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Ignore:
Timestamp:
01/03/19 19:05:37 (6 years ago)
Author:
gkronber
Message:

#2957: merged r16264, r16394, r16431 from trunk to stable

Location:
stable
Files:
7 edited
1 copied

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  • stable

  • stable/HeuristicLab.Problems.Instances.DataAnalysis

  • stable/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/Physics/AircraftLift.cs

    r16264 r16495  
    2626
    2727namespace HeuristicLab.Problems.Instances.DataAnalysis {
    28   class AircraftLift : ArtificialRegressionDataDescriptor {
    29     public override string Name { get { return "Aircraft Lift Coefficient C_L = x1*(x2 - 2) + x3*x4*x5/x6"; } }
     28  public class AircraftLift : ArtificialRegressionDataDescriptor {
     29    public override string Name { get { return "Aircraft Lift Coefficient C_L = C_La (a - a0) + C_Ld_e d_e S_HT / S_ref"; } }
    3030
    3131    public override string Description {
    3232      get {
    33         return "A full description of this problem instance is given in the paper: A multilevel block building algorithm for fast modeling generalized separable systems. " + Environment.NewLine +
    34                "Authors: Chen Chen, Changtong Luo, Zonglin Jiang" + Environment.NewLine +
    35                "Function: f(X) = x1*(x2 - 2) + x3*x4*x5/x6" + Environment.NewLine +
    36                "with x1 in [0.4, 0.8], x2 in [5, 10], x3 in [0.4, 0.8], x4 in [5, 10], x5 in [1, 1.5], x6 in [5, 7]";
     33        return "A full description of this problem instance is given in: " + Environment.NewLine +
     34          "Chen Chen, Changtong Luo, Zonglin Jiang, \"A multilevel block building algorithm for fast " +
     35          "modeling generalized separable systems\", Expert Systems with Applications, Volume 109, 2018, " +
     36          "Pages 25-34 https://doi.org/10.1016/j.eswa.2018.05.021. " + Environment.NewLine +
     37          "Function: C_L = C_La (a - a0) + C_Ld_e d_e S_HT / S_ref" + Environment.NewLine +
     38          "with C_La ∈ [0.4, 0.8]," + Environment.NewLine +
     39          "a ∈ [5°, 10°]," + Environment.NewLine +
     40          "C_Ld_e ∈ [0.4, 0.8]," + Environment.NewLine +
     41          "d_e ∈ [5°, 10°]," + Environment.NewLine +
     42          "S_HT ∈ [1m², 1.5m²]," + Environment.NewLine +
     43          "S_ref ∈ [5m², 7m²]," + Environment.NewLine +
     44          "a0 is set to -2°";
    3745      }
    3846    }
    3947
    40     protected override string TargetVariable { get { return "f(X)"; } }
    41     protected override string[] VariableNames { get { return new string[] { "x1", "x2", "x3", "x4", "x5", "x6", "f(X)" }; } }
    42     protected override string[] AllowedInputVariables { get { return new string[] { "x1", "x2", "x3", "x4", "x5", "x6" }; } }
     48    protected override string TargetVariable { get { return "C_L"; } }
     49    protected override string[] VariableNames { get { return new string[] { "C_La", "a", "a0", "C_Ld_e", "d_e", "S_HT", "C_L" }; } }
     50    protected override string[] AllowedInputVariables { get { return new string[] { "C_La", "a", "a0", "C_Ld_e", "d_e", "S_HT" }; } }
    4351    protected override int TrainingPartitionStart { get { return 0; } }
    4452    protected override int TrainingPartitionEnd { get { return 100; } }
    … …  
    5866
    5967      List<List<double>> data = new List<List<double>>();
    60       var x1 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.4, 0.8).ToList();
    61       var x2 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 10.0).ToList();
    62       var x3 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.4, 0.8).ToList();
    63       var x4 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 10.0).ToList();
    64       var x5 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 1.0, 1.5).ToList();
    65       var x6 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 7.0).ToList();
     68      var C_La = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.4, 0.8).ToList();
     69      var a = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 10.0).ToList();
     70      var C_Ld_e = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.4, 0.8).ToList();
     71      var d_e = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 10.0).ToList();
     72      var S_HT = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 1.0, 1.5).ToList();
     73      var S_ref = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 7.0).ToList();
    6674
    67       List<double> fx = new List<double>();
    68       data.Add(x1);
    69       data.Add(x2);
    70       data.Add(x3);
    71       data.Add(x4);
    72       data.Add(x5);
    73       data.Add(x6);
    74       data.Add(fx);
     75      List<double> C_L = new List<double>();
     76      data.Add(C_La);
     77      data.Add(a);
     78      data.Add(C_Ld_e);
     79      data.Add(d_e);
     80      data.Add(S_HT);
     81      data.Add(S_ref);
     82      data.Add(C_L);
    7583
    76       for (int i = 0; i < x1.Count; i++) {
    77         double fxi = x1[i] * (x2[i] - 2.0) + x3[i] * x4[i] * x5[i] / x6[i];
    78         fx.Add(fxi);
     84      double a0 = -2.0;
     85
     86      for (int i = 0; i < C_La.Count; i++) {
     87        double C_Li = C_La[i] * (a[i] - a0) + C_Ld_e[i] * d_e[i] * S_HT[i] / S_ref[i];
     88        C_L.Add(C_Li);
    7989      }
    8090

