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Integration: simpify weird double-exponential transformation design

pull/163/head
Christoph Ruegg 13 years ago
parent
65c44cf560
commit
dab0fb03d2
3 changed files with 440 additions and 487 deletions
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  1. 9
      src/Numerics/Integrate.cs
  2. 914
      src/Numerics/Integration/DoubleExponentialTransformation.cs
  3. 4
      src/UnitTests/IntegrationTests/IntegrationTest.cs

9
src/Numerics/Integrate.cs
View File

@ -38,11 +38,6 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
public static class Integrate public static class Integrate
{ {
/// <summary>
/// Shared internal DET algorithm.
/// </summary>
private static readonly DoubleExponentialTransformation Det = new DoubleExponentialTransformation();
/// <summary> /// <summary>
/// Approximation of the definite integral of an analytic smooth function on a closed interval. /// Approximation of the definite integral of an analytic smooth function on a closed interval.
/// </summary> /// </summary>
@ -53,7 +48,7 @@ namespace MathNet.Numerics
/// <returns>Approximation of the finite integral in the given interval.</returns> /// <returns>Approximation of the finite integral in the given interval.</returns>
public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd, double targetAbsoluteError) public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd, double targetAbsoluteError)
{ {
return Det.Integrate(f, intervalBegin, intervalEnd, targetAbsoluteError); return DoubleExponentialTransformation.Integrate(f, intervalBegin, intervalEnd, targetAbsoluteError);
} }
/// <summary> /// <summary>
@ -65,7 +60,7 @@ namespace MathNet.Numerics
/// <returns>Approximation of the finite integral in the given interval.</returns> /// <returns>Approximation of the finite integral in the given interval.</returns>
public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd) public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd)
{ {
return Det.Integrate(f, intervalBegin, intervalEnd, 1e-8); return DoubleExponentialTransformation.Integrate(f, intervalBegin, intervalEnd, 1e-8);
} }
} }
} }

914
src/Numerics/Integration/DoubleExponentialTransformation.cs
View File

@ -29,7 +29,7 @@
// </copyright> // </copyright>
using System; using System;
using System.Collections.Generic; using System.Linq;
namespace MathNet.Numerics.Integration namespace MathNet.Numerics.Integration
{ {
@ -37,7 +37,7 @@ namespace MathNet.Numerics.Integration
/// Analytic integration algorithm for smooth functions with no discontinuities /// Analytic integration algorithm for smooth functions with no discontinuities
/// or derivative discontinuities and no poles inside the interval. /// or derivative discontinuities and no poles inside the interval.
/// </summary> /// </summary>
public class DoubleExponentialTransformation public static class DoubleExponentialTransformation
{ {
/// <summary> /// <summary>
/// Maximum number of iterations, until the asked /// Maximum number of iterations, until the asked
@ -45,16 +45,6 @@ namespace MathNet.Numerics.Integration
/// </summary> /// </summary>
const int NumberOfMaximumLevels = 10; const int NumberOfMaximumLevels = 10;
/// <summary>
/// Abscissa vector per level provider.
/// </summary>
IEnumerable<double[]> _levelAbcissas;
/// <summary>
/// Weight vector per level provider.
/// </summary>
IEnumerable<double[]> _levelWeights;
/// <summary> /// <summary>
/// Approximate the integral by the double exponential transformation /// Approximate the integral by the double exponential transformation
/// </summary> /// </summary>
@ -63,43 +53,15 @@ namespace MathNet.Numerics.Integration
/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param> /// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
/// <param name="targetRelativeError">The expected relative accuracy of the approximation.</param> /// <param name="targetRelativeError">The expected relative accuracy of the approximation.</param>
/// <returns>Approximation of the finite integral in the given interval.</returns> /// <returns>Approximation of the finite integral in the given interval.</returns>
public double Integrate(Func<double, double> f, double intervalBegin, double intervalEnd, double targetRelativeError) public static double Integrate(Func<double, double> f, double intervalBegin, double intervalEnd, double targetRelativeError)
{ {
if (_levelAbcissas == null)
{
_levelAbcissas = ProvideLevelAbcissas();
_levelWeights = ProvideLevelWeights();
}
return NewtonCotesTrapeziumRule.IntegrateAdaptiveTransformedOdd( return NewtonCotesTrapeziumRule.IntegrateAdaptiveTransformedOdd(
f, f,
intervalBegin, intervalEnd, intervalBegin, intervalEnd,
_levelAbcissas, _levelWeights, Enumerable.Range(0, NumberOfMaximumLevels).Select(EvaluateAbcissas),
1, targetRelativeError); Enumerable.Range(0, NumberOfMaximumLevels).Select(EvaluateWeights),
} 1.0,
targetRelativeError);
/// <summary>
/// Abscissa vector per level provider.
