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Program.cs
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Program.cs
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace JA
{
using System.Diagnostics;
using JA.Parsing;
static class Program
{
static void Main(string[] args)
{
TestNamedConstants();
TestUnaryFunctions();
TestBinaryFunctions();
TestParse1();
TestParse2();
TestParse3();
TestArrayParse1();
TestArrayParse2();
TestCubicSpline();
TestMatrix();
#if DEBUG
Console.WriteLine("Press ENTER to end.");
Console.ReadLine();
#endif
}
private static void TestMatrix()
{
var A = Expr.Parse("[[1,-x],[x,2*x-1]]");
Console.WriteLine($"Matrix: {A}");
var rows = A.ToArray();
var jagged = rows.Select((row)=>row.ToArray()).ToArray();
Console.WriteLine("By Rows");
foreach (var row in A.ToArray())
{
foreach (var item in row.ToArray())
{
Console.Write($"{item,-7} ");
}
Console.WriteLine();
}
Console.WriteLine($"tr(A)={Expr.Transpose(A)}");
var B = A.Partial("x");
Console.WriteLine($"Rate: {B}");
var input = "tr([[1,2],[3,4]])/4";
Console.WriteLine($"Input: F={input}");
var F = Expr.Parse(input);
Console.WriteLine($"F={F}");
}
static void TestNamedConstants()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Named Constants:");
Console.ForegroundColor = ConsoleColor.Gray;
foreach (var (sym, val) in Expr.Constants)
{
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.Write($"{sym,5}");
Console.ForegroundColor = ConsoleColor.Gray;
Console.Write($" = ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"{val}");
}
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine();
Console.WriteLine("Test Substitutions:");
Console.ForegroundColor = ConsoleColor.Cyan;
Expr expr = "(2*x+1)/(y^2+1)";
Console.WriteLine($"f={expr}");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.Write($"Substitute: x=>10, ");
Expr sub = expr.Substitute("x", 10);
Console.WriteLine($"f={sub}");
Console.ForegroundColor = ConsoleColor.DarkMagenta;
Console.Write($"Substitute: x=>z/2, ");
sub = expr.Substitute("x", "z/2");
Console.WriteLine($"f={sub}");
Console.ForegroundColor = ConsoleColor.DarkYellow;
Console.Write($"Substitute: x=>0.5*y-1, ");
sub = expr.Substitute("x", "0.5*y-1");
Console.WriteLine($"f={sub}");
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.Write($"Substitute: y=>sqrt(x), ");
sub = expr.Substitute("y", "sqrt(x)");
Console.WriteLine($"f={sub}");
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine();
}
static void TestUnaryFunctions()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Unary Functions:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr a = "a";
double x = 2/Math.PI;
string fstr = $"f({x})", fpstr = $"f'({x})";
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{"f",-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"f'",-28} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{fstr,-22} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fpstr,-28}");
Console.WriteLine();
foreach (var op in Enum.GetValues(typeof(UnaryOp)) as UnaryOp[])
{
if (op==UnaryOp.Undefined) continue;
if (op==UnaryOp.Sum) continue;
if (op==UnaryOp.Transpose) continue;
var f_expr = Expr.Unary(op, a);
var dfda = f_expr.Partial(a);
var f = f_expr[a];
var fp = dfda[a];
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{f_expr,-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{dfda,-28:g4} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{f(x),-22:g4} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fp(x),-28:g4}");
Console.WriteLine();
}
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine();
}
static void TestBinaryFunctions()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Binary Functions:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr a = "a", b = "b";
double x = 5, y = 2;
string fstr = $"f({x},{y})", fpstr = $"f'({x},{y})";
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{"f",-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"f'",-28} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{fstr,-22} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fpstr,-28}");
Console.WriteLine();
foreach (var op in Enum.GetValues(typeof(BinaryOp)) as BinaryOp[])
{
if (op==BinaryOp.Undefined) continue;
var f_expr = Expr.Binary(op, a, b);
var dfda = f_expr.Partial(a);
var f = f_expr[a, b];
var fp = dfda[a, b];
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{f_expr,-12} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{dfda,-28:g4} ");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{f(x,y),-22:g4} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{fp(x,y),-28:g4}");
Console.WriteLine();
}
Console.WriteLine();
}
