/// <summary>
/// Computes e to the power of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of e^<sup>x1</sup>.</returns>
public static UncertainValue Exp(UncertainValue x)
{
double v = Math.Exp(x.Value);
double u = v * x.Uncertainty;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes an uncertain value raised to an arbitrary power.
/// </summary>
/// <param name="x">The argument.</param>
/// <param name="p">The power.</param>
/// <returns>The argument raised to the specified power.</returns>
public static UncertainValue Pow(UncertainValue x, double p)
{
double v = Math.Pow(x.Value, p);
double u = Math.Abs(p * v * x.RelativeUncertainty);
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the natural logarithm of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of ln(x1).</returns>
public static UncertainValue Log(UncertainValue x)
{
double v = Math.Log(x.Value);
double u = x.RelativeUncertainty;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the hyperbolic sine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The hyperbolic sine of the argument.</returns>
public static UncertainValue Sinh(UncertainValue x)
{
double v = Math.Sinh(x.Value);
double u = Math.Cosh(x.Value) * x.Uncertainty;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the arctangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arctanget of the argument.</returns>
public static UncertainValue Atan(UncertainValue x)
{
double xv = x.Value;
double v = Math.Atan(xv);
double u = x.Uncertainty / (1 + xv * xv);
return (new UncertainValue(v, u));
}
/// <summary>
/// Computes the hyperbolic tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The hyperbolic tanget of the argument.</returns>
public static UncertainValue Tanh(UncertainValue x)
{
double v = Math.Tanh(x.Value);
double u = x.Uncertainty / MoreMath.Sqr(Math.Cosh(x.Value));
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the arccosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arccosine of the argument.</returns>
public static UncertainValue Acos(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Acos(x.Value);
y.Uncertainty = x.Uncertainty / Math.Abs(Math.Sin(y.Value));
return (y);
}
// basic functions of uncertain values
/// <summary>
/// Computes the square root of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The square root of the argument.</returns>
public static UncertainValue Sqrt(UncertainValue x)
{
double v = Math.Sqrt(x.Value);
double u = 0.5 * x.Uncertainty / v;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the cosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The cosine of the argument.</returns>
public static UncertainValue Cos(UncertainValue x)
{
double v = Math.Cos(x.Value);
double u = Math.Abs(Math.Sin(x.Value)) * x.Uncertainty;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The tanget of the argument.</returns>
public static UncertainValue Tan(UncertainValue x)
{
double v = Math.Tan(x.Value);
double u = (1.0 + v * v) * x.Uncertainty;
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the arccosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arccosine of the argument.</returns>
public static UncertainValue Acos(UncertainValue x)
{
double v = Math.Acos(x.Value);
double u = x.Uncertainty / Math.Abs(Math.Sin(v));
return(new UncertainValue(v, u));
}
public void UncertainMathSinASin()
{
UncertainValue y = new UncertainValue(0.5, 0.1);
UncertainValue x = UncertainMath.Asin(y);
UncertainValue sx = UncertainMath.Sin(x);
Assert.IsTrue(TestUtilities.IsNearlyEqual(sx.Value, y.Value));
Assert.IsTrue(TestUtilities.IsNearlyEqual(sx.Uncertainty, y.Uncertainty));
}
/// <summary>
/// Computes the sine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The sine of the argument.</returns>
public static UncertainValue Sin(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Sin(x.Value);
y.Uncertainty = Math.Abs(Math.Cos(x.Value)) * x.Uncertainty;
return(y);
}
/// <summary>
/// Divides two uncertain values.
/// </summary>
/// <param name="v1">The first uncertain value.</param>
/// <param name="v2">The second uncertain value.</param>
/// <returns>The quotient of the two uncertain values.</returns>
public static UncertainValue operator /(UncertainValue v1, UncertainValue v2)
{
UncertainValue v = new UncertainValue();
v.Value = v1.Value / v2.Value;
v.Uncertainty = Math.Abs(v.Value) * MoreMath.Hypot(v1.RelativeUncertainty, v2.RelativeUncertainty);
return(v);
}
/// <summary>
/// Computes e to the power of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of e^<sup>x1</sup>.</returns>
public static UncertainValue Exp(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Exp(x.Value);
y.Uncertainty = y.Value * x.Uncertainty;
return(y);
}
/// <summary>
/// Computes the natural logarithm of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of ln(x1).</returns>
public static UncertainValue Log(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Log(x.Value);
y.Uncertainty = x.RelativeUncertainty;
return(y);
}
/// <summary>
/// Computes the arccosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arccosine of the argument.</returns>
public static UncertainValue Acos(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Acos(x.Value);
y.Uncertainty = x.Uncertainty / Math.Abs(Math.Sin(y.Value));
return(y);
}
/// <summary>
/// Computes an uncertain value raised to an arbitrary power.
