Reduced row echelon form: Difference between revisions

rowCount := M.Count() ; the number of rows in M

columnCount := M.1.Count() ; the number of columns in M

r := lead := 1

while (r <= rowCount) {

if (columnCount < lead)

return M

i := r

while (M[i, lead] = 0) {

i++

if (rowCount+1 = i) {

i := r, lead++

if (columnCount+1 = lead)

return M

}

}

if (i<>r)

for col, v in M[i] ; Swap rows i and r

tempVal := M[i, col], M[i, col] := M[r, col], M[r, col] := tempVal

num := M[r, lead]

if (M[r, lead] <> 0)

for col, val in M[r]

M[r, col] /= num ; If M[r, lead] is not 0 divide row r by M[r, lead]

i := 2

while (i <= rowCount) {

num := M[i, lead]

if (i <> r)

for col, val in M[i] ; Subtract M[i, lead] multiplied by row r from row i

M[i, col] -= num * M[r, col]

i++

}

lead++, r++

}

return M

Examples:<lang AutoHotkey>M := [[1 , 2, -1, -4 ]

, [2 , 3, -1, -11]

, [-2, 0, -3, 22]]

for col, v in obj

output .= RegExReplace(v, "\.0+$|0+$") "`t"

output .= "`n"