  • stable/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/Physics/AircraftMaximumLift.cs

    r16264 r16495  
    2626
    2727namespace HeuristicLab.Problems.Instances.DataAnalysis {
    28   class AircraftMaximumLift : ArtificialRegressionDataDescriptor {
    29     public override string Name { get { return "Aircraft Maximum Lift Coefficient"; } }
     28  public class AircraftMaximumLift : ArtificialRegressionDataDescriptor {
     29    public override string Name { get { return "Aircraft Maximum Lift Coefficient f(X) = x1 - 1/4 x4 x5 x6 (4 + 0.1 x2/x3 - x2²/x3²) + x13 x14/x15 x18 x7 - x13 x14/x15 x8 + x13 x14/x15 x9 + x16 x17/x15 x18 x10 - x16 x17/x15 x11 + x16 x17/x15 x12"; } }
    3030
    3131    public override string Description {
    3232      get {
    33         return "A full description of this problem instance is given in the paper: A multilevel block building algorithm for fast modeling generalized separable systems. " + Environment.NewLine +
    34                "Authors: Chen Chen, Changtong Luo, Zonglin Jiang" + Environment.NewLine +
    35                "Function: f(X) = x1 - 0.25 x4 x5 x6 (4 + 0.1 x2/x3 - x2²/x3²) + x13 x14/x15 x18 x7 - x13 x14/x15 x8 + x13 x14/x15 x9 + x16 x17/x15 x18 x10 - x16 x17/x15 x11 + x16 x17/x15 x12" + Environment.NewLine +
    36                "with x1 in [0.4, 0.8], " +
    37                "x2 in [3, 4], " +
    38                "x3 in [20, 30], " +
    39                "x4, x13, x16 in [2, 5]," +
    40                "x14, x17 in [1, 1.5], " +
    41                "x15 in [5, 7]," +
    42                "x18 in [10, 20]," +
    43                "x8, x11 in [1, 1.5]," +
    44                "x9, x12 in [1, 2]," +
    45                "x7, x10 in [0.5, 1.5]";
     33        return "Slightly changed version of the problem instance given in: " + Environment.NewLine +
     34          "Chen Chen, Changtong Luo, Zonglin Jiang, \"A multilevel block building algorithm for fast " +
     35          "modeling generalized separable systems\", " +
     36          "pre-print on arXiv: https://arxiv.org/abs/1706.02281 ." + Environment.NewLine +
     37          "Notably, this problem is missing from the peer-reviewed version of the article in Expert Systems with Applications, Volume 109" + Environment.NewLine +
     38          "Function: f(X) = x1 - 0.25 x4 x5 x6 (4 + 0.1 x2/x3 - x2²/x3²) + x13 x14/x15 x18 x7 - x13 x14/x15 x8 + x13 x14/x15 x9 + x16 x17/x15 x18 x10 - x16 x17/x15 x11 + x16 x17/x15 x12" + Environment.NewLine +
     39          "with x1 ∈ [0.4, 0.8]," + Environment.NewLine +
     40          "x2 ∈ [3, 4]," + Environment.NewLine +
     41          "x3 ∈ [20, 30]," + Environment.NewLine +
     42          "x4, x13, x16 ∈ [2, 5]," + Environment.NewLine +
     43          "x14, x17 ∈ [1, 1.5]," + Environment.NewLine +
     44          "x15 ∈ [5, 7]," + Environment.NewLine +
     45          "x18 ∈ [10, 20]," + Environment.NewLine +
     46          "x8, x11 ∈ [1, 1.5]," + Environment.NewLine +
     47          "x9, x12 ∈ [1, 2]," + Environment.NewLine +
     48          "x7, x10 ∈ [0.5, 1.5]." + Environment.NewLine +
     49          "Values for x5 and x6 have not been specified in the reference paper." +
     50          " We therefore only use a single (x5) variable in place of ∆αW/c and set x6 to a constant value of 1.0." + Environment.NewLine +
     51          "The range for x5 is [0..20].";
    4652      }
    4753    }
    … …  
    7884
    7985
    80       var x5 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 1.0, 1.5).ToList(); // TODO: range for X5 is not specified in the paper
    81       var x6 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 7.0).ToList(); // TODO: range for X6 is not specified in the paper
     86      // in the reference paper \Delta alpha_w/c is replaced by two variables x5*x6.
     87      var x5 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0, 20).ToList(); // range for X5 is not specified in the paper, we use [0°..20°] for ∆αW/c
     88      var x6 = Enumerable.Repeat(1.0, x5.Count).ToList(); // range for X6 is not specified in the paper. In the maximum lift formular there is only a single variable ∆αW/c in place of x5*x6.
    8289
    8390      var x7 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.5, 1.5).ToList();
    … …  
    96103
    97104      var x18 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 10.0, 20.0).ToList();
     105
    98106
    99107      List<double> fx = new List<double>();

