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Working on amcli info #4

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a6e2398
Working on amcli info
WhiteBlackGoose Nov 16, 2022
266e2bc
extrema analysis
WhiteBlackGoose Nov 16, 2022
557e83e
Improved, WIP
WhiteBlackGoose Nov 17, 2022
b63d505
upd
WhiteBlackGoose Nov 18, 2022
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3 changes: 3 additions & 0 deletions .gitmodules
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Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
[submodule "AngouriMath"]
path = AngouriMath
url = git@github.com:asc-community/AngouriMath.git
1 change: 1 addition & 0 deletions AngouriMath
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Submodule AngouriMath added at 18c127
4 changes: 2 additions & 2 deletions CLI.csproj
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,6 @@
<TargetFramework>net7.0</TargetFramework>
<ImplicitUsings>enable</ImplicitUsings>
<Nullable>enable</Nullable>

<SelfContained>true</SelfContained>
<PublishAot>true</PublishAot>
<PublishTrimmed>true</PublishTrimmed>
Expand All @@ -17,8 +16,9 @@
</PropertyGroup>

<ItemGroup>
<PackageReference Include="AngouriMath" Version="10.0.0-master-1664389750-0b77b8d" />
<Compile Remove="**/publishing/**" />
<Compile Remove="AngouriMath/**" />
<ProjectReference Include="./AngouriMath/Sources/AngouriMath/AngouriMath/AngouriMath.csproj" />
</ItemGroup>

</Project>
153 changes: 148 additions & 5 deletions Program.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -16,13 +16,15 @@

using AngouriMath;
using AngouriMath.Extensions;
using HonkSharp;
using HonkSharp.Functional;
using HonkSharp.Fluency;
using PeterO.Numbers;

var cliArgs = System.Environment.GetCommandLineArgs();
var reader = new ArgReader(cliArgs);


IArgReader reader = new ArgReader(cliArgs);
// IArgReader reader = new ArgReader(new [] { "", "info", "-66 x_1 2 - 6 x_1 x_2 + 24 x_1 x_3 - 12 x_1 x_4 + 270 x_1 - 74 x_2 2 - 8 x_2 x_3 + 4 x_2 x_4 - 440 x_2 - 59 x_3 2 - 16 x_3 x_4 - 190 x_3 - 71 x_4 2 + 20 x_4" });
var prec = GetEnv<int>("AMCLI_PRECISION", 20);
MathS.Settings.DecimalPrecisionContext.Set(new EContext(prec, ERounding.HalfUp, -prec, 10 * prec, false));
Entity expr;
Entity.Variable v;
string res;
Expand Down Expand Up @@ -170,6 +172,13 @@ is equivalent to
Here the result of `echo` is substituted instead of the second argument
of `amcli sub`, not the last one.

SETTINGS

All settings are set using environment variables.

AMCLI_PRECISION - precision/number of digits in decimal numbers.
Default - 100.

OTHER

You can bind amcli to @ using aliases. On Unix-like operating systems,
Expand Down Expand Up @@ -228,12 +237,141 @@ Here the result of `echo` is substituted instead of the second argument
Console.WriteLine(expr.Substitute(v, withWhat));
break;

case "info":
expr = reader.Next();
var splitter = new string('-', 20);
Console.WriteLine($"expr: {expr}");
Console.WriteLine(splitter);
Console.WriteLine($"vars: {expr.Vars.ToLList()}");
Console.WriteLine(splitter);
var vars = expr.Vars.ToArray();
foreach (var vx in vars)
{
Console.Write($"diff over {vx}: ");
Console.WriteLine(expr.Differentiate(vx).InnerSimplified);
Console.WriteLine(splitter);
}
foreach (var vx in vars)
{
Console.Write($"roots over {vx}: ");
Console.WriteLine(expr.Equalizes(0).Solve(vx).InnerSimplified);
Console.WriteLine(splitter);
}
if (vars.Length is 1)
{
var fx = expr.Differentiate(vars[0]);
var crit = fx.Equalizes(0).Solve(vars[0]);
if (crit is not Entity.Set.FiniteSet fins)
goto notOneVar;
var fxx = fx.Differentiate(vars[0]);
foreach (var (i, sol) in fins.Enumerate())
{
Console.WriteLine($"Extremum #{i}");
Console.WriteLine($"Point: {sol}");
Console.WriteLine($"Value: {expr.Substitute(vars[0], sol).Evaled}");
var fxxValue = fxx.Substitute(vars[0], sol).EvalNumerical();
Console.WriteLine($"2nd derivative value: {fxxValue}");
Console.Write("Type of extremum: ");
if (fxxValue is not Entity.Number.Real rVal)
continue;
if (rVal == 0)
Console.WriteLine("Saddle");
if ((double)rVal > 0.0)
Console.WriteLine("Minimum");
if ((double)rVal < 0.0)
Console.WriteLine("Maximum");
Console.WriteLine();
}
}
notOneVar:
if (vars.Length is > 1)
{
var diffs = new List<Entity>();
foreach (var vx in vars)
diffs.Add(expr.Differentiate(vx).InnerSimplified);