/// </summary>
/// <returns>Level Enumerator.</returns>
internal static IEnumerable<double[]> ProvideLevelAbcissas()
{
for (int i = 0; i < NumberOfMaximumLevels; i++)
{
yield return EvaluateAbcissas(i);
}
}
/// <summary>
/// Weight vector per level provider.
/// </summary>
/// <returns>Level Enumerator.</returns>
internal static IEnumerable<double[]> ProvideLevelWeights()
{
for (int i = 0; i < NumberOfMaximumLevels; i++)
{
yield return EvaluateWeights(i);
}
} }
/// <summary> /// <summary>
@ -167,445 +129,443 @@ namespace MathNet.Numerics.Integration
/// Precomputed abscissa vector per level. /// Precomputed abscissa vector per level.
/// </summary> /// </summary>
static readonly double[][] PrecomputedAbscissas = static readonly double[][] PrecomputedAbscissas =
{
new[] new[]
{ {
new[] 0.00000000000000000000,
{ 0.95136796407274694574,
0.00000000000000000000, 0.99997747719246159286,
0.95136796407274694574, 0.99999999999995705839
0.99997747719246159286, },
0.99999999999995705839 new[]
}, {
new[] 0.67427149224843582608,
{ 0.99751485645722438683,
0.67427149224843582608, 0.99999998887566488198
0.99751485645722438683, },
0.99999998887566488198 new[]
}, {
new[] 0.37720973816403417379,
{ 0.85956905868989663517,
0.37720973816403417379, 0.98704056050737689169,
0.85956905868989663517, 0.99968826402835320905,
0.98704056050737689169, 0.99999920473711471266,
0.99968826402835320905, 0.99999999995285644818
0.99999920473711471266, },
0.99999999995285644818 new[]
}, {
new[] 0.19435700332493543161,
{ 0.53914670538796776905,
0.19435700332493543161, 0.78060743898320029925,
0.53914670538796776905, 0.91487926326457461091,
0.78060743898320029925, 0.97396686819567744856,
0.91487926326457461091, 0.99405550663140214329,
0.97396686819567744856, 0.99906519645578584642,
0.99405550663140214329, 0.99990938469514399984,
0.99906519645578584642, 0.99999531604122052843,
0.99990938469514399984, 0.99999989278161241838,
0.99999531604122052843, 0.99999999914270509218,
0.99999989278161241838, 0.99999999999823216531
0.99999999914270509218, },
0.99999999999823216531 new[]
}, {
new[] 0.097923885287832333262,
{ 0.28787993274271591456,
0.097923885287832333262, 0.46125354393958570440,
0.28787993274271591456, 0.61027365750063894488,
0.46125354393958570440, 0.73101803479256151149,
0.61027365750063894488, 0.82331700550640237006,
0.73101803479256151149, 0.88989140278426019808,
0.82331700550640237006, 0.93516085752198468323,
0.88989140278426019808, 0.96411216422354729193,
0.93516085752198468323, 0.98145482667733517003,
0.96411216422354729193, 0.99112699244169880223,
0.98145482667733517003, 0.99610866543750854254,
0.99112699244169880223, 0.99845420876769773751,
0.99610866543750854254, 0.99945143443527460584,
0.99845420876769773751, 0.99982882207287494166,
0.99945143443527460584, 0.99995387100562796075,
0.99982882207287494166, 0.99998948201481850361,
0.99995387100562796075, 0.99999801714059543208,
0.99998948201481850361, 0.99999969889415261122,
0.99999801714059543208, 0.99999996423908091534,
0.99999969889415261122, 0.99999999678719909830,
0.99999996423908091534, 0.99999999978973286224,
0.99999999678719909830, 0.99999999999039393352,
0.99999999978973286224, 0.99999999999970809734
0.99999999999039393352, },
0.99999999999970809734 new[]
}, {
new[] 0.049055967305077886315,
{ 0.14641798429058794053,
0.049055967305077886315, 0.24156631953888365838,
0.14641798429058794053, 0.33314226457763809244,
0.24156631953888365838, 0.41995211127844715849,
