10"int1_type: an algebraic integrand of the form f(x) = x**2 / (x**2 + 1) / (x**2 + 4) for x in (lb, ub)"
19if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
20getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
210.592319847946765693983261139952398973,
0.592319847946765693983261139951656719,
0.122995853428115837177070158359807283E-22,
0.742253400566840697767773899072230989E-30 (unbiased)? TRUE
28if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
29getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
300.592319847946765693983261139952398973,
0.592319847946765693983261139951656623,
0.122995853428115837177070158261927716E-22,
0.742349697064060059560426697969360235E-30 (unbiased)? TRUE
35"int2_type: an algebraic integrand of the form f(x) = 1 / sqrt(a - b * x) for x in (0, a / b) with a > 0 and b > 0 with a singularity at the upper bound of integration"
44if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
46 ******** Integration did NOT converge
. ********
48getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
490.942809041582063365867792482806465323,
0.942809041582063358489159110539769991,
0.274189625236721766830515122145815584E-15,
0.737863337226669533225571680774701636E-17 (unbiased)? TRUE
56if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
57getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
580.942809041582063365867792482806465323,
0.942809041582063365867792482806451456,
0.747866619686254516023298199584791888E-27,
0.138666955995880981420030411866114767E-31 (unbiased)? TRUE
63"int3_type: an algebraic integrand of the form f(x) = log(x) / sqrt(x) for x in (0, ub) with a singularity at the lower limit of integration"
72if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
73getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
74-3.12249862669012531099145873075559453,
-3.12249862669012531099145800385027096,
0.871742302516757365494019872303469907E-22,
0.726905323565232669836577649328480277E-24 (unbiased)? TRUE
81if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
82getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
83-3.12249862669012531099145873075559453,
-3.12249862669012531099145873075553329,
0.638742935999207969456768107027576605E-25,
0.612445722315141001271800985742006887E-31 (unbiased)? TRUE
88"int4_type: an algebraic integrand of the form f(x) = log(x) / (1. + log(x)**2)**2 for x in (0, 1) with a singularity at the lower limit"
97if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
98getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
99-0.189275187882093321180367135892330336,
-0.189275187882093321180367139193492826,
0.439350295463286972817507956603694862E-23,
0.330116248974192359134514995223265581E-26 (unbiased)? TRUE
106if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
107getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
108-0.189275187882093321180367135892330336,
-0.189275187882093321180367392427969773,
0.530509501355781083785828386429659476E-23,
0.256535639436815431080742250597631077E-24 (unbiased)? TRUE
113"intSinCos_typer(): a highly oscillatory integrand of the form f(x) = cos(a * sin(b * x)) for x in (lb, ub)"
122if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
123getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
124-6.18103992684276605416490727881801341,
-6.18103992684276605416490727881796180,
0.204459144829722446056783263048240039E-21,
0.516149225095779208619002088612760521E-31 (unbiased)? TRUE
131if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
132getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
133-6.18103992684276605416490727881801341,
-6.18103992684276605416490727881796180,
0.204459144829722446056783263048240039E-21,
0.516149225095779208619002088612760521E-31 (unbiased)? TRUE
138"intNormPDF_type: f(x) = exp(-0.5 * (log(x) - mu)**2 / sigma**2) / (sigma * sqrt(2 * acos(-1.))) for x in (lb, ub)"
147if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
148getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
1490.997300203936739810946696370464810073,
0.997300203936739810946696370464810073,
0.863216418769238025171827058295059452E-23,
0.00000000000000000000000000000000000 (unbiased)? TRUE
156if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
157getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
1580.997300203936739810946696370464810073,
0.997300203936739810946696370464810073,
0.863216418769238025171827058295059452E-23,
0.00000000000000000000000000000000000 (unbiased)? TRUE
163"intLogNormPDF_type: f(x) = exp(-0.5 * (log(x) - mu)**2 / sigma**2) / (x * sigma * sqrt(2 * acos(-1.))) for x in (0 <= lb, ub)"
172if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
173getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
1740.999999998026824709924603718598271714,
0.999999998026824709924603718597611697,
0.287685113478269648540938767224899488E-23,
0.660016191941505726842283640923854592E-30 (unbiased)? TRUE
181if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
182getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
1830.999999998026824709924603718598271714,
0.999999998026824709924603718597611601,
0.287685113534716101717891864391506212E-23,
0.660112488438725088634936439820983838E-30 (unbiased)? TRUE
198"int5_type: an algebraic integrand of the form f(x) = x**3 log(abs((x**2 - 1) * (x**2 - 2))) for x in (0., 3.) with 4 possible singularities: [-sqrt(2.), -1., 1., sqrt(2.)]"
