Functions
blitz::Array< double, 2 >	FullPhysics::cholesky_decomposition (const blitz::Array< double, 2 > &A)
	This calculates the Cholesky Decompostion of A so that A = L L^T. More...

template<class T >
void	FullPhysics::fortran_resize (blitz::Array< T, 1 > &M, int sz1)
	If matrix is in Fortran order, resize it. More...

template<class T >
void	FullPhysics::fortran_resize (blitz::Array< T, 2 > &M, int sz1, int sz2)
	If matrix is in Fortran order, resize it. More...

template<class T >
void	FullPhysics::fortran_resize (blitz::Array< T, 3 > &M, int sz1, int sz2, int sz3)
	If matrix is in Fortran order, resize it. More...

blitz::Array< double, 2 >	FullPhysics::generalized_inverse (const blitz::Array< double, 2 > &A, double Rcond=std::numeric_limits< double >::epsilon())
	This returns the generalized inverse of the given matrix. More...

blitz::Array< double, 2 >	FullPhysics::generalized_inverse (const blitz::Array< double, 2 > &A, const blitz::Array< bool, 1 > &Zero_unused, double Rcond=std::numeric_limits< double >::epsilon())
	This returns the generalized inverse of the given matrix. More...

blitz::Array< double, 2 >	FullPhysics::multifit_covar (const blitz::Array< double, 2 > &J, double Eps_rel=std::numeric_limits< double >::epsilon())

bool	FullPhysics::multifit_test_delta (const blitz::Array< double, 1 > &dx, const blitz::Array< double, 1 > &x, double Eps_abs=std::numeric_limits< double >::epsilon(), double Eps_rel=std::numeric_limits< double >::epsilon())

bool	FullPhysics::multifit_test_gradient (const blitz::Array< double, 1 > &g, double Eps_abs=std::numeric_limits< double >::epsilon())

blitz::Array< double, 1 >	FullPhysics::solve_least_squares (const blitz::Array< double, 2 > &A, const blitz::Array< double, 1 > &B, double Rcond=1e-12)
	This solves the least squares system A*x = b, returning the minimum norm solution. More...

blitz::Array< double, 1 >	FullPhysics::solve_least_squares_qr (const blitz::Array< double, 2 > &A, const blitz::Array< double, 1 > &B)
	This finds the least squares solution to the overdetermined system A x = b where the matrix A has more rows than columns. More...

double	FullPhysics::sqr (double x)

void	FullPhysics::svd (const blitz::Array< double, 2 > &A, blitz::Array< double, 1 > &S, blitz::Array< double, 2 > &U, blitz::Array< double, 2 > &VT)
	Compute the SVD decomposition of a matrix A = U * SIGMA * V^T. More...

template<class T , int D>
blitz::Array< T, D >	FullPhysics::to_c_order (const blitz::Array< T, D > &In)
	Ensure that a given blitz::Array is contiguous, not reversed, and in C RowMajorArray format. More...

template<class T , int D>
blitz::Array< T, D >	FullPhysics::to_c_order_const (const blitz::Array< T, D > &In)
	Ensure that a given blitz::Array is contiguous, not reversed, and in C RowMajorArray format. More...

template<class T , int D>
blitz::Array< T, D >	FullPhysics::to_fortran (const blitz::Array< T, D > &In)
	Ensure that a given blitz::Array is contiguous, not reversed, and in fortran ColumnMajorArray format. More...

template<class T , int D>
blitz::Array< T, D >	FullPhysics::to_fortran_const (const blitz::Array< T, D > &In)
	Ensure that a given blitz::Array is contiguous, not reversed, and in fortran ColumnMajorArray format. More...

Detailed Description

Function Documentation

◆ cholesky_decomposition()

blitz::Array< double, 2 > FullPhysics::cholesky_decomposition ( const blitz::Array< double, 2 > & A )

This calculates the Cholesky Decompostion of A so that A = L L^T.

