public void GetExceptionExtrapolatingValues2ArgsFunction()
{
IVariable <double> x = new Variable <double>("x");
IVariable <double> y = new Variable <double>("y");
IVariable <double> f1 = new Variable <double>("f1");
IFunction function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
var xValues = new[] { 1.0, 2.0, 3.0 };
var yValues = new[] { 10.0, 20.0, 30.0, 40.0 };
var fValues = new[, ]
{
{ 100.0, 200.0, 300.0, 400.0 },
{ 1000.0, 2000.0, 3000.0, 4000.0 },
{ 10000.0, 20000.0, 30000.0, 40000.0 }
};
function.SetValues(fValues, new VariableValueFilter <double>(x, xValues), new VariableValueFilter <double>(y, yValues),
new ComponentFilter(f1));
//no interpolation..on a defined spot
Assert.AreEqual(100,
f1.Evaluate <double>(new VariableValueFilter <double>(x, 0.5),
(new VariableValueFilter <double>(y, 10.0))));
Assert.AreEqual(100,
f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.5),
(new VariableValueFilter <double>(y, 10.0))));
}
public void InterpolatedConstant2D()
{
IVariable <double> x = new Variable <double>("x");
IVariable <double> y = new Variable <double>("y");
IVariable <double> f1 = new Variable <double>("f1");
Function function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
x.InterpolationType = ApproximationType.Constant;
y.InterpolationType = ApproximationType.Constant;
var xValues = new double[] { 1.0, 2.0, 3.0 };
var yValues = new double[] { 10.0, 20.0, 30.0, 40.0 };
var fValues = new[, ]
{
{ 100.0, 200.0, 300.0, 400.0 },
{ 1000.0, 2000.0, 3000.0, 4000.0 },
{ 10000.0, 20000.0, 30000.0, 40000.0 }
};
function.SetValues(fValues, new VariableValueFilter <double>(x, xValues), new VariableValueFilter <double>(y, yValues), new ComponentFilter(f1));
//interpolation among first argument
Assert.AreEqual(100.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.6), (new VariableValueFilter <double>(y, 10.0))));
//interpolation among second argument
Assert.AreEqual(200.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.0), (new VariableValueFilter <double>(y, 26.0))));
//interpolation among two arguments
Assert.AreEqual(200.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.6), (new VariableValueFilter <double>(y, 26.0))), 0.001);
}
public void InterpolatedLinear2D()
{
IVariable <double> x = new Variable <double>("x");
IVariable <double> y = new Variable <double>("y");
IVariable <double> f1 = new Variable <double>("f1");
var function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
var xValues = new[] { 1.0, 2.0, 3.0 };
var yValues = new[] { 10.0, 20.0, 30.0, 40.0 };
var fValues = new[, ]
{
{ 100.0, 200.0, 300.0, 400.0 },
{ 1000.0, 2000.0, 3000.0, 4000.0 },
{ 10000.0, 20000.0, 30000.0, 40000.0 }
};
function.SetValues(fValues, new VariableValueFilter <double>(x, xValues), new VariableValueFilter <double>(y, yValues), new ComponentFilter(f1));
//no interpolation..on a defined spot
Assert.AreEqual(100, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.0), (new VariableValueFilter <double>(y, 10.0))));
//interpolation among first argument
Assert.AreEqual(640.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.6), (new VariableValueFilter <double>(y, 10.0))), 0.001);
//interpolation among second argument
Assert.AreEqual(260.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.0), (new VariableValueFilter <double>(y, 26.0))), 0.001);
//interpolation among two arguments
Assert.AreEqual(1664.0, f1.Evaluate <double>(new VariableValueFilter <double>(x, 1.6), (new VariableValueFilter <double>(y, 26.0))), 0.001);
}
public void GetUniformInterpolatedValue()
{
IVariable <double> x = new Variable <double>("x");
IVariable <double> y = new Variable <double>("y");
IVariable <double> f1 = new Variable <double>("f1");
f1.Arguments.Add(x);
f1.Arguments.Add(y);
var xValues = new[] { 1.0, 2.0 };
var yValues = new[] { 1.0, 2.0 };
var fValues = new[, ]
{
{ 100.0, 100.0 },
{ 100.0, 100.0 }
};
f1.SetValues(fValues,
new VariableValueFilter <double>(x, xValues),
new VariableValueFilter <double>(y, yValues));
var value = f1.Evaluate <double>(
new VariableValueFilter <double>(x, 1.5),
new VariableValueFilter <double>(y, 1.5));
Assert.AreEqual(100, value);
}
public object Call(jsObject Context, jsObject ArgList, object This = null, Engine Engine = null)
{
var Args = GetFunctionArguments(this, Context, ArgList);
if (!Args.ContainsKey("this"))
{
Variable.Set(
"this",
Args,
This == null && Object != null ?