static void TestParse1()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Parsing Strings");
Console.ForegroundColor = ConsoleColor.Gray;
var pi = Expr.Const("pi");
Console.WriteLine($"π={pi.Value}");
var s_input = "x+y+z";
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"Input: {s_input}");
var s_expr = Expr.Parse(s_input);
Console.WriteLine($"Expr: {s_expr}");
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine($"vars={string.Join(",", s_expr.GetVariables().AsEnumerable())}");
var f_input = "2.5*(1-exp(-π*t))";
Console.WriteLine($"Input: {f_input}");
var f_expr = Expr.Parse(f_input);
var f_fun = f_expr.GetFunction("t");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"x={f_expr}");
Console.ForegroundColor = ConsoleColor.Green;
Console.WriteLine($"{"t",-12} {"x",-12}");
for (int i = 0; i < 10; i++)
{
var t = 0.125 * i-0.5;
var x = f_fun(t);
Console.WriteLine($"{t,-12:g4} {x,-12:g4}");
}
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine();
}
static void TestParse2()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Multivariate Calculus:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr x = "x", y="y";
Console.ForegroundColor = ConsoleColor.Cyan;
var w_input = "x^2 + 2*x*y + x/y";
Console.WriteLine($"Input: {w_input}");
Console.ForegroundColor = ConsoleColor.Gray;
var w = Expr.Parse(w_input);
Console.WriteLine($"w={w}");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.WriteLine($"vars={string.Join(",", w.GetVariables().AsEnumerable())}");
Console.ForegroundColor = ConsoleColor.Gray;
var wx = w.Partial(x);
Console.WriteLine($"wx={wx}");
var wy = w.Partial(y);
Console.WriteLine($"wy={wy}");
var wp = w.TotalDerivative(x, y);
Console.WriteLine($"wp={wp}");
var f_input = "(x^2-pi)/(x^2+pi)";
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"Input: {f_input}");
Console.ForegroundColor = ConsoleColor.Gray;
var f = Expr.Parse(f_input);
Console.WriteLine($"f={f}");
var fx = f["x"];
Console.WriteLine($"f(0.5)={fx(0.5)}");
Console.ForegroundColor = ConsoleColor.DarkGreen;
var df = f.Partial(x);
Console.WriteLine($"df={df}");
Console.ForegroundColor = ConsoleColor.DarkYellow;
var fp = f.TotalDerivative();
Console.WriteLine($"fp={fp}");
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine();
}
static void TestParse3()
{
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Test Kinematics:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr q = "q", r = "r";
VariableExpr qp = q.Rate(), rp = r.Rate();
VariableExpr qpp = qp.Rate(), rpp = rp.Rate();
Console.ForegroundColor = ConsoleColor.DarkYellow;
Console.WriteLine($"Variables: {string.Join(", ", q, r)}");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.WriteLine($"Rates: {string.Join(", ", qp, rp)}");
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.WriteLine($"Accelerations: {string.Join(", ", qpp, rpp)}");
Expr pos = Expr.FromArray(r*Expr.Sin(q), -r*Expr.Cos(q));
Console.ForegroundColor = ConsoleColor.Yellow;
Console.WriteLine($"pos = {pos}");
Console.ForegroundColor = ConsoleColor.Cyan;
Expr vel = pos.TotalDerivative();
Console.WriteLine($"vel = {vel}");
Console.ForegroundColor = ConsoleColor.Blue;
Expr J = vel.Jacobian(rp,qp);
Console.WriteLine($"jacobian = {J}");
Console.ForegroundColor = ConsoleColor.Green;
Expr acc = vel.TotalDerivative();
Console.WriteLine($"acc = {acc}");
Console.WriteLine();
}
static void TestArrayParse1()
{
const int colWidth = 12;
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Vectorizing Array Parsing:");
Console.ForegroundColor = ConsoleColor.Gray;
var input = @"[x^3,6*x^2*(1-x),6*x*(1-x)^2,(1-x)^3]/6";
Console.WriteLine($"Input: {input}");
var expr = Expr.Parse(input);
Console.WriteLine($"y={expr}");
var f_expr = expr.GetArray("x");
var d_expr = expr.TotalDerivative();
Console.WriteLine($"dy={expr}");
var sum_expr = Expr.Sum(expr);
var f_sum = sum_expr.GetFunction("x");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"Σy={sum_expr}");
Console.ForegroundColor = ConsoleColor.Gray;
var d_sum_expr = sum_expr.Partial("x");
var df_sum = d_sum_expr.GetFunction("x");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine($"dΣy={d_sum_expr}");
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{"x",-colWidth} ");
Console.ForegroundColor = ConsoleColor.Yellow;
for (int j = 0; j < expr.ResultCount; j++)
{
var str = $"y[{j}]";
Console.Write($"{str,-colWidth} ");
}
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"Σy",-colWidth} ");
Console.Write($"{"dΣy/dx",-colWidth} ");
Console.WriteLine();
const int n = 12;
for (int i = 0; i <= n; i++)
{
Console.ForegroundColor = ConsoleColor.Gray;
double x_i = (double)i/n;
Console.ForegroundColor = ConsoleColor.Magenta;