207if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
208getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
20952.7407483834714449977291997202299809,
52.7407483834714449977291765299254724,
0.172884396198263085498243239907807437E-20,
0.231903045085095141212385933523689371E-22 (unbiased)? TRUE
216if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
217getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
21852.7407483834714449977291997202299809,
52.7407483834714449977292388198386134,
0.157545601084532647841636140405395188E-20,
0.390996086324092930047679517794757520E-22 (unbiased)? TRUE
225break
= integrand
%break
227+1.00000000000000000000000000000000000,
+1.41421356237309504880168872420969798
228if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
229getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
23052.7407483834714449977291997202299809,
52.7407483834714449977291997201071898,
0.145935898758650954111037868386060001E-21,
0.122791130278308118836119374489798694E-27 (unbiased)? TRUE
235"int5_type: an algebraic integrand of the form f(x) = x**3 log(abs((x**2 - 1) * (x**2 - 2))) for x in (-2., 5.) with 4 possible singularities: [-sqrt(2.), -1., 1., sqrt(2.)]"
244if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
245getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
246808.362636933094758891687400938039628,
808.362636933094758891687268473760062,
0.255379463719878359511890040859317480E-19,
0.132464279565495221439626229092202295E-21 (unbiased)? TRUE
253if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
254getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
255808.362636933094758891687400938039628,
808.362636933094758891681251389789229,
0.334323235794388144484139093037256979E-20,
0.614954825039840811287942669490845986E-20 (unbiased)? FALSE
262break
= integrand
%break
264-1.41421356237309504880168872420969798,
-1.00000000000000000000000000000000000,
+1.00000000000000000000000000000000000,
+1.41421356237309504880168872420969798
265if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
266getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
267808.362636933094758891687400938039628,
808.362636933094758891687400937280645,
0.990216586020630180919255548708256071E-21,
0.758982798435765983281759345872700701E-27 (unbiased)? TRUE
282"intGamUpp_type: an algebraic integrand of the form f(x; lb, alpha, beta) = (x / lb)**alpha * exp(-beta * (x - lb)) for x in (lb, +Inf), lb > 0."