0.33314226457763809244, 0.50101338937930910152,
0.41995211127844715849, 0.57558449063515165995,
0.50101338937930910152, 0.64317675898520470128,
0.57558449063515165995, 0.70355000514714201566,
0.64317675898520470128, 0.75669390863372994941,
0.70355000514714201566, 0.80279874134324126576,
0.75669390863372994941, 0.84221924635075686382,
0.80279874134324126576, 0.87543539763040867837,
0.84221924635075686382, 0.90301328151357387064,
0.87543539763040867837, 0.92556863406861266645,
0.90301328151357387064, 0.94373478605275715685,
0.92556863406861266645, 0.95813602271021369012,
0.94373478605275715685, 0.96936673289691733517,
0.95813602271021369012, 0.97797623518666497298,
0.96936673289691733517, 0.98445883116743083087,
0.97797623518666497298, 0.98924843109013389601,
0.98445883116743083087, 0.99271699719682728538,
0.98924843109013389601, 0.99517602615532735426,
0.99271699719682728538, 0.99688031812819187372,
0.99517602615532735426, 0.99803333631543375402,
0.99688031812819187372, 0.99879353429880589929,
0.99803333631543375402, 0.99928111192179195541,
0.99879353429880589929, 0.99958475035151758732,
0.99928111192179195541, 0.99976797159956083506,
0.99958475035151758732, 0.99987486504878034648,
0.99976797159956083506, 0.99993501992508242369,
0.99987486504878034648, 0.99996759306794345976,
0.99993501992508242369, 0.99998451990227082442,
0.99996759306794345976, 0.99999293787666288565,
0.99998451990227082442, 0.99999693244919035751,
0.99999293787666288565, 0.99999873547186590954,
0.99999693244919035751, 0.99999950700571943689,
0.99999873547186590954, 0.99999981889371276701,
0.99999950700571943689, 0.99999993755407837378,
0.99999981889371276701, 0.99999997987450320175,
0.99999993755407837378, 0.99999999396413420165,
0.99999997987450320175, 0.99999999832336194826,
0.99999999396413420165, 0.99999999957078777261,
0.99999999832336194826, 0.99999999989927772326,
0.99999999957078777261, 0.99999999997845533741,
0.99999999989927772326, 0.99999999999582460688,
0.99999999997845533741, 0.99999999999927152627,
0.99999999999582460688, 0.99999999999988636130
0.99999999999927152627, },
0.99999999999988636130 new[]
}, {
new[] 0.024539763574649160379,
{ 0.073525122985671294475,
0.024539763574649160379, 0.12222912220155764235,
0.073525122985671294475, 0.17046797238201051811,
0.12222912220155764235, 0.21806347346971200463,
0.17046797238201051811, 0.26484507658344795046,
0.21806347346971200463, 0.31065178055284596083,
0.26484507658344795046, 0.35533382516507453330,
0.31065178055284596083, 0.39875415046723775644,
0.35533382516507453330, 0.44078959903390086627,
0.39875415046723775644, 0.48133184611690504422,
0.44078959903390086627, 0.52028805069123015958,
0.48133184611690504422, 0.55758122826077823080,
0.52028805069123015958, 0.59315035359195315880,
0.55758122826077823080, 0.62695020805104287950,
0.59315035359195315880, 0.65895099174335012438,
0.62695020805104287950, 0.68913772506166767176,
0.65895099174335012438, 0.71750946748732412721,
0.68913772506166767176, 0.74407838354734739913,
0.71750946748732412721, 0.76886868676824658459,
0.74407838354734739913, 0.79191549237614211447,
0.76886868676824658459, 0.81326360850297385168,
0.79191549237614211447, 0.83296629391941087564,
0.81326360850297385168, 0.85108400798784873261,
0.83296629391941087564, 0.86768317577564598669,
0.85108400798784873261, 0.88283498824466895513,
0.86768317577564598669, 0.89661425428007602579,
0.88283498824466895513, 0.90909831816302043511,
