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Gaussian elimination: Difference between revisions
add rust solution
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=={{header|Rust}}==
<lang rust>
// using a Vec<f32> might be a better idea
// for now, let us create a fixed size array
// of size:
const SIZE: usize = 6;
pub fn eliminate(mut system: [[f32; SIZE+1]; SIZE]) -> Option<Vec<f32>> {
// produce the row reduced echelon form
//
// for every row...
for i in 0..SIZE-1 {
// for every column in that row...
for j in i..SIZE-1 {
if system[i][i] == 0f32 {
continue;
} else {
// reduce every element under that element to 0
let factor = system[j + 1][i] as f32 / system[i][i] as f32;
for k in i..SIZE+1 {
// potential optimization: set every element to zero, instead of subtracting
// i think subtraction helps showcase the process better
system[j + 1][k] -= factor * system[i][k] as f32;
}
}
}
}
// produce gaussian eliminated array
//
// the process follows a similar pattern
// but this one reduces the upper triangular
// elements
for i in (1..SIZE).rev() {
if system[i][i] == 0f32 {
continue;
} else {
for j in (1..i+1).rev() {
let factor = system[j - 1][i] as f32 / system[i][i] as f32;
for k in (0..SIZE+1).rev() {
system[j - 1][k] -= factor * system[i][k] as f32;
}
}
}
}
// produce solutions through back substitution
let mut solutions: Vec<f32> = vec![];
for i in 0..SIZE {
if system[i][i] == 0f32 {
return None;
}
else {
system[i][SIZE] /= system[i][i] as f32;
system[i][i] = 1f32;
println!("X{} = {}", i + 1, system[i][SIZE]);
solutions.push(system[i][SIZE])
}
}
return Some(solutions);
}
#[cfg(test)]
mod tests {
use super::*;
// sample run of the program
#[test]
fn eliminate_seven_by_six() {
let system: [[f32; SIZE +1]; SIZE] = [
[1.00 , 0.00 , 0.00 , 0.00 , 0.00 , 0.00 , -0.01 ] ,
[1.00 , 0.63 , 0.39 , 0.25 , 0.16 , 0.10 , 0.61 ] ,
[1.00 , 1.26 , 1.58 , 1.98 , 2.49 , 3.13 , 0.91 ] ,
[1.00 , 1.88 , 3.55 , 6.70 , 12.62 , 23.80 , 0.99 ] ,
[1.00 , 2.51 , 6.32 , 15.88 , 39.90 , 100.28 , 0.60 ] ,
[1.00 , 3.14 , 9.87 , 31.01 , 97.41 , 306.02 , 0.02 ]
] ;
let solutions = eliminate(system).unwrap();
assert_eq!(6, solutions.len());
let assert_solns = vec![-0.01, 1.60278, -1.61320, 1.24549, -0.49098, 0.06576];
for (ans, key) in solutions.iter().zip(assert_solns.iter()) {
if (ans - key).abs() > 1E-4 { panic!("Test Failed!") }
}
}
}
</lang>
=={{header|Stata}}==
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