var system = MathS.Equations((IEnumerable<Entity>)diffs);
Console.WriteLine("First order condition:");
Console.WriteLine(system);
var sols2 = system.Solve(vars);
if (sols2 is null)
{
Console.WriteLine("amcli wasn't able to find any extremas");
break;
}

var hessian = new Entity.Matrix(dims =>
expr
.Differentiate(vars[dims[0]])
.Differentiate(vars[dims[1]])
.InnerSimplified,
vars.Length,
vars.Length);

foreach (var (i, sol) in sols2.Enumerate())
{
var exprToSub = expr;
Entity hessianToSub = hessian;
var msol = ((Entity.Matrix)sol).T;
foreach (var (val, vr) in msol.Zip(vars))
{
exprToSub = exprToSub.Substitute(vr, val);
hessianToSub = hessianToSub.Substitute(vr, val);
}
var fValue = exprToSub.Evaled;
var hessienEvaled = (Entity.Matrix)hessianToSub.Evaled;
var det = hessienEvaled.Determinant!.EvalNumerical();
Console.WriteLine($"Extrema #{i}:");
Console.WriteLine($"Point: {msol.T}");
Console.WriteLine($"Value: {fValue}");
Console.WriteLine($"Hessien:");
Console.WriteLine(hessienEvaled.ToString(multilineFormat: true));

var uniqueVar = MathS.Var("lambda_quackfrog");
var eigenMatrix = (Entity.Matrix)(hessianToSub - MathS.IdentityMatrix(hessian.RowCount) * uniqueVar).InnerSimplified;
var eigenDet = eigenMatrix.Determinant!;
var eigenValues = eigenDet.InnerSimplified.Equalizes(0).Solve(uniqueVar).Evaled;
if (eigenValues is Entity.Set.FiniteSet eigens)
{
if (eigens.Count is 0)
Console.WriteLine("amcli wasn't able to find eigen values and the type of extremum");
else
{
Console.WriteLine($"Eigen values of hessian: {eigens}");
if (eigens.All(val => val.EvalNumerical() is Entity.Number.Real r1 && r1.IsPositive))
Console.WriteLine("Type of extremum: Minimum");
else if (eigens.All(val => val.EvalNumerical() is Entity.Number.Real r2 && r2.IsNegative))
Console.WriteLine("Type of extremum: Negative");
else if (eigens.All(val => val.EvalNumerical() is Entity.Number.Real r3 && r3.IsNegative || val.EvalNumerical() is Entity.Number.Real r4 && r4.IsPositive))
Console.WriteLine("Type of extremum: Saddle");
else
Console.WriteLine("Cannot detect type of extremum");
}
}
Console.WriteLine();
Console.WriteLine();
}
}

break;

default:
Console.WriteLine($"Unrecognized command `{cmd}`");
break;
}

public sealed class ArgReader
static T GetEnv<T>(string name, T def)
{
if (Environment.GetEnvironmentVariable(name) is not string value)
return def;
if (typeof(T) == typeof(int))
return (T)(object)int.Parse(value);
if (typeof(T) == typeof(string))
return (T)(object)value;
throw new();
}

public sealed class ArgReader : IArgReader
{
private readonly string[] args;
private int curr = 1;
Expand All @@ -252,3 +390,8 @@ public string Next()
return Console.ReadLine()!;
}
}

public interface IArgReader
{
public string Next();
}