Factorio-Paranoidal_mod/helmod/math/Readme.md

Solver Matrix

Current Solver:

• Matrix.lua: Contain class of Matrix
• SolverMatrix.lua: Common code of solvers
• SolverMatrixAlgebra.lua: Specifique code of Algebra calculation
• SolverMatrixSimplex.lua: Specifique code of Simplex method calculation

Classes

Matrix

Container for all informations

• field objectives is the input value, key column/value
• field objective_values is the input value, index column/value, is use with icol value in the code

---@class Matrix
---@field columns {[integer] : MatrixHeader}
---@field headers {[integer] : MatrixHeader}
---@field rows {[integer] : {[integer] : number}}
---@field columnIndex {[string] : integer}
---@field parameters {[integer] : MatrixRowParameters}
---@field objectives {[string] : number}
---@field objective_values {[integer] : number}

MatrixHeader

Header of row or column

---@class MatrixHeader
---@field index uint
---@field key string
---@field type string
---@field name string
---@field sysname string
---@field tooltip string
---@field is_ingredient boolean
---@field product table

MatrixRow

Row of matrix

---@class MatrixRow
---@field type string
---@field name string
---@field tooltip string
---@field header MatrixHeader
---@field columns {[integer] : MatrixHeader}
---@field values {[integer] : number}
---@field columnIndex {[string] : integer}

MatrixRowParameters

Parameters on recipe of row This stores all values for a recipe

---@class MatrixRowParameters
---@field base string
---@field contraint table
---@field factory_count number
---@field factory_speed number
---@field recipe_count number
---@field recipe_production number
---@field recipe_energy number
---@field coefficient number

Matrix Debugger in factorio

To active the debugger: find it in the menu Settings/Mod Settings/Map, in helmod section enable "Active the debug solver"

After to see something use refresh in helmod to generate cache of matrix (only need one time)

Click on Open debug button

Simplex code algorithm

1. Prepare initial matrix SolverMatrix.get_block_matrix(block, parameters)
2. Inject objectives in matrix SolverMatrix:prepare_z_and_objectives(matrix, reverse)
3. Start of program SolverMatrixSimplex:solve_matrix(Mbase, debug, by_factory, time)
4. Add ingredient recipes in rows and Inject initial recipes in columns SolverMatrixSimplex:prepare(matrix)
5. Search a pivot, greater positive value in row Z is the column, the greater division of coefficient bettween positive value of the colum is the row SolverMatrixSimplex:get_pivot(matrix)
6. Apply Gaussian pivot SolverMatrixSimplex:pivot(matrix, xrow, xcol)
7. Loop at "Search a pivot" while a pivot found
8. Compute the final Matrix, copy the recipe result in the parameters and compute the % production on each recipe SolverMatrixSimplex:table_compute(matrix, matrix_result) and SolverMatrixSimplex:line_compute(matrix, xrow)
9. Finalize the row Z SolverMatrix:finalize(matrix)
10. Apply status on products/ingredients SolverMatrix:apply_state(matrix)