/*
* This function is used to get a lower bound on the condition number. as it stands this is pretty straight forward:
*
* a random point (x) and vector (v) are generated, the Raleigh quotient ( v.H(x).v / v.v ) is then taken which provides both
* a lower bound on the largest eigenvalue, and an upper bound on the smallest eigenvalue. This can then be used to
* come up with a lower bound on the condition number of the hessian.
*/
public virtual double TestConditionNumber(int samples)
{
double maxSeen = 0.0;
double minSeen = 0.0;
double[] thisV = new double[thisFunc.DomainDimension()];
double[] thisX = new double[thisV.Length];
gradFD = new double[thisV.Length];
HvFD = new double[thisV.Length];
double thisVHV;
bool isNeg = false;
bool isPos = false;
bool isSemi = false;
thisFunc.method = StochasticCalculateMethods.ExternalFiniteDifference;
for (int j = 0; j < samples; j++)
{
for (int i = 0; i < thisV.Length; i++)
{
thisV[i] = generator.NextDouble();
}
for (int i_1 = 0; i_1 < thisX.Length; i_1++)
{
thisX[i_1] = generator.NextDouble();
}
log.Info("Evaluating Hessian Product");
System.Array.Copy(thisFunc.DerivativeAt(thisX, thisV, testBatchSize), 0, gradFD, 0, gradFD.Length);
thisFunc.recalculatePrevBatch = true;
System.Array.Copy(thisFunc.HdotVAt(thisX, thisV, gradFD, testBatchSize), 0, HvFD, 0, HvFD.Length);
thisVHV = ArrayMath.InnerProduct(thisV, HvFD);
if (System.Math.Abs(thisVHV) > maxSeen)
{
maxSeen = System.Math.Abs(thisVHV);
}
if (System.Math.Abs(thisVHV) < minSeen)
{
minSeen = System.Math.Abs(thisVHV);
}
if (thisVHV < 0)
{
isNeg = true;
}
if (thisVHV > 0)
{
isPos = true;
}
if (thisVHV == 0)
{
isSemi = true;
}
log.Info("It:" + j + " C:" + maxSeen / minSeen + "N:" + isNeg + "P:" + isPos + "S:" + isSemi);
}
System.Console.Out.WriteLine("Condition Number of: " + maxSeen / minSeen);
System.Console.Out.WriteLine("Is negative: " + isNeg);
System.Console.Out.WriteLine("Is positive: " + isPos);
System.Console.Out.WriteLine("Is semi: " + isSemi);
return(maxSeen / minSeen);
}
protected internal override void Init(AbstractStochasticCachingDiffFunction func)
{
sList = new List <double[]>();
yList = new List <double[]>();
dir = new double[func.DomainDimension()];
}
