# Hcubature + spherical from CoordinateTransformations
**URL:** https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042
**Category:** Specific Domains
**Tags:** question
**Created:** [July 14, 2024, 10:13pm UTC](https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042 "2024-07-14T22:13:39Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)
#### Post date: [July 14, 2024, 10:13pm UTC](https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042/1 "2024-07-14T22:13:39Z")
I am trying integration over a spherical shell by combining hcubature and spherical from CoordinateTransformations. I do get a method error. Code and error message below. Advice is much appreciated.
```julia
function foo(r)
return CartesianFromSpherical()(r)
end
hcubature(r -> foo(r)*r.r^2*sin(r.θ), (1,0,-pi/2), (2,2*π,π/2))
```
MethodError: no method matching (::CartesianFromSpherical)(::SVector{3, Float64})
Closest candidates are:
(::CartesianFromSpherical)(::Spherical) at ~/.julia/packages/CoordinateTransformations/jYKYg/src/coordinatesystems.jl:182
Stacktrace:
[1] foo(r::SVector{3, Float64})
@ Main ./In[61]:2
[2] (::var"#33#34")(r::SVector{3, Float64})
@ Main ./In[62]:1
[3] (::HCubature.GenzMalik{3, Float64})(f::var"#33#34", a::SVector{3, Float64}, b::SVector{3, Float64}, norm::typeof(norm))
@ HCubature ~/.julia/packages/HCubature/gOo1d/src/genz-malik.jl:121
[4] hcubature\_(f::var"#33#34", a::SVector{3, Float64}, b::SVector{3, Float64}, norm::typeof(norm), rtol\_::Int64, atol::Int64, maxevals::Int64, initdiv::Int64, buf::Nothing)
@ HCubature ~/.julia/packages/HCubature/gOo1d/src/HCubature.jl:110
[5] hcubature\_(f::Function, a::Tuple{Int64, Int64, Float64}, b::Tuple{Int64, Float64, Float64}, norm::Function, rtol::Int64, atol::Int64, maxevals::Int64, initdiv::Int64, buf::Nothing)
@ HCubature ~/.julia/packages/HCubature/gOo1d/src/HCubature.jl:182
[6] #hcubature#4
@ ~/.julia/packages/HCubature/gOo1d/src/HCubature.jl:235 [inlined]
[7] hcubature(f::Function, a::Tuple{Int64, Int64, Float64}, b::Tuple{Int64, Float64, Float64})
@ HCubature ~/.julia/packages/HCubature/gOo1d/src/HCubature.jl:235
[8] top-level scope
@ In[62]:1
---
### Author:  [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)
#### Post date: [July 15, 2024, 6:10am UTC](https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042/2 "2024-07-15T06:10:38Z")
Is this a good solution?
```julia
function foo(r)
r2 = Spherical(r[1],r[2],r[3])
return CartesianFromSpherical()(r2)
end
hcubature(r -> foo(r)*r[1]^2*sin(r[2]), (1,0,-pi/2), (2,2*π,π/2))
```
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [July 15, 2024, 12:47pm UTC](https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042/3 "2024-07-15T12:47:55Z")
> [@Domenico\_Lahaye](#):
>
> Is this a good solution?
Seems reasonable to me, except shouldn’t your third coordinate go from [0,\pi]?
(In this particular example, I believe your integral is zero; you might want to specify an absolute tolerance `atol` if this is a possibility in your real problem. I would also generally specify a relative tolerance `rtol`, as the default tolerance `1e-8` is fairly aggressive in multidimensional problems.)
---
### Author:  [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)
#### Post date: [July 15, 2024, 3:05pm UTC](https://discourse.julialang.org/t/hcubature-spherical-from-coordinatetransformations/117042/4 "2024-07-15T15:05:57Z")
Many thanks again!
1/ The way I understand the definition of the spherical coordinate system in CoordinateTransform.jl is that the latitude coordinate \phi runs from -pi/2 (negative z-axis) to +pi/2 (positive z-axis) (see docstring of Spherical). But it is indeed good to cross check.
2/ Thanks for the guideline on the tolerance settings. Will do.
3/ sin(r[2]) in the Jacobian should be cos(r[3]) instead