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JOptimizer is a java library for solving general convex optimization problems, like for example LP, QP, QCQP, SOCP, SDP, GP and many more.
/*
* Copyright 2011-2014 JOptimizer
*
* 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 com.joptimizer.functions;
import cern.colt.matrix.DoubleFactory1D;
import cern.colt.matrix.DoubleFactory2D;
import cern.colt.matrix.DoubleMatrix1D;
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.linalg.Algebra;
import cern.jet.math.Functions;
import cern.jet.math.Mult;
/**
* This function represents the logarithm of a posynomial after a change of variables x->y=log(x).
*
It represents a posynomial:
*
*
(1) f(x) = Sum[k=1, K](c[k]*x[1]^a[1,k]*x[2]^a[2,k]*****x[n]^a[n,k]), c[k]>0
*
*
in the form of:
*
*
(2) g(y) = log(Sum[k=1, K](e^(aT[k]*y+b[k])))
*
*
where a[k]=(a[1,k],..,a[n,k]) and b[k]=log(c[k])
*
*
It is useful in geometric programming.
*
* @see "S.Boyd and L.Vandenberghe, Convex Optimization, 4.5.3"
* @author alberto trivellato ([email protected])
*/
public class LogTransformedPosynomial implements ConvexMultivariateRealFunction {
private DoubleMatrix2D A = null;
private DoubleMatrix2D AT = null;
private DoubleMatrix1D b = null;
private int dim = -1;
private Algebra ALG = Algebra.DEFAULT;
/**
* A representation of a posynomial (1) in the form (2).
* @param akArray the matrix (a[1,k],..,a[n,k]) in expression (2)
* @param bkArray the vector b[k] in expression (2)
*/
public LogTransformedPosynomial(double[][] akArray, double[] bkArray){
this.A = DoubleFactory2D.dense.make(akArray);
this.b = DoubleFactory1D.dense.make(bkArray);
if(A.rows() != b.size()){
throw new IllegalArgumentException("Impossible to create the function");
}
this.AT = ALG.transpose(A);
this.dim = A.columns();
}
public double value(double[] X) {
DoubleMatrix1D x = DoubleFactory1D.dense.make(X);
DoubleMatrix1D g = ALG.mult(A, x).assign(b, Functions.plus).assign(Functions.exp);
return Math.log(g.zSum());
}
public double[] gradient(double[] X) {
DoubleMatrix1D x = DoubleFactory1D.dense.make(X);
DoubleMatrix1D g = ALG.mult(A, x).assign(b, Functions.plus).assign(Functions.exp);
double den = g.zSum();
double[] R = new double[dim];
for(int i=0; i