gaussian_elimination.ts

/**
 * Solves a system of linear equations using Gaussian Elimination with partial pivoting.
 *
 * @param {number[][]} matrix - The augmented matrix representing the system of equations.
 * @returns {number[]} An array representing the solutions to the equations.
 */
export function gaussianElimination(matrix: number[][]): number[] {
  const result: number[] = new Array(matrix.length)

  function partialPivot(): void {
    for (let row = 0; row < matrix.length; row++) {
      let pivotRow = row

      for (let column = row + 1; column < matrix.length; column++) {
        if (Math.abs(matrix[column][row]) > Math.abs(matrix[pivotRow][row])) {
          pivotRow = column
        }
      }

      if (pivotRow !== row) {
        for (let column = row; column <= matrix.length; column++) {
          ;[matrix[row][column], matrix[pivotRow][column]] = [
            matrix[pivotRow][column],
            matrix[row][column]
          ]
        }
      }

      for (let column = row + 1; column < matrix.length; column++) {
        const factor = matrix[column][row] / matrix[row][row]
        for (let k = row; k <= matrix.length; k++) {
          matrix[column][k] -= factor * matrix[row][k]
        }
      }
    }
  }

  function backSubstitute(): void {
    for (let row = matrix.length - 1; row >= 0; row--) {
      let sum = 0
      for (let column = row + 1; column < matrix.length; column++) {
        sum += matrix[row][column] * result[column]
      }
      result[row] = (matrix[row][matrix.length] - sum) / matrix[row][row]
    }
  }

  partialPivot()
  backSubstitute()

  return result
}