What is a "scalar" in numpy?

Question

The documentation states the purpose of scalars, such as the fact that conventional Python numbers like float and integer are too primitive therefore more complex data types are neccessary.

It also states certain kinds of scalars(data type hierarchy); as well as a couple attributes of scalar.
But it never gives a concrete definition of exactly what a scalar is in the context of Python.

I want to get to the heart of the issue on this. So my question is, in the simplest terms possible, explain to me what a pythonic scalar is.

Answer 1

A NumPy scalar is any object which is an instance of np.generic or whose type is in np.ScalarType:

In [12]: np.ScalarType
Out[13]: 
(int,
 float,
 complex,
 long,
 bool,
 str,
 unicode,
 buffer,
 numpy.int16,
 numpy.float16,
 numpy.int8,
 numpy.uint64,
 numpy.complex192,
 numpy.void,
 numpy.uint32,
 numpy.complex128,
 numpy.unicode_,
 numpy.uint32,
 numpy.complex64,
 numpy.string_,
 numpy.uint16,
 numpy.timedelta64,
 numpy.bool_,
 numpy.uint8,
 numpy.datetime64,
 numpy.object_,
 numpy.int64,
 numpy.float96,
 numpy.int32,
 numpy.float64,
 numpy.int32,
 numpy.float32)

This definition comes from looking at the source code for np.isscalar:

def isscalar(num):
    if isinstance(num, generic):
        return True
    else:
        return type(num) in ScalarType

---

Note that you can test if something is a scalar by using np.isscalar:

>>> np.isscalar(3.1)
True
>>> np.isscalar([3.1])
False
>>> np.isscalar(False)
True

---

How do we know what we know? I like learning how people know what they know -- more than the answers themselves. So let me try to explain where the above answer comes from.

Having the right tools can help you figure out things like this for yourself.

I found this out by using IPython. Using its TAB-completion feature, typing

In [19]: import numpy as np
In [20]: np.[TAB]

causes IPython to display all variables in the np module namespace. A search for the string "scalar" will lead you to np.ScalarType and np.isscalar. Typing

In [20]: np.isscalar?

(note the question mark at the end) prompts IPython to show you where np.isscalar is defined:

File:       /data1/unutbu/.virtualenvs/dev/lib/python2.7/site-packages/numpy/core/numeric.py

which is how I got to the definition of isscalar. Alternatively, the numpy documentation for isscalar has a link to the source code as well.

Answer 2

In this context, a scalar is one of the things you put in an array. A single 64-bit float or 32-bit int, for example, rather than a whole array of them.

Answer 3

Just non-vectors. numpy tries to parse it's vectors to a single numbers (namely, python scalars) when passed as arguments, and would fail when the length of vector is not 1:

In [44]: float(a)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-44-93d25633ffc4> in <module>()
----> 1 float(a)

TypeError: only length-1 arrays can be converted to Python scalars