ldmat Class Reference

Matrix stored in LD form, (typically known as UD). More...

#include <libDC.h>

Inheritance diagram for ldmat:

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Collaboration diagram for ldmat:

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List of all members.

Public Member Functions
	ldmat (const mat &L, const vec &D)
	Construct by copy of L and D.
	ldmat (const mat &V)
	Construct by decomposition of full matrix V.
	ldmat (vec D0)
	Construct diagonal matrix with diagonal D0.
	ldmat ()
	Default constructor.
	ldmat (const int dim0)
	Default initialization with proper size.
virtual	~ldmat ()
	Destructor for future use;.
void	opupdt (const vec &v, double w)
mat	to_mat ()
	Conversion to full matrix.
void	mult_sym (const mat &C)
	Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$.
void	mult_sym_t (const mat &C)
	Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$.
void	add (const ldmat &ld2, double w=1.0)
	Add another matrix in LD form with weight w.
double	logdet () const
	Logarithm of a determinant.
double	qform (const vec &v) const
	Evaluates quadratic form $x= v'*V*v$;.
void	clear ()
	Clearing matrix so that it corresponds to zeros.
int	cols () const
	access function
int	rows () const
	access function
vec	sqrt_mult (const vec &v) const
	Multiplies square root of $V$ by vector $x$.
virtual void	inv (ldmat &Inv) const
	Matrix inversion preserving the chosen form.
void	mult_sym (const mat &C, ldmat &U) const
	Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class.
void	mult_sym_t (const mat &C, ldmat &U) const
	Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class.
void	ldform (const mat &A, const vec &D0)
	Transforms general $A'D0 A$ into pure $L'DL$.
void	setD (const vec &nD)
	Access functions.
void	setD (const vec &nD, int i)
	Access functions.
void	setL (const vec &nL)
	Access functions.
ldmat &	operator+= (const ldmat &ldA)
	add another ldmat matrix
ldmat &	operator-= (const ldmat &ldA)
	subtract another ldmat matrix
ldmat &	operator *= (double x)
	multiply by a scalar
Protected Attributes
vec	D
	Positive vector $D$.
mat	L
	Lower-triangular matrix $L$.
Friends
std::ostream &	operator<< (std::ostream &os, const ldmat &sq)
	print both L and D

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Detailed Description

Matrix stored in LD form, (typically known as UD).

Matrix is decomposed as follows:

where only $L$ and $D$ matrices are stored. All inplace operations modifies only these and the need to compose and decompose the matrix is avoided.

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Member Function Documentation

void ldmat::opupdt	(	const vec &	v,
		double	w
	)			[virtual]

Perfroms a rank-1 update by outer product of vectors: $V = V + w v v'$.

Parameters:

	v	Vector forming the outer product to be added
	w	weight of updating; can be negative

BLAS-2b operation.

Implements sqmat.

void ldmat::mult_sym

(

const mat &

C

)

[virtual]

Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$.

Parameters:

C

multiplying matrix,

Implements sqmat.

void ldmat::mult_sym_t

(

const mat &

C

)

[virtual]

Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$.

Parameters:

C

multiplying matrix,

Implements sqmat.

vec ldmat::sqrt_mult

(

const vec &

v

)

const [virtual]

Multiplies square root of $V$ by vector $x$.

Used e.g. in generating normal samples.

Implements sqmat.

void ldmat::inv

(

ldmat &

Inv

)

const [virtual]

Matrix inversion preserving the chosen form.

Parameters:

Inv

a space where the inverse is stored.

void ldmat::mult_sym	(	const mat &	C,
		ldmat &	U
	)			const

Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class.

Parameters:

	C	matrix to multiply with
	U	a space where the inverse is stored.

void ldmat::mult_sym_t	(	const mat &	C,
		ldmat &	U
	)			const

Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class.

Parameters:

	C	matrix to multiply with
	U	a space where the inverse is stored.

void ldmat::ldform	(	const mat &	A,
		const vec &	D0
	)

Transforms general $A'D0 A$ into pure $L'DL$.

The new decomposition fullfills: $A'*diag(D)*A = self.L'*diag(self.D)*self.L$

Parameters:

	A	general matrix
	D0	general vector

ldmat & ldmat::operator+=

(

const ldmat &

ldA

)

[inline]

add another ldmat matrix

Operations: mapping of add operation to operators

ldmat & ldmat::operator-=

(

const ldmat &

ldA

)

[inline]

subtract another ldmat matrix

mapping of negative add operation to operators

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The documentation for this class was generated from the following files:

• work/mixpp/bdm/math/libDC.h
• work/mixpp/bdm/math/libDC.cpp

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