Line data    Source code

       1             : /**
       2             :  * @file gensvm_simplex.c
       3             :  * @author G.J.J. van den Burg
       4             :  * @date 2016-05-01
       5             :  * @brief Function for generating the simplex matrix
       6             :  *
       7             :  * @details
       8             :  * Contains the function for generating the simplex matrix for a given number
       9             :  * of classes.
      10             :  *
      11             :  * @copyright
      12             :  Copyright 2016, G.J.J. van den Burg.
      13             : 
      14             :  This file is part of GenSVM.
      15             : 
      16             :  GenSVM is free software: you can redistribute it and/or modify
      17             :  it under the terms of the GNU General Public License as published by
      18             :  the Free Software Foundation, either version 3 of the License, or
      19             :  (at your option) any later version.
      20             : 
      21             :  GenSVM is distributed in the hope that it will be useful,
      22             :  but WITHOUT ANY WARRANTY; without even the implied warranty of
      23             :  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
      24             :  GNU General Public License for more details.
      25             : 
      26             :  You should have received a copy of the GNU General Public License
      27             :  along with GenSVM. If not, see <http://www.gnu.org/licenses/>.
      28             : 
      29             :  */
      30             : 
      31             : #include "gensvm_simplex.h"
      32             : 
      33             : /**
      34             :  * @brief Generate matrix of simplex vertex coordinates
      35             :  *
      36             :  * @details
      37             :  * Generate the simplex matrix. Each row of the created matrix contains the 
      38             :  * coordinate vector of a single vertex of the K-simplex in K-1 dimensions.  
      39             :  * The simplex generated is a special simplex with edges of length 1. The 
      40             :  * simplex matrix U of the GenModel must already have been allocated.
      41             :  *
      42             :  * @param[in,out]       model   a GenModel structure
      43             :  */
      44          13 : void gensvm_simplex(struct GenModel *model)
      45             : {
      46          13 :         long i, j, K = model->K;
      47             : 
      48          56 :         for (i=0; i<K; i++) {
      49         147 :                 for (j=0; j<K-1; j++) {
      50         104 :                         if (i <= j) {
      51          52 :                                 matrix_set(model->U, K-1, i, j,
      52             :                                                 -1.0/sqrt(2.0*(j+1)*(j+2)));
      53          52 :                         } else if (i == j+1) {
      54          30 :                                 matrix_set(model->U, K-1, i, j,
      55             :                                                 sqrt((j+1)/(2.0*(j+2))));
      56             :                         } else {
      57          22 :                                 matrix_set(model->U, K-1, i, j, 0.0);
      58             :                         }
      59             :                 }
      60             :         }
      61          13 : }
      62             : 
      63             : /**
      64             :  * @brief Generate the simplex difference matrix
      65             :  *
      66             :  * @details
      67             :  * The simplex difference matrix is a 2D block matrix which is constructed
      68             :  * as follows. For each class i, we have a block of K rows and K-1 columns.
      69             :  * Each row in the block for class i contains a row vector with the difference
      70             :  * of the simplex matrix, U(i, :) - U(j, :).
      71             :  *
      72             :  * In the paper the notation @f$\boldsymbol{\delta}_{kj}'@f$ is used for the
      73             :  * difference vector of @f$\textbf{u}_k' - \textbf{u}_j'@f$, where
      74             :  * @f$\textbf{u}_k'@f$ corresponds to row k of @f$\textbf{U}@f$. Due to the
      75             :  * indexing in the paper being 1-based and C indexing is 0 based, the vector
      76             :  * @f$\boldsymbol{\delta}_{kj}'@f$ corresponds to the row (k-1)*K+(j-1) in the
      77             :  * UU matrix generated here.
      78             :  *
      79             :  * @param[in,out]       model   the corresponding GenModel
      80             :  *
      81             :  */
      82           9 : void gensvm_simplex_diff(struct GenModel *model)
      83             : {
      84           9 :         long i, j, l, K = model->K;
      85             :         double value;
      86             : 
      87             :         // UU is a 2D block matrix, where block i has the differences:
      88             :         // U(i, :) - U(j, :) for all j
      89          40 :         for (i=0; i<K; i++) {
      90         140 :                 for (j=0; j<K; j++) {
      91         391 :                         for (l=0; l<K-1; l++) {
      92         282 :                                 value = matrix_get(model->U, K-1, i, l);
      93         282 :                                 value -= matrix_get(model->U, K-1, j, l);
      94         282 :                                 matrix_set(model->UU, K-1, i*K+j, l, value);
      95             :                         }
      96             :                 }
      97             :         }
      98           9 : }