simplex method coding in swift (by ChatGPT)

simplex.swift

struct LinearProgram {
    let objective: [Double]
    let constraints: [[Double]]
    let sense: [Character]
    let rhs: [Double]
}

func simplex(lp: LinearProgram) -> [Double]? {
    var tableau = lp.constraints
    tableau.append(lp.objective)
    
    let m = lp.constraints.count
    let n = lp.objective.count
    
    var basis = [Int]()
    for i in 0..<m {
        basis.append(n + i)
    }
    
    while true {
        // Find the pivot column
        var pivotColumn = -1
        var minRatio = Double.greatestFiniteMagnitude
        for j in 0..<n {
            if tableau[m][j] > 0 {
                for i in 0..<m {
                    if tableau[i][j] < 0 {
                        let ratio = -tableau[i][n] / tableau[i][j]
                        if ratio < minRatio {
                            pivotColumn = j
                            minRatio = ratio
                        }
                    }
                }
            }
        }
        
        // Check for optimality
        if pivotColumn == -1 {
            break
        }
        
        // Find the pivot row
        var pivotRow = -1
        minRatio = Double.greatestFiniteMagnitude
        for i in 0..<m {
            if tableau[i][pivotColumn] < 0 {
                let ratio = -tableau[i][n] / tableau[i][pivotColumn]
                if ratio < minRatio {
                    pivotRow = i
                    minRatio = ratio
                }
            }
        }
        
        // Update the basis
        basis[pivotRow] = pivotColumn
        
        // Update the tableau
        let pivot = tableau[pivotRow][pivotColumn]
        for j in 0...n {
            tableau[pivotRow][j] /= pivot
        }
        for i in 0..<m+1 {
            if i != pivotRow {
                let factor = tableau[i][pivotColumn]
                for j in 0...n {
                    tableau[i][j] -= factor * tableau[pivotRow][j]
                }
            }
        }
    }
    
    // Extract the solution
    var solution = [Double](repeating: 0, count: n)
    for i in 0..<m {
        if basis[i] < n {
            solution[basis[i]] = tableau[i][n]
        }
    }
    
    return solution
}

// Example usage
let objective = [3, 5, 2]
let constraints = [[1, 2, 1], [3, 2, 0]]
let sense = ["<=", "<="]
let rhs = [5, 6]
let lp = LinearProgram(objective: objective, constraints: constraints, sense: sense, rhs: rhs)
let solution = simplex(lp: lp)
print(solution)