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JoshuaLampert
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Non-breaking internal restructuring (#79)
* Remove sole author credit, bump version * Bump compat minimums for consistency with Meshes * Generalize GaussLegendre rules * Bump test versions * Move dim specializations into _integral wrappers * Bugfix * Change to product of ntuple of Returns * Bugfix * Make jacobian arg ts generic (vector or tuple) * Fix copy/paste error * Make differential arg ts generic * Remove obsoleted methods * Allocate and zero ev in one step * Add explicit rtol's where needed * Combine methods with optional argument * Switch to generalized GaussLegendre method * Split IntegrationAlgorithm into separate file * Split BezierCurve methods into separate file * Split Line methods into separate file * Split Tetrahedron methods into separate file * Split Triangle methods into separate file * Split Ray methods into separate file * Split CylinderSurface methods into separate file * Split ConeSurface methods into separate file * Split FrustumSurface methods into separate file * Split Plane methods into separate file * Move GaussKronrod specializations into single section * Consolidate conic methods under new structure * Split Ring and Rope methods into separate files * Fix typo * Remove obsolete files * Point alias functions directly toward worker methods * Undo last commit * Revert to a minor version bump * Fix docstring typos Co-authored-by: Joshua Lampert <[email protected]> * Remove MeshIntegrals from test Project * Add conditional for selecting default integration rule * Update comment * Reduce Meshes lower bound --------- Co-authored-by: Joshua Lampert <[email protected]>
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-846
lines changed

Diff for: ‎Project.toml

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Original file line numberDiff line numberDiff line change
@@ -1,7 +1,6 @@
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name = "MeshIntegrals"
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uuid = "dadec2fd-bbe0-4da4-9dbe-476c782c8e47"
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authors = ["Mike Ingold <[email protected]>"]
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version = "0.13.4"
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version = "0.13.5"
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[deps]
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CoordRefSystems = "b46f11dc-f210-4604-bfba-323c1ec968cb"

Diff for: ‎src/MeshIntegrals.jl

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@@ -11,11 +11,23 @@ module MeshIntegrals
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include("utils.jl")
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export jacobian, derivative, unitdirection
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include("integration_algorithms.jl")
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export GaussKronrod, GaussLegendre, HAdaptiveCubature
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include("integral.jl")
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include("integral_aliases.jl")
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include("integral_line.jl")
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include("integral_surface.jl")
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include("integral_volume.jl")
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export GaussKronrod, GaussLegendre, HAdaptiveCubature
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export integral, lineintegral, surfaceintegral, volumeintegral
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# Integration methods specialized for particular geometries
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include("specializations/BezierCurve.jl")
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include("specializations/ConeSurface.jl")
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include("specializations/CylinderSurface.jl")
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include("specializations/FrustumSurface.jl")
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include("specializations/Line.jl")
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include("specializations/Plane.jl")
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include("specializations/Ray.jl")
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include("specializations/Ring.jl")
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include("specializations/Rope.jl")
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include("specializations/Tetrahedron.jl")
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include("specializations/Triangle.jl")
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end

