OpenTissue::math::big::details Namespace Reference

Functions
template<class T >
T	hypot (T const &a, T const &b)
template<typename ME >
void	svd_impl1 (ublas::matrix_expression< ME > const &AE, ublas::matrix< typename ME::value_type > &U, ublas::vector< typename ME::value_type > &s, ublas::matrix< typename ME::value_type > &V)
template<typename ME >
void	svd_impl_atlas (ublas::matrix_expression< ME > const &A, ublas::matrix< typename ME::value_type, ublas::column_major > &U, ublas::vector< typename ME::value_type > &s, ublas::matrix< typename ME::value_type, ublas::column_major > &VT)

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Function Documentation

template<class T >

T OpenTissue::math::big::details::hypot	(	T const &	a,
		T const &	b
	)			[inline]

Hypotenuse.

Parameters:

	a	A real value
	b	A real vlaue

Returns:

hypotenuse of real (non-complex) scalars a and b by avoiding underflow/overflow using (a * sqrt( 1 + (b/a) * (b/a))), rather than sqrt(a*a + b*b).

template<typename ME >

void OpenTissue::math::big::details::svd_impl1	(	ublas::matrix_expression< ME > const &	AE,
		ublas::matrix< typename ME::value_type > &	U,
		ublas::vector< typename ME::value_type > &	s,
		ublas::matrix< typename ME::value_type > &	V
	)			[inline]

Compute Singular Value Decomposition of a matrix.

A = U S VT

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'.

The singular values, sigma(k) = S(k,k), are ordered so that sigma(0) >= sigma(1) >= ... >= sigma(n-1).

The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).

Parameters:

	AE	The input matrix.
	U	Upon return this matrix holds orthogonal columns.
	s	A vector containing the singular values.
	V	Upon return this matrix is an orthogonal matrix.

template<typename ME >

void OpenTissue::math::big::details::svd_impl_atlas	(	ublas::matrix_expression< ME > const &	A,
		ublas::matrix< typename ME::value_type, ublas::column_major > &	U,
		ublas::vector< typename ME::value_type > &	s,
		ublas::matrix< typename ME::value_type, ublas::column_major > &	VT
	)			[inline]

Compute Singular Value Decomposition of a matrix.

A = U S VT

Parameters:

	A	The matrix.
	U	Upon return this matrix holds orthogonal columns.
	s	A vector containing the singular values.
	VT	Upon return this matrix is an orthogonal matrix.