determinant method

dynamic determinant({ DeterminantMethod method = DeterminantMethod.LU, })

Computes the determinant of the matrix.

Throws an Exception if the matrix is not square.

Takes an optional method parameter to specify the method for calculating the determinant. The default method is DeterminantMethod.LU.

Example:

var matrix = Matrix([
  [1, 2],
  [3, 4]
]);
var det = matrix.determinant();  // Output: -2.0
var detLaplace = matrix.determinant(method: DeterminantMethod.Laplace);  // Output: -2.0

[ \text{Determinant} = 1 \times 4 - 2 \times 3 = -2 ]

@param method The method used for calculating the determinant. One of DeterminantMethod.Laplace or DeterminantMethod.LU. @return The determinant of the matrix as a dynamic.

Implementation

dynamic determinant({DeterminantMethod method = DeterminantMethod.LU}) {
  int n = rowCount;
  if (n != columnCount) {
    throw Exception('Matrix must be square to calculate determinant');
  }
  Number det = Complex.one();
  if (method == DeterminantMethod.LU) {
    // Perform LU decomposition
    // (Replace with your actual LU decomposition implementation)
    var lu = decomposition.luDecompositionDoolittle();
    // var l = lu.L;
    var u = lu.U;

    // Compute the product of the diagonal elements of U

    for (int i = 0; i < n; i++) {
      det *= u[i][i];
    }
    return det;
  } else {
    // Laplace Expansion
    if (n == 1) {
      return this[0][0];
    }

    if (n == 2) {
      return (_data[0][0] * _data[1][1]) - (_data[0][1] * _data[1][0]);
    }

    for (int p = 0; p < n; p++) {
      Matrix subMatrix = Matrix([
        for (int i = 1; i < n; i++)
          [
            for (int j = 0; j < n; j++)
              if (j != p) _data[i][j]
          ]
      ]);

      det += _data[0][p] * (p % 2 == 0 ? 1 : -1) * subMatrix.determinant();
    }
  }

  return det;
}