Object.Evaluate(Context) :
This
);
}
return(this.Evaluate(Args));
}
public void GetInterpolatedValueReturnsDefaultValueOnEmpty2ArgsFunction()
{
IVariable<double> x = new Variable<double>("x");
IVariable<double> y = new Variable<double>("y");
x.ExtrapolationType = ExtrapolationType.Constant;
y.ExtrapolationType = ExtrapolationType.Constant;
IVariable<double> f1 = new Variable<double>("f1");
IFunction function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
f1.DefaultValue = 100.0;
Assert.AreEqual(100,
f1.Evaluate<double>(x.CreateValueFilter(7.5),
(new VariableValueFilter<double>(y, 68.2))));
}
public void GetInterpolatedValueReturnsDefaultValueOnEmpty2ArgsFunction()
{
IVariable <double> x = new Variable <double>("x");
IVariable <double> y = new Variable <double>("y");
x.ExtrapolationType = ExtrapolationType.Constant;
y.ExtrapolationType = ExtrapolationType.Constant;
IVariable <double> f1 = new Variable <double>("f1");
IFunction function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
f1.DefaultValue = 100.0;
Assert.AreEqual(100,
f1.Evaluate <double>(x.CreateValueFilter(7.5),
(new VariableValueFilter <double>(y, 68.2))));
}
public void GetUniformInterpolatedValue()
{
IVariable<double> x = new Variable<double>("x");
IVariable<double> y = new Variable<double>("y");
IVariable<double> f1 = new Variable<double>("f1");
f1.Arguments.Add(x);
f1.Arguments.Add(y);
var xValues = new[] { 1.0, 2.0 };
var yValues = new[] { 1.0, 2.0 };
var fValues = new[,]
{
{100.0, 100.0},
{100.0, 100.0}
};
f1.SetValues(fValues,
new VariableValueFilter<double>(x, xValues),
new VariableValueFilter<double>(y, yValues));
var value = f1.Evaluate<double>(
new VariableValueFilter<double>(x, 1.5),
new VariableValueFilter<double>(y, 1.5));
Assert.AreEqual(100,value);
}
public void InterpolatedLinear2D()
{
IVariable<double> x = new Variable<double>("x");
IVariable<double> y = new Variable<double>("y");
IVariable<double> f1 = new Variable<double>("f1");
var function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
var xValues = new[] { 1.0, 2.0, 3.0 };
var yValues = new[] { 10.0, 20.0, 30.0, 40.0 };
var fValues = new[,]
{
{100.0, 200.0, 300.0, 400.0},
{1000.0, 2000.0, 3000.0, 4000.0},
{10000.0, 20000.0, 30000.0, 40000.0}
};
function.SetValues(fValues, new VariableValueFilter<double>(x, xValues), new VariableValueFilter<double>(y, yValues), new ComponentFilter(f1));
//no interpolation..on a defined spot
Assert.AreEqual(100, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.0), (new VariableValueFilter<double>(y, 10.0))));
//interpolation among first argument
Assert.AreEqual(640.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.6), (new VariableValueFilter<double>(y, 10.0))), 0.001);
//interpolation among second argument
Assert.AreEqual(260.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.0), (new VariableValueFilter<double>(y, 26.0))), 0.001);
//interpolation among two arguments
Assert.AreEqual(1664.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.6), (new VariableValueFilter<double>(y, 26.0))), 0.001);
}
public void ExpressionBase_Evaluation_Add_PlusOverload()
{
var expression = new Variable("x") + 1.0;
Assert.AreEqual(1.5, expression.Evaluate(_replacements));
}
public void ExpressionBase_Evaluation_Variable_KeyNotFoundException()
{
ExpressionBase expression = new Variable("s");
expression.Evaluate(_replacements);
}
public void ExpressionBase_IFunction_Evaluation_Constant_IFunction()
{
IFunction expression = new Variable("y");
Assert.AreEqual(0.75, expression.Evaluate(0.75));
}
public void ExpressionBase_Evaluation_Multiply_DivideOverload()
{
var expression = new Variable("x") / 1.0;
Assert.AreEqual(0.5, expression.Evaluate(_replacements));
}
public void InterpolatedConstant2D()
{
IVariable<double> x = new Variable<double>("x");
IVariable<double> y = new Variable<double>("y");
IVariable<double> f1 = new Variable<double>("f1");
Function function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
x.InterpolationType = ApproximationType.Constant;
y.InterpolationType = ApproximationType.Constant;
var xValues = new double[] { 1.0, 2.0, 3.0 };
var yValues = new double[] { 10.0, 20.0, 30.0, 40.0 };
