Merge pull request #67 from shahriariravanian/main

update to ver 1.3

Author: shahriariravanian

Project.toml

@@ -1,14 +1,13 @@
 name = "SymbolicNumericIntegration"
 uuid = "78aadeae-fbc0-11eb-17b6-c7ec0477ba9e"
 authors = ["Shahriar Iravanian <[email protected]>"]
-version = "1.2.0"
+version = "1.3.0"
 
 [deps]
 DataDrivenDiffEq = "2445eb08-9709-466a-b3fc-47e12bd697a2"
 DataDrivenSparse = "5b588203-7d8b-4fab-a537-c31a7f73f46b"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
@@ -18,7 +17,6 @@ Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 DataDrivenDiffEq = "1.0"
 DataDrivenSparse = "0.1.2"
 DataStructures = "0.18"
-Optim = "1"
 SymbolicUtils = "1"
 Symbolics = "5"
 SpecialFunctions = "2"

README.md

@@ -21,19 +21,19 @@ the documentation, which contains the unreleased features.
 ## Example
 
 ```julia
-julia> using SymbolicNumericIntegration
-julia> using Symbolics
+using Symbolics
+using SymbolicNumericIntegration
 
-julia> @variables x a b
+@variables x a b
 
-julia> integrate(3x^3 + 2x - 5)
-(x^2 + (3//4)*(x^4) - (5//1)*x, 0, 0)
+integrate(3x^3 + 2x - 5)
+(x^2 + (3 // 4) * (x^4) - (5 // 1) * x, 0, 0)
 
-julia> integrate(exp(a * x), x; symbolic = true)
-(exp(a*x) / a, 0, 0)
+integrate(exp(a * x), x; symbolic = true)
+(exp(a * x) / a, 0, 0)
 
-julia> integrate(sin(a * x) * cos(b * x), x; symbolic = true, detailed = false)
-(-a*cos(a*x)*cos(b*x) - b*sin(a*x)*sin(b*x)) / (a^2 - (b^2))
+integrate(sin(a * x) * cos(b * x), x; symbolic = true, detailed = false)
+(-a * cos(a * x) * cos(b * x) - b * sin(a * x) * sin(b * x)) / (a^2 - (b^2))
 ```
 
 # Citation
@@ -43,7 +43,7 @@ If you use SymbolicNumericIntegration.jl in your research, please cite [this pap
 ```
 
 @article{Iravanian2022,
-author = {Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Julia Computing and Yingbo Ma and Chris Rackauckas},
+author = {Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Yingbo Ma and Chris Rackauckas},
 doi = {10.48550/arxiv.2201.12468},
 month = {1},
 title = {Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression},

docs/make.jl

@@ -9,7 +9,7 @@ makedocs(sitename = "SymbolicNumericIntegration.jl",
     authors = "Shahriar Iravanian",
     modules = [SymbolicNumericIntegration],
     clean = true, doctest = false, linkcheck = true,
-    warnonly = [:missing_docs],
+    # warnonly = [:missing_docs],
     format = Documenter.HTML(assets = ["assets/favicon.ico"],
         canonical = "https://docs.sciml.ai/SymbolicNumericIntegration/stable/"),
     pages = pages)

docs/src/index.md

@@ -22,53 +22,53 @@ Pkg.add("SymbolicNumericIntegration")
 Examples:
 
 ```julia
-julia> using SymbolicNumericIntegration
-julia> using Symbolics
+using Symbolics
+using SymbolicNumericIntegration
 
-julia> @variables x a b
+@variables x a b
 
 # if `detailed = true` (default), the output is a tuple of (solution, unsolved portion, err)
 
-julia> integrate(3x^3 + 2x - 5)
-(x^2 + (3//4)*(x^4) - (5x), 0, 0)
+integrate(3x^3 + 2x - 5)
+(x^2 + (3 // 4) * (x^4) - (5x), 0, 0)
 
-julia> integrate((5 + 2x)^-1)
-((1//2)*log((5//2) + x), 0, 0.0)
+integrate((5 + 2x)^-1)
+((1 // 2) * log((5 // 2) + x), 0, 0.0)
 
 # `detailed = false` simplifies the output to just the resulting integral
 
-julia> integrate(x^2 / (16 + x^2); detailed = false)
-x + 4atan((-1//4)*x)
+integrate(x^2 / (16 + x^2); detailed = false)
+x + 4atan((-1 // 4) * x)
 
-julia> integrate(x^2 * log(x); detailed = false)
-(1//3)*(x^3)*log(x) - (1//9)*(x^3)
+integrate(x^2 * log(x); detailed = false)
+(1 // 3) * (x^3) * log(x) - (1 // 9) * (x^3)
 
-julia> integrate(sec(x) * tan(x); detailed = false)
+integrate(sec(x) * tan(x); detailed = false)
 sec(x)
 