This returns L. A must be symmetric positive definite.

Definition at line 212 of file linear_algebra.cc.

◆ fortran_resize() [1/3]

template<class T >

void FullPhysics::fortran_resize	(	blitz::Array< T, 1 > &	M,
		int	sz1
	)

If matrix is in Fortran order, resize it.

Otherwise, set it to a Fortran matrix of the given size.

Definition at line 91 of file linear_algebra.h.

◆ fortran_resize() [2/3]

template<class T >

void FullPhysics::fortran_resize	(	blitz::Array< T, 2 > &	M,
		int	sz1,
		int	sz2
	)

If matrix is in Fortran order, resize it.

Otherwise, set it to a Fortran matrix of the given size.

Definition at line 110 of file linear_algebra.h.

◆ fortran_resize() [3/3]

template<class T >

void FullPhysics::fortran_resize	(	blitz::Array< T, 3 > &	M,
		int	sz1,
		int	sz2,
		int	sz3
	)

If matrix is in Fortran order, resize it.

Otherwise, set it to a Fortran matrix of the given size.

Definition at line 129 of file linear_algebra.h.

◆ generalized_inverse() [1/2]

Array< double, 2 > FullPhysics::generalized_inverse	(	const blitz::Array< double, 2 > &	A,
		double	Rcond = `std::numeric_limits<double>::epsilon()`
	)

This returns the generalized inverse of the given matrix.

This is the same as the inverse, except that if A is rank deficient we set the SVD value to 0.

Parameters

A	Matrix to get inverse of
Rcond	We set singular values < Rcond * max singular value to 0.

Definition at line 136 of file linear_algebra.cc.

◆ generalized_inverse() [2/2]

Array< double, 2 > FullPhysics::generalized_inverse	(	const blitz::Array< double, 2 > &	A,
		const blitz::Array< bool, 1 > &	Zero_unused,
		double	Rcond = `std::numeric_limits<double>::epsilon()`
	)

This returns the generalized inverse of the given matrix.

This is the same as the inverse, except that if A is rank deficient we set the SVD value to 0.

This variation takes a boolean array indicating which parameters are to be held at zero.

Parameters

A	Matrix to get inverse of
Zero_unused	Boolean array indicating parameters that are unused and should be held to zero
Rcond	We set singular values < Rcond * max singular value to 0.

Definition at line 164 of file linear_algebra.cc.

◆ multifit_covar()

blitz::Array< double, 2 > FullPhysics::multifit_covar	(	const blitz::Array< double, 2 > &	J,
		double	Eps_rel = `std::numeric_limits<double>::epsilon()`
	)

Definition at line 226 of file linear_algebra.cc.

◆ multifit_test_delta()

bool FullPhysics::multifit_test_delta	(	const blitz::Array< double, 1 > &	dx,
		const blitz::Array< double, 1 > &	x,
		double	Eps_abs = `std::numeric_limits<double>::epsilon()`,
		double	Eps_rel = `std::numeric_limits<double>::epsilon()`
	)

Definition at line 239 of file linear_algebra.cc.

◆ multifit_test_gradient()

bool FullPhysics::multifit_test_gradient	(	const blitz::Array< double, 1 > &	g,
		double	Eps_abs = `std::numeric_limits<double>::epsilon()`
	)

Definition at line 234 of file linear_algebra.cc.

◆ solve_least_squares()

Array< double, 1 > FullPhysics::solve_least_squares	(	const blitz::Array< double, 2 > &	A,
		const blitz::Array< double, 1 > &	B,
		double	Rcond = `1e-12`
	)

This solves the least squares system A*x = b, returning the minimum norm solution.

It is perfectly ok for A to be rank deficient.

Parameters

A	a M x N matrix, which may be rank deficient.
B	the right hand side, a M vector
Rcond	a singular value <= Rcond * max singular value is treated as 0. You can pass Rcond < 0 to use machine precision if desired.

