Gauss-Seidel Method

gauss_seidel.dart

void main() {
  final i = IterativeMethods();

  i.gaussSeidel(
    precision: 4,
    initialAproximation: [0, 0, 0],
    maxIterations: 10,
    matrix: [
      [5, 2, 1, 0],
      [2, 4, 1, 2],
      [0, -2, 3, -1]
    ],
  );
}

class IterativeMethods {
  void gaussSeidel({
    List<List<num>> matrix,
    List<num> initialAproximation,
    maxIterations = 10,
    precision = 3,
  }) {
    if (_isDiagonallyDominant(matrix)) {
      print('Gauss-Seidel method\n');
      var variables = List.generate(matrix.length, (_) => 0.0);
      var identityMatrix = List.generate(matrix.length, (_) => 0.0);
      var aproximation =
          initialAproximation ?? List.generate(matrix.length, (_) => 0.0);
      for (var i = 0; i < matrix.length; i++) {
        identityMatrix[i] = matrix[i][i];
      }

      for (var k = 0; k < maxIterations; k++) {
        for (var i = 0; i < matrix.length; i++) {
          var multiplication = 0.0;

          for (var j = 0; j < matrix[i].length - 1; j++) {
            if (i != j) {
              multiplication += matrix[i][j] * aproximation[j];
            }
          }

          final total = matrix[i].last - multiplication;
          variables[i] = total / identityMatrix[i];

          aproximation = variables;
        }

        _printValues(
          index: k,
          aproximation: aproximation,
          precision: precision,
        );
      }
    } else {
      print('Error');
    }
  }

  bool _isDiagonallyDominant(List<List<num>> matrix) {
    var isDiagonallyDominant = true;

    for (var i = 0; i < matrix.length; i++) {
      var sum = 0;

      for (var k = 0; k < matrix[i].length - 1; k++) {
        if (i != k) {
          sum += matrix[i][k].abs();
        }
      }

      if (matrix[i][i].abs() < sum) {
        isDiagonallyDominant = false;
        break;
      }
    }

    return isDiagonallyDominant;
  }

  void _printValues({List<num> aproximation, int precision = 3, int index}) {
    var truncated = <String>[];
    aproximation
        .forEach((value) => truncated.add(value.toStringAsFixed(precision)));

    print(index != null ? '$index - $truncated' : '$truncated');
  }
}