 # Symbolic integration. Here, a is a symbolic constant; therefore, we need 
 # to explicitly define the independent variable (say, x). Also, we set
 # `symbolic = true` to force using the symbolic solver
 
-julia> integrate(sin(a * x), x; detailed = false, symbolic = true)
-(-cos(a*x)) / a
+integrate(sin(a * x), x; detailed = false, symbolic = true)
+(-cos(a * x)) / a
 
-julia> integrate(x^2 * cos(a * x), x; detailed = false, symbolic = true)
-((a^2)*(x^2)*sin(a*x) + 2.0a*x*cos(a*x) - 2.0sin(a*x)) / (a^3)
+integrate(x^2 * cos(a * x), x; detailed = false, symbolic = true)
+((a^2) * (x^2) * sin(a * x) + 2.0a * x * cos(a * x) - 2.0sin(a * x)) / (a^3)
 
-julia> integrate(log(log(a * x)) / x, x; detailed = false, symbolic = true)
-log(a*x)*log(log(a*x)) - log(a*x)
+integrate(log(log(a * x)) / x, x; detailed = false, symbolic = true)
+log(a * x) * log(log(a * x)) - log(a * x)
 
 # multiple symbolic constants
 
-julia> integrate(cosh(a * x) * exp(b * x), x; detailed = false, symbolic = true)
-(a*sinh(a*x)*exp(b*x) - b*cosh(a*x)*exp(b*x)) / (a^2 - (b^2))
+integrate(cosh(a * x) * exp(b * x), x; detailed = false, symbolic = true)
+(a * sinh(a * x) * exp(b * x) - b * cosh(a * x) * exp(b * x)) / (a^2 - (b^2))
 
 # definite integration, passing a tuple of (x, lower bound, higher bound) in the 
 # second argument
 
-julia> integrate(x * sin(a * x), (x, 0, 1); symbolic = true, detailed = false)
-(sin(a) - a*cos(a)) / (a^2)
+integrate(x * sin(a * x), (x, 0, 1); symbolic = true, detailed = false)
+(sin(a) - a * cos(a)) / (a^2)
 ```
 
 SymbolicNumericIntegration.jl exports some special integral functions (defined over Complex numbers) and uses them in solving integrals:
@@ -81,13 +81,13 @@ SymbolicNumericIntegration.jl exports some special integral functions (defined o
 For examples:
 
 ```julia
-julia> integrate(exp(x + 1) / (x + 1))
+integrate(exp(x + 1) / (x + 1))
 (SymbolicNumericIntegration.Ei(1 + x), 0, 0.0)
 
-julia> integrate(x * cos(a*x^2 - 1) / (a*x^2 - 1), x; detailed=false, symbolic=true)
-((1//2)*SymbolicNumericIntegration.Ci(a*(x^2) - 1)) / a
+integrate(x * cos(a * x^2 - 1) / (a * x^2 - 1), x; detailed = false, symbolic = true)
+((1 // 2) * SymbolicNumericIntegration.Ci(a * (x^2) - 1)) / a
 
-julia> integrate(1 / (x*log(log(x))), x; detailed=false, symbolic=true)
+integrate(1 / (x * log(log(x))), x; detailed = false, symbolic = true)
 SymbolicNumericIntegration.Li(log(x))
 ```
 
@@ -213,4 +213,4 @@ file and the
 [project]($link_project)
 file.
 """)
-```
+```

src/SymbolicNumericIntegration.jl

@@ -3,12 +3,21 @@ module SymbolicNumericIntegration
 using SymbolicUtils
 using SymbolicUtils: istree, operation, arguments
 using Symbolics
-using Symbolics: value, get_variables, expand_derivatives
+using Symbolics: value, get_variables, expand_derivatives, coeff, Equation
 using SymbolicUtils.Rewriters
 using SymbolicUtils: exprtype, BasicSymbolic
 
 using DataDrivenDiffEq, DataDrivenSparse
 
+struct NumericalPlan
+    abstol::Float64
+    radius::Float64
+    complex_plane::Bool
+    opt::DataDrivenDiffEq.AbstractDataDrivenAlgorithm
+end
+
+default_plan() = NumericalPlan(1e-6, 5.0, true, STLSQ(exp.(-10:1:0)))
+
 include("utils.jl")
 include("tree.jl")
 include("special.jl")
@@ -24,10 +33,10 @@ export Ei, Si, Ci, Li
 
 include("numeric_utils.jl")
 include("sparse.jl")
-include("optim.jl")
+# include("optim.jl")
 include("integral.jl")
 
-export integrate, generate_basis
+export integrate, generate_basis, best_hints
 
 include("symbolic.jl")
 

src/candidates.jl

@@ -1,6 +1,6 @@
 using DataStructures
 
-# this is the main heurisctic used to find the test fragments
+# this is the old heurisctic used to find the test fragments
 function generate_basis(eq, x, try_kernel = true)
     if !try_kernel
         S = sum(generate_homotopy(expr(eq), x))