/// <summary>
/// Checks stability of polynom
/// </summary>
/// <param name="polynom">Polynom</param>
/// <returns>True if stable and false otherwise</returns>
public static bool IsStablePolynom(double[] polynom)
{
if (polynom.Length == 1)
{
return(true);
}
if (polynom.Length == 2)
{
return((polynom[0] * polynom[1]) > 0);
}
double[,] a = GetGurvitzMatrix(polynom);
double det = RealMatrix.Det(a);
if (det <= 0)
{
return(false);
}
for (int i = 1; i < a.GetLength(0); i++)
{
double[,] b = RealMatrix.GetMainMinor(a, i);
det = RealMatrix.Det(b);
if (det <= 0)
{
return(false);
}
}
return(true);
}
public RealMatrixDetailPage(RealMatrix current_matrix)
{
//Matrix at top
//Number of rows
//Number of columns
//Row reduced form
//Transpose
//Rank
//Nullity
//Determinant
//Inverse (if it exists)
//Characteristic polynomial
StackLayout s = new StackLayout {
Spacing = 20, BackgroundColor = Color.FromHex("046875")
};
Label num_rows = new Label {
Text = current_matrix.NumRows().ToString() + " rows", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(num_rows);
Label num_columns = new Label {
Text = current_matrix.NumColumns().ToString() + " columns", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(num_columns);
Label rref = new Label {
Text = "Row-Reduced Echelon Form:", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(rref);
Label rref_matrix = new Label {
Text = current_matrix.Rref().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(rref_matrix);
Label tranpose = new Label {
Text = "Transpose(" + current_matrix.name + ") :", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(tranpose);
Label transpose_matrix = new Label {
Text = current_matrix.Transpose().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(transpose_matrix);
// Condition for matrix to have an inverse (must be square with non-zero determinant)
if (current_matrix.NumRows() == current_matrix.NumColumns() && current_matrix.Det() != 0)
{
Label inv = new Label {
Text = "Inverse", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
Label inverse_matrix = new Label {
Text = current_matrix.Rref().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(inv);
s.Children.Add(inverse_matrix);
}
else
{
Label no_inv = new Label {
Text = "The matrix has 0 determinant so has no inverse", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(no_inv);
}
Label rank = new Label {
Text = "Rank(" + current_matrix.name + ") = " + current_matrix.Rank().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(rank);
Label nullity = new Label {
Text = "Nullity(" + current_matrix.name + ") = " + current_matrix.Nullity().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(nullity);
if (current_matrix.NumRows() == current_matrix.NumColumns())
{
Label det = new Label {
Text = "det(" + current_matrix.name + ") = " + current_matrix.Det().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(det);
Label characteristic_polynomial = new Label {
Text = "Characteristic(" + current_matrix.name + ") = " + current_matrix.CharPolynomial().ToString(), TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(characteristic_polynomial);
}
else
{
Label no_det = new Label {
Text = "The matrix is not square so has no characteristic polynomial", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(no_det);
Label no_char = new Label {
Text = "The matrix is not square so has no characteristic polynomial", TextColor = Color.WhiteSmoke, HorizontalOptions = LayoutOptions.Center, FontSize = 16
};
s.Children.Add(no_char);
}
ScrollView scroll = new ScrollView {
Content = s
};
Content = scroll;
}
