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", ySpectrum["InterpolationPointsSubdivision",0.2,0.3] gives zero, while ySpectrum["AdaptiveMonteCarlo",0.2,0.3] is non-zero (as it should be, if looking at the initial data). … But how to make "InterpolationPointsSubdivision" work correctly? It does not work properly with non-rectangular regions of integration. …

1}]; var = Flatten[Table[co[i, j], {j, 0, jm, 1}, {i, 0, 2^j - 1, 1}]]; varM = Join[{co[-1, -1]}, var]; eq[x_] := Sum[NIntegrate[Cot[(x - t)/2]*h[t, i, 2^j], {t, -ac, x, ac}, Method -> {"InterpolationPointsSubdivision … ", Method -> {"PrincipalValue", "SymbolicProcessing" -> 0}}]* co[i, j], {j, 0, jm, 1}, {i, 0, 2^j - 1, 1}] + NIntegrate[Cot[(x - t)/2]*h1[t], {t, -ac, x, ac}, Method -> {"InterpolationPointsSubdivision …

= s}}], (* subtract singular part *) {s, -L, x, L}, Method -> {"InterpolationPointsSubdivision", (* divide interval at nodes *) "SymbolicProcessing" -> 0}, PrecisionGoal - … = xp}}], {xp, -L, x, L}, Method -> {"InterpolationPointsSubdivision", "SymbolicProcessing" -> 0}, PrecisionGoal -> 4] + dux*((2*L) Log[(L + x)/(L - x)])/π]]; Single-call timings …

Verify how many interpolation points are used in the integration interval of interest: Count[Flatten[derPhi["Grid"]], x_ /; 1/4 < x < 1/2] 63 We can then use the "InterpolationPointsSubdivision" … The count above is well within the default setting of "MaxSubregions", so that doesn't need to be adjusted: NIntegrate[derPhi[x], {x, 1/4, 1/2}, Method -> {"InterpolationPointsSubdivision" …

You can specify the singularities sometimes with Method -> "InterpolationPointsSubdivision", but it does not work here, maybe because of the complexity of p1. …

NumericQ, t_ /; t == 0] := (cnt++; NIntegrate[inicos'''[xp]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method -> "PrincipalValue"}, PrecisionGoal … NumericQ, t_ /; t == 0] := (cnt++; NIntegrate[ inicos'''[xp]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method -> "PrincipalValue" …

NumericQ, t_ /; t == 0] := (cnt++; NIntegrate[inicos'''[xp]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method -> "PrincipalValue"}, PrecisionGoal … NumericQ] := Function[x, cnt++; NIntegrate[Interpolation[periodize@Transpose@{xv, uppp}, xp, PeriodicInterpolation -> True]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision …

NumericQ, t_ /; t == 0] := (cnt++; c*NIntegrate[D[ic[xp], {xp, 3}]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method -> {"PrincipalValue", " … NumericQ, t_ /; t == 0] := (cnt2++; c*NIntegrate[D[ic[xp], {xp, 2}]*int[D[ic[xp], xp], x, t]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method …

NumericQ, t_ /; t == 0] := (cnt++; NIntegrate[-Cos[xp]/ (x - xp), {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method -> "PrincipalValue"}, PrecisionGoal -> 8 … VectorQ, t_] := Function[x, cnt++; NIntegrate[ Interpolation[periodize@Transpose@{xv, uppp}, xp, PeriodicInterpolation -> True]/ (x - xp), {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision …

weak singularities, which require dense sampling to get an accurate estimate or require the integration region to be broken up according to the pieces of the piecewise interpolation, which is what the "InterpolationPointsSubdivision … i1 = NIntegrate[ DistrToyInterpolated[thh, Eh], {thh, 0, Pi}, {Eh, 125, 3000}, Method -> {"InterpolationPointsSubdivision", "MaxSubregions" -> 315*3000/5, (* slight overestimate from interpolation …

The "InterpolationPointsSubdivision" preprocessor of NIntegrate seems like the right move, but it was much faster and with a much better result to do a simple, straightforward implementation of an integration …

From here, we can use the sRGB conversion functions from this answer, and then use NIntegrate[] with the setting Method -> "InterpolationPointsSubdivision": (* gamma correction *) sRGBGamma = Function … 12.92 z, z <= 0.0031308}}, 1.055 z^(1/2.4) - 0.055]], Listable]; NIntegrate[Clip[#, {0, 1}]/λ^4, {λ, 385, 700}, Method -> "InterpolationPointsSubdivision …

NumericQ, t_ /; t == 0] := (cnt++; NIntegrate[ D[0.1*Cos[\[Pi]/L*xp], {xp, 3}]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision", Method … cnt++; NIntegrate[ Interpolation[periodize@Transpose@{xv, uppp}, xp, PeriodicInterpolation -> True]*Cot[\[Pi] (x - xp)/(2*L)], {xp, x - L, x, x + L}, Method -> {"InterpolationPointsSubdivision …

To do that, I the function Si2[a_, b_] := NIntegrate[Sin[x - y]/(x y), {x, a, b}, {y, x, b}, AccuracyGoal -> 25, PrecisionGoal -> 25, WorkingPrecision -> 40, MaxRecursion -> 1000000, Method -> "InterpolationPointsSubdivision … Note that I use the InterpolationPointsSubdivision method because I saw in various answers that it is a good method to evaluate numerically a highly-oscillatory integrand. …

opts = {{}, Method -> "InterpolationPointsSubdivision", {Method -> {Automatic, "SymbolicProcessing" -> 0}, PrecisionGoal -> 3}}; res = Table[ With[{x = 5, y = 5, o1 = o}, Prepend …