/// <summary>
/// Produces the determinant of a square matrix
/// </summary>
/// <param name="mat">The matrix</param>
/// <returns>The determinant of the matrix</returns>
public static T Determinant <T>(this T[,] mat)
{
MatrixDimensions d = mat.GetDimensions();
if (d.IsSquare())
{
switch (d.rows)
{
case 0:
throw new MatrixSizeException("A matrix cannot have no elements.");
case 1:
return(mat[0, 0]);
case 2:
return(mat[0, 0] * (dynamic)mat[1, 1] - mat[0, 1] * (dynamic)mat[1, 0]);
default:
T sum = mat[0, 0] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, 1).Determinant());
for (int i = 1; i < d.rows; i++)
{
if (i % 2 == 0)
{
sum += mat[0, i] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, i + 1).Determinant());
}
else
{
sum -= mat[0, i] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, i + 1).Determinant());
}
}
return(sum);
}
}
throw new IllegalOperationException("Only squre matricies have determinants.");
}
/// <summary>
/// Inserts a row or column vector into a matrix
/// </summary>
/// <param name="mat">The matrix</param>
/// <param name="direction">The type of vector to insert (row or column)</param>
/// <param name="insertIndex">The vector index to insert at</param>
/// <param name="vector">The vector to insert at the index. If not incuded or null, the vector is populated with default values.</param>
/// <returns>The matrix with an additional row/column at the specified index</returns>
public static T[,] InsertVector <T>(this T[,] mat, VectorDirection direction, int insertIndex, T[] vector = null)
{
MatrixDimensions d = mat.GetDimensions();
T[,] newMat;
if (vector != null && d.InDirection(direction) != vector.Length)
{
throw new VectorSizeException("A vector cannot be inserted into a matrix of a different size");
}
if (direction == VectorDirection.Column)
{
if (insertIndex > d.cols + 1 || insertIndex < 1)
{
throw new IndexOutOfRangeException("That column index does not and will not exist in the new matrix.");
}
newMat = new T[d.rows, d.cols + 1];
return(newMat.Apply((v, r, c) => {
if (c < insertIndex)
{
return mat[r - 1, c - 1];
}
else if (c > insertIndex)
{
return mat[r - 1, c - 2];
}
if (vector != null)
{
return vector[r - 1];
}
return v;
}));
}
else
{
if (insertIndex > d.rows + 1 || insertIndex < 1)
{
throw new IndexOutOfRangeException("That row index does not and will not exist in the new matrix.");
}
newMat = new T[d.rows + 1, d.cols];
return(newMat.Apply((v, r, c) => {
if (r < insertIndex)
{
return mat[r - 1, c - 1];
}
else if (r > insertIndex)
{
return mat[r - 2, c - 1];
}
if (vector != null)
{
return vector[c - 1];
}
return v;
}));
}
}
/// <summary>
/// Convert a matrix of one type to another type through a specified function
/// </summary>
/// <typeparam name="T">The type of the original matrix</typeparam>
/// <typeparam name="T2">The type of the new matrix</typeparam>
/// <param name="matrix">The matrix</param>
/// <param name="castFunc">The conversion function</param>
/// <returns>A matrix of the new type</returns>
public static T2[,] Cast <T, T2>(this T[,] matrix, Func <T, T2> castFunc)
{
T2[,] newMatrix = matrix.GetDimensions().CreateMatrix <T2>();
MatrixDimensions d = matrix.GetDimensions();
for (int r = 0; r < d.rows; r++)
{
for (int c = 0; c < d.cols; c++)
{
newMatrix[r, c] = castFunc.Invoke(matrix[r, c]);
}
}
return(newMatrix);
}
/// <summary>
/// Produces a vector in the form [R(1), R(2), R(3), ..., R(n)]
/// </summary>
/// <param name="mat">The matrix to flatten</param>
/// <returns>A vector resulting from the flattened matrix</returns>
public static T[] FlattenToVector <T>(this T[,] mat)
{
MatrixDimensions d = mat.GetDimensions();
T[] vector = new T[d.rows * d.cols];
for (int r = 0; r < d.rows; r++)
{
for (int c = 0; c < d.cols; c++)
{
vector[r * d.cols + c] = mat[r, c];
}
}
return(vector);
}
/// <summary>
/// Applies a scalar function to a matrix
/// </summary>
/// <param name="mat">The matrix to be acted on</param>
/// <param name="f">The function to be applied to each element of the matrix.
