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, and therefore more complex data types are necessary. It also states certain kinds of scalars (data type hierarchy); as well as a couple of 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. In the simplest terms possible, what is a Pythonic scalar?

Accepted Answer

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.

What is a "scalar" in NumPy?

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