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A fast and easy to use dense and sparse matrix linear algebra library written in Java.
/*
* Copyright (c) 2009-2017, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.dense.row.misc;
import org.ejml.data.DMatrixRMaj;
import org.ejml.data.FMatrixRMaj;
/**
* Computes the determinant using different very simple and computationally expensive algorithms.
*
* @author Peter Abeles
*/
public class NaiveDeterminant {
/**
*
* Computes the determinant of the matrix using Leibniz's formula
*
*
*
* A direct implementation of Leibniz determinant equation. This is of little practical use
* because of its slow runtime of O(n!) where n is the width of the matrix. LU decomposition
* should be used instead. One advantage of Leibniz's equation is how simplistic it is.
*
*
* det(A) = Sum( σ in Sn ; sgn(σ) Prod( i = 1 to n ; ai,σ(i)) )
*
*
* - sgn is the sign function of permutations. +1 or -1 for even and odd permutations
* - a set of permutations. if n=3 then the possible permutations are (1,2,3) (1,3,2), (3,2,1), ... etc
*
*
* @param mat The matrix whose determinant is computed.
* @return The value of the determinant
*/
public static double leibniz( DMatrixRMaj mat )
{
PermuteArray perm = new PermuteArray( mat.numCols );
double total = 0;
int p[] = perm.next();
while( p != null ) {
double prod = 1;
for( int i = 0; i < mat.numRows; i++ ) {
prod *= mat.get(i,p[i]);
}
total += perm.sgn()*prod;
p = perm.next();
}
return total;
}
/**
*
* A simple and inefficient algorithm for computing the determinant. This should never be used.
* It is at least two orders of magnitude slower than {@link DeterminantFromMinor_DDRM}. This is included
* to provide a point of comparison for other algorithms.
*
* @param mat The matrix that the determinant is to be computed from
* @return The determinant.
*/
public static double recursive( DMatrixRMaj mat )
{
if(mat.numRows == 1) {
return mat.get(0);
} else if(mat.numRows == 2) {
return mat.get(0) * mat.get(3) - mat.get(1) * mat.get(2);
} else if( mat.numRows == 3 ) {
return UnrolledDeterminantFromMinor_DDRM.det3(mat);
}
double result = 0;
for(int i = 0; i < mat.numRows; i++) {
DMatrixRMaj minorMat = new DMatrixRMaj(mat.numRows-1,mat.numRows-1);
for(int j = 1; j < mat.numRows; j++) {
for(int k = 0; k < mat.numRows; k++) {
if(k < i) {
minorMat.set(j-1,k,mat.get(j,k));
} else if(k > i) {
minorMat.set(j-1,k-1,mat.get(j,k));
}
}
}
if( i % 2 == 0 )
result += mat.get(0,i) * recursive(minorMat);
else
result -= mat.get(0,i) * recursive(minorMat);
}
return result;
}
public static float recursive( FMatrixRMaj mat )
{
if(mat.numRows == 1) {
return mat.get(0);
} else if(mat.numRows == 2) {
return mat.get(0) * mat.get(3) - mat.get(1) * mat.get(2);
} else if( mat.numRows == 3 ) {
return UnrolledDeterminantFromMinor_FDRM.det3(mat);
}
float result = 0;
for(int i = 0; i < mat.numRows; i++) {
FMatrixRMaj minorMat = new FMatrixRMaj(mat.numRows-1,mat.numRows-1);
for(int j = 1; j < mat.numRows; j++) {
for(int k = 0; k < mat.numRows; k++) {
if(k < i) {
minorMat.set(j-1,k,mat.get(j,k));
} else if(k > i) {
minorMat.set(j-1,k-1,mat.get(j,k));
}
}
}
if( i % 2 == 0 )
result += mat.get(0,i) * recursive(minorMat);
else
result -= mat.get(0,i) * recursive(minorMat);
}
return result;
}
}