# NumPy refresher¶

- Here are some quick guides to NumPy:

## Matrix conventions for machine learning¶

Rows are horizontal and columns are vertical. Every row is an example. Therefore, inputs[10,5] is a matrix of 10 examples where each example has dimension 5. If this would be the input of a neural network then the weights from the input to the first hidden layer would represent a matrix of size (5, #hid).

Consider this array:

```
>>> numpy.asarray([[1., 2], [3, 4], [5, 6]])
array([[ 1., 2.],
[ 3., 4.],
[ 5., 6.]])
>>> numpy.asarray([[1., 2], [3, 4], [5, 6]]).shape
(3, 2)
```

This is a 3x2 matrix, i.e. there are 3 rows and 2 columns.

To access the entry in the 3rd row (row #2) and the 1st column (column #0):

```
>>> numpy.asarray([[1., 2], [3, 4], [5, 6]])[2, 0]
5.0
```

To remember this, keep in mind that we read left-to-right, top-to-bottom, so each thing that is contiguous is a row. That is, there are 3 rows and 2 columns.

## Broadcasting¶

Numpy does *broadcasting* of arrays of different shapes during
arithmetic operations. What this means in general is that the smaller
array (or scalar) is *broadcasted* across the larger array so that they have
compatible shapes. The example below shows an instance of
*broadcasting*:

```
>>> a = numpy.asarray([1.0, 2.0, 3.0])
>>> b = 2.0
>>> a * b
array([ 2., 4., 6.])
```

The smaller array `b`

(actually a scalar here, which works like a 0-d array) in this case is *broadcasted* to the same size
as `a`

during the multiplication. This trick is often useful in
simplifying how expression are written. More detail about *broadcasting*
can be found in the numpy user guide.