Multivariate integration

[Alexander-Murray]

Hey, I tried following the tutorial examples here but I can't seem to figure out the right syntax for multivariate integration. Here is what I am trying:

deg = [3, 5, 6, 4]
d = minimum(deg)
op1 = GaussOrthoPoly(deg[1], addQuadrature=true);
op2 = Uniform01OrthoPoly(deg[2], addQuadrature=true);
op3 = Beta01OrthoPoly(deg[3], 2, 1.2, addQuadrature=true);
ops = [op1, op2, op3];
mop = MultiOrthoPoly(ops, d);
integrate((a,b,c,d) -> a*b*c*d, mop)

however, I get the following error:

type MultiOrthoPoly has no field quad

Stacktrace:
 [1] getproperty(::MultiOrthoPoly{ProductMeasure,Quad{Float64,Array{Float64,1}},Array{AbstractCanonicalOrthoPoly{Array{Float64,1},M,Quad{Float64,Array{Float64,1}}} where M,1}}, ::Symbol) at .\Base.jl:33
 [2] integrate(::Function, ::MultiOrthoPoly{ProductMeasure,Quad{Float64,Array{Float64,1}},Array{AbstractCanonicalOrthoPoly{Array{Float64,1},M,Quad{Float64,Array{Float64,1}}} where M,1}}) at C:\Users\mrra\.julia\packages\PolyChaos\AlY80\src\auxfuns.jl:96
 [3] top-level scope at In[5]:8
 [4] include_string(::Function, ::Module, ::String, ::String) at .\loading.jl:1091

Is there any way of doing this with the PolyChaos package?

[Alexander-Murray]

One solution is to use multiple univariate integrals:

deg = [3, 5, 6, 4]
op1 = GaussOrthoPoly(deg[1], addQuadrature=true);
op2 = Uniform01OrthoPoly(deg[2], addQuadrature=true);
op3 = Beta01OrthoPoly(deg[3], 2, 1.2, addQuadrature=true);
ops = [op1, op2, op3];
integrate(c->integrate(b->integrate((a)->a*b*c, op1),op2),op3)

however, I'd be interested to hear about other approaches.

[timueh]

hi Alex, yes, multiple univariate integrals is the way to proceed.

Put differently, there is not support for generic multivariate integration, only integration of product measures for which you can decompose the $n$-variate integral to $n$ univariate integrals. For each of the $n$ univariate integrals you can then use the quad rules.