matrix_util.h File Reference

Utility functions for matrices. More...

#include "Matrix.h"
#include "rwimg.h"

Functions
int	matrix_normalize (Matrix &m)
	Normalizes a matrix. More...
double	matrix_find_cutoff_for_number (Matrix m, int n)
	Calculates a cutoff to ensure that the given number of elements fall below it. More...
int	matrix_log_1_R (Matrix matrix)
	Calculates the logarithmic derivative of an R-factor in a matrix. More...
int *	matrix_find_linear_sequence (Matrix, int window)
	Finds a linear sequence of elements based on a pairwise matrix. More...
int	matrix_permute (int i, int j, Matrix, int *order, double *best_R, int *best_order)
	Permutes the order of a pairwise matrix and calculate a distance criterion. More...
double	matrix_calc_dist_fit (Matrix, int *order)
	Calculates an R-factor for a specific order of elements in a pairwise matrix. More...

Detailed Description

Utility functions for matrices.

Author

Bernard Heymann

Date

Created: 20010723

Modified: 20190911

Function Documentation

matrix_calc_dist_fit()

double matrix_calc_dist_fit	(	Matrix	matrix,
		int *	order
	)

Calculates an R-factor for a specific order of elements in a pairwise matrix.

Parameters

matrix	pairwise square matrix.
*order	n-value array holding the order.

Returns

double the R-factor.

A new matrix is composed with the lower triangle taken from the input
matrix in the given order, and the upper triangle calculated as the 
sum of the diagonal elements between the indices of the element. 
I.e, if i and j are the indices of an upper triangle element, then 
it is the sum of all the diagonal elements from i to j:
    up(i,j) = sum(mat(k,k+1)) for i<=k<j
The difference between the lower and upper triangles is then calculated
as:
              1      up(i,j) - upmin   lo(j,i) - lomin
    R = sum(----- * (--------------- - ---------------) )
            i - j     upmax - upmin     lomax - lomin
where upmin, upmax, lomin, and lomax are the extremes in each triangle.

matrix_find_cutoff_for_number()

double matrix_find_cutoff_for_number	(	Matrix	m,
		int	n
	)

Calculates a cutoff to ensure that the given number of elements fall below it.

Parameters

m	pairwise square matrix.
n	number of elements below cutoff.

Returns

double cutoff.

Each column is scanned and the cutoff adjusted so that at least the
given number of elements will fall below it.

matrix_find_linear_sequence()

int * matrix_find_linear_sequence	(	Matrix	matrix,
		int	window
	)

Finds a linear sequence of elements based on a pairwise matrix.

Parameters

matrix	pairwise square matrix.
window	range of elements to permute.

Returns

int* the best order, NULL on error.

matrix_log_1_R()

int matrix_log_1_R

(

Matrix

matrix

)

Calculates the logarithmic derivative of an R-factor in a matrix.

Parameters

matrix

pairwise square matrix.

Returns

int 0.

matrix_normalize()

int matrix_normalize

(

Matrix &

m

)

Normalizes a matrix.

Parameters

&m

matrix.

Returns

int 0.

The rows and columns are alternatively iteratively normalized until
the error is small enough.

matrix_permute()

int matrix_permute	(	int	i,
		int	j,
		Matrix	matrix,
		int *	order,
		double *	best_R,
		int *	best_order
	)

Permutes the order of a pairwise matrix and calculate a distance criterion.

Parameters

i	start of window within the order array.
j	end of window within the order array.
matrix	pairwise square matrix.
*order	n-value array holding the current order.
*best_R	R-factor for the best order.
*best_order	n-value array holding the best order.

Returns

int 0.

A recursive function to pass through all possible permutations
within a given window.