/// <summary>Extracts this object.</summary>
/// <param name="m">Input Matrix.</param>
/// <param name="x">Matrix x.</param>
/// <param name="y">The y coordinate.</param>
/// <param name="width">The width.</param>
/// <param name="height">The height.</param>
/// <param name="safe">(Optional) true to safe.</param>
/// <returns>A Matrix.</returns>
public static Matrix Extract(Matrix m, int x, int y, int width, int height, bool safe = true)
{
Matrix m2 = Matrix.Zeros(height, width);
for (int i = y; i < y + height; i++)
{
for (int j = x; j < x + width; j++)
{
if (safe && i < m.Rows && j < m.Cols)
{
m2[i - y, j - x] = m[i, j];
}
}
}
return(m2);
}
/// <summary>Subtraction operator.</summary>
/// <exception cref="InvalidOperationException">Thrown when the requested operation is invalid.</exception>
/// <param name="m1">The first Matrix.</param>
/// <param name="m2">The second Matrix.</param>
/// <returns>The result of the operation.</returns>
public static Matrix operator -(Matrix m1, Matrix m2)
{
if (m1.Rows != m2.Rows || m1.Cols != m2.Cols)
{
throw new InvalidOperationException("Dimensions do not match");
}
var result = Matrix.Zeros(m1.Rows, m1.Cols);
for (int i = 0; i < m1.Rows; i++)
{
for (int j = 0; j < m1.Cols; j++)
{
result[i, j] = m1[i, j] - m2[i, j];
}
}
return(result);
}
/// <summary>Modified Gram-Schmidt QR Factorization.</summary>
/// <param name="A">Matrix A.</param>
/// <returns>Tuple(Q, R)</returns>
public static Tuple <Matrix, Matrix> QR(Matrix A)
{
int n = A.Rows;
Matrix R = Matrix.Zeros(n);
Matrix Q = A.Copy();
for (int k = 0; k < n; k++)
{
R[k, k] = Q[k, VectorType.Col].Norm();
Q[k, VectorType.Col] = Q[k, VectorType.Col] / R[k, k];
for (int j = k + 1; j < n; j++)
{
R[k, j] = Vector.Dot(Q[k, VectorType.Col], A[j, VectorType.Col]);
Q[j, VectorType.Col] = Q[j, VectorType.Col] - (R[k, j] * Q[k, VectorType.Col]);
}
}
return(new Tuple <Matrix, Matrix>(Q, R));
}
/// <summary>matrix multiplication.</summary>
/// <exception cref="InvalidOperationException">Thrown when the requested operation is invalid.</exception>
/// <param name="m1">left hand side.</param>
/// <param name="m2">right hand side.</param>
/// <returns>matrix.</returns>
public static Matrix operator *(Matrix m1, Matrix m2)
{
if (m1.Cols != m2.Rows)
{
throw new InvalidOperationException("Invalid multiplication dimenstion");
}
var result = Matrix.Zeros(m1.Rows, m2.Cols);
for (int i = 0; i < m1.Rows; i++)
{
for (int j = 0; j < m2.Cols; j++)
{
for (int k = 0; k < m1.Cols; k++)
{
result[i, j] += m1[i, k] * m2[k, j];
}
}
}
return(result);
}
//---------------- structural
/// <summary>Stack a set of vectors into a matrix.</summary>
/// <exception cref="InvalidOperationException">Thrown when the requested operation is invalid.</exception>
/// <param name="type">.</param>
/// <param name="vectors">.</param>
/// <returns>A Matrix.</returns>
internal static Matrix Stack(VectorType type, params Vector[] vectors)
{
if (vectors.Length == 0)
{
throw new InvalidOperationException("Cannot construct Matrix from empty vector set!");
}
if (!vectors.All(v => v.Length == vectors[0].Length))
{
throw new InvalidOperationException("Vectors must all be of the same length!");
}
int n = type == VectorType.Row ? vectors.Length : vectors[0].Length;
int d = type == VectorType.Row ? vectors[0].Length : vectors.Length;
Matrix m = Matrix.Zeros(n, d);
for (int i = 0; i < vectors.Length; i++)
{
m[i, type] = vectors[i];
}
return(m);
}