/// <summary>
/// Creates an upper bound inequality for a variable
/// </summary>
/// <param name="var"></param>
/// <returns></returns>
public static Inequality FromUpperBound(Variable var)
{
Inequality ineq = new Inequality(new Label(var.Name, var.Name.name + "_hi"),
IneqType.Le, new LinearFunction(var), new LpNumber(var.UBound), false);
return(ineq);
}
// Adds an indexed inequality to a dictionary
private void AddIndexedIneq(Inequality ineq, LpNumber marginal, ListHyp hypermap)
{
IndexedInequality newIneq = new IndexedInequality(ineq, marginal, hypermap);
string name = ineq.Id.name;
// Ad hoc treatment of sums over faces
if (name == "sol_sum" || name == "tau_sum")
{
DartList face = hypermap.Manager.TranslateIneq(hypermap, ineq.Id) as DartList;
if (face == null)
{
throw new Exception("A face is expected for the constraint " + name);
}
name += face.list.Count.ToString();
}
if (ineq.type == Inequality.IneqType.Eq && ineq.NegFlag)
{
name += "_neg";
}
if (dict.ContainsKey(name))
{
dict[name].Add(newIneq);
}
else
{
var list = new List <IndexedInequality>();
list.Add(newIneq);
dict.Add(name, list);
ineqNames.Add(name);
}
}
/// <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>
/// Computes the index automatically
/// </summary>
public IndexedInequality(Inequality ineq, LpNumber marginal, ListHyp hypermap)
{
this.ineq = ineq;
this.marginal = marginal;
if (ineq.Id.index == null || ineq.Id.index == "")
{
this.index = 0;
}
else
{
this.index = hypermap.Manager.FindIneqIndex(hypermap, ineq.Id);
}
}
/// <summary>
/// Prints the given inequality into a stream
/// </summary>
private void WriteIneqText(Inequality ineq, LpNumber marginal, int precision,
StreamWriter writer, ListHyp hypermap)
{
// Relabel
HypermapElement element = hypermap.Manager.TranslateIneq(hypermap, ineq.Id);
int index = hypermap.Manager.FindIneqIndex(hypermap, ineq.Id);
// Write out
if (ineq.NegFlag && ineq.type == Inequality.IneqType.Eq)
{
writer.Write("-");
}
writer.Write(ineq.Id + " & ");
writer.Write(index + " & ");
writer.Write(element + ": ");
writer.Write(ineq.ToHOLString(precision, vars));
writer.Write("\t (");
writer.Write(marginal.ToHOLString(precision));
writer.WriteLine(")");
}
// Adds an indexed inequality to a dictionary
private void AddIndexedIneq(Inequality ineq, LpNumber marginal, ListHyp hypermap)
{
IndexedInequality newIneq = new IndexedInequality(ineq, marginal, hypermap);
string name = ineq.Id.name;
if (ineq.type == Inequality.IneqType.Eq && ineq.NegFlag)
{
name += "_neg";
}
if (dict.ContainsKey(name))
{
dict[name].Add(newIneq);
}
else
{
var list = new List <IndexedInequality>();
list.Add(newIneq);
dict.Add(name, list);
ineqNames.Add(name);
}
}
/// <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)
{
if (sol.NumberOfVariables != vars.Number)
{
throw new Exception("Inconsistent number of variables");
}
if (sol.NumberOfConstraints != originalIneqs.Count)
{
throw new Exception("Inconsistent number of constraints");
}
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 = 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);
}
/// <summary>
/// Parses a LP
/// </summary>
/// <param name="scanner"></param>
/// <returns></returns>
public static LP ParseLP(Scanner scanner)
{
LP lp = new LP();
// Maximize
Token t = scanner.nextToken();
if (t.Type != TokenType.Identifier && t.StringValue != "Maximize")
{
throw new Exception("Maximize expected: " + t);
}
// objective
t = scanner.nextToken();
if (t.Type != TokenType.Identifier)
{
throw new Exception("Identifier expected: " + t);
}
// :
t = scanner.nextToken();
if (t.Type != TokenType.Colon)
{
throw new Exception(": expected: " + t);
}
// objective function
lp.objective = LinearFunction.ParseFunction(scanner);
