public void RandomRectangularSVD()
{
for (int c = 1; c < 64; c += 11)
{
Console.WriteLine(c);
RectangularMatrix R = GenerateRandomMatrix(64, c);
SingularValueDecomposition SVD = R.SingularValueDecomposition();
Assert.IsTrue(SVD.RowCount == R.RowCount);
Assert.IsTrue(SVD.ColumnCount == SVD.ColumnCount);
Assert.IsTrue(SVD.Dimension == SVD.ColumnCount);
SquareMatrix U = SVD.LeftTransformMatrix();
Assert.IsTrue(U.Dimension == R.RowCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(U.Transpose() * U, TestUtilities.CreateSquareUnitMatrix(U.Dimension)));
SquareMatrix V = SVD.RightTransformMatrix();
Assert.IsTrue(V.Dimension == R.ColumnCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V.Transpose() * V, TestUtilities.CreateSquareUnitMatrix(V.Dimension)));
RectangularMatrix S = U.Transpose() * R * V;
for (int i = 0; i < SVD.Dimension; i++)
{
double w = SVD.SingularValue(i);
Console.WriteLine(" {0} {1}", w, S[i, i]);
Assert.IsTrue(w >= 0.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S[i, i], w));
Assert.IsTrue(TestUtilities.IsNearlyEqual(R * SVD.RightSingularVector(i), w * SVD.LeftSingularVector(i)));
}
}
}
public void SquareMatrixArithmetic()
{
SquareMatrix M = CreateSquareRandomMatrix(5);
// addition is same a multiplication by two
SquareMatrix MA = M + M;
SquareMatrix M2 = 2.0 * M;
Assert.IsTrue(MA == M2);
// subraction of self same as multiplication by zero
SquareMatrix MS = M - M;
SquareMatrix M0 = 0.0 * M;
Assert.IsTrue(MS == M0);
// check transpose
SquareMatrix MT = M.Transpose();
Assert.IsTrue(MT != M);
// matrix multiplication is not ableian
SquareMatrix MMT = M * MT;
SquareMatrix MTM = MT * M;
Assert.IsFalse(MMT == MTM);
// check that transpose of transpose is original
SquareMatrix MTT = MT.Transpose();
Assert.IsTrue(MTT == M);
}
public void SquareMatrixArithmetic()
{
SquareMatrix M = CreateSquareRandomMatrix(5);
// Addition is same as multiplication by two
SquareMatrix MA = M + M;
SquareMatrix M2 = 2.0 * M;
Assert.IsTrue(MA == M2);
// Division by two returns us to original
SquareMatrix MB = MA / 2.0;
Assert.IsTrue(MB == M);
// Subraction of self same as multiplication by zero
SquareMatrix MS = M - M;
SquareMatrix M0 = 0.0 * M;
Assert.IsTrue(MS == M0);
// Negation is same as multiplication by negative one
SquareMatrix MN = -M;
SquareMatrix MM = -1.0 * M;
Assert.IsTrue(MN == MM);
// check transpose
SquareMatrix MT = M.Transpose();
Assert.IsTrue(MT != M);
// matrix multiplication is not ableian
SquareMatrix MMT = M * MT;
SquareMatrix MTM = MT * M;
Assert.IsFalse(MMT == MTM);
// check that transpose of transpose is original
SquareMatrix MTT = MT.Transpose();
Assert.IsTrue(MTT == M);
}
public void RectangularQRDecomposition()
{
RectangularMatrix M = GenerateRandomMatrix(30, 10);
QRDecomposition QRD = M.QRDecomposition();
Assert.IsTrue(QRD.RowCount == M.RowCount);
Assert.IsTrue(QRD.ColumnCount == M.ColumnCount);
SquareMatrix Q = QRD.QMatrix;
Assert.IsTrue(Q.Dimension == M.RowCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(Q * Q.Transpose(), TestUtilities.CreateSquareUnitMatrix(Q.Dimension)));
RectangularMatrix R = QRD.RMatrix;
Assert.IsTrue(R.RowCount == M.RowCount);
Assert.IsTrue(R.ColumnCount == M.ColumnCount);
RectangularMatrix QR = Q * R;
Assert.IsTrue(TestUtilities.IsNearlyEqual(QR, M));
}