  • stable/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/Physics/FluidDynamics.cs

    r16264 r16495  
    2626
    2727namespace HeuristicLab.Problems.Instances.DataAnalysis {
    28   class FluidDynamics : ArtificialRegressionDataDescriptor {
    29     public override string Name { get { return "Flow psi = x1*x2*x5*(1 - x4²/x5²) + 1/(2*Pi) * x3*log(x5/x4)"; } }
     28  public class FluidDynamics : ArtificialRegressionDataDescriptor {
     29    public override string Name { get { return "Flow Psi = V_inf r sin(th) (1 - R²/r²) + G/(2 π) ln(r/R)"; } }
    3030
    3131    public override string Description {
    3232      get {
    33         return "A full description of this problem instance is given in the paper: A multilevel block building algorithm for fast modeling generalized separable systems. " + Environment.NewLine +
    34                "Authors: Chen Chen, Changtong Luo, Zonglin Jiang" + Environment.NewLine +
    35                "Function: f(X) = x1*x2*x5*(1 - x4²/x5²) + 1/(2*Pi) * x3*log(x5/x4)" + Environment.NewLine +
    36                "with x1 in [60,65], x2 in [30, 40], x3 in [5,10], x4 in [0.5,0.8], x5 in [0.2,0.5]";
     33        return "A full description of this problem instance is given in: " + Environment.NewLine +
     34          "Chen Chen, Changtong Luo, Zonglin Jiang, \"A multilevel block building algorithm for fast " +
     35          "modeling generalized separable systems\", Expert Systems with Applications, Volume 109, 2018, " +
     36          "Pages 25-34 https://doi.org/10.1016/j.eswa.2018.05.021. " + Environment.NewLine +
     37          "Function: Psi = V_inf r sin(th) (1 - R²/r²) + G/(2 π) ln(r/R)" + Environment.NewLine +
     38          "with V_inf ∈ [60 m/s, 65 m/s]," + Environment.NewLine +
     39          "th ∈ [30°, 40°]," + Environment.NewLine +
     40          "r ∈ [0.2m, 0.5m]," + Environment.NewLine +
     41          "R ∈ [0.5m, 0.8m]," + Environment.NewLine +
     42          "G ∈ [5 m²/s, 10 m²/s]";
    3743      }
    3844    }
    3945
    40     protected override string TargetVariable { get { return "f(X)"; } }
    41     protected override string[] VariableNames { get { return new string[] { "x1", "x2", "x3", "x4", "x5", "f(X)" }; } }
    42     protected override string[] AllowedInputVariables { get { return new string[] { "x1", "x2", "x3", "x4", "x5" }; } }
     46    protected override string TargetVariable { get { return "Psi"; } }
     47    protected override string[] VariableNames { get { return new string[] { "V_inf", "th", "r", "R", "G", "Psi" }; } }
     48    protected override string[] AllowedInputVariables { get { return new string[] { "V_inf", "th", "r", "R", "G" }; } }
    4349    protected override int TrainingPartitionStart { get { return 0; } }
    4450    protected override int TrainingPartitionEnd { get { return 100; } }
    … …  
    5864
    5965      List<List<double>> data = new List<List<double>>();
    60       var x1 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 60.0, 65.0).ToList();
    61       var x2 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 30.0, 40.0).ToList();
    62       var x3 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5.0, 10.0).ToList();
    63       var x4 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.5, 0.8).ToList();
    64       var x5 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.2, 0.5).ToList();
     66      var V_inf = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 60.0, 65.0).ToList();
     67      var th = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 30.0, 40.0).ToList();
     68      var r = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.2, 0.5).ToList();
     69      var R = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.5, 0.8).ToList();
     70      var G = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 5, 10).ToList();
    6571
    66       List<double> fx = new List<double>();
    67       data.Add(x1);
    68       data.Add(x2);
    69       data.Add(x3);
    70       data.Add(x4);
    71       data.Add(x5);
    72       data.Add(fx);
     72      List<double> Psi = new List<double>();
     73      data.Add(V_inf);
     74      data.Add(th);
     75      data.Add(r);
     76      data.Add(R);
     77      data.Add(G);
     78      data.Add(Psi);
    7379
    74       for (int i = 0; i < x1.Count; i++) {
    75         double fxi = x1[i] * x2[i] * x5[i] * (1 - (x4[i] * x4[i]) / (x5[i] * x5[i])) +
    76                      (1 / (2 * Math.PI)) * x3[i] * Math.Log(x5[i] / x4[i]);
    77         fx.Add(fxi);
     80      for (int i = 0; i < V_inf.Count; i++) {
     81        var th_rad = Math.PI * th[i] / 180.0;
     82        double Psi_i = V_inf[i] * r[i] * Math.Sin(th_rad) * (1 - (R[i] * R[i]) / (r[i] * r[i])) +
     83                     (G[i] / (2 * Math.PI)) * Math.Log(r[i] / R[i]);
     84        Psi.Add(Psi_i);
    7885      }
    7986

