Mad Wombat - 5 months ago 13

Python Question

I want to make a list of integer sequences with random start points. The way I would do this in pure python is

x = np.zeros(1000, 10) # 1000 sequences of 10 elements each

starts = np.random.randint(1, 1000, 1000)

for i in range(len(x)):

x[i] = np.arange(starts[i], starts[i] + 10)

I wonder if there is a more elegant way of doing this using Numpy functionality.

Answer

You can use `broadcasting`

after extending `starts`

to a `2D`

version and adding in the `1D`

range array, like so -

```
x = starts[:,None] + np.arange(10)
```

**Explanation**

Let's take a small example for `starts`

to see what that `broadcasting`

does in this case.

```
In [382]: starts
Out[382]: array([3, 1, 3, 2])
In [383]: starts.shape
Out[383]: (4,)
In [384]: starts[:,None]
Out[384]:
array([[3],
[1],
[3],
[2]])
In [385]: starts[:,None].shape
Out[385]: (4, 1)
In [386]: np.arange(10).shape
Out[386]: (10,)
```

Thus, looking at the shapes and putting those together, a schematic diagram of the same would look something like this -

```
starts : 4
np.arange(10) : 10
```

After extending `starts`

:

```
starts[:,None] : 4 x 1
np.arange(10) : 10
```

Thus, when we add `starts[:,None]`

with `np.arange(10)`

, the elems of `starts[:,None]`

would be broadcasted along its second axis `10`

times corresponding to the length of the other array along that axis. For `np.arange(10)`

, it would be converted to `2D`

with its first dim being a singleton dim and its elems being broadcasted along it `4`

times correspoinding to the length of `4`

for the other array `starts[:,None]`

along that axis. Please note that there aren't explicit replications, as under the hood the elems are broadcasted and added on the fly.

Thus, functionally we would have the replications, like so -

```
In [391]: np.repeat(starts[:,None],10,axis=1)
Out[391]:
array([[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2]])
In [392]: np.repeat(np.arange(10)[None],4,axis=0)
Out[392]:
array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])
```

These broadcasted elems are then added to give us the desired output `x`

.