Reduced row echelon form: Difference between revisions

=={{header|Julia}}==

<lang julia>

function ToReducedRowEchelonForm(matrix)

lead = 1

rowCount,columnCount = size(matrix)

for row = 1:rowCount

if lead > columnCount

return

end

i = row

while matrix[i,lead] == 0

i += 1

if i == rowCount

i = row

lead += 1

if columnCount == lead

return

end

end

end

matrix[i,:],matrix[row,:] =matrix[row,:],matrix[i,:]

leadValue = matrix[row,lead]

matrix[row,:] = [ val / leadValue for val in matrix[row,:]]

for i=1:rowCount

if i != row

leadValue = matrix[i,lead]

matrix[i,:] = [ (ivalue - leadValue*rowvalue) for (rowvalue,ivalue) in zip(matrix[row,:],matrix[i,:])]

end

end

lead += 1

end

end

</lang>

Output:

<pre>

julia> matrix = [1 2 -1 -4 ; 2 3 -1 -11 ; -2 0 -3 22]

3x4 Int32 Array:

1 2 -1 -4

2 3 -1 -11

-2 0 -3 22

julia> ToReducedRowEchelonForm(matrix)

julia> matrix

3x4 Int32 Array:

1 0 0 -8

0 1 0 1

0 0 1 -2

</pre>