  • stable/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/Physics/PhysicsInstanceProvider.cs

    r16264 r16495  
    2222using System;
    2323using System.Collections.Generic;
     24using HeuristicLab.Random;
    2425
    2526namespace HeuristicLab.Problems.Instances.DataAnalysis {
    26   class PhysicsInstanceProvider : ArtificialRegressionInstanceProvider {
     27  public class PhysicsInstanceProvider : ArtificialRegressionInstanceProvider {
     28    public override string Name { get { return "Physics Benchmark Problems"; } }
     29    public override string Description { get { return ""; } }
     30    public override Uri WebLink { get { return new Uri(@"https://doi.org/10.1016/j.eswa.2018.05.021"); } }
     31    public override string ReferencePublication {
     32      get {
     33        return "Chen Chen, Changtong Luo, Zonglin Jiang, \"A multilevel block building algorithm for fast modeling generalized separable systems\", Expert Systems with Applications, Volume 109, 2018, Pages 25-34 https://doi.org/10.1016/j.eswa.2018.05.021 as well as the (slightly different) pre-print on arXiv: https://arxiv.org/abs/1706.02281";
     34      }
     35    }
     36
     37    public int Seed { get; private set; }
     38
     39    public PhysicsInstanceProvider() : this((int)DateTime.Now.Ticks) { }
     40
     41    public PhysicsInstanceProvider(int seed) : base() {
     42      Seed = seed;
     43    }
     44
    2745    public override IEnumerable<IDataDescriptor> GetDataDescriptors() {
     46      var rand = new FastRandom(Seed);
     47
    2848      return new List<IDataDescriptor>()
    2949      {
    30          new RocketFuelFlow(123),
    31          new AircraftLift(456),
    32          new FluidDynamics(789),
    33          new AircraftMaximumLift(321)
     50         new RocketFuelFlow(rand.Next()),
     51         new AircraftLift(rand.Next()),
     52         new FluidDynamics(rand.Next()),
     53         new AircraftMaximumLift(rand.Next())
    3454      };
    35     }
    36 
    37     public override string Name { get { return "Physics Benchmark Problems"; } }
    38     public override string Description { get { return ""; } }
    39     public override Uri WebLink { get { return new Uri(@"https://arxiv.org/abs/1706.02281"); } }
    40     public override string ReferencePublication {
    41       get {
    42         return "Chen Chen, Changtong Luo, Zonglin Jiang, 2017 " +
    43 "\"A multilevel block search algorithm for fast modeling generalized separable systems.\" arXiv preprint arXiv:1706.02281, v3";
    44       }
    4555    }
    4656  }