/// </summary>
/// <param name="x">The argument.</param>
/// <param name="p">The power.</param>
/// <returns>The argument raised to the specified power.</returns>
public static UncertainValue Pow(UncertainValue x, double p)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Pow(x.Value, p);
y.Uncertainty = Math.Abs(p * y.Value * x.RelativeUncertainty);
return(y);
}
public void UncertainMathCosACos()
{
UncertainValue y = new UncertainValue(0.5, 0.1);
UncertainValue x = UncertainMath.Acos(y);
UncertainValue cx = UncertainMath.Cos(x);
Assert.IsTrue(TestUtilities.IsNearlyEqual(cx.Value, y.Value));
Assert.IsTrue(TestUtilities.IsNearlyEqual(cx.Uncertainty, y.Uncertainty));
}
/// <summary>
/// Computes the hyperbolic tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The hyperbolic tanget of the argument.</returns>
public static UncertainValue Tanh(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Tanh(x.Value);
y.Uncertainty = y.Uncertainty / Math.Pow(Math.Cosh(x.Value), 2);
return(y);
}
/// <summary>
/// Computes the arctangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arctanget of the argument.</returns>
public static UncertainValue Atan(UncertainValue x)
{
double xv = x.Value;
double v = Math.Atan(xv);
double u = x.Uncertainty / (1 + xv * xv);
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the arcsine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arcsine of the argument.</returns>
public static UncertainValue Asin(UncertainValue x)
{
double v = Math.Asin(x.Value);
double u = x.Uncertainty / Math.Abs(Math.Cos(v));
return (new UncertainValue(v, u));
//UncertainValue y = new UncertainValue();
//y.Value = Math.Asin(x.Value);
//y.Uncertainty = x.Uncertainty / Math.Abs(Math.Cos(y.Value));
//return (y);
}
/// <summary>
/// Computes the arctangent of the ratio of two uncertain values.
/// </summary>
/// <param name="x">The argument of the numerator.</param>
/// <param name="y">The argument of the denominator.</param>
/// <returns>The arctangent of the quotient.</returns>
public static UncertainValue Atan2(UncertainValue x, UncertainValue y)
{
double xv = x.Value;
double yv = y.Value;
double v = Math.Atan2(xv, yv);
double u1 = x.Uncertainty * yv;
double u2 = y.Uncertainty * xv;
double u = Math.Sqrt(u1 * u1 + u2 * u2) / (xv * xv + yv * yv);
return (new UncertainValue(v, u));
}
/// <summary>
/// Computes the cosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The cosine of the argument.</returns>
public static UncertainValue Cos(UncertainValue x)
{
double v = Math.Cos(x.Value);
double u = Math.Abs(Math.Sin(x.Value)) * x.Uncertainty;
return (new UncertainValue(v, u));
//UncertainValue y = new UncertainValue();
//y.Value = Math.Cos(x.Value);
//y.Uncertainty = Math.Abs(Math.Sin(x.Value)) * x.Uncertainty;
//return (y);
}
/// <summary>
/// Computes the arctangent of the ratio of two uncertain values.
/// </summary>
/// <param name="x">The argument of the numerator.</param>
/// <param name="y">The argument of the denominator.</param>
/// <returns>The arctangent of the quotient.</returns>
public static UncertainValue Atan2(UncertainValue x, UncertainValue y)
{
double xv = x.Value;
double yv = y.Value;
double v = Math.Atan2(xv, yv);
double u1 = x.Uncertainty * yv;
double u2 = y.Uncertainty * xv;
double u = Math.Sqrt(u1 * u1 + u2 * u2) / (xv * xv + yv * yv);
return(new UncertainValue(v, u));
}
/// <summary>
/// Computes the tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The tanget of the argument.</returns>
public static UncertainValue Tan(UncertainValue x)
{
double v = Math.Tan(x.Value);
double u = (1.0 + MoreMath.Pow2(v)) * x.Uncertainty;
return(new UncertainValue(v, u));
//UncertainValue y = new UncertainValue();
//y.Value = Math.Tan(x.Value);
//y.Uncertainty = (1.0 + Math.Pow(y.Value, 2)) * x.Uncertainty;
//return (y);
}
/// <summary>
/// Computes the arcsine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The arcsine of the argument.</returns>
public static UncertainValue Asin(UncertainValue x)
{
double v = Math.Asin(x.Value);
double u = x.Uncertainty / Math.Abs(Math.Cos(v));
return(new UncertainValue(v, u));
//UncertainValue y = new UncertainValue();
//y.Value = Math.Asin(x.Value);
//y.Uncertainty = x.Uncertainty / Math.Abs(Math.Cos(y.Value));
//return (y);
}
/// <summary>
/// Determines whether the given object represents the same uncertain value.