0.89661425428007602579, 0.92036605303195280235,
0.90909831816302043511, 0.93049693799715340631,
0.92036605303195280235, 0.93957022393327475539,
0.93049693799715340631, 0.94766419061515309734,
0.93957022393327475539, 0.95485549580502268541,
0.94766419061515309734, 0.96121861515111640753,
0.95485549580502268541, 0.96682537031235585284,
0.96121861515111640753, 0.97174454156548730892,
0.96682537031235585284, 0.97604156025657673933,
0.97174454156548730892, 0.97977827580061576265,
0.97604156025657673933, 0.98301279148110110558,
0.97977827580061576265, 0.98579936302528343597,
0.98301279148110110558, 0.98818835380074264243,
0.98579936302528343597, 0.99022624046752774694,
0.98818835380074264243, 0.99195566300267761562,
0.99022624046752774694, 0.99341551316926403900,
0.99195566300267761562, 0.99464105571251119672,
0.99341551316926403900, 0.99566407681695316965,
0.99464105571251119672, 0.99651305464025377317,
0.99566407681695316965, 0.99721334704346870224,
0.99651305464025377317, 0.99778739195890653083,
0.99721334704346870224, 0.99825491617199629344,
0.99778739195890653083, 0.99863314864067747762,
0.99825491617199629344, 0.99893703483351217373,
0.99863314864067747762, 0.99917944893488591716,
0.99893703483351217373, 0.99937140114093768690,
0.99917944893488591716, 0.99952223765121720422,
0.99937140114093768690, 0.99963983134560036519,
0.99952223765121720422, 0.99973076151980848263,
0.99963983134560036519, 0.99980048143113838630,
0.99973076151980848263, 0.99985347277311141171,
0.99980048143113838630, 0.99989338654759256426,
0.99985347277311141171, 0.99992317012928932869,
0.99989338654759256426, 0.99994518061445869309,
0.99992317012928932869, 0.99996128480785666613,
0.99994518061445869309, 0.99997294642523223656,
0.99996128480785666613, 0.99998130127012072679,
0.99997294642523223656, 0.99998722128200062811,
0.99998130127012072679, 0.99999136844834487344,
0.99998722128200062811, 0.99999423962761663478,
0.99999136844834487344, 0.99999620334716617675,
0.99999423962761663478, 0.99999752962380516793,
0.99999620334716617675, 0.99999841381096473542,
0.99999752962380516793, 0.99999899541068996962,
0.99999841381096473542, 0.99999937270733536947,
0.99999899541068996962, 0.99999961398855024275,
0.99999937270733536947, 0.99999976602333243312,
0.99999961398855024275, 0.99999986037121459941,
0.99999976602333243312, 0.99999991800479471056,
0.99999986037121459941, 0.99999995264266446185,
0.99999991800479471056, 0.99999997311323594362,
0.99999995264266446185, 0.99999998500307631173,
0.99999997311323594362, 0.99999999178645609907,
0.99999998500307631173, 0.99999999558563361584,
0.99999999178645609907, 0.99999999767323673790,
0.99999999558563361584, 0.99999999879798350040,
0.99999999767323673790, 0.99999999939177687583,
0.99999999879798350040, 0.99999999969875436925,
0.99999999939177687583, 0.99999999985405611550,
0.99999999969875436925, 0.99999999993088839501,
0.99999999985405611550, 0.99999999996803321674,
0.99999999993088839501, 0.99999999998556879008,
0.99999999996803321674, 0.99999999999364632387,
0.99999999998556879008, 0.99999999999727404948,
0.99999999999364632387, 0.99999999999886126543,
0.99999999999727404948, 0.99999999999953722654,
0.99999999999886126543, 0.99999999999981720098,
0.99999999999953722654, 0.99999999999992987953
0.99999999999981720098, }
0.99999999999992987953 };
}
};
/// <summary> /// <summary>
/// Precomputed weight vector per level. /// Precomputed weight vector per level.