Returns: The vector X, which is a N vector

Definition at line 27 of file linear_algebra.cc.

◆ solve_least_squares_qr()

Array< double, 1 > FullPhysics::solve_least_squares_qr	(	const blitz::Array< double, 2 > &	A,
		const blitz::Array< double, 1 > &	B
	)

This finds the least squares solution to the overdetermined system A x = b where the matrix A has more rows than columns.

The least squares solution minimizes the Euclidean norm of the residual, ||Ax - b||. The solution is determined using a QR decomposition of A.

Parameters

A	a M x N matrix, which may be rank deficient.
B	the right hand side, a M vector

Returns: The vector X, which is a N vector

Definition at line 66 of file linear_algebra.cc.

◆ sqr()

double FullPhysics::sqr ( double x )

inline

Todo:: Move this to a better location

Definition at line 11 of file linear_algebra.h.

◆ svd()

void FullPhysics::svd	(	const blitz::Array< double, 2 > &	A,
		blitz::Array< double, 1 > &	S,
		blitz::Array< double, 2 > &	U,
		blitz::Array< double, 2 > &	VT
	)

Compute the SVD decomposition of a matrix A = U * SIGMA * V^T.

Parameters

A	Matrix to get decomposition for.
S	On exit, Singular values
U	On exit, U matrix. Note that this is the "thin" version of U, this is M x N rather than M x M. The "full" version would just have extra columns of zeros.
VT	On exit, V^T matrix

Definition at line 103 of file linear_algebra.cc.

◆ to_c_order()

template<class T , int D>

blitz::Array<T, D> FullPhysics::to_c_order ( const blitz::Array< T, D > & In )

Ensure that a given blitz::Array is contiguous, not reversed, and in C RowMajorArray format.

If it already is, then we just return the array. Otherwise, we create a copy of this in C order.

Definition at line 44 of file linear_algebra.h.

◆ to_c_order_const()

template<class T , int D>

blitz::Array<T, D> FullPhysics::to_c_order_const ( const blitz::Array< T, D > & In )

Ensure that a given blitz::Array is contiguous, not reversed, and in C RowMajorArray format.

If it already is, then we just return the array. Otherwise, we create a copy of this in C order.

Unfortunately, this removes the "const" from the calling argument, so we have a version of this where you explicitly say this ok.

Definition at line 70 of file linear_algebra.h.

◆ to_fortran()

template<class T , int D>

blitz::Array<T, D> FullPhysics::to_fortran ( const blitz::Array< T, D > & In )

Ensure that a given blitz::Array is contiguous, not reversed, and in fortran ColumnMajorArray format.

If it already is, then we just return the array. Otherwise, we create a copy of this suitable for passing to Fortran.

Definition at line 21 of file linear_algebra.h.

◆ to_fortran_const()

template<class T , int D>

blitz::Array<T, D> FullPhysics::to_fortran_const ( const blitz::Array< T, D > & In )

Ensure that a given blitz::Array is contiguous, not reversed, and in fortran ColumnMajorArray format.

If it already is, then we just return the array. Otherwise, we create a copy of this suitable for passing to Fortran.

Unfortunately, this removes the "const" from the calling argument, so we have a version of this where you explicitly say this ok.

Definition at line 156 of file linear_algebra.h.

Functions

Detailed Description

Function Documentation

◆ cholesky_decomposition()

◆ fortran_resize() [1/3]

◆ fortran_resize() [2/3]

◆ fortran_resize() [3/3]

◆ generalized_inverse() [1/2]

◆ generalized_inverse() [2/2]

◆ multifit_covar()

◆ multifit_test_delta()

◆ multifit_test_gradient()

◆ solve_least_squares()

◆ solve_least_squares_qr()

◆ sqr()

◆ svd()

◆ to_c_order()

◆ to_c_order_const()

◆ to_fortran()

◆ to_fortran_const()