291if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
292getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
2932.00000000000000000000000000000000039,
2.00000000000000000000000000000000039,
0.503988260578339162149833493686791185E-24,
0.00000000000000000000000000000000000 (unbiased)? TRUE
300if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
301getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
3022.00000000000000000000000000000000039,
2.00000000000000000000000000000000039,
0.503988260578338140171031197806738174E-24,
0.00000000000000000000000000000000000 (unbiased)? TRUE
307"intLogNormPDF_type: f(x) = exp(-0.5 * (log(x) - mu)**2 / sigma**2) / (x * sigma * sqrt(2 * acos(-1.))) for x in (0 <= lb, ub)"
316if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
317getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
3181.00000000000000000000000000000000000,
1.00000000000000000000000005509718469,
0.185875326636098607607964145008442373E-22,
0.550971846938518212456720189377984095E-25 (unbiased)? TRUE
325if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
326getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
3271.00000000000000000000000000000000000,
1.00000000000000000000000005509718469,
0.185875326636098606689609183428530258E-22,
0.550971846938518212456720189377984095E-25 (unbiased)? TRUE
332"intDoncker1_type: f(x) = 1 / (1 + x) / sqrt(x) for x in (0 <= lb, ub) with a square-root singularity at 0"
341if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
343 ******** Integration did NOT converge
. ********
345getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
3463.14159265358979323846264338327950280,
3.14159265358979319764120376296608615,
0.114874526811124567747394666325693956E-14,
0.408214396203134166514689154707924291E-16 (unbiased)? TRUE
353if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
354getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
3553.14159265358979323846264338327950280,
3.14159265358979323846264338346019817,
0.105499447763580851205123272015818952E-22,
0.180695369614276997099759184920380085E-27 (unbiased)? TRUE
360"int6_type: an algebraic integrand of the form f(x) = log(x) / (1 + 100 * x**2) for x in (0, +Inf) with a singularity at the lower limit"
369if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
370getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
371-0.361689220620773240624502327513089541,
-0.361689220620773240624502327908133835,
0.118682246318398965349923011739062857E-22,
0.395044294632030724453129549211143496E-27 (unbiased)? TRUE
378if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
379getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
380-0.361689220620773240624502327513089541,
-0.361689220620773240624502327510642406,
0.120941504830908329737177699048668687E-23,
0.244713473558703155578925197329697327E-29 (unbiased)? TRUE
385"int7_type: an algebraic integrand of the form f(x) = -log(abs((1 - x**2) * (1 - 2 * x**2)) / x**4) / x**5 for x in (1./3., +Inf) with two singularities at [1 / sqrt(2), 1]"
394if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
395getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
39652.7407483834714449977291997202299809,
52.7407483834714449977292221649683846,
0.168283512274674281393657004006737318E-20,
0.224447384036677384031379327649902600E-22 (unbiased)? TRUE
403if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
404getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
40552.7407483834714449977291997202299809,
52.7407483834714449977306706202548049,
0.169942945536630143394077258382982232E-20,
0.147090002482391233646949135657205724E-20 (unbiased)? TRUE
412break
= integrand
%break
414+0.707106781186547524400844362104849088,
+1.00000000000000000000000000000000000
415if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
416getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
41752.7407483834714449977291997202299809,
52.7407483834714449977291997199544774,
0.550213208024888852525213619612864128E-21,
0.275503508172616333885316422295596819E-27 (unbiased)? TRUE
432"int8_type: an algebraic integrand of the form f(x) = log(abs((1 - x**2) * (1 - 2 * x**2)) / x**4) / x**5 for x in (-Inf, -1./3.) with two singularities at [-1, -1 / sqrt(2)]"
441if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
442getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
44352.7407483834714449977291997202299809,
52.7407483834714449977292221649683846,
0.168283512274674281393657004006737318E-20,
0.224447384036677384031379327649902600E-22 (unbiased)? TRUE
450if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
451getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
45252.7407483834714449977291997202299809,
52.7407483834714449977306706202548049,
0.169942945536630143394077258382982232E-20,
0.147090002482391233646949135657205724E-20 (unbiased)? TRUE
459break
= integrand
%break
