/// <summary>
/// Loads solutions from a stream (a file)
/// </summary>
/// <param name="r"></param>
/// <returns></returns>
public static LPSolution LoadSolution(StreamReader r, int precision, LpNumber upperBound)
{
LPSolution sol = new LPSolution();
sol.UpperBound = upperBound;
string str = r.ReadLine();
if (str == null)
throw new Exception("Two numbers are expected on the first line");
string[] els = str.Split(' ');
if (els.Length != 2)
throw new Exception("Two numbers are expected on the first line");
// Subtract one since we don't count the objective function
sol.NumberOfConstraints = int.Parse(els[0]) - 1;
sol.NumberOfVariables = int.Parse(els[1]);
// Optimal
var vals = ReadThirdValue(r, 1, precision);
sol.Optimal = vals[0];
// Skip one line (the objective function)
ReadThirdValue(r, 1, precision);
// Constraints
sol.ConstraintMarginals = ReadThirdValue(r, sol.NumberOfConstraints, precision);
// Bounds
sol.VariableMarginals = ReadThirdValue(r, sol.NumberOfVariables, precision);
return sol;
}
/// <summary>
/// Private constructor
/// </summary>
private Inequality(Label id, IneqType type, LinearFunction lhs, LpNumber rhs, bool negFlag)
{
this.Id = id;
this.type = type;
this.lhs = lhs;
this.rhs = rhs;
this.NegFlag = negFlag;
}
/// <summary>
/// Loads solutions from a stream (a file)
/// </summary>
/// <param name="r"></param>
/// <returns></returns>
public static LPSolution LoadSolution(StreamReader r, int precision, LpNumber upperBound, bool infeasible)
{
LPSolution sol = new LPSolution();
sol.UpperBound = upperBound;
if (infeasible)
{
sol.UpperBound = new LpNumber(0);
}
string str = r.ReadLine();
if (str == null)
throw new Exception("Two numbers are expected on the first line");
string[] els = str.Split(' ');
if (els.Length != 2)
throw new Exception("Two numbers are expected on the first line");
int nc = int.Parse(els[0]);
int nv = int.Parse(els[1]);
if (infeasible)
{
sol.NumberOfConstraints = nc;
// Do not count slack variables
sol.NumberOfVariables = nv - nc;
}
else
{
// Subtract one since we don't count the objective function for a feasible solution
sol.NumberOfConstraints = nc - 1;
sol.NumberOfVariables = nv;
}
// Optimal
var vals = ReadThirdValue(r, 1, precision);
sol.Optimal = vals[0];
if (!infeasible)
{
// Skip one line (the objective function)
ReadThirdValue(r, 1, precision);
}
// Constraints
sol.ConstraintMarginals = ReadThirdValue(r, sol.NumberOfConstraints, precision);
if (infeasible)
{
// Skip slack variables
ReadThirdValue(r, nc, precision);
}
// Bounds
sol.VariableMarginals = ReadThirdValue(r, sol.NumberOfVariables, precision);
return sol;
}
/// <summary>
/// Generates a test for arithmetic
/// </summary>
static void GenerateArithTest()
{
FileStream fs = new FileStream("arith_test_data.hl", FileMode.Create);
StreamWriter w = new StreamWriter(fs);
Random rnd = new Random(0);
w.WriteLine("let data = [");
for (int i = 0; i < 1000; i++)
{
decimal n1 = rnd.Next(1000000000, 2000000000);
decimal n2 = rnd.Next(1000000000, 2000000000);
// n1 *= rnd.Next(1000000000, 2000000000);
// n2 *= rnd.Next(1000000000, 2000000000);
n1 *= rnd.Next(100000, 500000);
n2 *= rnd.Next(100000, 500000);
int x1 = (int)Math.Log10((double)n1);
int x2 = (int)Math.Log10((double)n2);
LpNumber m1 = new LpNumber(n1);
LpNumber m2 = new LpNumber(n2);
w.Write(m1.ToHOLExplicit(0));
w.Write(",");
w.Write(m2.ToHOLExplicit(0));
if (i < 999)
w.Write(";");
w.Write("(* {0}, {1} *)", x1, x2);
w.WriteLine();
}
w.WriteLine("];;");
w.Flush();
fs.Close();
}
/// <summary>
/// Creates files for a formal proof for a general linear program
/// </summary>
static bool processLPGeneral(string fname, int precision, LpNumber upperBound)
{
if (precision > 10)
throw new Exception("Cannot solve the problem (precision > 10): " + fname);
LP lp;
LPSolution sol;
// Load an LP
FileStream fs = new FileStream(fname + ".lp", FileMode.Open);
using (fs)
{
StreamReader r = new StreamReader(fs);
Scanner scanner = new Scanner(r, fname + ".lp");
lp = LP.ParseLP(scanner);
}
// Load solutions
