Improve code readability and reduce OOP allocations for StaticArrays (#183)

* created function basic_patankar_step for oop

* revised MPRK43

* revised SSPMPRK oop implementations

* format

* fix SSPMPRK43

* bugfix SSPMPRK43

* more structure, more dispatch

* bugfix

* revised SSPMPRK schemes

* bugfix

* revised lincomb function

* added @muladd

* build_mprk_matrix for StaticMatrix

* bugfix build_mprk_matrix for StaticMatrix

* build_mprk_matrix for StaticMatrix without slicing allocations

* format

* Revised implementation of build_mprk_matrix for StaticMatrix. Now tests pass as before.

* lincomb! in MPRK schemes

* bugfix MPRK22

* remove stale explicit imports

* introduced basic_patankar_step! and basic_patankar_step_conservative!

* revised sspmprk

* removed comments

* add diagonal of sparse matrix efficiently

* use naive loop to add diagonal of sparse matrices

* consolidate broadcasts

* removed @unpack

* additional comments in source file

* Update src/mprk.jl

Co-authored-by: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com>

* format

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

* Apply more suggestions from code review

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

---------

Co-authored-by: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com>
Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

Author: 3 people

Project.toml

@@ -12,7 +12,6 @@ OrdinaryDiffEqCore = "bbf590c4-e513-4bbe-9b18-05decba2e5d8"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-SimpleUnPack = "ce78b400-467f-4804-87d8-8f486da07d0a"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
@@ -34,7 +33,6 @@ OrdinaryDiffEqCore = "1.21, 2"
 RecipesBase = "1.3.4"
 Reexport = "1.2.2"
 SciMLBase = "2.78"
-SimpleUnPack = "1"
 SparseArrays = "1"
 StaticArrays = "1.9.7"
 Statistics = "1"

src/PositiveIntegrators.jl

@@ -4,13 +4,12 @@ module PositiveIntegrators
 using LinearAlgebra: LinearAlgebra, Tridiagonal, I, diag, mul!
 using Statistics: median
 
-using SparseArrays: SparseArrays, AbstractSparseMatrix,
+using SparseArrays: SparseArrays, AbstractSparseMatrix, SparseMatrixCSC,
                     issparse, nonzeros, nzrange, rowvals, spdiagm
-using StaticArrays: SVector, SMatrix, StaticArray, @SVector, @SMatrix, MMatrix
+using StaticArrays: SVector, SMatrix, StaticArray, StaticMatrix, @SVector, @SMatrix, MMatrix
 
 using FastBroadcast: @..
 using MuladdMacro: @muladd
-using SimpleUnPack: @unpack
 
 using Reexport: @reexport
 
@@ -28,8 +27,7 @@ using LinearSolve: LinearSolve, LinearProblem, LUFactorization, solve!
 
 import SciMLBase: interp_summary
 
-using OrdinaryDiffEqCore: @cache,
-                          OrdinaryDiffEqAdaptiveAlgorithm,
+using OrdinaryDiffEqCore: OrdinaryDiffEqAdaptiveAlgorithm,
                           OrdinaryDiffEqConstantCache, OrdinaryDiffEqMutableCache,
                           False,
                           _vec

src/mpdec.jl

@@ -564,8 +564,8 @@ function _build_mpdec_matrix_and_rhs!(M::AbstractSparseMatrix, rhs, P::AbstractS
 end
 
 @muladd function perform_step!(integrator, cache::MPDeCConstantCache, repeat_step = false)
-    @unpack alg, t, dt, uprev, f, p = integrator
-    @unpack K, M, nodes, theta, small_constant, ValM = cache
+    (; alg, t, dt, uprev, f, p) = integrator
+    (; K, M, nodes, theta, small_constant, ValM) = cache
 
     C = cmatrix(uprev, ValM)
     C2 = cmatrix(uprev, ValM)
@@ -702,9 +702,9 @@ function initialize!(integrator, cache::Union{MPDeCCache, MPDeCConservativeCache
 end
 
 @muladd function perform_step!(integrator, cache::MPDeCCache, repeat_step = false)
-    @unpack t, dt, uprev, u, f, p = integrator
-    @unpack tmp, P, P2, d, σ, C, C2, linsolve_rhs, linsolve = cache
-    @unpack K, M, nodes, theta, small_constant = cache.tab
+    (; t, dt, uprev, u, f, p) = integrator
+    (; tmp, P, P2, d, σ, C, C2, linsolve_rhs, linsolve) = cache
+    (; K, M, nodes, theta, small_constant) = cache.tab
 
     # Initialize C matrices
     for i in 1:(M + 1)
@@ -743,9 +743,9 @@ end
 
 @muladd function perform_step!(integrator, cache::MPDeCConservativeCache,
                                repeat_step = false)
-    @unpack t, dt, uprev, u, f, p = integrator
-    @unpack tmp, P, P2, σ, C, C2, linsolve_rhs, linsolve = cache
-    @unpack K, M, nodes, theta, small_constant = cache.tab
+    (; t, dt, uprev, u, f, p) = integrator
+    (; tmp, P, P2, σ, C, C2, linsolve_rhs, linsolve) = cache
+    (; K, M, nodes, theta, small_constant) = cache.tab
 
     # Initialize right hand side of linear system
     linsolve_rhs .= uprev