is .FALSE..

	   INFO

		     INFO is INTEGER
		  = 0:	Successful exit.
		  < 0:	if INFO = -i, the ith argument to DLA_SYRFSX_EXTENDED had an illegal
			value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 394 of file dla_syrfsx_extended.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012		 dla_syrfsx_extended.f(3)


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