public static DoubleVector GenerateRow(IMatrix A, int r, int c1, int c2)
{
int cu = c2 - c1 + 1;
DoubleVector u = new DoubleVector(cu);
for (int j = c1; j <= c2; j++)
{
u[j - c1] = A[r, j];
A[r, j] = 0.0;
}
double norm = u.GetNorm();
if (c1 == c2 || norm == 0)
{
A[r, c1] = -u[0];
u[0] = (double)System.Math.Sqrt(2);
return(u);
}
double scale = 1.0 / norm;
if (u[0] < 0.0)
{
scale *= -1.0;
}
A[r, c1] = -1.0 / scale;
for (int j = 0; j < cu; j++)
{
u[j] *= scale;
}
u[0] = u[0] + 1.0;
double s = (double)System.Math.Sqrt(1 / u[0]);
for (int j = 0; j < cu; j++)
{
u[j] *= s;
}
return(u);
}
public static DoubleVector GenerateColumn(IMatrix A, int r1, int r2, int c)
{
int ru = r2 - r1 + 1;
DoubleVector u = new DoubleVector(r2 - r1 + 1);
for (int i = r1; i <= r2; i++)
{
u[i - r1] = A[i, c];
A[i, c] = 0.0;
}
double norm = u.GetNorm();
if (r1 == r2 || norm == 0)
{
A[r1, c] = -u[0];
u[0] = (double)System.Math.Sqrt(2);
return(u);
}
double scale = 1.0 / norm;
if (u[0] < 0.0)
{
scale *= -1.0;
}
A[r1, c] = -1.0 / scale;
for (int i = 0; i < ru; i++)
{
u[i] *= scale;
}
u[0] += 1.0;
double s = (double)System.Math.Sqrt(1 / u[0]);
for (int i = 0; i < ru; i++)
{
u[i] *= s;
}
return(u);
}
///<summary> Initialize the optimization method </summary>
///<remarks> The use of this function is intended for testing/debugging purposes only </remarks>
public override void InitializeMethod(DoubleVector initialvector)
{
g = GradientEvaluation(initialvector);
// Calculate Diagonal preconditioner
DoubleMatrix h = HessianEvaluation(initialvector);
DoubleMatrix m_inv = new DoubleMatrix(initialvector.Length,initialvector.Length);
for (int i=0; i<initialvector.Length; i++)
m_inv[i,i] = 1/h[i,i];
s = m_inv*g;
DoubleVector d = -s;
delta_new = g.GetDotProduct(d);
restartCounter=0;
/* ------------------------------ */
this.iterationVectors_ = new DoubleVector[endCriteria_.maxIteration+1];
this.iterationVectors_[0] = initialvector;
this.iterationValues_ = new double[endCriteria_.maxIteration+1];
this.iterationValues_[0] = FunctionEvaluation(this.iterationVectors_[0]);
this.iterationGradients_ = new DoubleVector[endCriteria_.maxIteration+1];
this.iterationGradients_[0] = new DoubleVector(g);
this.iterationGradientNorms_ = new double[endCriteria_.maxIteration+1];
this.iterationGradientNorms_[0] = g.GetNorm();
this.iterationDirections_ = new DoubleVector[endCriteria_.maxIteration+1];
this.iterationDirections_[0] = d;
this.iterationTrialSteps_ = new double[endCriteria_.maxIteration+1];
this.iterationTrialSteps_[0] = 1/this.iterationGradientNorms_[0];
}
///<summary> Perform a single iteration of the optimization method </summary>
///<remarks> The use of this function is intended for testing/debugging purposes only </remarks>
public override void IterateMethod()
{
DoubleVector d = this.iterationDirections_[endCriteria_.iterationCounter-1];
DoubleVector x = this.iterationVectors_[endCriteria_.iterationCounter-1];
DoubleVector g = this.iterationGradients_[endCriteria_.iterationCounter-1];