/// <para>Its arguments are the row, col, and the value for each element in the matrix</para></param>
/// <returns>A copy of the old matrix with a scalar function applied to it</returns>
public static T[,] Apply <T>(this T[,] mat, Func <T, int, int, T> f)
{
T[,] newMat = new T[mat.GetLength(0), mat.GetLength(1)];
MatrixDimensions dim = mat.GetDimensions();
for (int r = 0; r < dim.rows; r++)
{
for (int c = 0; c < dim.cols; c++)
{
newMat[r, c] = f.Invoke(mat[r, c], r + 1, c + 1);
}
}
return(newMat);
}
/// <summary>
/// Transposes a matrix
/// </summary>
/// <param name="mat">The matrix to transpose</param>
/// <returns>The transposed matrix</returns>
public static T[,] Transpose <T>(this T[,] mat)
{
MatrixDimensions d = mat.GetDimensions().Flip();
T[,] newMat = d.CreateMatrix <T>();
for (int r = 0; r < d.rows; r++)
{
for (int c = 0; c < d.cols; c++)
{
newMat[r, c] = mat[c, r];
}
}
return(newMat);
}
/// <summary>
/// Calculates the inverse of a matrix, if it has one
/// </summary>
/// <param name="matrix">The matrix</param>
/// <returns>The matrix's inverse</returns>
public static T[,] Inverse <T>(this T[,] matrix)
{
MatrixDimensions d = matrix.GetDimensions();
if (!d.IsSquare())
{
throw new MatrixSizeException("A non-square matrix cannot have an inverse.");
}
T[][,] aug = matrix.Augment(Matrix <T> .IdentityMatrix(d.cols)).RREF().Separate(d.cols, d.cols);
if (!aug[0].IsIdentity())
{
throw new IllegalOperationException("A matrix with no identity has no inverse.");
}
return(aug[1]);
}
/// <summary>
/// Produces a human-readable matrix
/// </summary>
/// <param name="mat">The matrix</param>
/// <returns>A human-readable representation of the matrix</returns>
public static string ToMatrixString <T>(this T[,] mat)
{
MatrixDimensions d = mat.GetDimensions();
string[] lines = new string[d.rows];
for (int r = 0; r < d.rows; r++)
{
string[] line = new string[d.cols];
for (int c = 0; c < d.cols; c++)
{
line[c] = mat[r, c].ToString();
}
lines[r] = "[" + String.Join(" ", line) + "]";
}
return("[" + String.Join("\n", lines) + "]");
}
/// <summary>
/// Matrix multiplication
/// </summary>
/// <param name="mat1">Left matrix</param>
/// <param name="mat2">Right matrix</param>
/// <returns>The product of the two matricies</returns>
public static T[,] Multiply <T>(this T[,] mat1, T[,] mat2)
{
MatrixDimensions d1 = mat1.GetDimensions();
MatrixDimensions d2 = mat2.GetDimensions();
if (d1.cols == d2.rows)
{
T[,] productMatrix = new T[d1.rows, d2.cols];
for (int r = 0; r < d1.rows; r++)
{
for (int c = 0; c < d2.cols; c++)
{
productMatrix[r, c] = mat1.GetVector(VectorDirection.Row, r + 1).DotProduct(mat2.GetVector(VectorDirection.Column, c + 1));
}
}
return(productMatrix);
}
throw new MatrixSizeException($"A matrix of size {d1.ToString()} cannot be multiplied by a matrix of size {d2.ToString()}");
}
/// <summary>
/// Removes a row or column vector in a matrix
/// </summary>
/// <param name="mat">The matrix</param>
/// <param name="direction">The type of vector to remove (row or column)</param>
/// <param name="removeIndex">The vector index to remove at</param>
/// <returns>The matrix with an removed row/column at the specified index</returns>
public static T[,] RemoveVector <T>(this T[,] mat, VectorDirection direction, int removeIndex)
{
MatrixDimensions d = mat.GetDimensions();
T[,] newMat;
if (direction == VectorDirection.Column)
{
if (removeIndex > d.cols || removeIndex < 1)
{
throw new IndexOutOfRangeException("That column index does not exist in the matrix.");
}
newMat = new T[d.rows, d.cols - 1];
return(newMat.Apply((v, r, c) => {
if (c < removeIndex)
{
return mat[r - 1, c - 1];
}
else
{
return mat[r - 1, c];
}
}));
}
else
{
if (removeIndex > d.rows || removeIndex < 1)
{
throw new IndexOutOfRangeException("That row index does not exist in the matrix.");
}