/// </summary> /// </summary>
static readonly double[][] PrecomputedWeights = static readonly double[][] PrecomputedWeights =
{
new[]
{
1.5707963267948966192,
0.230022394514788685,
0.00026620051375271690866,
1.3581784274539090834e-12
},
new[]
{
0.96597657941230114801,
0.018343166989927842087,
2.1431204556943039358e-7
},
new[]
{
1.3896147592472563229,
0.53107827542805397476,
0.076385743570832304188,
0.0029025177479013135936,
0.000011983701363170720047,
1.1631165814255782766e-9
},
new[]
{
1.5232837186347052132,
1.1934630258491569639,
0.73743784836154784136,
0.36046141846934367417,
0.13742210773316772341,
0.039175005493600779072,
0.0077426010260642407123,
0.00094994680428346871691,
0.000062482559240744082891,
1.8263320593710659699e-6,
1.8687282268736410132e-8,
4.9378538776631926964e-11
},
new[] new[]
{ {
new[] 1.5587733555333301451,
{ 1.466014426716965781,
1.5707963267948966192, 1.297475750424977998,
0.230022394514788685, 1.0816349854900704074,
0.00026620051375271690866, 0.85017285645662006895,
1.3581784274539090834e-12 0.63040513516474369106,
}, 0.44083323627385823707,
new[] 0.290240679312454185,
{ 0.17932441211072829296,
0.96597657941230114801, 0.10343215422333290062,
0.018343166989927842087, 0.055289683742240583845,
2.1431204556943039358e-7 0.027133510013712003219,
}, 0.012083543599157953493,
new[] 0.0048162981439284630173,
{ 0.0016908739981426396472,
1.3896147592472563229, 0.00051339382406790336017,
0.53107827542805397476, 0.00013205234125609974879,
0.076385743570832304188, 0.000028110164327940134749,
0.0029025177479013135936, 4.8237182032615502124e-6,
0.000011983701363170720047, 6.4777566035929719908e-7,
1.1631165814255782766e-9 6.5835185127183396672e-8,
}, 4.8760060974240625869e-9,
new[] 2.5216347918530148572e-10,
{ 8.6759314149796046502e-12
1.5232837186347052132, },
1.1934630258491569639, new[]
0.73743784836154784136, {
0.36046141846934367417, 1.5677814313072218572,
0.13742210773316772341, 1.5438811161769592204,
0.039175005493600779072, 1.4972262225410362896,
0.0077426010260642407123, 1.4300083548722996676,
0.00094994680428346871691, 1.3452788847662516615,
0.000062482559240744082891, 1.2467012074518577048,
1.8263320593710659699e-6, 1.1382722433763053734,
1.8687282268736410132e-8, 1.0240449331118114483,
4.9378538776631926964e-11 0.90787937915489531693,
}, 0.79324270082051671787,
new[] 0.68306851634426375464,
{ 0.57967810308778764708,
1.5587733555333301451, 0.48475809121475539287,
1.466014426716965781, 0.39938474152571713515,
1.297475750424977998, 0.32408253961152890402,
1.0816349854900704074, 0.258904639514053516,
0.85017285645662006895, 0.20352399885860174519,
0.63040513516474369106, 0.15732620348436615027,
0.44083323627385823707, 0.11949741128869592428,
0.290240679312454185, 0.089103139240941462841,
0.17932441211072829296, 0.065155533432536205042,
0.10343215422333290062, 0.046668208054846613644,
0.055289683742240583845, 0.032698732726609031113,
0.027133510013712003219, 0.022379471063648476483,
0.012083543599157953493, 0.014937835096050129696,
0.0048162981439284630173, 0.0097072237393916892692,
0.0016908739981426396472, 0.0061300376320830301252,
0.00051339382406790336017, 0.0037542509774318343023,
0.00013205234125609974879, 0.0022250827064786427022,
0.000028110164327940134749, 0.0012733279447082382027,
4.8237182032615502124e-6, 0.0007018595156842422708,
6.4777566035929719908e-7, 0.00037166693621677760301,
6.5835185127183396672e-8, 0.00018856442976700318572,
4.8760060974240625869e-9, 0.000091390817490710122732,
2.5216347918530148572e-10, 0.000042183183841757600604,
8.6759314149796046502e-12 0.000018481813599879217116,
}, 7.6595758525203162562e-6,
