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/**
* @file gensvm_simplex.c
* @author G.J.J. van den Burg
* @date 2016-05-01
* @brief Function for generating the simplex matrix
*
* @details
* Contains the function for generating the simplex matrix for a given number
* of classes.
*
* @copyright
Copyright 2016, G.J.J. van den Burg.
This file is part of GenSVM.
GenSVM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
GenSVM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with GenSVM. If not, see <http://www.gnu.org/licenses/>.
*/
#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 of the GenModel must already have been allocated.
*
* @param[in,out] model a GenModel structure
*/
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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