ldmat Class Reference

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

#include <square_mat.h>

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 (const ldmat &V0, const ivec &perm)

Construct by restructuring of V0 accordint to permutation vector perm.

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 () const

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 $x= v'*V*v$ ;.

double invqform (const vec &v) const

Evaluates quadratic form $x= v'*inv(V)*v$ ;.

void clear ()

Clearing matrix so that it corresponds to zeros.

vec sqrt_mult (const vec &v) const

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

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.

const vec & _D () const

Access functions.

const mat & _L () const

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

int cols () const

Reimplementing common functions of mat: cols().

int rows () const

Reimplementing common functions of mat: rows().

Protected Attributes

vec D

Positive vector $D$ .

mat L

Lower-triangular matrix $L$ .

int dim

dimension of the square matrix

Friends

std::ostream & operator<< (std::ostream &os, const ldmat &sq)

print both L and D

Detailed Description

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

Matrix is decomposed as follows:

$M = L'DL$

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.

Member Function Documentation

void ldmat::inv ( ldmat & Inv ) const

Matrix inversion preserving the chosen form.

Parameters:

Inv

a space where the inverse is stored.

References clear(), D, L, and ldform().

Referenced by bdm::egiw::variance().

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

References D, sqmat::dim, and L.

Referenced by inv(), ldmat(), mult_sym(), and mult_sym_t().

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.

References D, L, and ldform().

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.

References D, L, and ldform().

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.

References D, L, and ldform().

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.

References D, L, and ldform().

ldmat & ldmat::operator+= ( const ldmat & ldA ) [inline]

add another ldmat matrix

Operations: mapping of add operation to operators

References add().

ldmat & ldmat::operator-= ( const ldmat & ldA ) [inline]

subtract another ldmat matrix

mapping of negative add operation to operators

References add().

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.

References D, sqmat::dim, and L.

Referenced by add(), bdm::ARX::bayes(), and bdm::ARX::logpred().

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.

References D, sqmat::dim, and L.

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

square_mat.h
square_mat.cpp


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 (const ldmat &V0, const ivec &perm)
	Construct by restructuring of V0 accordint to permutation vector perm.
	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 () const
	Conversion to full matrix.
void	mult_sym (const mat &C)
	Inplace symmetric multiplication by a SQUARE matrix , i.e. .
void	mult_sym_t (const mat &C)
	Inplace symmetric multiplication by a SQUARE transpose of matrix , i.e. .
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 ;.
double	invqform (const vec &v) const
	Evaluates quadratic form ;.
void	clear ()
	Clearing matrix so that it corresponds to zeros.
vec	sqrt_mult (const vec &v) const
	Multiplies square root of by vector .
void	inv (ldmat &Inv) const
	Matrix inversion preserving the chosen form.
void	mult_sym (const mat &C, ldmat &U) const
	Symmetric multiplication of by a general matrix , result of which is stored in the current class.
void	mult_sym_t (const mat &C, ldmat &U) const
	Symmetric multiplication of by a transpose of a general matrix , result of which is stored in the current class.
void	ldform (const mat &A, const vec &D0)
	Transforms general into pure .
void	setD (const vec &nD)
	Access functions.
void	setD (const vec &nD, int i)
	Access functions.
void	setL (const vec &nL)
	Access functions.
const vec &	_D () const
	Access functions.
const mat &	_L () const
	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
int	cols () const
	Reimplementing common functions of mat: cols().
int	rows () const
	Reimplementing common functions of mat: rows().
Protected Attributes
vec	D
	Positive vector .
mat	L
	Lower-triangular matrix .
int	dim
	dimension of the square matrix
Friends
std::ostream &	operator<< (std::ostream &os, const ldmat &sq)
	print both `L` and `D`