newMat = new T[d.rows - 1, d.cols];
return(newMat.Apply((v, r, c) => {
if (r < removeIndex)
{
return mat[r - 1, c - 1];
}
else
{
return mat[r, c - 1];
}
}));
}
}
/// <summary>
/// Compares if two matricies are equal
/// </summary>
/// <param name="matrix1">The first matrix</param>
/// <param name="matrix2">The second matrix</param>
/// <returns>Whether or not the two matricies have equal elements</returns>
public static bool MatrixEquals <T>(this T[,] matrix1, T[,] matrix2)
{
MatrixDimensions d = matrix1.GetDimensions();
if (!d.Equals(matrix2.GetDimensions()))
{
return(false);
}
for (int r = 0; r < d.rows; r++)
{
for (int c = 0; c < d.cols; c++)
{
if (!matrix1[r, c].Equals(matrix2[r, c]))
{
return(false);
}
}
}
return(true);
}
/// <summary>
/// Augments a matrix
/// </summary>
/// <param name="matrix">The matrix to augment</param>
/// <param name="otherMatrix">The matrix to append</param>
/// <returns>The augmented matrix</returns>
public static T[,] Augment <T>(this T[,] matrix, T[,] otherMatrix)
{
MatrixDimensions d1 = matrix.GetDimensions();
MatrixDimensions d2 = otherMatrix.GetDimensions();
if (d1.rows != d2.rows)
{
throw new MatrixSizeException("A matrix cannot be augmented if the second matrix has a different number of rows.");
}
T[,] augmentedMatrix = new T[d1.rows, d1.cols + d2.cols];
return(augmentedMatrix.Apply((v, r, c) =>
{
if (c > d1.cols)
{
return otherMatrix[r - 1, c - d1.cols - 1];
}
return matrix[r - 1, c - 1];
}));
}
/// <summary>
/// Calculates the sum of all elements in the matrix
/// </summary>
/// <param name="mat">The matrix to be summed</param>
/// <returns>The sum of all elements in the matrix</returns>
public static T Sum <T>(this T[,] mat)
{
if (mat.Length == 0)
{
throw new MatrixSizeException("A matrix cannot have no elements");
}
T sum = mat[0, 0];
MatrixDimensions d = mat.GetDimensions();
for (int r = 0; r < d.rows; r++)
{
for (int c = 0; c < d.cols; c++)
{
if (r != 0 || c != 0)
{
sum += (dynamic)mat[r, c];
}
}
}
return(sum);
}
/// <summary>
/// Produces the RREF form of the matrix
/// </summary>
/// <param name="matrix">The matrix</param>
/// <returns>The matrix in RREF form</returns>
public static T[,] RREF <T>(this T[,] matrix)
{
MatrixDimensions d = matrix.GetDimensions();
T[,] newMatrix = matrix;
int i = 0, j = 0;
while (i < d.rows && j < Math.Min(d.rows, d.cols))
{
bool pass = false;
if (newMatrix[i, j] == (dynamic)0)
{
pass = true;
for (int r = i + 1; r < d.rows; r++)
{
if (!(matrix[r, j] == (dynamic)0))
{
pass = false;
newMatrix = newMatrix.RowSwap(i + 1, r + 1);
r = d.rows;
}
}
}
if (!pass)
{
newMatrix = newMatrix.RowDivide(i + 1, newMatrix[i, j]);
for (int r = 0; r < d.rows; r++)
{
if (i != r && !matrix[r, j].Equals(0))
{
newMatrix = newMatrix.RowSubtract(r + 1, i + 1, newMatrix[r, j]);
}
}
i++;
}
j++;
}
return(newMatrix);
}
/// <summary>
/// Splits an augmented matrix
/// </summary>
/// <param name="matrix">The matrix to split</param>
/// <param name="augmentLengths">The number of columns in each constituent matrix. The sum of these lengths must equal the length of the matrix</param>
/// <returns>A list of sub-matricies</returns>
public static T[][,] Separate <T>(this T[,] matrix, params int[] augmentLengths)
{
MatrixDimensions d = matrix.GetDimensions();
if (augmentLengths.Sum() != d.cols)
{
throw new MatrixSizeException("An augmented matrix can't be split up into more sub-matricies than the augmented matrix contains.");
}
T[][,] splitMatricies = new T[augmentLengths.Length][, ];
int colOff = 0;
for (int i = 0; i < augmentLengths.Length; i++)
{
if (augmentLengths[i] <= 0)
{
throw new MatrixSizeException("A sub-matrix cannot have zero or fewer columns.");
}
splitMatricies[i] = new T[d.rows, augmentLengths[i]].Apply((v, r, c) => matrix[r - 1, c - 1 + colOff]);
colOff += augmentLengths[i];
}
return(splitMatricies);
}