# What does -1 mean in numpy reshape?

The criterion to satisfy for providing the new shape is that *'The new shape should be compatible with the original shape'*

numpy allow us to give one of new shape parameter as -1 (eg: (2,-1) or (-1,3) but not (-1, -1)). It simply means that it is an unknown dimension and we want numpy to figure it out. And numpy will figure this by looking at the *'length of the array and remaining dimensions'* and making sure it satisfies the above mentioned criteria

Now see the example.

```python
z = np.array([[1, 2, 3, 4],
         [5, 6, 7, 8],
         [9, 10, 11, 12]])
z.shape
(3, 4)
```

Now trying to reshape with (-1) . Result new shape is (12,) and is compatible with original shape (3,4)

```python
z.reshape(-1)
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])
```

Now trying to reshape with (-1, 1) . We have provided column as 1 but rows as unknown . So we get result new shape as (12, 1).again compatible with original shape(3,4)

```python
z.reshape(-1,1)
array([[ 1],
   [ 2],
   [ 3],
   [ 4],
   [ 5],
   [ 6],
   [ 7],
   [ 8],
   [ 9],
   [10],
   [11],
   [12]])
```

New shape as (-1, 2). row unknown, column 2. we get result new shape as (6, 2)

```python
z.reshape(-1, 2)
array([[ 1,  2],
   [ 3,  4],
   [ 5,  6],
   [ 7,  8],
   [ 9, 10],
   [11, 12]])
```

Now trying to keep column as unknown. New shape as (1,-1). i.e, row is 1, column unknown. we get result new shape as (1, 12)

```python
z.reshape(1,-1)
array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12]])
```

New shape (2, -1). Row 2, column unknown. we get result new shape as (2,6)

```python
z.reshape(2, -1)
array([[ 1,  2,  3,  4,  5,  6],
   [ 7,  8,  9, 10, 11, 12]])
```

New shape as (3, -1). Row 3, column unknown. we get result new shape as (3,4)

```python
z.reshape(3, -1)
array([[ 1,  2,  3,  4],
   [ 5,  6,  7,  8],
   [ 9, 10, 11, 12]])
```

And finally, if we try to provide both dimension as unknown i.e new shape as (-1,-1). It will throw an error

```python
z.reshape(-1, -1)
ValueError: can only specify one unknown dimension
```


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