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Remove substitution rule for [a, b] => [-1, 1] from DoubleExponential method.

pull/655/head
diluculo 6 years ago
parent
ab1f608345
commit
e0cd83b648
3 changed files with 42 additions and 63 deletions
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  1. 15
      src/Numerics.Tests/IntegrationTests/IntegrationTest.cs
  2. 66
      src/Numerics/Integrate.cs
  3. 24
      src/Numerics/Integration/GaussKronrodRule.cs

15
src/Numerics.Tests/IntegrationTests/IntegrationTest.cs
View File

@ -181,16 +181,13 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests
TargetAreaC,
Integrate.DoubleExponential(TargetFunctionC, StartC, StopC, 1e-10),
1e-10,
"DoubleExponential, Target 1e-10");
// integrate_(0)^(1) log(x) dx = -1
// Note that DoubleExponential returns -oo.
"DoubleExponential");
Assert.AreEqual(
TargetAreaD,
Integrate.OnClosedInterval(TargetFunctionD, StartD, StopD),
Integrate.DoubleExponential(TargetFunctionD, StartD, StopD),
1e-10,
"Interval");
"DoubleExponential");
Assert.AreEqual(
TargetAreaD,
@ -474,19 +471,19 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests
expected,
factor * Integrate.DoubleExponential((x) => 1 / (1 + x * x), a, b),
1e-10,
"DET Integral of sin(pi*x)/(pi*x) from -oo to oo");
"DET Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
factor * Integrate.GaussKronrod((x) => 1 / (1 + x * x), a, b),
1e-10,
"GK Integral of sin(pi*x)/(pi*x) from -oo to oo");
"GK Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
Assert.AreEqual(
expected,
factor * Integrate.GaussLegendre((x) => 1 / (1 + x * x), a, b, order: 128),
1e-10,
"GL Integral of sin(pi*x)/(pi*x) from -oo to oo");
"GL Integral of sin(pi*x)/(pi*x) from {0} to {1}", a, b);
}
// integral_(-oo)^(oo) 1/(1 + j x^2) dx = -(-1)^(3/4) ¥ð

66
src/Numerics/Integrate.cs
View File

@ -102,7 +102,7 @@ namespace MathNet.Numerics
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if (double.IsInfinity(intervalBegin) && double.IsInfinity(intervalEnd))
@ -115,8 +115,8 @@ namespace MathNet.Numerics
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (double.IsInfinity(intervalEnd))
@ -129,8 +129,8 @@ namespace MathNet.Numerics
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (double.IsInfinity(intervalBegin))
@ -141,18 +141,9 @@ namespace MathNet.Numerics
};
return DoubleExponentialTransformation.Integrate(u, -1, 0, targetAbsoluteError);
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else
{
Func<double, double> u = (t) =>
{
return f((intervalEnd - intervalBegin) / 4 * t * (3 - t * t) + (intervalEnd + intervalBegin) / 2) * 3 * (intervalEnd - intervalBegin) / 4 * (1 - t * t);
};
return DoubleExponentialTransformation.Integrate(u, -1, 1, targetAbsoluteError);
return DoubleExponentialTransformation.Integrate(f, intervalBegin, intervalEnd, targetAbsoluteError);
}
}
@ -178,7 +169,7 @@ namespace MathNet.Numerics
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if (double.IsInfinity(intervalBegin) && double.IsInfinity(intervalEnd))
@ -191,8 +182,8 @@ namespace MathNet.Numerics
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (double.IsInfinity(intervalEnd))
@ -205,8 +196,8 @@ namespace MathNet.Numerics
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (double.IsInfinity(intervalBegin))
@ -219,7 +210,7 @@ namespace MathNet.Numerics
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(a)^(b) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else
@ -292,7 +283,7 @@ namespace MathNet.Numerics
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if (double.IsInfinity(intervalBegin) && double.IsInfinity(intervalEnd))
@ -305,8 +296,8 @@ namespace MathNet.Numerics
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (double.IsInfinity(intervalEnd))
@ -319,8 +310,8 @@ namespace MathNet.Numerics
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (double.IsInfinity(intervalBegin))
@ -331,18 +322,9 @@ namespace MathNet.Numerics
};
return DoubleExponentialTransformation.ContourIntegrate(u, -1, 0, targetAbsoluteError);
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else
{
Func<double, Complex> u = (t) =>
{
return f((intervalEnd - intervalBegin) / 4 * t * (3 - t * t) + (intervalEnd + intervalBegin) / 2) * 3 * (intervalEnd - intervalBegin) / 4 * (1 - t * t);
};
return DoubleExponentialTransformation.ContourIntegrate(u, -1, 1, targetAbsoluteError);
return DoubleExponentialTransformation.ContourIntegrate(f, intervalBegin, intervalEnd, targetAbsoluteError);
}
}
@ -368,7 +350,7 @@ namespace MathNet.Numerics
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if (double.IsInfinity(intervalBegin) && double.IsInfinity(intervalEnd))
@ -381,8 +363,8 @@ namespace MathNet.Numerics
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (double.IsInfinity(intervalEnd))
@ -395,8 +377,8 @@ namespace MathNet.Numerics
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (double.IsInfinity(intervalBegin))
@ -409,7 +391,7 @@ namespace MathNet.Numerics
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(a)^(b) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else