// Subject To
t = scanner.nextToken();
if (t.Type != TokenType.Identifier && t.StringValue != "Subject")
{
throw new Exception("Subject To expected: " + t);
}
t = scanner.nextToken();
if (t.Type != TokenType.Identifier && t.StringValue != "To")
{
throw new Exception("Subject To expected: " + t);
}
// Constraints
while (true)
{
t = scanner.peekToken();
if (t.Type == TokenType.Identifier && t.StringValue == "Bounds")
{
break;
}
if (t.Type == TokenType.EOF)
{
break;
}
Inequality ineq = Inequality.ParseInequality(scanner);
lp.originalIneqs.Add(ineq);
}
// Bounds
t = scanner.nextToken();
if (t.Type != TokenType.Identifier && t.StringValue != "Bounds")
{
throw new Exception("Bounds expected: " + t);
}
// Bounds
while (true)
{
t = scanner.peekToken();
if (t.Type == TokenType.Identifier && t.StringValue == "End")
{
break;
}
if (t.Type == TokenType.EOF)
{
break;
}
ParseBound(scanner, lp);
}
return(lp);
}
/// <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>
/// Creates an upper bound inequality for a variable
/// </summary>
/// <param name="var"></param>
/// <returns></returns>
public static Inequality FromUpperBound(Variable var)
{
Inequality ineq = new Inequality(new Label(var.Name, var.Name.name + "_hi"),
IneqType.Le, new LinearFunction(var), new LpNumber(var.UBound), false);
return ineq;
}
/// <summary>
/// Computes the index automatically
/// </summary>
public IndexedInequality(Inequality ineq, LpNumber marginal, ListHyp hypermap)
{
this.ineq = ineq;
this.marginal = marginal;
this.index = hypermap.Manager.FindIneqIndex(hypermap, ineq.Id);
}
/// <summary>
/// Converts the LP into HOL data
/// </summary>
/// <param name="writer"></param>
public void ConvertToHOL(StreamWriter writer, int precision)
{
// Find target variables
foreach (var term in objective.Terms)
{
vars[term.varName].TargetVariable = true;
}
// Compute the precision constant
decimal mul = 1;
for (int i = 0; i < precision; i++)
{
mul *= 10;
}
// Dependencies
writer.WriteLine("module Lp = struct");
// writer.WriteLine("needs \"arith/prove_lp.hl\";;");
// writer.WriteLine("open Prove_lp;;");
// Target
writer.WriteLine("let target = `" + objective.ToHOLString(precision, vars) + "`;;");
// Target bound
writer.WriteLine("let target_bound = `" + upperBound.ToHOLString(100) + "`;;");
// Precision
// LpNumber precision_constant = new LpNumber(mul * mul * mul);
writer.Write("let precision_constant = ");
writer.Write("Int " + mul);
// writer.Write(precision_constant.ToHOLExplicit(0));
writer.WriteLine(";;");
// Constraints
int counter = 0;
writer.WriteLine("let ineqs = [");
vars.MakeSimpleNames();
for (int i = 0; i < ineqs.Count; i++)
{
Inequality ineq = ineqs[i];
LpNumber m = ineq.Marginal; //ineqMarginals[i];
if (ineq.Id.name == "lnsum_def")
{
throw new Exception("lnsum_def cannot be active");
}
// Ignore zero values
if (m.IsZero(precision))
{
continue;
}
// m *= mul * mul;
m *= mul;
ineq = ineq * mul;
writer.Write("ASSUME (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write("), ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(";");
counter++;
}
writer.WriteLine("];;");
int constraintIneqs = counter;
// Variables
// Sort variables
varIneqs.Sort(new VarsComparer(vars));
// Save target variables first
writer.WriteLine("let target_vars = [");
counter = 0;
for (; counter < varIneqs.Count; counter++)
{
Inequality ineq = varIneqs[counter];
if (!vars[ineq.lhs.Terms.First().varName].TargetVariable)
{
break;
}
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
m *= mul * mul;
ineq = ineq * mul;
writer.Write("ASSUME (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write("), ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(";");
}
writer.WriteLine("];;\n\n");
