Python: confusion between types and dtypes

Question

Suppose I enter:

a = uint8(200)
a*2

Then the result is 400, and it is recast to be of type uint16.

However:

a = array([200],dtype=uint8)
a*2

and the result is

array([144], dtype=uint8)

The multiplication has been performed modulo 256, to ensure that the result stays in one byte.

I'm confused about "types" and "dtypes" and where one is used in preference to another. And as you see, the type may make a significant difference in the output.

Can I, for example, create a single number of dtype uint8, so that operations on that number will be performed modulo 256? Alternatively, can I create an array of type (not dtype) uint8 so that operations on it will produce values outside the range 0-255?

Answer 1

The type of a NumPy array is numpy.ndarray; this is just the type of Python object it is (similar to how type("hello") is str for example).

dtype just defines how bytes in memory will be interpreted by a scalar (i.e. a single number) or an array and the way in which the bytes will be treated (e.g. int/float). For that reason you don't change the type of an array or scalar, just its dtype.

As you observe, if you multiply two scalars, the resulting datatype is the smallest "safe" type to which both values can be cast. However, multiplying an array and a scalar will simply return an array of the same datatype. The documentation for the function np.inspect_types is clear about when a particular scalar or array object's dtype is changed:

Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array's type takes precedence and the actual value of the scalar is taken into account.

The documentation continues:

If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with promote_types to produce the return value.

So for np.uint8(200) * 2, two scalars, the resulting datatype will be the type returned by np.promote_types:

>>> np.promote_types(np.uint8, int)
dtype('int32')

For np.array([200], dtype=np.uint8) * 2 the array's datatype takes precedence over the scalar int and a np.uint8 datatype is returned.

To address your final question about retaining the dtype of a scalar during operations, you'll have to restrict the datatypes of any other scalars you use to avoid NumPy's automatic dtype promotion:

>>> np.array([200], dtype=np.uint8) * np.uint8(2)
144

The alternative, of course, is to simply wrap the single value in a NumPy array (and then NumPy won't cast it in operations with scalars of different dtype).

To promote the type of an array during an operation, you could wrap any scalars in an array first:

>>> np.array([200], dtype=np.uint8) * np.array([2])
array([400])