fs = new FileStream(fname + ".txt", FileMode.Open);
using (fs)
{
sol = LPSolution.LoadSolution(new StreamReader(fs), precision, upperBound);
}
if (!lp.SetSolution(sol, precision))
return false;
// Create a test file containing all inequalities explicitly
FileStream test = new FileStream(fname + "_test.hl", FileMode.Create);
lp.ConvertToHOL(new StreamWriter(test), precision);
test.Close();
return true;
}
/// <summary>
/// Creates files for producing a formal proof for the given linear program
/// </summary>
static bool ProcessLP(string fname, LpNumber upperBound, int precision, ListHyp hypermap)
{
if (precision > 5)
throw new Exception("Cannot solve the problem: " + fname);
LP lp;
LPSolution sol;
// Load an LP
FileStream fs = new FileStream(fname + ".lp", FileMode.Open);
using (fs)
{
StreamReader r = new StreamReader(fs);
Scanner scanner = new Scanner(r, fname + ".lp");
lp = LP.ParseLP(scanner);
}
// Load solutions
fs = new FileStream(fname + ".txt", FileMode.Open);
using (fs)
{
sol = LPSolution.LoadSolution(new StreamReader(fs), precision, upperBound);
}
if (sol.Optimal.value > upperBound.value)
throw new Exception("Optimal value is greater than " + upperBound.value + ": " + fname);
if (!lp.SetSolution(sol, precision))
return false;
// Create a test file containing all inequalities explicitly
FileStream test = new FileStream(fname + "_test.hl", FileMode.Create);
lp.ConvertToHOL(new StreamWriter(test), precision);
test.Close();
// Create a certificate file
FileStream main = new FileStream(fname + "_out.hl", FileMode.Create);
lp.PrintCertificate(new StreamWriter(main), precision, hypermap, log);
main.Close();
return true;
}
/// <summary>
/// Creates files for producing a formal proof for the given linear program.
/// The precision is selected automatically
/// </summary>
static void ProcessLP(string fname, LpNumber upperBound, ListHyp hypermap)
{
Console.WriteLine("Processing {0}...", fname);
try
{
for (int precision = 3; ; precision++)
{
Console.WriteLine("Precision = {0}", precision);
if (hypermap != null)
{
if (ProcessLP(fname, upperBound, precision, hypermap))
break;
}
else
{
if (processLPGeneral(fname, precision, upperBound))
break;
}
}
}
catch (Exception e)
{
Console.Error.WriteLine("ERROR: {0}", e.Message);
}
Console.WriteLine("done\n");
}
// Main
static void Main(string[] args)
{
FileStream flog = new FileStream("log.txt", FileMode.Create);
log = new StreamWriter(flog);
using (log)
{
// GenerateArithTest();
// return;
// Flyspeck
if (args.Length == 0)
{
Console.WriteLine("Processing Flyspeck linear programs");
Console.WriteLine();
ProcessFlyspeckLP();
return;
}
// Incorrect number of arguments
if (args.Length != 2)
{
Console.WriteLine("Usage: LP-HL lp_name upper_bound");
Console.WriteLine("Files {lp_name}.lp and {lp_name}.txt must be in the current directory.");
Console.WriteLine("{upper_bound} is a decimal number");
return;
}
// Specific LP
string name = args[0];
LpNumber upperBound = new LpNumber(decimal.Parse(args[1]));
ProcessLP(name, upperBound, null);
}
}
/// <summary>
/// Reads k third values from the input stream
/// </summary>
/// <param name="k"></param>
/// <returns></returns>
private static List<LpNumber> ReadThirdValue(StreamReader r, int k, int precision)
{
List<LpNumber> result = new List<LpNumber>();
for (int i = 0; i < k; i++)
{
string str = r.ReadLine();
if (str == null)
throw new Exception("Unexpected end of file");
string[] els = str.Split(' ');
if (els.Length != 3)
throw new Exception("Triples are expected: " + str);
LpNumber val = new LpNumber(double.Parse(els[2]), precision);
result.Add(val);
}
return result;
}
/// <summary>
/// Returns the equality 0 = 0
/// </summary>
public static Inequality Zero()
{
Label id = new Label("ZERO", "");
LinearFunction lhs = new LinearFunction(new List<decimal>(), new List<string>());
LpNumber rhs = new LpNumber(0);
Inequality ineq = new Inequality(id, IneqType.Eq, lhs, rhs, false);
return ineq;
}
/// <summary>
/// Parses an inequality
/// </summary>
/// <param name="scanner"></param>
/// <returns></returns>
