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, UnitMatrix.OfDimension(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));
}