writer.WriteLine("let var_ineqs = [");
// writer.WriteLine("let vars = [");
// counter = 0;
for (int i = counter; i < varIneqs.Count; i++)
{
Inequality ineq = varIneqs[i];
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
if (m.IsZero(precision))
{
throw new Exception("Unexpected zero");
}
if (i < varIneqs.Count - 1)
{
Inequality ineq2 = varIneqs[i + 1];
LpNumber m2 = ineq2.Marginal;
if (m2.IsZero(precision))
{
throw new Exception("Unexpected zero");
}
if (ineq.lhs.Terms.First().varName == ineq2.lhs.Terms.First().varName)
{
m *= mul * mul;
m2 *= mul * mul;
ineq = ineq * mul;
ineq2 = ineq2 * mul;
writer.Write("var2_le_transform (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m.ToHOLExplicit(precision));
writer.Write(") ");
writer.Write("(");
writer.Write(ineq2.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m2.ToHOLExplicit(precision));
writer.WriteLine(");");
i++;
continue;
}
}
m *= mul * mul;
ineq = ineq * mul;
writer.Write("var1_le_transform (");
writer.Write(ineq.ToHOLExplicit(precision, vars));
writer.Write(", ");
writer.Write(m.ToHOLExplicit(precision));
writer.WriteLine(");");
// writer.WriteLine(";");
}
writer.WriteLine("];;");
Console.WriteLine("Inequalities for constraints: {0}", constraintIneqs);
Console.WriteLine("Inequalities for variables: {0}", varIneqs.Count);
Console.WriteLine("Number of variables: {0}", vars.Number);
Console.WriteLine("Total constraints: {0}", constraintIneqs + varIneqs.Count);
writer.WriteLine("let start = Sys.time();;");
writer.WriteLine("let result = prove_lp ineqs var_ineqs target_vars target_bound precision_constant;;");
// writer.WriteLine("let result = Prove_lp.prove_lp ineqs vars target_bound precision_constant;;");
writer.WriteLine("end;;");
writer.WriteLine("Sys.time() -. Lp.start;;");
// writer.WriteLine("let done_message = \"{0} done\";;", fname);
writer.WriteLine("concl (Lp.result);;");
writer.Flush();
}
/// <summary>
/// Prints all inequalities in a text file using HOL syntax
/// </summary>
/// <param name="writer"></param>
/// <param name="precision"></param>
public void PrintAllText(StreamWriter writer, int precision, ListHyp hypermap)
{
// Find target variables
foreach (var term in objective.Terms)
{
vars[term.varName].TargetVariable = true;
}
// Compute the precision constant
decimal mul = 1;
for (int i = 0; i < precision; i++)
{
mul *= 10;
}
// Target
writer.WriteLine("target: " + objective.ToHOLString(precision, vars));
// Precision
writer.WriteLine("precision_constant: " + mul);
// Constraints
int counter = 0;
vars.RelabelAllVariables(hypermap);
for (int i = 0; i < ineqs.Count; i++)
{
Inequality ineq = ineqs[i];
LpNumber m = ineq.Marginal;
if (ineq.Id.name == "lnsum_def")
{
throw new Exception("lnsum_def cannot be active");
}
// Ignore zero values
if (m.IsZero(precision))
{
continue;
}
WriteIneqText(ineq * mul, m * mul, precision, writer, hypermap);
counter++;
}
writer.WriteLine();
writer.WriteLine("Inequalities for constraints: {0}", counter);
writer.WriteLine("-------------------------------------------------------");
writer.WriteLine();
// Variables
// Sort variables
varIneqs.Sort(new VarsComparer(vars));
// Target variables first
writer.WriteLine("Target variables:");
counter = 0;
for (; counter < varIneqs.Count; counter++)
{
Inequality ineq = varIneqs[counter];
if (!vars[ineq.lhs.Terms.First().varName].TargetVariable)
{
break;
}
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
m *= mul * mul;
ineq = ineq * mul;
WriteIneqText(ineq, m, precision, writer, hypermap);
}
writer.WriteLine("-------------------------------------------------------");
writer.WriteLine();
// All other variables
writer.WriteLine("Variables:");
for (int i = counter; i < varIneqs.Count; i++)
