/*
* $RCSfile: LinearSubspace.java,v $
* $Revision: 1.6 $
* $Date: 2007/06/30 17:30:33 $
* $Author: wojna $
*
* Copyright (C) 2002 - 2007 Logic Group, Institute of Mathematics, Warsaw University
*
* This file is part of Rseslib.
*
* Rseslib 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.
*
* Rseslib 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 this program. If not, see <http://www.gnu.org/licenses/>.
*/
package rseslib.structure.vector.subspace;
import rseslib.structure.vector.Vector;
/**
* Multidimensional linear real value subspace
* spanned by DoubleVectors with implemented projections.
*
* @author Rafal Falkowski
*/
public class LinearSubspace {
/** Vectors that span the subspace. */
private Vector[] m_nSpanningVectors;
/**
* Constructor spans the Subspace on vectors from given table.
*
* @param vec Table of vectors.
*/
public LinearSubspace(Vector[] vec) {
m_nSpanningVectors = new Vector[vec.length];
for (int i = 0; i < vec.length; i++)
m_nSpanningVectors[i] = new Vector(vec[i]);
}
/**
* Constructor spans the null Subspace on null vectors.
*
* @param sDim Dimension of the subspace.
* @param vDim Dimension of spanning vectors.
*/
public LinearSubspace(int sDim, int vDim) {
m_nSpanningVectors = new Vector[sDim];
for (int i = 0; i < sDim; i++)
m_nSpanningVectors[i] = new Vector(vDim);
}
/**
* Gets the dimension of the subspace.
*
* @return Dimension of the subspace.
*/
public int getDimension() {
return m_nSpanningVectors.length;
}
/**
* Gets vectors spanning the subspace.
*
* @return Spanning vectors.
*/
public Vector[] getSpanningVectors() {
return m_nSpanningVectors;
}
/**
* Gets the ith spanning vector.
*
* @return Ith spanning vector.
*/
public Vector getSpanningVector(int i) {
return m_nSpanningVectors[i];
}
/**
* Sets the ith spanning vector.
*/
public void setSpanningVector(Vector vec, int i) {
m_nSpanningVectors[i] = vec;
}
/**
* Calculates the projection of DataVector
* onto the subspace spanned by first n vectors.
*
* @param dVec Vector to be projected.
* @param n Dimension of the subspace.
* It should be less to the DataVector dimension.
*
* @return Projected vector.
*/
public Vector projection(Vector dVec, int n) {
double[] y = new double[n];
for (int i = 0; i < n; i++) // y = W^T x'
y[i] = dVec.scalarProduct(m_nSpanningVectors[i]);
Vector vecProjection = new Vector(m_nSpanningVectors[0].dimension()); // z
for (int att = 0; att < m_nSpanningVectors[0].dimension(); att++) // z = W y
{
double sum = 0;
for (int j = 0; j < n; j++) //to chyba malo efektywne? Ale poprawne :-)
sum += y[j]*m_nSpanningVectors[j].get(att);
vecProjection.set(att, sum);
}
return vecProjection;
}
/**
* Calculates the projection of DataVector
* onto the subspace of the Subspace Dimension, i.e. to
* the number of spanning vectors.
*
* @param dVec Vector to be projected.
*
* @return Projected vector.
*/
public Vector projection(Vector dVec) {
return projection(dVec, m_nSpanningVectors.length);
}
/**
* Calculates the projections of DataVector
* onto the subspaces for dimensions
* from 1 to the Subspace Dimension, i.e. to the number
* of spanning vectors. For calculation of each projection
* are taken first k vectors from m_nSpanningVectors.
*
* @param dVec Vector to be projected.
*
* @return Table of projected vectors.
*/
public Vector[] projections(Vector dVec) { //Liczona jest tu cala tabela projekcji.
double[] y = new double[m_nSpanningVectors.length];
Vector vecProjection[] = new Vector[m_nSpanningVectors.length]; // z
for (int i = 0; i < m_nSpanningVectors.length; i++) // y = W^T x'
{
y[i] = dVec.scalarProduct(m_nSpanningVectors[i]);
vecProjection[i] = new Vector(m_nSpanningVectors[0].dimension());
}
for (int att = 0; att < m_nSpanningVectors[0].dimension(); att++) // z = W y
{
double sum = 0;
for (int j = 0; j < m_nSpanningVectors.length; j++) //to chyba malo efektywne? Ale poprawne :-)
{
sum += y[j]*m_nSpanningVectors[j].get(att);
vecProjection[j].set(att, sum);
}
}
return vecProjection;
}
/**
* Calculates distance between given DoubleVector
* and its projection onto the subspace
* on the basis of the Euclidean norm.
*
* @param dVec Vector to be projected.
*
* @return Square of the distance.
*/
public double euclideanDist(Vector dVec) {
Vector vecProjection = projection(dVec, m_nSpanningVectors.length);
vecProjection.subtract(dVec); // W y - dVec
return vecProjection.euclideanNorm();
}
/**
* Calculates distance between given DoubleVector
* and its projection onto the subspace
* on the basis of the Manhattan city norm.
*
* @param dVec Vector to be projected.
*
* @return Square of the distance.
*/
public double cityDist(Vector dVec) {
Vector vecProjection = projection(dVec, m_nSpanningVectors.length);
vecProjection.subtract(dVec); // W y - dVec
return vecProjection.cityNorm();
}
}
