mpqc.Math.Matrix

Matrix and Vector classes and function, derived from Eigen. More...

Classes
struct	mpqc::matrix< T, Order >
	Matrix class derived from Eigen::Matrix with additional MPQC integration. More...
struct	mpqc::vector< T >
	Vector class derived from Eigen::Matrix with additional MPQC integration. More...

Typedefs
typedef matrix< double >	mpqc::Matrix
	Convience double matrix type.
typedef vector< double >	mpqc::Vector
	Convience double vector type.

Functions
template<class E >
double	mpqc::absmax (const E &e)
	absolute max of an Eigen type
template<class T >
T	mpqc::dot (const matrix< T > &a, const matrix< T > &b)
	element-wise dot product of two matrices
template<class T >
Eigen::SelfAdjointEigenSolver< Matrix::EigenType >	mpqc::symmetric (const matrix< T > &a)
	Computes (Eigen::SelfAdjointEigenSolver) eigensystem of a matrix.
template<class T >
T	mpqc::norm (const matrix< T > &a)
	Matrix norm.
template<class T >
void	mpqc::normalize (matrix< T > &a)
	Normalize matrix.
template<class T >
void	mpqc::orthonormalize (matrix< T > &d, const matrix< T > &b)
	orthormalize matrix d wrt to normalized matrix b d = normalize(d - (<d|b>*b))

Detailed Description

Matrix and Vector classes and function, derived from Eigen.

The matrix and vector objects overide operator(), s.t. if one of the arguments is a range, a block is returned rather than a single element. Example:

matrix(0,range(0,4)); // returns 1x4 sub-matrix (0,0:3)
matrix(0,0); // returns matrix element (0,0);
vector(range(2,4)); // returns sub-vector (2:3)

Function Documentation

absmax()

template<class E >

double mpqc::absmax

(

const E &

e

)

absolute max of an Eigen type

Todo

Refactor to accept EigenBase types and return proper type

dot()

template<class T >

T mpqc::dot	(	const matrix< T > &	a,
		const matrix< T > &	b )

element-wise dot product of two matrices

Todo

Refactor to work with EigenBase types

Referenced by mpqc::orthonormalize().

norm()

template<class T >

T mpqc::norm

(

const matrix< T > &

a

)

Matrix norm.

Todo

Refactor to work with EigenBase types

normalize()

template<class T >

void mpqc::normalize

(

matrix< T > &

a

)

Normalize matrix.

Todo

Refactor to work with EigenBase types

Referenced by mpqc::orthonormalize().

orthonormalize()

template<class T >

void mpqc::orthonormalize	(	matrix< T > &	d,
		const matrix< T > &	b )

orthormalize matrix d wrt to normalized matrix b d = normalize(d - (<d|b>*b))

Todo

Refactor to work with EigenBase types

References mpqc::dot(), and mpqc::normalize().

symmetric()

template<class T >

Eigen::SelfAdjointEigenSolver< Matrix::EigenType > mpqc::symmetric

(

const matrix< T > &

a

)

Computes (Eigen::SelfAdjointEigenSolver) eigensystem of a matrix.

Matrix must be symmetric.

Todo

Find a better name

Referenced by mpqc::ci::direct().