{
Inequality ineq = varIneqs[i];
LpNumber m = ineq.Marginal; //varIneqMarginals[i];
if (m.IsZero(precision))
{
throw new Exception("Unexpected zero");
}
/* if (i < varIneqs.Count - 1)
* {
* Inequality ineq2 = varIneqs[i + 1];
* LpNumber m2 = ineq2.Marginal;
*
* if (m2.IsZero(precision))
* throw new Exception("Unexpected zero");
*
* if (ineq.lhs.Terms.First().varName == ineq2.lhs.Terms.First().varName)
* {
* m *= mul * mul;
* m2 *= mul * mul;
* ineq = ineq * mul;
* ineq2 = ineq2 * mul;
*
* writer.Write("var2_le_transform (");
* writer.Write(ineq.ToHOLExplicit(precision, vars));
* writer.Write(", ");
* writer.Write(m.ToHOLExplicit(precision));
* writer.Write(") ");
*
* writer.Write("(");
* writer.Write(ineq2.ToHOLExplicit(precision, vars));
* writer.Write(", ");
* writer.Write(m2.ToHOLExplicit(precision));
* writer.WriteLine(");");
*
* i++;
* continue;
* }
* }
*/
m *= mul * mul;
ineq = ineq * mul;
WriteIneqText(ineq, m, precision, writer, hypermap);
}
writer.WriteLine("Inequalities for variables: {0}", varIneqs.Count);
writer.Flush();
}
/// <summary>
/// Creates a HOL certificate
/// </summary>
public void PrintCertificate(StreamWriter writer, int precision, ListHyp hypermap, StreamWriter log)
{
// Find target variables
foreach (var term in objective.Terms)
{
vars[term.varName].TargetVariable = true;
}
// Compute the precision constant
decimal mul = 1;
for (int i = 0; i < precision; i++)
{
mul *= 10;
}
// Head
writer.WriteLine("needs \"nobranching_lp.hl\";;\n");
writer.WriteLine("module Test_case = struct");
// Parameters
writer.WriteLine("let hypermap_string = \"" + hypermap.rawString + "\";;");
writer.WriteLine("let precision = " + precision + ";;");
dict.Clear();
ineqNames.Clear();
// Constraints
int counter = 0;
vars.RelabelAllVariables(hypermap);
writer.WriteLine("(***************)");
writer.WriteLine("(* Constraints *)");
writer.WriteLine("(***************)");
for (int i = 0; i < ineqs.Count; i++)
{
Inequality ineq = ineqs[i];
LpNumber m = ineq.Marginal;
if (ineq.Id.name == "lnsum_def")
{
throw new Exception("lnsum_def cannot be active");
}
// Ignore zero values
if (m.IsZero(precision))
{
continue;
}
ineq *= mul;
m *= mul;
AddIndexedIneq(ineq, m, hypermap);
}
writer.WriteLine("let constraints = [");
SaveIndexedIneqs(writer, precision);
writer.WriteLine("];;");
// Variables
writer.WriteLine();
writer.WriteLine("(***************)");
writer.WriteLine("(* Variables *)");
writer.WriteLine("(***************)");
// Sort variables
varIneqs.Sort(new VarsComparer(vars));
// Target variables first
dict.Clear();
ineqNames.Clear();
counter = 0;
for (; counter < varIneqs.Count; counter++)
{
Inequality ineq = varIneqs[counter];
if (!vars[ineq.lhs.Terms.First().varName].TargetVariable)
{
break;
}
LpNumber m = ineq.Marginal;
m *= mul * mul;
ineq = ineq * mul;
AddIndexedIneq(ineq, m, hypermap);
}
writer.WriteLine("let target_variables = [");
SaveIndexedIneqs(writer, precision);
writer.WriteLine("];;");
writer.WriteLine();
writer.WriteLine("(*************************)");
writer.WriteLine();
// All other variables
dict.Clear();
ineqNames.Clear();
for (int i = counter; i < varIneqs.Count; i++)
{
Inequality ineq = varIneqs[i];
LpNumber m = ineq.Marginal;
m *= mul * mul;
ineq = ineq * mul;
AddIndexedIneq(ineq, m, hypermap);
}
writer.WriteLine("let variable_bounds = [");
SaveIndexedIneqs(writer, precision);
writer.WriteLine("];;");
// Tail
writer.WriteLine("let result = prove_hypermap_lp hypermap_string precision constraints target_variables variable_bounds;;");
writer.WriteLine("end;;");
writer.WriteLine();
writer.WriteLine("concl (Test_case.result)");
writer.Flush();
log.WriteLine("{0}\t{1}\t{2}", hypermap.Id, ineqs.Count + varIneqs.Count, vars.Number);
}