public static Inequality ParseInequality(Scanner scanner)
{
Token t;
// Identifier
Label id = Label.ParseLabel(scanner);
// :
t = scanner.nextToken();
if (t.Type != TokenType.Colon)
throw new Exception(": expected: " + t);
// lhs
LinearFunction lhs = LinearFunction.ParseFunction(scanner);
// type
t = scanner.nextToken();
IneqType type;
switch (t.Type)
{
case TokenType.Le:
type = IneqType.Le;
break;
case TokenType.Ge:
type = IneqType.Ge;
break;
case TokenType.Eq:
type = IneqType.Eq;
break;
default:
throw new Exception("<=, =>, or = expected: " + t);
}
// rhs
t = scanner.nextToken();
if (t.Type != TokenType.Integer && t.Type != TokenType.Double)
throw new Exception("A number is expected: " + t);
LpNumber rhs = new LpNumber(decimal.Parse(t.StringValue));
return new Inequality(id, type, lhs, rhs, false);
}
/// <summary>
/// Processes all inequalities based on the given solution
/// </summary>
/// <param name="sol"></param>
/// <param name="precision"></param>
/// <returns></returns>
public bool SetSolution(LPSolution sol, int precision, bool infeasible)
{
if (sol.NumberOfVariables != vars.Number)
throw new Exception("Inconsistent number of variables");
if (sol.NumberOfConstraints != originalIneqs.Count)
throw new Exception("Inconsistent number of constraints");
if (infeasible)
{
ResortVariables();
}
ineqs = new List<Inequality>();
// ineqMarginals = new List<LpNumber>();
// Constraints
for (int i = 0; i < sol.NumberOfConstraints; i++)
{
LpNumber m = sol.ConstraintMarginals[i];
if (m.IsZero(precision))
continue;
Inequality ineq = originalIneqs[i];
if (m.value < 0)
{
ineq = -ineq;
m = -m;
}
ineq = ineq.Round(precision);
ineq.Marginal = m;
ineqs.Add(ineq);
// ineqMarginals.Add(m);
}
// Variables
List<Inequality> tmpIneqs = new List<Inequality>();
for (int i = 0; i < sol.NumberOfVariables; i++)
{
Variable var = vars[i];
LpNumber m = sol.VariableMarginals[i];
if (m.IsZero(precision))
continue;
Inequality ineq;
if (m.value < 0)
{
var.LMarginal = -m;
ineq = -Inequality.FromLowerBound(var);
ineq = ineq.Round(precision) * (-m.value);
}
else
{
var.UMarginal = m;
ineq = Inequality.FromUpperBound(var);
ineq = ineq.Round(precision) * m.value;
}
tmpIneqs.Add(ineq);
}
// Compute additional inequality
// Inequality sum1 = ineqs[0] * ineqs[0].Marginal.value; //ineqMarginals[0].value;
Inequality sum1 = Inequality.Zero();
for (int i = 0; i < ineqs.Count; i++)
{
sum1 += ineqs[i] * ineqs[i].Marginal.value; //ineqMarginals[i].value;
}
Inequality sum2 = sum1;
for (int i = 0; i < tmpIneqs.Count; i++)
{
sum2 += tmpIneqs[i];
}
// df
LinearFunction df;
if (infeasible)
{
df = -sum2.lhs;
}
else
{
df = objective - sum2.lhs;
}
// Compute corrections for marginals
foreach (var term in df.Terms)
{
LpNumber c = term.c;
if (c.value < 0)
{
vars[term.varName].LMarginal -= c;
}
else
{
vars[term.varName].UMarginal += c;
}
}
// Verification
LpNumber sum = sum1.rhs;
for (int i = 0; i < vars.Number; i++)
{
Variable var = vars[i];
if (!var.LMarginal.IsZero(precision))
{
sum -= var.LMarginal * LpNumber.RoundDown(var.LBound, precision);
}
if (!var.UMarginal.IsZero(precision))
{
sum += var.UMarginal * LpNumber.RoundUp(var.UBound, precision);
}
}
LpNumber eps = sol.UpperBound - sum;
Console.WriteLine("eps = {0}", eps);
if (eps.value < 0)
return false;
// Set the upper bound
upperBound = sol.UpperBound;
// Generate inequalities for variables
Console.Write("Generating inequalities for variables...");
varIneqs = new List<Inequality>();
// varIneqMarginals = new List<LpNumber>();
for (int i = 0; i < vars.Number; i++)
{
Variable var = vars[i];
Inequality ineq;
if (!var.LMarginal.IsZero(precision))
{
ineq = -Inequality.FromLowerBound(var);
ineq = ineq.Round(precision);
ineq.Marginal = var.LMarginal;
varIneqs.Add(ineq);
// varIneqMarginals.Add(var.LMarginal);
}
if (!var.UMarginal.IsZero(precision))
{
ineq = Inequality.FromUpperBound(var);
ineq = ineq.Round(precision);
ineq.Marginal = var.UMarginal;
varIneqs.Add(ineq);
// varIneqMarginals.Add(var.UMarginal);
}
}
Console.WriteLine("done");
return true;
}
