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Functions
static void	aprod_free (BCLS *ls, const int mode, const int m, const int nFree, double dxFree[], double y[])
	Mat-vec routine called by CGLS.
static int	bcls_cgls (BCLS ls, int m, int n, int kmax, double tol, double damp, double c[], double x[], double r[], double s[], double p[], int itns, double opt, FILE nout)
	CG for least squares.
int	bcls_newton_step_cgls (BCLS ls, int m, int nFree, int ix[], double damp, int itnLim, double tol, double dxFree[], double x[], double c[], double r[], int itns, double *opt)
	Compute a Newton step using CGLS.

Detailed Description

Function Documentation

static void aprod_free	(	BCLS *	ls,
		const int	mode,
		const int	m,
		const int	nFree,
		double	dxFree[],
		double	y[]
	)			`[static]`

Mat-vec routine called by CGLS.

CGLS call this routine, which in turn calls bcls_aprod:

If mode == BCLS_PROD_A, y = A dxFree.
else if mode == BCLS_PROD_At, dxFree = A'y.

This routine is declared "static" so that it won't be confused with the user's own Aprod routine.

Parameters:

`[in,out]`	ls	BCLS solver context.
`[in]`	mode	Specifies if the product with A or A' is required.
`[in]`	m	Number of rows in A.
`[in]`	nFree	Length of dxFree (and ix which is recovered via ls).
`[in,out]`	dxFree	RHS or LHS (depending on the mode).
`[in,out]`	y	RHS or LHS (depending on the mode).

Definition at line 67 of file bccgls.c.

References bcls_aprod(), bcls_gather(), BCLS_PROD_A, BCLS_PROD_At, bcls_scatter(), BCLS::dx, and BCLS::ix.

Referenced by bcls_cgls().

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static int bcls_cgls	(	BCLS *	ls,
		int	m,
		int	n,
		int	kmax,
		double	tol,
		double	damp,
		double	c[],
		double	x[],
		double	r[],
		double	s[],
		double	p[],
		int *	itns,
		double *	opt,
		FILE *	nout
	)			`[static]`

CG for least squares.

This routine implements CG for solving the symmetric linear system

( N'N + damp I ) x = N'r + c

where N is an m-by-n submatrix of the general matrix A. This implementation is adapted from Hestenes and Stiefel's CG for least-squares method to accomodate the damping term and the additional vector on the RHS. (See, eg, Bjork, Numerical Methods for Least-Squares Problems, 1996, p. 289.)

Parameters:

`[in,out]`	ls	BCLS solver context.
`[in]`	m	No. of rows in A.
`[in]`	n	No. of cols in A.
`[in]`	kmax	Maximum no. of CG iterations.
`[in]`	tol	Required optimality tolerance: norm( A'A x - A'b ) / norm(A'b)
`[in]`	damp	Regularization term on x.
`[in]`	c	Additional vector (set NULL if not present).
`[out]`	x	Solution vector.
`[in,out]`	r	On entry, r must be defined. On exit, r is the residual.
`[in,out]`	s	Work vector.
`[in,out]`	p	Work vector.
`[out]`	itns	No. of CG iterations.
`[out]`	opt	Relative residual (see tol, above).
`[in]`	nout	File for log output (set NULL if not needed).

Returns:

0: Required accuracy was achieved.
1: The iteration limit (kmax) was reached.
2: N'N appears to be singular.

Todo:: Update normx rather than recompute at each iteration.

Definition at line 129 of file bccgls.c.

References aprod_free(), bcls_dload(), BCLS_PROD_A, BCLS_PROD_At, cblas_daxpy(), cblas_dcopy(), cblas_dnrm2(), and cblas_dscal().

Referenced by bcls_newton_step_cgls().

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int bcls_newton_step_cgls	(	BCLS *	ls,
		int	m,
		int	nFree,
		int	ix[],
		double	damp,
		int	itnLim,
		double	tol,
		double	dxFree[],
		double	x[],
		double	c[],
		double	r[],
		int *	itns,
		double *	opt
	)

Compute a Newton step using CGLS.

See the description of bcls_newton_step.

Parameters:

`[in,out]`	ls	BCLS solver context
`[in]`	m	No. of rows in A.
`[in]`	nFree	No. of free columns, i.e., no. of cols in N.
`[in]`	ix	Index of vars for which a Newton step is computed.
`[in]`	damp	Regularization term on dxFree.
`[in]`	itnLim	Maximum no. of CG iterations.
`[in]`	tol	Required optimality tolerance: norm( N'N x - N'b ) / norm(N'b).
`[in]`	dxFree	Newton direction in the free vars (len = nFree).
`[in]`	x	Current iterate.
`[in]`	c	Linear term. (Set to NULL if not present.)
`[in,out]`	r	On entry, r is current residual: r = b - Ax. Will be used as workspace.
`[in]`	itns	No. of CG iterations.
`[in]`	opt	Relative residual (see tol, above).

Returns:: The termination flag returned by bcls_cgls.

Definition at line 258 of file bccgls.c.

References bcls_cgls(), bcls_gather(), cblas_dscal(), BCLS::minor_file, BCLS::wrk_u, BCLS::wrk_v, and BCLS::wrk_w.

Referenced by bcls_newton_step().

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bccgls.c File Reference

Functions

Detailed Description

Function Documentation