nmrLSMinNorm.h File Reference

#include <cisstNumerical/nmrNetlib.h>
#include <cisstVector/vctDynamicMatrix.h>
#include <cisstNumerical/nmrExport.h>

Go to the source code of this file.

Classes
class	nmrLSMinNorm
class	nmrLSMinNorm::Data

Functions
vctDynamicMatrix< double > CISST_EXPORT	nmrLSMinNorm (vctDynamicMatrix< double > &A, vctDynamicMatrix< double > &b, CISSTNETLIB_DOUBLE r=-1.0)
	Computes the minimum norm solution to a real linear least squares problem.
vctDynamicMatrix< double > CISST_EXPORT	nmrLSMinNorm (vctDynamicMatrix< double > &A, vctDynamicMatrix< double > &b, nmrLSMinNorm::Data &data, CISSTNETLIB_DOUBLE r=-1.0)
	Computes the minimum norm solution to a real linear least squares problem.

Function Documentation

nmrLSMinNorm() [1/2]

vctDynamicMatrix< double > CISST_EXPORT nmrLSMinNorm	(	vctDynamicMatrix< double > &	A,
		vctDynamicMatrix< double > &	b,
		CISSTNETLIB_DOUBLE	r = -1.0 )

Computes the minimum norm solution to a real linear least squares problem.

Computes the minimum norm solution to a real linear least squares problem: \( \min_{\mathbf{x}} \| \mathbf{b} - A\mathbf{x} \| \)

Parameters

[in]	A	The \( M \times N \) column major matrix.
[out]	A	The first \( \min ( M \times N ) \) right singular vectors.
[in]	b	The \( M \times O \) column major matrix. The matrix can be overwritten.
	r	Used to determine the effective rank of A. Singular values \( \sigma_i \leq r\sigma_1 \) are treated as zero (low rank approximation). If \( r<0 \), machine precision is used instead.

Returns

The \( N \times O \) minimum norm solutions \( \mathbf{x} \).

nmrLSMinNorm() [2/2]

vctDynamicMatrix< double > CISST_EXPORT nmrLSMinNorm	(	vctDynamicMatrix< double > &	A,
		vctDynamicMatrix< double > &	b,
		nmrLSMinNorm::Data &	data,
		CISSTNETLIB_DOUBLE	r = -1.0 )

Computes the minimum norm solution to a real linear least squares problem.

Computes the minimum norm solution to a real linear least squares problem: \( \min_{\mathbf{x}} \| \mathbf{b} - A\mathbf{x} \| \)

Parameters

[in]	A	A \( M \times N \) column major matrix.
[out]	A	The first \( \min ( M \times N ) \) right singular vectors.
[in]	b	A \( M \times O \) column major matrix. The matrix can be overwritten.
[in]	data	Provide pre-allocated workspace. If the workspace is not adequate it will be reallocated.
	r	Used to determine the effective rank of A. Singular values \( \sigma_i \leq r\sigma_1 \) are treated as zero (low rank approximation). If \( r<0 \), machine precision is used instead.

Returns

The \( N \times O \) minimum norm solutions \( \mathbf{x} \).