def rref(matrix, augment=None):
    def row_swap(i, j):
        matrix[i,:], matrix[j,:] = matrix[j,:], matrix[i,:].copy()
        augment[i,:], augment[j,:] = augment[j,:], augment[i,:].copy()
    def row_xor(i, j):
        matrix[i,:] = matrix[i,:] ^ matrix[j,:]
        augment[i,:] = augment[i,:] ^ augment[j,:]
    matrix = matrix.copy()
    if augment is None:
        augment = np.matrix(np.zeros(matrix.shape), dtype=dt)
    else:
        augment = augment.copy()
    height, width = matrix.shape
    pivots = []
    print("reducing")
    for i in range(width):
        col = matrix[:,i]
        pivot_row = len(pivots)
        if pivot_row >= height:
            break
        if col.take(pivot_row) == 0:
            nonzeros = col.flat[pivot_row:].nonzero()[1]
            if len(nonzeros) == 0:
                continue
            else:
                row_swap(pivot_row, pivot_row + nonzeros[0])
        pivots.append(i)
        nonzeros = col.nonzero()[0]
        for nonzero in nonzeros:
            if nonzero != pivot_row:
                row_xor(nonzero, pivot_row)
    return matrix, augment