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/**
* @file gensvm_simplex.c
* @author Gertjan van den Burg
* @date May, 2016
* @brief Function for generating the simplex matrix
*
* @details
* Contains the function for generating the simplex matrix for a given number
* of classes.
*
*/
#include "gensvm_simplex.h"
/**
* @brief Generate matrix of simplex vertex coordinates
*
* @details
* Generate the simplex matrix. Each row of the created
* matrix contains the coordinate vector of a single
* vertex of the K-simplex in K-1 dimensions. The simplex
* generated is a special simplex with edges of length 1.
* The simplex matrix U must already have been allocated.
*
* @param[in] K number of classes
* @param[in,out] U simplex matrix of size K * (K-1)
*/
void gensvm_simplex(struct GenModel *model)
{
long i, j, K = model->K;
for (i=0; i<K; i++) {
for (j=0; j<K-1; j++) {
if (i <= j) {
matrix_set(model->U, K-1, i, j,
-1.0/sqrt(2.0*(j+1)*(j+2)));
} else if (i == j+1) {
matrix_set(model->U, K-1, i, j,
sqrt((j+1)/(2.0*(j+2))));
} else {
matrix_set(model->U, K-1, i, j, 0.0);
}
}
}
}
/**
* @brief Generate the simplex difference matrix
*
* @details
* The simplex difference matrix is a 2D block matrix which is constructed
* as follows. For each class i, we have a block of K rows and K-1 columns.
* Each row in the block for class i contains a row vector with the difference
* of the simplex matrix, U(i, :) - U(j, :).
*
* In the paper the notation @f$\boldsymbol{\delta}_{kj}'@f$ is used for the
* difference vector of @f$\textbf{u}_k' - \textbf{u}_j'@f$, where
* @f$\textbf{u}_k'@f$ corresponds to row k of @f$\textbf{U}@f$. Due to the
* indexing in the paper being 1-based and C indexing is 0 based, the vector
* @f$\boldsymbol{\delta}_{kj}'@f$ corresponds to the row (k-1)*K+(j-1) in the
* UU matrix generated here.
*
* @param[in,out] model the corresponding GenModel
*
*/
void gensvm_simplex_diff(struct GenModel *model)
{
long i, j, l, K = model->K;
double value;
// UU is a 2D block matrix, where block i has the differences:
// U(i, :) - U(j, :) for all j
for (i=0; i<K; i++) {
for (j=0; j<K; j++) {
for (l=0; l<K-1; l++) {
value = matrix_get(model->U, K-1, i, l);
value -= matrix_get(model->U, K-1, j, l);
matrix_set(model->UU, K-1, i*K+j, l, value);
}
}
}
}
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