Solver for linear systems of equations (using the Gaussian method)

linear-system-solver.dart

import 'dart:math';

void main() {
  final matrix = <List<double>>[
    [1, -4, 5, 3],
    [3, 3, 7, 13],
    [0, -2, -3, -1],
  ];

  print('Input:');
  printMatrix(matrix);

  final numberOfRows = matrix.length;
  final numberOfColumns = matrix[0].length;

  for (var i = 0; i < numberOfRows - 1; i++) {
    for (var row = i + 1; row < numberOfRows; row++) {
      final factor = matrix[row][i] / matrix[i][i];
      for (var column = i; column < numberOfColumns; column++) {
        matrix[row][column] = matrix[row][column] - factor * matrix[i][column];
      }
    }
  }

  print('\nReduced row echelon form:');
  printMatrix(matrix);

  final reversedResults = [];
  for (var i = numberOfRows - 1; i >= 0; i--) {
    var result = matrix[i].last;

    for (var j = 0; j < reversedResults.length; j++) {
      result -= matrix[i][numberOfColumns - 2 - j] * reversedResults[j];
    }

    result /= matrix[i][numberOfColumns - 2 - reversedResults.length];

    reversedResults.add(result);
  }

  print('\nResult:');
  printResult(List.from(reversedResults.reversed));
}

extension DoubleToPrettyString on double {
  String toPrettyString() => ((this * 100).round() / 100).toString();
}

void printMatrix(List<List<double>> matrix) {
  final numberOfRows = matrix.length;
  final numberOfColumns = matrix[0].length;

  final columnWidths = <int>[];
  for (var column = 0; column < numberOfColumns; column++) {
    var width = 1;
    for (var row = 0; row < numberOfRows; row++) {
      width = max(width, matrix[row][column].toPrettyString().length);
    }
    columnWidths.add(width);
  }

  String stringifyRow(int row) {
    final result = [];
    for (var i = 0; i < numberOfColumns; i++) {
      final width = columnWidths[i];
      final string = matrix[row][i].toPrettyString();
      final rightPadding = ' ' *
          ((width - string.length) ~/ 2); // Right padding takes precedence
      final leftPadding = ' ' * (width - string.length - rightPadding.length);
      result.add('$leftPadding$string$rightPadding');
    }
    return result.join(' ');
  }

  print('⎡ ${stringifyRow(0)} ⎤');
  for (var i = 1; i < matrix.length - 1; i++) {
    print('⎢ ${stringifyRow(i)} ⎥');
  }
  print('⎣ ${stringifyRow(numberOfRows - 1)} ⎦');
}

void printResult(List<double> result) {
  print('{ (${result.map((e) => e.toPrettyString()).join('|')}) }');
}