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package optimization.projections;
import optimization.util.MathUtils;
import optimization.util.MatrixOutput;
import util.ArrayMath;
import util.Printing;
public abstract class Projection {
public abstract void project(double[] original);
/**
* From the projection theorem "Non-Linear Programming" page
* 201 fact 2.
*
* Given some z in R, and a vector x* in X;
* x* = z+ iif for all x in X
* (z-x*)'(x-x*) <= 0 where 0 is when x*=x
* See figure 2.16 in book
*
* @param original
* @param projected
* @return
*/
public boolean testProjection(double[] original, double[] projected){
double[] original1 = original.clone();
//System.out.println(Printing.doubleArrayToString(original1, null, "original"));
//System.out.println(Printing.doubleArrayToString(projected, null, "projected"));
MathUtils.minusEquals(original1, projected, 1);
//System.out.println(Printing.doubleArrayToString(original1, null, "minus1"));
for(int i = 0; i < 10; i++){
double[] x = samplePoint(original.length);
// System.out.println(Printing.doubleArrayToString(x, null, "sample"));
//If the same this returns zero so we are there.
MathUtils.minusEquals(x, projected, 1);
// System.out.println(Printing.doubleArrayToString(x, null, "minus2"));
double dotProd = MathUtils.dotProduct(original1, x);
// System.out.println("dot " + dotProd);
if(dotProd > 0) return false;
}
//Perturbs the point a bit in all possible directions
for(int i = 0; i < original.length; i++){
double[] x = perturbePoint(projected,i);
// System.out.println(Printing.doubleArrayToString(x, null, "perturbed"));
//If the same this returns zero so we are there.
MathUtils.minusEquals(x, projected, 1);
// System.out.println(Printing.doubleArrayToString(x, null, "minus2"));
double dotProd = MathUtils.dotProduct(original1, x);
// System.out.println("dot " + dotProd);
if(dotProd > 0) return false;
}
return true;
}
//Samples a point from the constrained set
public abstract double[] samplePoint(int dimensions);
//Perturbs a point a bit still leaving it at the constraints set
public abstract double[] perturbePoint(double[] point, int parameter);
}
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