protected override GeneralMatrix CalculateNextHessianApproximation(GeneralMatrix previousH,
double[] prevX, double[] curX, double[] prevGrad, double[] curGrad)
{
GeneralMatrix currentH = new GeneralMatrix(_nDim, _nDim);
GeneralMatrix cX = new GeneralMatrix(curX, _nDim);
GeneralMatrix pX = new GeneralMatrix(prevX, _nDim);
GeneralMatrix cG = new GeneralMatrix(curGrad, _nDim);
GeneralMatrix pG = new GeneralMatrix(prevGrad, _nDim);
GeneralMatrix dX = cX.Subtract(pX);
GeneralMatrix dG = cG.Subtract(pG);
double aK1 = 1 / (dX.Transpose().Multiply(dG).GetElement(0, 0));
GeneralMatrix aK2 = dX.Multiply(dX.Transpose());
GeneralMatrix aK = aK2.Multiply(aK1);
double bK1 = -1 / (dG.Transpose().Multiply(previousH).Multiply(dG).GetElement(0, 0));
GeneralMatrix bK2 = previousH.Multiply(dG).Multiply(dG.Transpose()).Multiply(previousH.Transpose());
GeneralMatrix bK = bK2.Multiply(bK1);
currentH = previousH.Add(aK).Add(bK);
return(currentH);
}
/// <summary>
/// (
/// </summary>
/// <param name="matrix"></param>
/// <returns></returns>
public static GeneralMatrix ExpandUtility(GeneralMatrix matrix)
{
double val = 0.0;
int n = matrix.RowDimension;
int m = matrix.ColumnDimension;
if (n != m)
{
throw new ArgumentException("Criteria matrix must be symmetrical");
}
GeneralMatrix newMatrix = matrix.Transpose();
//for all transposed elements calculate their inverse values
//set diagonal elements to 0
for (int i = 0; i < n; i++)
{
for (int j = 0; j <= i; j++)
{
val = newMatrix.GetElement(i, j);
if (val == 0.0)
{
throw new ArgumentException("Criteria comparison values van't be 0");
}
newMatrix.SetElement(i, j, 1 / val);
if (i == j)
{
newMatrix.SetElement(i, j, 0);
}
}
}
//add transposed, inverse matrix to the original one
//create fully expanded matrix
return(newMatrix.Add(matrix));
}
public void SubstractAndAdd()
{
GeneralMatrix B = GeneralMatrix.Random(A.RowDimension, A.ColumnDimension);
GeneralMatrix C = A.Subtract(B);
Assert.IsTrue(GeneralTests.Check(C.Add(B), A));
}
protected override GeneralMatrix CalculateNextHessianApproximation(GeneralMatrix pH,
double[] prevX, double[] curX, double[] prevGrad, double[] curGrad)
{
GeneralMatrix cH = new GeneralMatrix(_nDim, _nDim);
GeneralMatrix cX = new GeneralMatrix(curX, _nDim);
GeneralMatrix pX = new GeneralMatrix(prevX, _nDim);
GeneralMatrix cG = new GeneralMatrix(curGrad, _nDim);
GeneralMatrix pG = new GeneralMatrix(prevGrad, _nDim);
GeneralMatrix sigma = cX.Subtract(pX);
GeneralMatrix gamma = cG.Subtract(pG);
double sigmaTGamma = sigma.Transpose().Multiply(gamma).GetElement(0, 0);
GeneralMatrix hGammaSigmaT = pH.Multiply(gamma.Multiply(sigma.Transpose()));
GeneralMatrix sigmaGammaTH = sigma.Multiply(gamma.Transpose().Multiply(pH));
double gammaTHGamma = (gamma.Transpose().Multiply(pH.Multiply(gamma))).GetElement(0, 0);
GeneralMatrix sigmaSigmaT = sigma.Multiply(sigma.Transpose());
GeneralMatrix term1 = (hGammaSigmaT.Add(sigmaGammaTH)).Multiply(1 / sigmaTGamma);
GeneralMatrix term2 = (sigmaSigmaT.Multiply(1 / sigmaTGamma)).Multiply(1 + gammaTHGamma / sigmaTGamma);
return(pH.Subtract(term1).Add(term2));
}
public static void Main(System.String[] argv)
{
/*
| Tests LU, QR, SVD and symmetric Eig decompositions.
|
| n = order of magic square.
| trace = diagonal sum, should be the magic sum, (n^3 + n)/2.
| max_eig = maximum eigenvalue of (A + A')/2, should equal trace.
| rank = linear algebraic rank,
| should equal n if n is odd, be less than n if n is even.
| cond = L_2 condition number, ratio of singular values.
| lu_res = test of LU factorization, norm1(L*U-A(p,:))/(n*eps).
| qr_res = test of QR factorization, norm1(Q*R-A)/(n*eps).
*/
print("\n Test of GeneralMatrix Class, using magic squares.\n");
print(" See MagicSquareExample.main() for an explanation.\n");
print("\n n trace max_eig rank cond lu_res qr_res\n\n");
System.DateTime start_time = System.DateTime.Now;
double eps = System.Math.Pow(2.0, -52.0);
for (int n = 3; n <= 32; n++)
{
print(fixedWidthIntegertoString(n, 7));
GeneralMatrix M = magic(n);
//UPGRADE_WARNING: Narrowing conversions may produce unexpected results in C#. 'ms-help://MS.VSCC.2003/commoner/redir/redirect.htm?keyword="jlca1042"'
int t = (int)M.Trace();
print(fixedWidthIntegertoString(t, 10));
EigenvalueDecomposition E = new EigenvalueDecomposition(M.Add(M.Transpose()).Multiply(0.5));
double[] d = E.RealEigenvalues;
print(fixedWidthDoubletoString(d[n - 1], 14, 3));
int r = M.Rank();
print(fixedWidthIntegertoString(r, 7));
double c = M.Condition();
print(c < 1 / eps ? fixedWidthDoubletoString(c, 12, 3):" Inf");
LUDecomposition LU = new LUDecomposition(M);
GeneralMatrix L = LU.L;
GeneralMatrix U = LU.U;
int[] p = LU.Pivot;
GeneralMatrix R = L.Multiply(U).Subtract(M.GetMatrix(p, 0, n - 1));
double res = R.Norm1() / (n * eps);
print(fixedWidthDoubletoString(res, 12, 3));
QRDecomposition QR = new QRDecomposition(M);
GeneralMatrix Q = QR.Q;
R = QR.R;
R = Q.Multiply(R).Subtract(M);
res = R.Norm1() / (n * eps);
print(fixedWidthDoubletoString(res, 12, 3));
print("\n");
}
System.DateTime stop_time = System.DateTime.Now;
double etime = (stop_time.Ticks - start_time.Ticks) / 1000.0;
print("\nElapsed Time = " + fixedWidthDoubletoString(etime, 12, 3) + " seconds\n");
print("Adios\n");
}
public void Negative_AddMatrix()
{
A.Add(S);
}
public void UnaryMinus()
{
A = R.UnaryMinus();
Z = new GeneralMatrix(A.RowDimension, A.ColumnDimension);
Assert.IsTrue(GeneralTests.Check(A.Add(R), Z));
}