/// </summary>
/// <param name="obj">The object.</param>
/// <returns>True if the object represents the same reference point, otherwise false.</returns>
public override bool Equals(object obj)
{
if (obj is UncertainValue)
{
UncertainValue uv = (UncertainValue)obj;
return(this == uv);
}
else
{
return(false);
}
}
internal IntegrationResult(UncertainValue estimate, int evaluationCount, EvaluationSettings settings)
: base(evaluationCount, settings)
{
this.estimate = estimate;
}
/// <summary>
/// Computes the hyperbolic tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The hyperbolic tanget of the argument.</returns>
public static UncertainValue Tanh(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Tanh(x.Value);
y.Uncertainty = y.Uncertainty / Math.Pow(Math.Cosh(x.Value), 2);
return (y);
}
/// <summary>
/// Computes the natural logarithm of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of ln(x1).</returns>
public static UncertainValue Log(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Log(x.Value);
y.Uncertainty = x.RelativeUncertainty;
return (y);
}
/// <summary>
/// Computes the hyperbolic cosine of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The hyperbolic cosine of the argument.</returns>
public static UncertainValue Cosh(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Cosh(x.Value);
y.Uncertainty = Math.Abs(Math.Sinh(x.Value)) * x.Uncertainty;
return (y);
}
/// <summary>
/// Computes the tangent of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The tanget of the argument.</returns>
public static UncertainValue Tan(UncertainValue x)
{
double v = Math.Tan(x.Value);
double u = (1.0 + MoreMath.Pow2(v)) * x.Uncertainty;
return (new UncertainValue(v, u));
//UncertainValue y = new UncertainValue();
//y.Value = Math.Tan(x.Value);
//y.Uncertainty = (1.0 + Math.Pow(y.Value, 2)) * x.Uncertainty;
//return (y);
}
// basic functions of uncertain values
/// <summary>
/// Computes the square root of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The square root of the argument.</returns>
public static UncertainValue Sqrt(UncertainValue x)
{
double v = Math.Sqrt(x.Value);
double u = 0.5 * x.Uncertainty / v;
return (new UncertainValue(v, u));
}
/// <summary>
/// Computes an uncertain value raised to an arbitrary power.
/// </summary>
/// <param name="x">The argument.</param>
/// <param name="p">The power.</param>
/// <returns>The argument raised to the specified power.</returns>
public static UncertainValue Pow(UncertainValue x, double p)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Pow(x.Value, p);
y.Uncertainty = Math.Abs(p * y.Value * x.RelativeUncertainty);
return (y);
}
public void UncertainValueConstructorTest()
{
UncertainValue u = new UncertainValue(1.0, -1.0);
}
public void UncertainValueZeroUncertaintiesTest()
{
UncertainValue p = new UncertainValue(3.141592653, 0.0);
UncertainValue q = new UncertainValue(2.718281828, 0.0);
UncertainValue sum = p + q;
Assert.IsTrue(sum.Value == p.Value + q.Value);
Assert.IsTrue(sum.Uncertainty == 0.0);
UncertainValue difference = p - q;
Assert.IsTrue(difference.Value == p.Value - q.Value);
Assert.IsTrue(difference.Uncertainty == 0.0);
UncertainValue product = p * q;
Assert.IsTrue(product.Value == p.Value * q.Value);
Assert.IsTrue(product.Uncertainty == 0.0);
UncertainValue quotient = p / q;
Assert.IsTrue(quotient.Value == p.Value / q.Value);
Assert.IsTrue(quotient.Uncertainty == 0.0);
UncertainValue exp = UncertainMath.Exp(p);
Assert.IsTrue(exp.Value == Math.Exp(p.Value));
Assert.IsTrue(exp.Uncertainty == 0.0);
UncertainValue log = UncertainMath.Log(q);
Assert.IsTrue(log.Value == Math.Log(q.Value));
Assert.IsTrue(log.Uncertainty == 0.0);
UncertainValue tan = UncertainMath.Tan(q);
Assert.IsTrue(TestUtilities.IsNearlyEqual(tan.Value, Math.Tan(q.Value)));
Assert.IsTrue(tan.Uncertainty == 0.0);
UncertainValue atan = UncertainMath.Atan(q);
Assert.IsTrue(TestUtilities.IsNearlyEqual(atan.Value, Math.Atan(q.Value)));
Assert.IsTrue(atan.Uncertainty == 0.0);
}
/// <summary>
/// Multiplies two uncertain values.
/// </summary>
/// <param name="v1">The first uncertain value.</param>
/// <param name="v2">The second uncertain value.</param>
/// <returns>The product of the two uncertain values.</returns>
public static UncertainValue operator *(UncertainValue v1, UncertainValue v2)
{
UncertainValue v = new UncertainValue();
v.Value = v1.Value * v2.Value;
v.Uncertainty = Math.Abs(v.Value) * MoreMath.Hypot(v1.RelativeUncertainty, v2.RelativeUncertainty);
return(v);
}
/// <summary>
/// Computes e to the power of an uncertain value.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of e^<sup>x1</sup>.</returns>
public static UncertainValue Exp(UncertainValue x)
{
UncertainValue y = new UncertainValue();
y.Value = Math.Exp(x.Value);
y.Uncertainty = y.Value * x.Uncertainty;
return (y);
}