Add transformations for infinite and semi infinite integral. #33
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@ChrisRackauckas I applied this to Quadrature Algorithms. Can you check this further so that I can apply this to Cubature as well? |
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What do you mean? Cubature is just multi-dimensional quadrature. |
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@ChrisRackauckas No, I meant have I done correctly ? I added the check only to |
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It looks like it's written always assuming that lb and ub is scalar or length 1 which isn't correct, but when that's fixed it should be good to go. |
No, I have checked this works for vector inputs as well. Should I add a test case as well? |
Yes, on scalar and vector. |
src/Quadrature.jl
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| function transform_inf(t , p , f) | ||
| v(t) = t ./ (1 .- t.^2) | ||
| if t isa Number | ||
| j = ForwardDiff.derivative(v, t) |
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can we just write down the analytical solution to the derivatives here?
src/Quadrature.jl
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| end | ||
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| function transformation_if_inf(prob) | ||
| if (!(prob.lb isa Number) && all(prob.lb .== -Inf) && all(prob.ub .== Inf)) || (prob.lb == -Inf && prob.ub == Inf) |
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I wonder if this could be selectively applied to the directions which are Inf.
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Oh, does the transformation hold for that case?
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You can cache the indexes to transform and then if transform, then X otherwise identity.
ashutosh-b-b
changed the title
src/Quadrature.jl
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| if lb isa Number && ub isa Number | ||
| if lb == -Inf && ub == Inf | ||
| j = (1 .+ t.^2 )/(1 .- t.^2).^2 | ||
| return f(v_inf(t) , p)*(j) | ||
| elseif lb != -Inf && ub == Inf | ||
| a = lb | ||
| j = 1 ./ ((1 .- t).^2) | ||
| return f(v_semiinf(t , a) , p)*(j) | ||
| elseif lb == -Inf && ub != Inf | ||
| error("Semi Infinte integrals of limits 0 to Inf are supported") | ||
| end | ||
| end |
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this should be a separate dispatch
src/Quadrature.jl
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| j = 1 ./ ((1 .- t).^2) | ||
| return f(v_semiinf(t , a) , p)*(j) | ||
| elseif lb == -Inf && ub != Inf | ||
| error("Semi Infinte integrals of limits 0 to Inf are supported") |
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can't you just flip the integral to handle this case?
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