new[] 2.9916615878138787094e-6,
{ 1.0968835125901264732e-6,
1.5677814313072218572, 3.7595411862360630091e-7,
1.5438811161769592204, 1.1992442782902770219e-7,
1.4972262225410362896, 3.5434777171421953043e-8,
1.4300083548722996676, 9.6498888961089633609e-9,
1.3452788847662516615, 2.4091773256475940779e-9,
1.2467012074518577048, 5.482835779709497755e-10,
1.1382722433763053734, 1.1306055347494680536e-10,
1.0240449331118114483, 2.0989335404511469109e-11,
0.90787937915489531693, 3.4841937670261059685e-12
0.79324270082051671787, },
0.68306851634426375464, new[]
0.57967810308778764708, {
0.48475809121475539287, 1.5700420292795931467,
0.39938474152571713515, 1.5640214037732320999,
0.32408253961152890402, 1.5520531698454121192,
0.258904639514053516, 1.5342817381543034316,
0.20352399885860174519, 1.5109197230741697127,
0.15732620348436615027, 1.48224329788553807,
0.11949741128869592428, 1.4485862549613225916,
0.089103139240941462841, 1.4103329714462590129,
0.065155533432536205042, 1.3679105116808964881,
0.046668208054846613644, 1.3217801174437728579,
0.032698732726609031113, 1.2724283455378627082,
0.022379471063648476483, 1.2203581095793582207,
0.014937835096050129696, 1.1660798699324345766,
0.0097072237393916892692, 1.1101031939653403796,
0.0061300376320830301252, 1.0529288799552666556,
0.0037542509774318343023, 0.99504180404613271514,
0.0022250827064786427022, 0.93690461274566793366,
0.0012733279447082382027, 0.87895234555278212039,
0.0007018595156842422708, 0.82158803526696470334,
0.00037166693621677760301, 0.7651792989089561367,
0.00018856442976700318572, 0.71005590120546898385,
0.000091390817490710122732, 0.65650824613162753076,
0.000042183183841757600604, 0.60478673057840362158,
0.000018481813599879217116, 0.55510187800363350959,
7.6595758525203162562e-6, 0.5076251588319080997,
2.9916615878138787094e-6, 0.4624903980553677613,
1.0968835125901264732e-6, 0.41979566844501548066,
3.7595411862360630091e-7, 0.37960556938665160999,
1.1992442782902770219e-7, 0.3419537959230168323,
3.5434777171421953043e-8, 0.30684590941791694932,
9.6498888961089633609e-9, 0.27426222968906810637,
2.4091773256475940779e-9, 0.24416077786983990868,
5.482835779709497755e-10, 0.21648020911729617038,
1.1306055347494680536e-10, 0.19114268413342749532,
2.0989335404511469109e-11, 0.16805663794826916233,
3.4841937670261059685e-12 0.14711941325785693248,
}, 0.12821973363120098675,
new[] 0.11123999898874453035,
{ 0.096058391865189467849,
1.5700420292795931467, 0.082550788110701737654,
1.5640214037732320999, 0.070592469906866999352,
1.5520531698454121192, 0.060059642358636300319,
1.5342817381543034316, 0.05083075757257047107,
1.5109197230741697127, 0.042787652157725676034,
1.48224329788553807, 0.035816505604196436523,
1.4485862549613225916, 0.029808628117310126969,
1.4103329714462590129, 0.024661087314753282511,
1.3679105116808964881, 0.020277183817500123926,
1.3217801174437728579, 0.016566786254247575375,
1.2724283455378627082, 0.013446536605285730674,
1.2203581095793582207, 0.010839937168255907211,
1.1660798699324345766, 0.0086773307495391815854,
1.1101031939653403796, 0.0068957859690660035329,
1.0529288799552666556, 0.0054388997976239984331,
0.99504180404613271514, 0.0042565295990178580165,
0.93690461274566793366, 0.0033044669940348302363,
0.87895234555278212039, 0.0025440657675291729678,
0.82158803526696470334, 0.0019418357759843675814,
0.7651792989089561367, 0.0014690143599429791058,
0.71005590120546898385, 0.0011011261134519383862,
0.65650824613162753076, 0.00081754101332469493115,
0.60478673057840362158, 0.00060103987991147422573,
0.55510187800363350959, 0.00043739495615911687786,
