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This small package contains the functions rref and rref!.
The code was initially part of Julia and was developed by Jeff Bezanson (see here).
Example of computing rref_with_pivots :
rref_with_pivots(A)
Compute the reduced row echelon form of the matrix A together with the position of the pivots. Since this algorithm is sensitive to numerical imprecision,
- Complex numbers are converted to ComplexF64
- Integer, Float16 and Float32 numbers are converted to Float64
- Rational are kept unchanged
julia> rref_with_pivots([ 1 2 -1 -4;
2 3 -1 -11;
-2 0 -3 22])
3×4 Array{Float64,2}:
1.0 0.0 0.0 -8.0
0.0 1.0 0.0 1.0
0.0 0.0 1.0 -2.0
Int64[3]:
1
2
3
julia> rref_with_pivots([16 2 3 13;
5 11 10 8;
9 7 6 12;
4 14 15 1])
4×4 Array{Float64,2}:
1.0 0.0 0.0 1.0
0.0 1.0 0.0 3.0
0.0 0.0 1.0 -3.0
0.0 0.0 0.0 0.0
Int64[3]:
1
2
3
julia> rref_with_pivots([ 1 2 0 3;
2 4 0 7])
2×4 Array{Float64,2}:
1.0 2.0 0.0 0.0
0.0 0.0 0.0 1.0
Int64[3]:
1
4
Example of computing rref :
rref(A)
Compute the reduced row echelon form of the matrix A. Since this algorithm is sensitive to numerical imprecision,
- Complex numbers are converted to ComplexF64
- Integer, Float16 and Float32 numbers are converted to Float64
- Rational are kept unchanged
julia> rref([ 1 2 -1 -4;
2 3 -1 -11;
-2 0 -3 22])
3×4 Array{Float64,2}:
1.0 0.0 0.0 -8.0
0.0 1.0 0.0 1.0
0.0 0.0 1.0 -2.0
julia> rref([16 2 3 13;
5 11 10 8;
9 7 6 12;
4 14 15 1])
4×4 Array{Float64,2}:
1.0 0.0 0.0 1.0
0.0 1.0 0.0 3.0
0.0 0.0 1.0 -3.0
0.0 0.0 0.0 0.0
julia> rref([ 1 2 0 3;
2 4 0 7])
2×4 Array{Float64,2}:
1.0 2.0 0.0 0.0
0.0 0.0 0.0 1.0