461-1.00000000000000000000000000000000000,
-0.707106781186547524400844362104849088
462if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
463getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
46452.7407483834714449977291997202299809,
52.7407483834714449977291997199544774,
0.550213208024888852525213619612864128E-21,
0.275503508172616333885316422295596819E-27 (unbiased)? TRUE
469"intDoncker2_type: f(x) = exp(x) / sqrt(-x) for x in (lb, ub <= 0) with a square-root singularity at 0"
478if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
480 ******** Integration did NOT converge
. ********
482getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
4831.77245385090551602729816748334114514,
1.77245385090551600687177993068626502,
0.574360549312137963665679582228894917E-15,
0.204263875526548801162109406012147667E-16 (unbiased)? TRUE
490if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
491getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
4921.77245385090551602729816748334114514,
1.77245385090551602729816748322058404,
0.316674820796741424790461948518443858E-23,
0.120561095995702138441865857630079607E-27 (unbiased)? TRUE
497"intDoncker2_type: f(x) = exp(x) / sqrt(-x) for x in (lb, ub <= 0) with a square-root singularity at 0"
506if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
507getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
5080.278805585280661976499232611077439155,
0.278805585280661976499232611077447244,
0.136847162139771908855491210817521382E-24,
0.808890576642639058283510735885669474E-32 (unbiased)? TRUE
515if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
516getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
5170.278805585280661976499232611077439155,
0.278805585280661976499232611077447292,
0.136847162139771908864182157536569162E-24,
0.813705401503607147916150680742131792E-32 (unbiased)? TRUE
532"int9_type: an algebraic piecewise integrand of the form f(x) = log(abs((1 - x**2) * (1 - 2 * x**2)) / x**4) / x**5 for x in (1./3., +Inf) and 1 / (acos(-1) * sqrt(-(x+10) * (x+9))) for x in (-10, 9), otherwise 0, with two singularities at [-10, -9, 1/3., 1 / sqrt(2), 1]"
541if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
543 ******** Integration did NOT converge
. ********
545getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
54653.7407483834714449977291997202299809,
53.7407483834714446968169568664147327,
0.297103187254200474475915711578675253E-14,
0.300912242853815248241860288447560029E-15 (unbiased)? TRUE
553if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
555 ******** Integration did NOT converge
. ********
557getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
55853.7407483834714449977291997202299809,
53.7407483834714786408368937861800291,
0.597341489232741586490157071452958427E-12,
0.336431076940659500481100214330126955E-13 (unbiased)? TRUE
565break
= integrand
%break
567-10.0000000000000000000000000000000000,
-9.00000000000000000000000000000000000,
+0.333333333333333333333333333333333317,
+0.707106781186547524400844362104849088,
+1.00000000000000000000000000000000000
568if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
569getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
57053.7407483834714449977291997202299809,
53.7407483834714449977291998296210022,
0.511241450110203608013944520330859404E-22,
0.109391021252254961020398451633034320E-24 (unbiased)? TRUE
575"intNormPDF_type: f(x) = exp(-0.5 * (log(x) - mu)**2 / sigma**2) / (sigma * sqrt(2 * acos(-1.))) for x in (lb, ub)"
584if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
585getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
5861.00000000000000000000000000000000000,
0.999999999999999999999999999999999133,
0.386431949672064481044988439592369946E-24,
0.866668474974256133875190074163217293E-33 (unbiased)? TRUE
593if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
594getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
5951.00000000000000000000000000000000000,
0.999999999999999999999999999999999133,
0.386431949672064466119465327815932357E-24,
0.866668474974256133875190074163217293E-33 (unbiased)? TRUE
600"intGenExpGammaPDF_type: f(x) = GenExpGamma(x; kappa = 1., omega = 1., logSigma = 0.) for x in (-Inf, Inf)"
609if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
610getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6111.00000000000000000000000000000000000,
1.00000000000000000000000000000013597,
0.148409338409973194577277535014189193E-22,
0.135970654073738851225752042746495869E-30 (unbiased)? TRUE
618if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
619getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6201.00000000000000000000000000000000000,
1.00000000000000000000000000000013597,
0.148409338409973194495421223865688864E-22,
0.135970654073738851225752042746495869E-30 (unbiased)? TRUE
