matrix.cpp File Reference

Matrix manipulation functions. More...

#include "Matrix.h"
#include "matrix_linear.h"
#include "math_util.h"
#include "random_numbers.h"
#include "utilities.h"

Macros
#define	SQR(x)   ((x)*(x))

Functions
ostream &	operator<< (ostream &output, Matrix &mat)
Vector3< double >	principal_axes (Vector3< double > avg, Vector3< double > avg2, Vector3< double > avgx, Vector3< double > *eigenvec)
	Calculates the principal axes of 3D coordinates. More...
Vector3< double >	principal_axes (vector< Vector3< double > > &coor, Matrix &a)
	Calculates the principal axes of 3D coordinates. More...
void	dsytrd3 (Matrix &A, vector< double > &d, vector< double > &e)
	Reduces a symmetric 3x3 matrix to tridiagonal form. More...
vector< double >	dsyevq3 (Matrix &A)
	Calculates the eigenvalues and normalized eigenvectors of a symmetric 3x3 matrix. More...

Variables
int	verbose

Detailed Description

Matrix manipulation functions.

Author

Bernard Heymann

Date

Created: 20000501

Modified: 20180723

Macro Definition Documentation

SQR

#define SQR

(

x

)

((x)*(x))

Function Documentation

dsyevq3()

vector< double > dsyevq3

(

Matrix &

A

)

Calculates the eigenvalues and normalized eigenvectors of a symmetric 3x3 matrix.

Parameters

A	matrix, replaced by normalized eigenvectors.

Returns

double* eigenvalues.

Calculates the eigenvalues and normalized eigenvectors of a symmetric 3x3
matrix A using the QL algorithm with implicit shifts, preceded by a
Householder reduction to tridiagonal form.
The function accesses only the diagonal and upper triangular parts of A.

Reference: Kopp (2008).

dsytrd3()

void dsytrd3	(	Matrix &	A,
		vector< double > &	d,
		vector< double > &	e
	)

Reduces a symmetric 3x3 matrix to tridiagonal form.

Parameters

A	matrix, replaced by tridiagonal matrix.
d	diagonal.
e	off-diagonal. Reduces a symmetric 3x3 matrix to tridiagonal form by applying (unitary) Householder transformations: [ d[0] e[0] ] A = Q . [ e[0] d[1] e[1] ] . Q^T [ e[1] d[2] ] The function accesses only the diagonal and upper triangular parts of A. Reference: Kopp (2008).

operator<<()

ostream & operator<<	(	ostream &	output,
		Matrix &	mat
	)

principal_axes() [1/2]

Vector3< double > principal_axes	(	Vector3< double >	avg,
		Vector3< double >	avg2,
		Vector3< double >	avgx,
		Vector3< double > *	eigenvec
	)

Calculates the principal axes of 3D coordinates.

Parameters

avg	average of vectors.
avg2	average of squared vectors.
avgx	average of cross products {xy, xz, yz}.
*eigenvec	3 return eigen vectors (can be NULL).

Returns

Vector3<double> principal axes.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

principal_axes() [2/2]

Vector3< double > principal_axes	(	vector< Vector3< double > > &	coor,
		Matrix &	a
	)

Calculates the principal axes of 3D coordinates.

Parameters

coor	vector of coordinates.
&a	matrix with eigen vectors.

Returns

Vector3<double> principal axes.

Reference: Press W.H. et al (1992) Numerical Recipes in C.

Variable Documentation

verbose

int verbose

extern