var fValues = new[,]
{
{100.0, 200.0, 300.0, 400.0},
{1000.0, 2000.0, 3000.0, 4000.0},
{10000.0, 20000.0, 30000.0, 40000.0}
};
function.SetValues(fValues, new VariableValueFilter<double>(x, xValues), new VariableValueFilter<double>(y, yValues), new ComponentFilter(f1));
//interpolation among first argument
Assert.AreEqual(100.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.6), (new VariableValueFilter<double>(y, 10.0))));
//interpolation among second argument
Assert.AreEqual(200.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.0), (new VariableValueFilter<double>(y, 26.0))));
//interpolation among two arguments
Assert.AreEqual(200.0, f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.6), (new VariableValueFilter<double>(y, 26.0))), 0.001);
}
public void GetExceptionExtrapolatingValues2ArgsFunction()
{
IVariable<double> x = new Variable<double>("x");
IVariable<double> y = new Variable<double>("y");
IVariable<double> f1 = new Variable<double>("f1");
IFunction function = new Function("testfunction");
function.Arguments.Add(x);
function.Arguments.Add(y);
function.Components.Add(f1);
var xValues = new[] {1.0, 2.0, 3.0};
var yValues = new[] {10.0, 20.0, 30.0, 40.0};
var fValues = new[,]
{
{100.0, 200.0, 300.0, 400.0},
{1000.0, 2000.0, 3000.0, 4000.0},
{10000.0, 20000.0, 30000.0, 40000.0}
};
function.SetValues(fValues, new VariableValueFilter<double>(x, xValues), new VariableValueFilter<double>(y, yValues),
new ComponentFilter(f1));
//no interpolation..on a defined spot
Assert.AreEqual(100,
f1.Evaluate<double>(new VariableValueFilter<double>(x, 0.5),
(new VariableValueFilter<double>(y, 10.0))));
Assert.AreEqual(100,
f1.Evaluate<double>(new VariableValueFilter<double>(x, 1.5),
(new VariableValueFilter<double>(y, 10.0))));
}
static void Main(string[] args)
{
// Create some constants.
Expression A = 2;
Constant B = Constant.New(3);
// Create some variables.
Expression x = "x";
Variable y = Variable.New("y");
// Create a basic expressions.
Expression f = A * x + B * y + 4;
// This expression uses the implicit conversion from string to
// Expression, which parses the string.
Expression g = "5*x + C*y + 8";
// Create a system of equations from the above expressions.
var system = new List <Equal>()
{
Equal.New(f, 0),
Equal.New(g, 0),
};
// We can now solve the system of equations for x and y. Since the
// equations have a variable 'C', the solutions will not be
// constants.
List <Arrow> solutions = system.Solve(x, y);
Console.WriteLine("The solutions are:");
foreach (Arrow i in solutions)
{
Console.WriteLine(i.ToString());
}
// A fundamental building block of ComputerAlgebra is the 'Arrow'
// expression. Arrow expressions define the value of one expression
// to be the value given by another expression. For example, 'x->2'
// defines the expression 'x' to have the value '2'.
// The 'Solve' function used above returns a list of Arrow
// expressions defining the solutions of the system.
// Arrow expressions are used by the 'Evaluate' function to
// substitute values for expressions into other expressions. To
// demonstrate the usage of Evaluate, let's validate the solution
// by using Evaluate to substitute the solutions into the original
// system of equations, and then substitute a value for C.
Expression f_xy = f.Evaluate(solutions).Evaluate(Arrow.New("C", 2));
Expression g_xy = g.Evaluate(solutions).Evaluate(Arrow.New("C", 2));
if ((f_xy == 0) && (g_xy == 0))
{
Console.WriteLine("Success!");
}
else
{
Console.WriteLine("Failure! f = {0}, g = {1}", f_xy, g_xy);
}
// Suppose we need to evaluate the solutions efficiently many times.
// We can compile the solutions to delegates where 'C' is a
// parameter to the delegate, allowing it to be specified later.
var x_C = x.Evaluate(solutions).Compile <Func <double, double> >("C");
var y_C = y.Evaluate(solutions).Compile <Func <double, double> >("C");
for (int i = 0; i < 20; ++i)
{
double C = i / 2.0;
Console.WriteLine("C = {0}: (x, y) = ({1}, {2})", C, x_C(C), y_C(C));
}
}
public void ExpressionBase_Evaluation_Variable()
{
ExpressionBase expression = new Variable("x");
Assert.AreEqual(0.5, expression.Evaluate(_replacements));
}
