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use ndarray::*;
use ndarray::{Array1, Array2};
use num_traits::Float;
#[cfg(test)]
mod test;
fn initial_table<T: Float + std::convert::From<i32>>(
objective: &Array1<T>,
constraints: &Array2<T>,
requirements: &Array1<T>,
) -> Array2<T> {
let n_variables = objective.len();
let dimension_j = 1 + n_variables + 1 + constraints.len_of(Axis(0));
let dimension_i = constraints.len_of(Axis(0)) + 1;
let mut table = Array2::<T>::zeros((dimension_i, dimension_j));
table[[0, 0]] = 1i32.into();
for j in 0..objective.len() {
table[[0, j + 1]] = objective[j];
table[[0, j + 1]] = table[[0, j + 1]] * (-1).into();
}
for i in 0..constraints.len_of(Axis(0)) {
for j in 0..constraints.len_of(Axis(1)) {
table[[i + 1, j + 1]] = constraints[[i, j]];
}
}
for i in 0..requirements.len() {
table[[i + 1, dimension_j - 1]] = requirements[i];
}
table
}
fn pivot_point<T: Float + std::convert::From<i32>>(table: &Array2<T>) -> Option<[usize; 2]> {
let mut out_var = None;
let mut out_var_max = 0.into();
let mut in_var = None;
let mut in_var_min = None;
for j in 1..(table.len_of(Axis(1)) - 1) {
if table[[0, j]] > out_var_max {
out_var_max = table[[0, j]];
out_var = Some(j);
}
}
if let Some(j) = out_var {
let req = table.len_of(Axis(1)) - 1;
for i in 1..table.len_of(Axis(0)) {
if let Some(m) = in_var_min {
if table[[i, req]] / table[[i, j]] < m && table[[i, req]] / table[[i, j]] > 0.into()
{
in_var_min = Some(table[[i, req]] / table[[i, j]]);
in_var = Some(i);
}
} else {
in_var_min = Some(table[[i, req]] / table[[i, j]]);
in_var = Some(i);
}
}
}
match (out_var, in_var) {
(Some(j), Some(i)) => Some([i, j]),
_ => None,
}
}
fn gauss<T>(pivot: [usize; 2], table: &mut Array2<T>)
where
T: Float
+ std::fmt::Debug
+ std::ops::MulAssign
+ std::ops::AddAssign
+ std::ops::DivAssign
+ ndarray::ScalarOperand,
{
for i in 0..table.len_of(Axis(0)) {
if i != pivot[0] {
let pivot_n = table[pivot];
let make_zero = table[[i, pivot[1]]];
{
let mut row_pivot = table.row_mut(pivot[0]);
row_pivot /= pivot_n;
}
let mut row_pivot = table.row(pivot[0]).to_owned();
let mut row_make_zero = table.row_mut(i);
row_make_zero *= pivot_n;
row_pivot *= -make_zero;
row_make_zero += &row_pivot;
}
}
let pivot_n = table[[0, 0]];
let mut row_pivot = table.row_mut(0);
row_pivot /= pivot_n;
}
#[allow(dead_code)]
fn check_optimus() {}
pub fn simplex<T>(
objective: Array1<T>,
constraints: Array2<T>,
requirements: Array1<T>,
) -> Array2<T>
where
T: Float
+ std::convert::From<i32>
+ std::fmt::Debug
+ std::ops::MulAssign
+ std::ops::AddAssign
+ std::ops::DivAssign
+ ndarray::ScalarOperand,
{
let mut table = initial_table(&objective, &constraints, &requirements);
while let Some(pivot) = pivot_point(&table) {
gauss(pivot, &mut table);
}
table
}