https://github.com/augustocl/gauss_jordan_elimination

Scratch implementation of Gaussian Elimination algo in Julia
https://github.com/augustocl/gauss_jordan_elimination

algorithm gauss-elimination gauss-jordan gauss-jordan-elimination julialang

Last synced: 2 days ago
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Scratch implementation of Gaussian Elimination algo in Julia

• Host: GitHub
• URL: https://github.com/augustocl/gauss_jordan_elimination
• Owner: AugustoCL
• License: mit
• Created: 2020-09-30T16:25:11.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2021-09-09T03:25:20.000Z (over 3 years ago)
• Last Synced: 2024-11-21T15:27:11.542Z (2 months ago)
• Topics: algorithm, gauss-elimination, gauss-jordan, gauss-jordan-elimination, julialang
• Language: Julia
• Homepage:
• Size: 52.7 KB
• Stars: 4
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
## Gauss-Jordan Elimination

This repo implements **from scratch** the **Gaussian Elimination** algorithm in [Julia Lang](julialang.org/).

If you need to refresh your memory about the technique, I suggest you read the [wikipedia page](https://en.wikipedia.org/wiki/Gaussian_elimination) of the method, which has a great introduction and applications in Linear Algebra disciplines.

## Example of the operation

![](imgs/gauss-jordan-operation.png) 

## Function implemented

```julia

function gauss_jordan(A::Matrix{T}) where {T<:Number}

    

    # convert to float to avoid InexactError: Int64()

    (T <: Integer) && (A = convert.(Float64, A))

    # check if matrix is singular

    m, n = size(A)

    if m == n

        @assert det(A) ≠ 0.0 "Must insert a non-singular matrix"

    else

        @assert det(A[:,1:end-1]) ≠ 0.0 "Must insert a non-singular matrix or a system matrix [A b]"

    end

    for i ∈ axes(A, 1)

        if A[i,i] == 0.0                            # check if need swap rows

            swap_rows(i, m)

        end

        @. A[i,:] = A[i,:] / A[i,i]                 # divide pivot line by pivot element

        for j ∈ axes(A, 1)                          # iterate each line for each pivot column, except pivot line

            if j ≠ i                                # jump pivot line

                @. A[j,:] = A[j,:] - A[i,:]*A[j,i]  # apply gauss jordan in each line

            end

        end

    end

    return A

end

function swap_rows(i::T, nlinha::T) where {T<:Integer}

    for n ∈ (i+1):nlinha        # iterate over lines above to check if could be swap

        if A[n,i] ≠ 0.0         # condition to swap row

            L = copy(A[i,:])    # copy line to swap

            A[i,:] = A[n,:]     # swap occur

            A[n,:] = L

            break

        end

    end

end

``` 

## Benchmark inputing Int vs Float

![](imgs/bench-float-int.png)