double stp = this.iterationTrialSteps_[endCriteria_.iterationCounter-1];
// Shanno-Phua's Formula for Trial Step
if (restartCounter==0 && endCriteria_.iterationCounter>1)
{
double dg = d.GetDotProduct(g);
double dg0 = this.iterationDirections_[endCriteria_.iterationCounter-2].GetDotProduct(
this.iterationGradients_[endCriteria_.iterationCounter-2])/stp;
stp = dg0/dg;
}
delta_mid = g.GetDotProduct(g);
// Conduct line search
x = lineSearchMethod_.Search(x,d,stp);
g = GradientEvaluation(x);
delta_old = delta_new;
delta_mid = g.GetDotProduct(s);
// Calculate Diagonal preconditioner
DoubleMatrix h = HessianEvaluation(x);
DoubleMatrix m_inv = new DoubleMatrix(x.Length,x.Length);
for (int i=0; i<x.Length; i++)
m_inv[i,i] = 1/h[i,i];
s = m_inv*g;
// Calculate Beta
delta_new = g.GetDotProduct(s);
double beta = (delta_new-delta_mid)/delta_old;
// Check for restart conditions
restartCounter++;
if (restartCounter==restartCount || (restartCounter==x.Length && restartCount==0) || beta<=0)
{
restartCount = 0;
beta=0;
}
// Calculate next line search direction
d = -s + beta*d;
this.iterationVectors_[endCriteria_.iterationCounter] = x;
this.iterationValues_[endCriteria_.iterationCounter] = FunctionEvaluation(x);
this.iterationGradients_[endCriteria_.iterationCounter] = g;
this.iterationGradientNorms_[endCriteria_.iterationCounter] = g.GetNorm();
this.iterationDirections_[endCriteria_.iterationCounter] = d;
this.iterationTrialSteps_[endCriteria_.iterationCounter] = stp;
}
public static DoubleVector GenerateRow(IMatrix A, int r, int c1, int c2)
{
int cu = c2 - c1 + 1;
DoubleVector u = new DoubleVector(cu);
for (int j = c1; j <= c2; j++)
{
u[j - c1] = A[r, j];
A[r, j] = 0.0;
}
double norm = u.GetNorm();
if (c1 == c2 || norm == 0)
{
A[r, c1] = -u[0];
u[0] = (double)System.Math.Sqrt(2);
return u;
}
double scale = 1.0 / norm;
if (u[0] < 0.0)
scale *= -1.0;
A[r, c1] = -1.0 / scale;
for (int j = 0; j < cu; j++)
{
u[j] *= scale;
}
u[0] = u[0] + 1.0;
double s = (double)System.Math.Sqrt(1 / u[0]);
for (int j = 0; j < cu; j++)
{
u[j] *= s;
}
return u;
}
public static DoubleVector GenerateColumn(IMatrix A, int r1, int r2, int c)
{
int ru = r2 - r1 + 1;
DoubleVector u = new DoubleVector(r2 - r1 + 1);
for (int i = r1; i <= r2; i++)
{
u[i - r1] = A[i, c];
A[i, c] = 0.0;
}
double norm = u.GetNorm();
if (r1 == r2 || norm == 0)
{
A[r1, c] = -u[0];
u[0] = (double)System.Math.Sqrt(2);
return u;
}
double scale = 1.0 / norm;
if (u[0] < 0.0)
scale *= -1.0;
A[r1, c] = -1.0 / scale;
for (int i = 0; i < ru; i++)
{
u[i] *= scale;
}
u[0] += 1.0;
double s = (double)System.Math.Sqrt(1 / u[0]);
for (int i = 0; i < ru; i++)
{
u[i] *= s;
}
return u;
}
public void GetNorm()
{
DoubleVector a = new DoubleVector(new double[4]{0,1,2,3});
DoubleVector b = new DoubleVector(new double[4]{4,5,6,7});
Assert.AreEqual(a.GetNorm(),System.Math.Sqrt(14));
Assert.AreEqual(a.GetNorm(),a.GetNorm(2));
Assert.AreEqual(a.GetNorm(0),3);
Assert.AreEqual(b.GetNorm(),3*System.Math.Sqrt(14));
Assert.AreEqual(b.GetNorm(),b.GetNorm(2));
Assert.AreEqual(b.GetNorm(0),7);
}