  • stable/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/Physics/RocketFuelFlow.cs

    r16264 r16495  
    2626
    2727namespace HeuristicLab.Problems.Instances.DataAnalysis {
    28   class RocketFuelFlow : ArtificialRegressionDataDescriptor {
    29     public override string Name { get { return "Rocket Fuel Flow f(X) = 4000*x1*x2/sqrt(x3)"; } }
     28  public class RocketFuelFlow : ArtificialRegressionDataDescriptor {
     29    public override string Name { get { return "Rocket Fuel Flow m_dot = p0 A / sqrt(T0) * sqrt(γ/R (2/(γ+1))^((γ+1) / (γ-1)))"; } }
    3030
    3131    public override string Description {
    3232      get {
    33         return "A full description of this problem instance is given in the paper: A multilevel block building algorithm for fast modeling generalized separable systems. " + Environment.NewLine +
    34                "Authors: Chen Chen, Changtong Luo, Zonglin Jiang" + Environment.NewLine +
    35                "Function: f(X) = 4000*x1*x2/sqrt(x3)" + Environment.NewLine +
    36                "with x1 in [4,6], x2 in [0.5, 1.5], x3 in [250,260]";
     33        return "A full description of this problem instance is given in: " + Environment.NewLine +
     34          "Chen Chen, Changtong Luo, Zonglin Jiang, \"A multilevel block building algorithm for fast " +
     35          "modeling generalized separable systems\", Expert Systems with Applications, Volume 109, 2018, " +
     36          "Pages 25-34 https://doi.org/10.1016/j.eswa.2018.05.021. " + Environment.NewLine +
     37          "Function: m_dot = p0 A / sqrt(T0) * sqrt(γ/R (2/(γ+1))^((γ+1) / (γ-1)))" + Environment.NewLine +
     38          "with p0 ∈ [4e5 Pa, 6e5 Pa]," + Environment.NewLine +
     39          "A ∈ [0.5m², 1.5m²]," + Environment.NewLine +
     40          "T0 ∈ [250°K, 260°K]," + Environment.NewLine +
     41          "γ=1.4 and R=287 J/(kg*K)" + Environment.NewLine +
     42          "The factor sqrt(γ/R (2/(γ+1))^((γ+1) / (γ-1))) is constant as γ and R are constants.";
    3743      }
    3844    }
    3945
    40     protected override string TargetVariable { get { return "f(X)"; } }
    41     protected override string[] VariableNames { get { return new string[] { "x1", "x2", "x3", "f(X)" }; } }
    42     protected override string[] AllowedInputVariables { get { return new string[] { "x1", "x2", "x3" }; } }
     46    protected override string TargetVariable { get { return "m_dot"; } }
     47    protected override string[] VariableNames { get { return new string[] { "p0", "A", "T0", "m_dot" }; } }
     48    protected override string[] AllowedInputVariables { get { return new string[] { "p0", "A", "T0" }; } }
    4349    protected override int TrainingPartitionStart { get { return 0; } }
    4450    protected override int TrainingPartitionEnd { get { return 100; } }
    … …  
    5864
    5965      List<List<double>> data = new List<List<double>>();
    60       var x1 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 4.0, 6.0).ToList();
    61       var x2 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.5, 1.5).ToList();
    62       var x3 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 250.0, 260.0).ToList();
     66      var p0 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 4.0e5, 6.0e5).ToList();
     67      var A = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 0.5, 1.5).ToList();
     68      var T0 = ValueGenerator.GenerateUniformDistributedValues(rand.Next(), TestPartitionEnd, 250.0, 260.0).ToList();
    6369
    64       List<double> fx = new List<double>();
    65       data.Add(x1);
    66       data.Add(x2);
    67       data.Add(x3);
    68       data.Add(fx);
    69 
    70       for (int i = 0; i < x1.Count; i++) {
    71         double fxi = 4000 * x1[i] * x2[i] / Math.Sqrt(x3[i]);
    72         fx.Add(fxi);
     70      List<double> m_dot = new List<double>();
     71      data.Add(p0);
     72      data.Add(A);
     73      data.Add(T0);
     74      data.Add(m_dot);
     75      double R = 287.0;
     76      double γ = 1.4;
     77      var c = Math.Sqrt(γ / R * Math.Pow(2 / (γ + 1), (γ + 1) / (γ - 1)));
     78      for (int i = 0; i < p0.Count; i++) {
     79        double m_dot_i = p0[i] * A[i] / Math.Sqrt(T0[i]) * c;
     80        m_dot.Add(m_dot_i);
    7381      }
    7482
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