/// <summary>
/// Calculates tangent of the interval of angles.
/// </summary>
/// <param name="x">An interval represents the angle in radians.</param>
public static Interval Tan(Interval x)
{
if (Cos(x).Contains(0))
{
throw new ArgumentException();
}
return new Interval(Math.Tan(x.A), Math.Tan(x.B), x.Epsilon);
}
/// <summary>
/// Calculates a cosine of the interval.
/// </summary>
/// <param name="x">A fuzzy number represents the angle in radians.</param>
public static Interval Cos(Interval x)
{
double a, b, extreme;
extreme = Math.Floor(x.A / Math.PI) * Math.PI;
if (x.Contains(extreme))
{
a = Math.Cos(extreme);
}
else
{
extreme += Math.PI;
if (x.Contains(extreme))
{
a = Math.Cos(extreme);
}
else
{
a = Math.Cos(x.A);
b = Math.Cos(x.B);
return b > a
? new Interval(a, b, x.Epsilon)
: new Interval(b, a, x.Epsilon);
}
}
extreme += Math.PI;
if (x.Contains(extreme))
{
b = Math.Cos(extreme);
}
else if (a > 0)
{
b = Math.Min(Math.Cos(x.A), Math.Cos(x.B));
}
else
{
b = Math.Max(Math.Cos(x.A), Math.Cos(x.B));
}
return b > a
? new Interval(a, b, x.Epsilon)
: new Interval(b, a, x.Epsilon);
}
/// <summary>
/// Calculates a value of the interval raised to the specified power.
/// </summary>
/// <param name="x">Base</param>
/// <param name="y">Exponent</param>
public static Interval Pow(Interval x, double y)
{
var a = Math.Pow(x.A, y);
var b = Math.Pow(x.B, y);
if (a > b)
{
var tmp = a;
a = b;
b = tmp;
}
if (x.Contains(0) && a > 0)
{
a = 0;
}
return new Interval(a, b, x.Epsilon);
}
private static Interval Atan2(Interval y, Interval x, bool rotated)
{
double a1, a2, a3, a4;
var epsilon = Math.Max(y.Epsilon, x.Epsilon);
if (rotated)
{
if (y.Contains(0) && x.Contains(0))
{
return new Interval(-1.5 * Math.PI, 0.5 * Math.PI, epsilon);
}
a1 = Atan2Rotated(y.A, x.A);
a2 = Atan2Rotated(y.A, x.B);
a3 = Atan2Rotated(y.B, x.B);
a4 = Atan2Rotated(y.B, x.A);
}
else
{
if (y.Contains(0) && x.Contains(0))
{
return new Interval(-Math.PI, Math.PI, epsilon);
}
a1 = Math.Atan2(y.A, x.A);
a2 = Math.Atan2(y.A, x.B);
a3 = Math.Atan2(y.B, x.B);
a4 = Math.Atan2(y.B, x.A);
}
return new Interval(
Math.Min(Math.Min(a1, a2), Math.Min(a3, a4)),
Math.Max(Math.Max(a1, a2), Math.Max(a3, a4)),
epsilon
);
}
/// <summary>
/// Calculates a sine of the interval of angles.
/// </summary>
/// <param name="x">A interval represents the angle in radians.</param>
public static Interval Sin(Interval x)
{
return Cos(x - Math.PI / 2);
}
/// <summary>
/// Returns the smaller of two intervals.
/// </summary>
public static Interval Min(Interval x, Interval y)
{
return new Interval(Math.Min(x.A, y.A), Math.Min(x.B, y.B), Math.Max(x.Epsilon, y.Epsilon));
}
/// <summary>
/// Calculates e raised to the specified interval.
/// </summary>
/// <param name="X">Exponent</param>
public static Interval Exp(Interval x)
{
return new Interval(Math.Exp(x.A), Math.Exp(x.B), x.Epsilon);
}