24
src/Numerics/Integration/GaussKronrodRule.cs
View File

@ -240,7 +240,7 @@ namespace MathNet.Numerics.Integration
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if ((intervalBegin < double.MinValue) && (intervalEnd > double.MaxValue))
@ -253,8 +253,8 @@ namespace MathNet.Numerics.Integration
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (intervalEnd > double.MaxValue)
@ -267,8 +267,8 @@ namespace MathNet.Numerics.Integration
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (intervalBegin < double.MinValue)
@ -281,7 +281,7 @@ namespace MathNet.Numerics.Integration
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(a)^(b) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else
@ -326,7 +326,7 @@ namespace MathNet.Numerics.Integration
// (-oo, oo) => [-1, 1]
//
// integral_{-oo}^{oo} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(-oo)^(oo) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = t / (1 - t^2)
// g'(t) = (1 + t^2) / (1 - t^2)^2
if ((intervalBegin < double.MinValue) && (intervalEnd > double.MaxValue))
@ -339,8 +339,8 @@ namespace MathNet.Numerics.Integration
}
// [a, oo) => [0, 1]
//
// integral_{a}^{oo} f(x) dx = integral_{0}^{oo} f(a + t^2) 2 t dt
// = integral_{0}^{1} f(a + g(s)^2) 2 g(s) g'(s) ds
// integral_(a)^(oo) f(x) dx = integral_(0)^(oo) f(a + t^2) 2 t dt
// = integral_(0)^(1) f(a + g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 - s)
// g'(s) = 1 / (1 - s)^2
else if (intervalEnd > double.MaxValue)
@ -353,8 +353,8 @@ namespace MathNet.Numerics.Integration
}
// (-oo, b] => [-1, 0]
//
// integral_{-oo}^{b} f(x) dx = -integral_{-oo}^{0} f(b - t^2) 2 t dt
// = -integral_{-1}^{0} f(b - g(s)^2) 2 g(s) g'(s) ds
// integral_(-oo)^(b) f(x) dx = -integral_(-oo)^(0) f(b - t^2) 2 t dt
// = -integral_(-1)^(0) f(b - g(s)^2) 2 g(s) g'(s) ds
// g(s) = s / (1 + s)
// g'(s) = 1 / (1 + s)^2
else if (intervalBegin < double.MinValue)
@ -367,7 +367,7 @@ namespace MathNet.Numerics.Integration
}
// [a, b] => [-1, 1]
//
// integral_{a}^{b} f(x) dx = integral_{-1}^{1} f(g(t)) g'(t) dt
// integral_(a)^(b) f(x) dx = integral_(-1)^(1) f(g(t)) g'(t) dt
// g(t) = (b - a) * t * (3 - t^2) / 4 + (b + a) / 2
// g'(t) = 3 / 4 * (b - a) * (1 - t^2)
else

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