function fully_reduce(matrix){
var echelon_result = row_echelon(matrix)
, echelon = echelon_result[0]
, change = echelon_result[1]
, augmentation = echelon_result[2]
, height = echelon.length
, width = echelon[0].length
, size = width < height ? width : height
, column_index = size
, row_index = column_index-1
, target
;
// make the diagonal 1
u.times(width < height ? width : height, function(row_index){
var row = echelon[row_index];
echelon[row_index] = m.disperse(echelon[row_index], row[row_index])
augmentation[row_index] = m.disperse(augmentation[row_index], row[row_index])
change = change.per(row[row_index])
})
while ( column_index -- > 0 ) {
row_index = column_index
while ( row_index -- > 0 ) {
target = echelon[row_index][column_index]
echelon[row_index] = m.sub(echelon[row_index], m.scale(echelon[column_index], target))
augmentation[row_index] = m.sub(augmentation[row_index], m.scale(augmentation[column_index], target))
}
}
return [echelon, augmentation]
}
matrix.forEach(function(row, row_index){
if ( row_index < row.length ) {
u.times(row_index, function(column_index){
if ( row[column_index] !== zero ) {
result = false
}
})
}
})
function determinant(matrix){
if ( matrix.length != matrix[0].length) return undefined
var echelon = row_echelon(matrix);
return u.times(echelon[0].length, function(row_index){
return echelon[0][row_index][row_index]
}).reduce(r.mul).per(echelon[1])
}
echelon.forEach(function(row, row_index){
u.times(row_index, function(column_index){
var pivot, pivot_row, lead, multiple;
pivot = echelon[column_index][column_index]
lead = echelon[row_index][column_index]
scalar = lead.per(pivot)
echelon[row_index] = m.sub(echelon[row_index]
, m.scale(echelon[column_index], scalar))
augmentation[row_index] = m.sub(augmentation[row_index]
, m.scale(augmentation[column_index], scalar))
})
})