625"intGenExpGammaPDF_type: f(x) = GenExpGamma(x; kappa = 5., omega = 10., logSigma = 2.) for x in (-Inf, Inf)"
634if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
635getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6361.00000000000000000000000000000000000,
1.00000000000000000000000000000000578,
0.132417436079502091744367222811402828E-22,
0.577778983316170755916793382775478196E-32 (unbiased)? TRUE
643if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
644getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6451.00000000000000000000000000000000000,
1.00000000000000000000000000000000578,
0.132417436079839015749459180202287325E-22,
0.577778983316170755916793382775478196E-32 (unbiased)? TRUE
650"intPentaGammaInf_type: f(x) = sum of five Gamma PDFs with five break points in the integration range x in (-Inf, +Inf)"
659if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
661 ******** Integration did NOT converge
. ********
663getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6645.00000000000000000000000000000000000,
4.99999999999999999999972410297847334,
0.200738257888944093088270474559436884E-19,
0.275897021526661457740995046287992818E-21 (unbiased)? TRUE
671if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
672getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6735.00000000000000000000000000000000000,
4.99999999999999999999999459738972784,
0.120968281919312175939861440033309516E-21,
0.540261027215530879807578922336193197E-23 (unbiased)? TRUE
680break
= integrand
%break
682-9.00000000000000000000000000000000000,
-5.00000000000000000000000000000000000,
+2.00000000000000000000000000000000000,
+5.00000000000000000000000000000000000,
+7.00000000000000000000000000000000000
683if (
isFailedQuad(getFunc, lb, ub, break, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
684getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
6855.00000000000000000000000000000000000,
4.99999999999999999999999999996475779,
0.454086489790053140200838733525734823E-22,
0.352422068663531514279007291757730680E-28 (unbiased)? TRUE
695"intCauchy1_type: an integrand of the form w(x) * f(x) with Cauchy weight w(x) 1 / (x - cs) and f(x) = 1 ~,~ x \in (lb < cs, cs < ub)"
704if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
706 ******** Integration did NOT converge
. ********
708getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
709-0.405465108108164381978013115464349228,
-2.04356971055286136189443548589605091,
7.24146052036062818462419495305868050,
1.63810460244469697991642237043170168 (unbiased)? TRUE
716if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
718 ******** Integration did NOT converge
. ********
720getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
721-0.405465108108164381978013115464349228,
-0.405465108108164381978013115464718525,
0.948013123403926992764805620933964846E-25,
0.369297066836252474823483770490659813E-30 (unbiased)? TRUE
729+1.00000000000000000000000000000000000
730if (
isFailedQuad(getFuncUnweighted, lb, ub, integrand
%wcauchy, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
731getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
732-0.405465108108164381978013115464349228,
-0.405465108108164381978013115464349036,
0.192592994438723585305597794258492732E-33,
0.192592994438723585305597794258492732E-33 (unbiased)? TRUE
737"intCauchy2_type: an integrand of the form w(x) * f(x) = 1 / (x + 2.) / (x - 3.) for x in (-3., 2.)"
746if (
isFailedQuad(getFunc, lb, ub, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
748 ******** Integration did NOT converge
. ********
750getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
751-0.635610766069589123929388320259411106,
-0.313635651749756707119425316680125425,
1.43562881981449143882504794728653286,
0.321975114319832416809963003579285681 (unbiased)? TRUE
758if (
isFailedQuad(getFunc, lb, ub,
weps, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
760 ******** Integration did NOT converge
. ********
762getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
763-0.635610766069589123929388320259411106,
-0.635610766069589123929388320259460313,
0.597574167278168521319843806854314588E-24,
0.492075100790938760455802364330448930E-31 (unbiased)? TRUE
771-2.00000000000000000000000000000000000
772if (
isFailedQuad(getFuncUnweighted, lb, ub, integrand
%wcauchy, integral, abserr, neval
= numFuncEval))
call disp%show(
' ******** Integration did NOT converge. ********', tmsize
= 1_IK, bmsize
= 1_IK)
773getStr([truth, integral, abserr, abs(integral
- truth)])
//SK_
' (unbiased)? '//getStr(abs(integral
- truth)
<= abserr)
774-0.635610766069589123929388320259411106,
-0.635610766069589123929388320259411106,
0.485640976828224618892203332811773371E-24,
0.00000000000000000000000000000000000 (unbiased)? TRUE
type(weps_type), parameter weps
The scalar constant object of type weps_type that indicates the use of Epsilon extrapolation method o...