Console.Write($"{x_i,-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.Yellow;
double[] y_i = f_expr(x_i);
for (int j = 0; j < y_i.Length; j++)
{
Console.Write($"{y_i[j],-colWidth:g4} ");
}
Console.ForegroundColor = ConsoleColor.Cyan;
double Sy = f_sum(x_i), dSy = df_sum(x_i);
Console.Write($"{Sy,-colWidth:g4} ");
Console.Write($"{dSy,-colWidth:g4} ");
Console.WriteLine();
}
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine("Dot Product:");
var ex1 = Expr.FromArray(1, Expr.Sin("x"), Expr.Cos("x"));
var ex2 = Expr.FromArray("c_0", "c_1", "c_2");
Console.WriteLine($"ex1={ex1}");
Console.WriteLine($"ex2={ex2}");
var y = Expr.Dot(ex1, ex2);
Console.WriteLine($"Dot(ex1,ex2)={y}");
var d_y = y.Partial("x");
Console.WriteLine($"dy/dx={d_y}");
var yp = y.TotalDerivative();
Console.WriteLine($"yp={yp}");
Console.WriteLine();
}
static void TestArrayParse2()
{
const int colWidth = 12;
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Mismatch Array Parsing:");
Console.ForegroundColor = ConsoleColor.Gray;
var input = @"[x, 1-x] + [1,2,3]";
Console.WriteLine($"Input: {input}");
var expr = Expr.Parse(input);
Console.ForegroundColor = ConsoleColor.Yellow;
Console.WriteLine($"y={expr}");
Console.ForegroundColor = ConsoleColor.Gray;
var f_expr = expr.GetArray("x");
var sum_expr = Expr.Sum(expr);
var f_sum = sum_expr.GetFunction("x");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.WriteLine($"Σy={sum_expr}");
var d_sum_expr = sum_expr.Partial("x");
var df_sum = d_sum_expr.GetFunction("x");
Console.ForegroundColor = ConsoleColor.Green;
Console.WriteLine($"dΣy={d_sum_expr}");
Console.ForegroundColor = ConsoleColor.DarkGray;
Console.Write($"{"x",-colWidth} ");
Console.ForegroundColor = ConsoleColor.DarkMagenta;
for (int j = 0; j < expr.ResultCount; j++)
{
var str = $"y[{j}]";
Console.Write($"{str,-colWidth} ");
}
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"Σy",-colWidth} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{"dΣy/dx",-colWidth} ");
Console.WriteLine();
const int n = 4;
for (int i = 0; i <= n; i++)
{
double x = (double)i/n;
Console.ForegroundColor = ConsoleColor.Gray;
Console.Write($"{x,-colWidth:g4} ");
double[] y = f_expr(x);
Console.ForegroundColor = ConsoleColor.Magenta;
for (int j = 0; j < y.Length; j++)
{
Console.Write($"{y[j],-colWidth:g4} ");
}
double Sy = f_sum(x), dSy = df_sum(x);
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{Sy,-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{dSy,-colWidth:g4} ");
Console.WriteLine();
}
Console.WriteLine();
}
static void TestCubicSpline()
{
const int colWidth = 12;
Console.ForegroundColor = ConsoleColor.White;
Console.WriteLine("Cubic Spline:");
Console.ForegroundColor = ConsoleColor.Gray;
VariableExpr a = "a";
var xi = new double[] {0, 2};
var yi = new double[] {1, 7};
var ypi = new double[] {0, 0};
var h = xi[1]-xi[0];
Console.WriteLine("Given Boundary Conditions:");
Console.ForegroundColor = ConsoleColor.DarkYellow;
Console.Write($"{"x",-colWidth} ");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.Write($"{"y",-colWidth} ");
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.Write($"{"yp",-colWidth} ");
Console.WriteLine();
for (int i = 0; i < xi.Length; i++)
{
Console.ForegroundColor = ConsoleColor.DarkYellow;
Console.Write($"{xi[i],-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.DarkCyan;
Console.Write($"{yi[i],-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.Write($"{ypi[i],-colWidth:g4} ");
Console.WriteLine();
}
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine("Calculated Interpolation:");
Expr ξ = a/h;
var basis = Expr.FromArray(
((1-ξ)^2)*(2*ξ+1),
(ξ^2)*(3-2*ξ),
h*ξ*((1-ξ)^2),
h*(ξ^2)*(ξ-1));
var coef = new Expr[] { yi[0], yi[1], ypi[0], ypi[1] };
Expr y_expr = Expr.Dot(basis, coef);
Console.WriteLine($"y={y_expr}");
var y_fun = y_expr["a"];
Expr dy_expr = y_expr.Partial("a");
Console.WriteLine($"yp={dy_expr}");
var dy_fun = dy_expr["a"];
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{"x",-colWidth} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{"y",-colWidth} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{"yp",-colWidth} ");
Console.WriteLine();
for (int i = 0; i < 12; i++)
{
double t = (double)i/11;
double x = (1-t)*xi[0] + t*xi[1];
double y = y_fun(x);
double yp = dy_fun(x);
Console.ForegroundColor = ConsoleColor.Yellow;
Console.Write($"{x,-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.Cyan;
Console.Write($"{y,-colWidth:g4} ");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write($"{yp,-colWidth:g4} ");
Console.WriteLine();
}
Console.ForegroundColor = ConsoleColor.Gray;
}
}
}