public void SubstractEquals()
{
A = R.Copy();
Assert.IsFalse(A.Norm1() == 0.0);
A.SubtractEquals(R);
Assert.IsTrue(A.Norm1() == 0.0);
}
/// <summary>Check norm of difference of Matrices.
/// </summary>
public static bool Check(GeneralMatrix X, GeneralMatrix Y)
{
bool result = false;
double eps = System.Math.Pow(2.0, -52.0);
if (X.Norm1() == 0.0 & Y.Norm1() < 10 * eps)
{
result = true;
}
else if (Y.Norm1() == 0.0 & X.Norm1() < 10 * eps)
{
result = true;
}
else if (X.Subtract(Y).Norm1() > 1000 * eps * System.Math.Max(X.Norm1(), Y.Norm1()))
{
throw new System.SystemException("The norm of (X-Y) is too large: " + X.Subtract(Y).Norm1().ToString());
}
else
{
result = true;
}
return(result);
}
public void Identity()
{
double[][] ivals = { new double[] { 1.0, 0.0, 0.0, 0.0 }, new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } };
GeneralMatrix I = new GeneralMatrix(ivals);
GeneralMatrix K = GeneralMatrix.Identity(3, 4);
Assert.IsTrue(I.Norm1() == K.Norm1() && I.Norm1() == 1);
}
public void TestNorm1()
{
GeneralMatrix _gm = new GeneralMatrix(2, 2);
_gm.SetElement(0, 0, 1);
_gm.SetElement(0, 1, 2);
_gm.SetElement(1, 0, 3);
_gm.SetElement(1, 1, 4);
Assert.AreEqual(6, _gm.Norm1());
}
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 Transpose2()
{
A.Transpose();
Assert.IsTrue(GeneralTests.Check(A.Norm1(), columnsummax));
}