Diff for: ‎src/integral.jl

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Original file line numberDiff line numberDiff line change
@@ -1,48 +1,3 @@
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################################################################################
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# Integration Algorithms
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################################################################################
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abstract type IntegrationAlgorithm end
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"""
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GaussKronrod(kwargs...)
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Numerically integrate using the h-adaptive Gauss-Kronrod quadrature rule implemented
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by QuadGK.jl. All standard `QuadGK.quadgk` keyword arguments are supported.
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"""
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struct GaussKronrod <: IntegrationAlgorithm
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kwargs
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GaussKronrod(; kwargs...) = new(kwargs)
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end
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"""
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GaussLegendre(n)
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Numerically integrate using an `n`'th-order Gauss-Legendre quadrature rule. nodes
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and weights are efficiently calculated using FastGaussQuadrature.jl.
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So long as the integrand function can be well-approximated by a polynomial of
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order `2n-1`, this method should yield results with 16-digit accuracy in `O(n)`
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time. If the function is know to have some periodic content, then `n` should
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(at a minimum) be greater than the expected number of periods over the geometry,
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e.g. `length(geometry)/lambda`.
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"""
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struct GaussLegendre <: IntegrationAlgorithm
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n::Int64
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end
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"""
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GaussKronrod(kwargs...)
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Numerically integrate areas and surfaces using the h-adaptive cubature rule
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implemented by HCubature.jl. All standard `HCubature.hcubature` keyword
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arguments are supported.
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"""
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struct HAdaptiveCubature <: IntegrationAlgorithm
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kwargs
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HAdaptiveCubature(; kwargs...) = new(kwargs)
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end
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################################################################################
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# Master Integral Function
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################################################################################
@@ -68,57 +23,38 @@ contrast, increasing `FP` to e.g. `BigFloat` will typically increase precision
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"""
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function integral end
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# If only f and geometry are specified, default to HAdaptiveCubature
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# If only f and geometry are specified, select default algorithm
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function integral(
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f::F,
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geometry::G
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) where {F<:Function, G<:Meshes.Geometry}
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_integral(f, geometry, HAdaptiveCubature())
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end
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# If algorithm is HAdaptiveCubature, use the generalized n-dim solution
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function integral(
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f::F,
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geometry::G,
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settings::HAdaptiveCubature
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) where {F<:Function, G<:Meshes.Geometry}
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_integral(f, geometry, settings)
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N = Meshes.paramdim(geometry)
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rule = (N == 1) ? GaussKronrod() : HAdaptiveCubature()
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_integral(f, geometry, rule)
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end
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# If algorithm is HAdaptiveCubature, and FP specified, use the generalized n-dim solution
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# with algorithm and T specified
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function integral(
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f::F,
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geometry::G,
92-
settings::HAdaptiveCubature,
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FP::Type{T}
94-
) where {F<:Function, G<:Meshes.Geometry, T<:AbstractFloat}
40+
settings::I,
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FP::Type{T} = Float64
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) where {F<:Function, G<:Meshes.Geometry, I<:IntegrationAlgorithm, T<:AbstractFloat}
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_integral(f, geometry, settings, FP)
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end
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# If algorithm is not HAdaptiveCubature, specialize on number of dimensions
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function integral(
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f::F,
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geometry::G,
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settings::I
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) where {F<:Function, G<:Meshes.Geometry, I<:IntegrationAlgorithm}
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# Run the appropriate integral type
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Dim = Meshes.paramdim(geometry)
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if Dim == 1
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return _integral_1d(f, geometry, settings)
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elseif Dim == 2
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return _integral_2d(f, geometry, settings)
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elseif Dim == 3
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return _integral_3d(f, geometry, settings)
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end
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end
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# If algorithm is not HAdaptiveCubature, and FP specified, specialize on number of dimensions
116-
function integral(
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f::F,
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geometry::G,
119-
settings::I,
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FP::Type{T}
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) where {F<:Function, G<:Meshes.Geometry, I<:IntegrationAlgorithm, T<:AbstractFloat}
47+
################################################################################
48+
# Generalized (n-Dimensional) Worker Methods
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################################################################################
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# GaussKronrod
52+
function _integral(
53+
f,
54+
geometry,
55+
settings::GaussKronrod,
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FP::Type{T} = Float64
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) where {T<:AbstractFloat}
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# Run the appropriate integral type
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Dim = Meshes.paramdim(geometry)
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if Dim == 1
@@ -130,12 +66,32 @@ function integral(
13066
end
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end
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69+
# GaussLegendre
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function _integral(
71+
f,
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geometry,
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settings::GaussLegendre,
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FP::Type{T} = Float64
75+
) where {T<:AbstractFloat}
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N = Meshes.paramdim(geometry)
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78+
# Get Gauss-Legendre nodes and weights for a region [-1,1]^N
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xs, ws = _gausslegendre(FP, settings.n)
80+
weights = Iterators.product(ntuple(Returns(ws), N)...)
81+
nodes = Iterators.product(ntuple(Returns(xs), N)...)
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134-
################################################################################
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# Generalized (n-Dimensional) Worker Methods
136-
################################################################################
83+
# Domain transformation: x [-1,1] ↦ t [0,1]
84+
t(x) = FP(1//2) * x + FP(1//2)
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138-
# General solution for HAdaptiveCubature methods
86+
function integrand((weights, nodes))
87+
ts = t.(nodes)
88+
prod(weights) * f(geometry(ts...)) * differential(geometry, ts)
89+
end
90+
91+
return FP(1//(2^N)) .* sum(integrand, zip(weights, nodes))
92+
end
93+
94+
# HAdaptiveCubature
13995
function _integral(
14096
f,
14197
geometry,
@@ -158,3 +114,38 @@ function _integral(
158114
# Reapply units
159115
return value .* integrandunits
160116
end
117+
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################################################################################
119+
# Specialized GaussKronrod Methods
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################################################################################
121+
122+
function _integral_1d(
123+
f,
124+
geometry,
125+
settings::GaussKronrod,
126+
FP::Type{T} = Float64
127+
) where {T<:AbstractFloat}
128+
integrand(t) = f(geometry(t)) * differential(geometry, [t])
129+
return QuadGK.quadgk(integrand, FP(0), FP(1); settings.kwargs...)[1]
130+
end
131+
132+
function _integral_2d(
133+
f,
134+
geometry2d,
135+
settings::GaussKronrod,
136+
FP::Type{T} = Float64
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) where {T<:AbstractFloat}
138+
integrand(u,v) = f(geometry2d(u,v)) * differential(geometry2d, [u,v])
139+
∫₁(v) = QuadGK.quadgk(u -> integrand(u,v), FP(0), FP(1); settings.kwargs...)[1]
140+
return QuadGK.quadgk(v -> ∫₁(v), FP(0), FP(1); settings.kwargs...)[1]
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end
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143+
# Integrating volumes with GaussKronrod not supported by default
144+
function _integral_3d(
145+
f,
146+
geometry,
147+
settings::GaussKronrod,
148+
FP::Type{T} = Float64
149+
) where {T<:AbstractFloat}
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error("Integrating this volume type with GaussKronrod not supported.")
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end

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