0.5076251588319080997, 0.00031497209186021200274,
0.4624903980553677613, 0.00022435965205008549104,
0.41979566844501548066, 0.00015802788400701191949,
0.37960556938665160999, 0.00011002112846666697224,
0.3419537959230168323, 0.000075683996586201477788,
0.30684590941791694932, 0.000051421497447658802092,
0.27426222968906810637, 0.0000344921247593431977,
0.24416077786983990868, 0.000022832118109036146591,
0.21648020911729617038, 0.000014908514031870608449,
0.19114268413342749532, 9.5981941283784710776e-6,
0.16805663794826916233, 6.0899100320949039256e-6,
0.14711941325785693248, 3.8061983264644899045e-6,
0.12821973363120098675, 2.3421667208528096843e-6,
0.11123999898874453035, 1.4183067155493917523e-6,
0.096058391865189467849, 8.4473756384859863469e-7,
0.082550788110701737654, 4.9458288702754198508e-7,
0.070592469906866999352, 2.8449923659159806339e-7,
0.060059642358636300319, 1.6069394579076224911e-7,
0.05083075757257047107, 8.9071395140242387124e-8,
0.042787652157725676034, 4.8420950198072369669e-8,
0.035816505604196436523, 2.579956822953589238e-8,
0.029808628117310126969, 1.3464645522302038796e-8,
0.024661087314753282511, 6.8784610955899001111e-9,
0.020277183817500123926, 3.4371856744650090511e-9,
0.016566786254247575375, 1.6788897682161906807e-9,
0.013446536605285730674, 8.0099784479729665356e-10,
0.010839937168255907211, 3.7299501843052790038e-10,
0.0086773307495391815854, 1.6939457789411646876e-10,
0.0068957859690660035329, 7.4967397573818224522e-11,
0.0054388997976239984331, 3.230446433325236576e-11,
0.0042565295990178580165, 1.3542512912336274432e-11,
0.0033044669940348302363, 5.5182369468174885821e-12,
0.0025440657675291729678, 2.1835922099233609052e-12
0.0019418357759843675814, }
0.0014690143599429791058, };
0.0011011261134519383862,
0.00081754101332469493115,
0.00060103987991147422573,
0.00043739495615911687786,
0.00031497209186021200274,
0.00022435965205008549104,
0.00015802788400701191949,
0.00011002112846666697224,
0.000075683996586201477788,
0.000051421497447658802092,
0.0000344921247593431977,
0.000022832118109036146591,
0.000014908514031870608449,
9.5981941283784710776e-6,
6.0899100320949039256e-6,
3.8061983264644899045e-6,
2.3421667208528096843e-6,
1.4183067155493917523e-6,
8.4473756384859863469e-7,
4.9458288702754198508e-7,
2.8449923659159806339e-7,
1.6069394579076224911e-7,
8.9071395140242387124e-8,
4.8420950198072369669e-8,
2.579956822953589238e-8,
1.3464645522302038796e-8,
6.8784610955899001111e-9,
3.4371856744650090511e-9,
1.6788897682161906807e-9,
8.0099784479729665356e-10,
3.7299501843052790038e-10,
1.6939457789411646876e-10,
7.4967397573818224522e-11,
3.230446433325236576e-11,
1.3542512912336274432e-11,
5.5182369468174885821e-12,
2.1835922099233609052e-12
}
};
#endregion #endregion
} }

4
src/UnitTests/IntegrationTests/IntegrationTest.cs
View File

@ -88,11 +88,9 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests
[TestCase(1e-13)] [TestCase(1e-13)]
public void TestDoubleExponentialTransformationAlgorithm(double targetRelativeError) public void TestDoubleExponentialTransformationAlgorithm(double targetRelativeError)
{ {
var algorithm = new DoubleExponentialTransformation();
Assert.AreEqual( Assert.AreEqual(
TargetAreaA, TargetAreaA,
algorithm.Integrate(TargetFunctionA, StartA, StopA, targetRelativeError), DoubleExponentialTransformation.Integrate(TargetFunctionA, StartA, StopA, targetRelativeError),
targetRelativeError * TargetAreaA, targetRelativeError * TargetAreaA,
"DET Adaptive {0}", "DET Adaptive {0}",
targetRelativeError); targetRelativeError);

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