ICpNonLinearDecomposition.Equations

Syntax

Equations: Array;

Description

The Equations property determines system equations.

Comments

Use the ICpNonLinearDecomposition.MethodType property to determine a method of solution search.

Example

The system of non-linear equations is created in this example:

Output variables: x1, x2.
Controlling variables: u, v.
Equations that form the system:
- x1[t] = 0.3 * x1[t-1] + 0.1 * x2[t+1] + u[t-1] * x1[t+1] *x2[t-1].
- x2[t] = -0.2 * x1[t-1] + 0.4 *x2[t+1] + (x1[t+1] * x2[t-1])/(v[t-1]+1).

Add links to the Cp, Stat system assemblies.

Sub UserProc;
Var
    Optima: NonLinearDecomposition;
    PeriodL, j, i: Integer;
    Vars: INonLDVariables;
    Vrbl: INonLDVariable;
    RetroX1, ForestX1: Array Of Double;
    RetroX2, ForestX2: Array Of Double;
    RetroU, ForestU: Array Of Double;
    RetroV, ForestV, InitApproximation: Array Of Double;
    Funstions: Array Of String;
    Res: INonLoResults;
    val: Double;
Begin
    Optima := New NonLinearDecomposition.Create;
    // Set value of calculation period
    PeriodL := 4;
    RetroX1 := New Double[PeriodL]; ForestX1 := New Double[PeriodL];
    RetroX2 := New Double[PeriodL]; ForestX2 := New Double[PeriodL];
    RetroU := New Double[PeriodL]; ForestU := New Double[PeriodL];
    RetroV := New Double[PeriodL]; ForestV := New Double[PeriodL];
    InitApproximation := New Double[PeriodL];
    For i := 0 To PeriodL - 1 Do
    RetroX1[i] := -2.1 - i; ForestX1[i] := 1.9 + i;
    RetroX2[i] := -2.2 - i; ForestX2[i] := 1.8 + i;
    RetroU[i] := -2.3 - i; ForestU[i] := 1.7 + i;
    RetroV[i] := -2.4 - i; ForestV[i] := 1.6 + i;
    InitApproximation[i] := 0.1;
    End For;
    // Add the first variable
    Vars := Optima.Variables;
    Vrbl := Vars.Add("x1");
    Vrbl.Retrospective := RetroX1;
    Vrbl.CoefficientsOrderRetrospective := "x1[t];x1[t-1]";
    Vrbl.Forestall := ForestX1;
    Vrbl.CoefficientsOrderForestall := "x1[t];x1[t+1]";
    Vrbl.InitApproximation := InitApproximation;
    // Add the second variable
    Vars := Optima.Variables;
    Vrbl := Vars.Add("x2");
    Vrbl.Retrospective := RetroX2;
    Vrbl.CoefficientsOrderRetrospective := "x2[t];x2[t-1]";
    Vrbl.Forestall := ForestX2;
    Vrbl.CoefficientsOrderForestall := "x2[t];x2[t+1]";
    Vrbl.InitApproximation := InitApproximation;
    // Set initial approximations for the first controlling variable
    For i := 0 To PeriodL - 1 Do
    InitApproximation[i] := 1.5 * (i + 1);
    End For;
    // Add the first controlling variable
    Vars := Optima.Variables;
    Vrbl := Vars.Add("u");
    Vrbl.Retrospective := RetroU;
    Vrbl.CoefficientsOrderRetrospective := "u[t];u[t-1]";
    Vrbl.Forestall := ForestU;
    Vrbl.CoefficientsOrderForestall := "u[t];u[t+1]";
    Vrbl.ControlVariable := True;
    Vrbl.InitApproximation := InitApproximation;
    // Set initial approximations for the second controlling variable
    For i := 0 To PeriodL - 1 Do
    InitApproximation[i] := 2 * (i + 1);
    End For;
    // Add the second controlling variable
    Vars := Optima.Variables;
    Vrbl := Vars.Add("v");
    Vrbl.Retrospective := RetroV;
    Vrbl.CoefficientsOrderRetrospective := "v[t];v[t-1]";
    Vrbl.Forestall := ForestV;
    Vrbl.CoefficientsOrderForestall := "v[t];v[t+1]";
    Vrbl.ControlVariable := True;
    Vrbl.InitApproximation := InitApproximation;
    // Create a system of non-linear equations
    Funstions := New String[2];
    Funstions[0] := "0.3 * x1[t-1] + 0.1 * x2[t+1] + u[t-1] * x1[t+1] *x2[t-1]";
    Funstions[1] := "-0.2 * x1[t-1] + 0.4 *x2[t+1] + (x1[t+1] * x2[t-1])/(v[t-1]+1)";
    Optima.Equations := Funstions;
    Optima.NodesCount := 2;
    Optima.Extremum := ExtremumType.Minimum;
    Optima.MaxIteration := 250;
    Optima.Tolerance := 0.000001;
    Optima.MethodType := NonLinearEquationsType.HMethod;
    // System calculation
    Res := Optima.Evaluate(PeriodL) As INonLoResults;
    Debug.WriteLine(Res.ErrorMsg);
    // Display results
    If (Res.Status = 0) Then
        Vars := Optima.Variables;
        For j := 0 To Vars.Count - 1 Do
            Vrbl := Vars.Item(j);
            Debug.WriteLine("Variable: " + Vrbl.Id);
            Debug.Indent;
            For i := 0 To PeriodL - 1 Do
                Val := Res.VarValues(Vrbl.Id)[i];
                Debug.WriteLine(Val);
            End For;
            Debug.Unindent;
        End For;
    End If;
End Sub UserProc;

After executing the example a system of non-linear equations is created and calculated. Calculation results are displayed in the console window.