public static double simpsonRuleM(Expr expr, string varName, double a, double b)
{
var f = expr.Compile(varName);
f = Differentiate.SecondDerivativeFunc(Differentiate.SecondDerivativeFunc(f));
return(max(f(a), f(b)));
}
public static double evaluate(
[Desc("The equation to evaluate.")] Expr expr,
[Desc("The name of the first variable in the equation.")] string aName, [Desc("The value of the first variable.")] double a,
[Desc("The name of the second variable in the equation.")] string bName, [Desc("The value of the second variable.")] double b)
{
var f = expr.Compile(aName, bName);
return(f(a, b));
}
public static double evaluate(
[Desc("The equation to evaluate.")] Expr expr,
[Desc("The name of the variable in the equation.")] string aName,
[Desc("The value of the variable.")] double a)
{
var f = expr.Compile(aName);
return(f(a));
}
public static double trapezoidalRuleEt(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
double trValue = NewtonCotesTrapeziumRule.IntegrateComposite(f, a, b, n);
double trueValue = Integrate.OnClosedInterval(f, a, b);
return(abs(trueValue - trValue));
}
public static double simpsonRuleEs(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
double srValue = SimpsonRule.IntegrateComposite(f, a, b, n);
double trueValue = Integrate.OnClosedInterval(f, a, b);
return(abs(trueValue - srValue));
}
public static double evaluate(
[Desc("The equation to evaluate.")] Expr expr,
[Desc("The name of the first variable in the equation.")] string aName, [Desc("The value of the first variable.")] double a,
[Desc("The name of the second variable in the equation.")] string bName, [Desc("The value of the second variable.")] double b,
[Desc("The name of the third variable in the equation.")] string cName, [Desc("The value of the third variable.")] double c,
[Desc("The name of the fourth variable in the equation.")] string dName, [Desc("The value of the fourth variable.")] double d)
{
var f = expr.Compile(aName, bName, cName, dName);
return(f(a, b, c, d));
}
public static double simpsonRule(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
return(SimpsonRule.IntegrateComposite(f, a, b, n));
}
public static double trapezoidalRuleError(Expr expr, string varName, double a, double b, double Et)
{
var f = expr.Compile(varName);
return(NewtonCotesTrapeziumRule.IntegrateAdaptive(f, a, b, Et));
}
public static double trapezoidalRule(Expr expr, string varName, double a, double b, int n)
{
var f = expr.Compile(varName);
return(NewtonCotesTrapeziumRule.IntegrateComposite(f, a, b, n));
}
public static double integral(Expr expr, string varName, double a, double b)
{
var f = expr.Compile(varName);
return(Integrate.OnClosedInterval(f, a, b));
}
public static double fourthDerivative(Expr expr, string varName, double x)
{
var f = expr.Compile(varName);
return(Differentiate.SecondDerivative(Differentiate.SecondDerivativeFunc(f), x));
}
public static double firstDerivative(Expr expr, string varName, double x)
{
var f = expr.Compile(varName);
return(Differentiate.FirstDerivative(f, x));
}
