Numpy and diff()

Question

I'm trying to create a diff of my sorted numpy array such that if I record the value of the first row, and the diffs, i can recreate the original table but store less data.

So here's an example of the table:

my_array = numpy.array([(0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0), 
                        (0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  1),
                        (0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  2), 
                        (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 34),
                        (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 35), 
                        (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36)
                       ],'uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8,uint8')

And after running numpy.diff(my_array) I would have expected something like this:

[(0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  1), 
 (0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  1),
 (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 32),
 (0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  1),
 (0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  0,   0,  0,  1)
]

Note: The data above comes from the first & last three rows of the 'real' data, which is much much larger. With the full dataset, most of the rows after a diff would be 0,0,0,0,0,0,0,0,0,0,0,0,1 -- which can a) be stored in a much smaller struct, and b) will compress fantastically well on disk since most rows contain very similar data.

I should probably point out that the reason I have a whole bunch of uint8's in the first place, is because I needed to store an array of extremely large numbers, in the smallest amount of memory possible. The largest number was 185439173519100986733232011757860, which is too big for uint64. In fact, the smallest number of bits to store it would be 108 bits, or 14 bytes (to the nearest byte). So to fit these large numbers into numpy, i use the following two functions:

def large_number_to_numpy(number,columns): return tuple((number >> (8*x)) & 255 for x in range(columns-1,-1,-1))

def numpy_to_large_number(numbers): return sum([y << (8*x) for x,y in enumerate(numbers[::-1])])

Which is used like this:

>>> large_number_to_numpy(185439173519100986733232011757860L,14) (9L, 36L, 146L, 73L, 36L, 146L, 73L, 36L, 146L, 73L, 36L, 146L, 73L, 36L)

numpy_to_large_number((9L, 36L, 146L, 73L, 36L, 146L, 73L, 36L, 146L, 73L, 36L, 146L, 73L, 36L)) 185439173519100986733232011757860L

With the array created like this:

my_array = numpy.zeros(TOTAL_ROWS,','.join(14*['uint8']))

And then populated with:

my_array[x] = large_number_to_numpy(large_number,14)

But instead I get this:

>>> my_array
array([(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
       (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1),
       (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2),
       (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 34),
       (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 35),
       (9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36)],
      dtype=[('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'u1'), ('f4', 'u1'), ('f5', 'u1'), ('f6', 'u1'), ('f7', 'u1'), ('f8', 'u1'), ('f9', 'u1'), ('f10', 'u1'), ('f11', 'u1'), ('f12', 'u1'), ('f13', 'u1')])
>>> numpy.diff(my_array)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python2.7/site-packages/numpy/lib/function_base.py", line 1567, in diff
    return a[slice1]-a[slice2]
TypeError: ufunc 'subtract' did not contain a loop with signature matching types dtype([('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'u1'), ('f4', 'u1'), ('f5', 'u1'), ('f6', 'u1'), ('f7', 'u1'), ('f8', 'u1'), ('f9', 'u1'), ('f10', 'u1'), ('f11', 'u1'), ('f12', 'u1'), ('f13', 'u1')]) dtype([('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'u1'), ('f4', 'u1'), ('f5', 'u1'), ('f6', 'u1'), ('f7', 'u1'), ('f8', 'u1'), ('f9', 'u1'), ('f10', 'u1'), ('f11', 'u1'), ('f12', 'u1'), ('f13', 'u1')]) dtype([('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'u1'), ('f4', 'u1'), ('f5', 'u1'), ('f6', 'u1'), ('f7', 'u1'), ('f8', 'u1'), ('f9', 'u1'), ('f10', 'u1'), ('f11', 'u1'), ('f12', 'u1'), ('f13', 'u1')])

Answer 1

The problem is that you have a structured array instead of a regular 2-dimensional array, so numpy does not know how to subtract one tuple from another.

Convert your structured array to a regular array (from this SO question):

my_array = my_array.view(numpy.uint8).reshape((my_array.shape[0], -1))

and then do numpy.diff(my_array, axis=0).

Or, if you can, avoid creating a structured array by defining my_array as

numpy.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
             [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
             [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2],
             [9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 34],
             [9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 35],
             [9, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36, 146, 73, 36]],
            dtype=numpy.uint8)