using System;
using Optimizer;
using System.Collections.Generic;
namespace Examples {
/// <summary>
/// Code example that uses a user function of type "multimapdelta".
/// </summary>
/// <remarks>
/// <code>
/// Xpress Optimizer Examples
/// =========================
///
/// Maximize the area of polygon of N vertices and diameter of 1
/// The position of vertices is indicated as (rho,theta) coordinates
/// where rho denotes the distance to the base point
/// (vertex with number N) and theta the angle from the x-axis.
///
/// (c) 2021-2024 Fair Isaac Corporation
/// </code>
///
/// Polygon example: maximise the area of an N sided polygon
///
/// *** Demonstrating using a multi-map (R^2->R^2) userfunction calculating its own derivatives ***
///
/// <code>
/// Variables:
///
/// rho : 0..N-1 ! Distance of vertex from the base point
/// theta : 0..N-1 ! Angle from x-axis
///
/// Objective:
/// (sum (i in 1..N-2) (rho(i)*rho(i-1)*sin(theta(i)-theta(i-1)))) * 0.5
///
/// Constraints:
/// Vertices in increasing degree order:
/// theta(i) >= theta(i-1) +.0001 : i = 1..N-2
/// Boundary conditions:
/// theta(N-1) <= Pi
/// 0.1 <= rho(i) <= 1 : i = 0..N-2
/// Third side of all triangles <= 1
/// rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1 : i in 0..N-3, j in i..N-2
/// </code>
/// </remarks>
public class PolygonMultiMapDelta {
/// <summary>
/// User function that maps two doubles to a double.
/// </summary>
/// <remarks>
/// Computes <c>sin(x[0] - x[1])</c>.
/// It also fills in the partial derivatives if requested.
/// </remarks>
/// <param name="value">The point at which to evaluate.</param>
/// <param name="delta">Non-zero whether partial derivatives are requested.</param>
/// <paran name="partials">Where to return the partial derivatives of the function.</paran>
/// <returns>the computed values of the function.</returns>
private static double[] MyTrigonometrics(double[] value, double[] deltas, double[] partials)
{
int nInput = 2;
// Assuming f:R^k->R^l, there will be a total of k*l derivatives,
// which must be written to the partials argument as:
// diff(f1(x), x1), diff(f1(x), x2) ... diff(f1(x), xk)
// diff(f2(x), x1), diff(f2(x), x2) ... diff(f1(x), xk)
// ...
// diff(fl(x), x1), diff(fl(x), x2) ... diff(fl(x), xk)
if (deltas != null) // Delta may be used as a suggestion for a finite difference step size
// however it also indicates if a partial is requested, saving on effort in case only an evaluation is needed
{
if (deltas[0] != 0.0)
{
partials[0 + 0] = Math.Cos(value[0] - value[1]);
partials[nInput + 0] = -Math.Sin(value[0] - value[1]);
}
if (deltas[1] != 0.0)
{
partials[0 + 1] = -Math.Cos(value[0] - value[1]);
partials[nInput + 1] = Math.Sin(value[0] - value[1]);
}
}
return new double[] {
Math.Sin(value[0] - value[1]),
Math.Cos(value[0] - value[1])
};
}
public static void Main(String[] args) {
using (XPRSprob prob = new XPRSprob(null)) {
// Number of sides of the Polygon
int nSide = 5;
// Theta
int[] theta = prob.VarArray('C', nSide - 1, 0.0, Math.PI,
i => "THETA" + (i + 1));
// Rho
int[] rho = prob.VarArray('C', nSide - 1, 0.01, 1.0,
i => "RHO" + (i + 1));
// Add the user function
XPRSprob.MultiMapDeltaFunction trig = prob.NlpAddUserFunction("myTrigonometrics", 2, 2, 0, MyTrigonometrics);
// Objective function. We build the objective function as
// a formula in infix notation. See below for submitting a
// formula as string.
List<int> tok = new List<int>();
List<double> val = new List<double>();
for (int i = 1; i < nSide - 1; ++i) {
if ( tok.Count > 0 ) {
tok.Add(Constants.TOK_OP);
val.Add(Constants.OP_PLUS);
}
tok.Add(Constants.TOK_COL); // RHO(i)
val.Add(rho[i]);
tok.Add(Constants.TOK_OP); // *
val.Add(Constants.OP_MULTIPLY);
tok.Add(Constants.TOK_COL); // RHO(i-1)
val.Add(rho[i-1]);
tok.Add(Constants.TOK_OP); // *
val.Add(Constants.OP_MULTIPLY);
tok.Add(Constants.TOK_FUN); // myTrigonometrics
val.Add(trig.GetId());
tok.Add(Constants.TOK_LB); // (
val.Add(Constants.TOK_LB);
tok.Add(Constants.TOK_COL); // THETA(i)
val.Add(theta[i]);
tok.Add(Constants.TOK_DEL); // -
val.Add(Constants.DEL_COMMA);
tok.Add(Constants.TOK_COL); // THETA(i-1)
val.Add(theta[i-1]);
tok.Add(Constants.TOK_DEL); // :
val.Add(Constants.DEL_COLON);
tok.Add(Constants.TOK_CON); // 1
val.Add(1);
tok.Add(Constants.TOK_RB); // )
val.Add(Constants.TOK_RB);
tok.Add(Constants.TOK_OP); // *
val.Add(Constants.OP_MULTIPLY);
tok.Add(Constants.TOK_CON); // 0.5
val.Add(0.5);
}
tok.Add(Constants.TOK_EOF);
val.Add(0.0);
// Since nonlinear objectives cannot be directly expressed in Xpress, we maximize a free
// variable objx and constrain this variable to be equal to the nonlinear objective.
int objx = prob.AddCol(1.0, XPRS.MINUSINFINITY, XPRS.PLUSINFINITY);
int objeq = prob.AddRow(new int[]{objx}, new double[]{-1.0}, 'E', 0.0);
prob.NlpChgFormula(objeq, 0,
tok.ToArray(),
val.ToArray());
prob.ChgObjSense(ObjSense.Maximize);
// Vertices in increasing degree order
for (int i = 0; i < nSide - 2; ++i)
prob.AddRow(new int[]{ theta[i], theta[i+1] },
new double[]{ -1.0, 1.0 },
'G',
0.001);
// Third side of all triangles <= 1
for (int i = 1; i < nSide - 1; i++) {
for (int j = i + 1; j < nSide; j++) {
int row = prob.AddRow(new int[0], new double[0], 'L', 1.0);
prob.NlpChgFormulaStr(row,
String.Format("RHO{0:d} ^ 2 + RHO{1:d} ^ 2 - RHO{2:d} * RHO{3:d} * 2 * myTrigonometrics ( THETA{4:d} , THETA{5:d} : 2 )",
i, j, i, j, j, i));
}
}
int solvestatus = -1;
int solstatus = -1;
prob.Optimize("s", out solvestatus, out solstatus);
System.Console.WriteLine("solvestatus: " + solvestatus);
System.Console.WriteLine("solstatus: " + solstatus);
System.Console.WriteLine("Solution value: " + prob.ObjVal);
double[] x = prob.GetSolution();
for (int i = 0; i < rho.Length; ++i)
System.Console.WriteLine("RHO" + (i+1) + " = " + x[rho[i]]);
for (int i = 0; i < theta.Length; ++i)
System.Console.WriteLine("THETA" + (i + 1) + " = " + x[theta[i]]);
}
}
}
}
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