What does -1 mean in numpy reshape?

Question

A numpy matrix can be reshaped into a vector using reshape function with parameter -1. But I don't know what -1 means here.

For example:

a = numpy.matrix([[1, 2, 3, 4], [5, 6, 7, 8]])
b = numpy.reshape(a, -1)

The result of b is: matrix([[1, 2, 3, 4, 5, 6, 7, 8]])

Does anyone know what -1 means here? And it seems python assign -1 several meanings, such as: array[-1] means the last element. Can you give an explanation?

Solution 1

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.

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)

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)

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

The above is consistent with numpy advice/error message, to use reshape(-1,1) for a single feature; i.e. single column

Reshape your data using array.reshape(-1, 1) if your data has a single feature

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

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)

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

The above is consistent with numpy advice/error message, to use reshape(1,-1) for a single sample; i.e. single row

Reshape your data using array.reshape(1, -1) if it contains a single sample

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

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)

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

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

Solution 2

Used to reshape an array.

Say we have a 3 dimensional array of dimensions 2 x 10 x 10:

r = numpy.random.rand(2, 10, 10) 

Now we want to reshape to 5 X 5 x 8:

numpy.reshape(r, shape=(5, 5, 8)) 

will do the job.

Note that, once you fix first dim = 5 and second dim = 5, you don't need to determine third dimension. To assist your laziness, Numpy gives the option of using -1:

numpy.reshape(r, shape=(5, 5, -1)) 

will give you an array of shape = (5, 5, 8).

Likewise,

numpy.reshape(r, shape=(50, -1)) 

will give you an array of shape = (50, 4)

You can read more at http://anie.me/numpy-reshape-transpose-theano-dimshuffle/

Solution 3

According to the documentation:

newshape : int or tuple of ints

The new shape should be compatible with the original shape. If an integer, then the result will be a 1-D array of that length. One shape dimension can be -1. In this case, the value is inferred from the length of the array and remaining dimensions.

Solution 4

numpy.reshape(a,newshape,order{})

check the below link for more info. https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html

for the below example you mentioned the output explains the resultant vector to be a single row.(-1) indicates the number of rows to be 1. if the

a = numpy.matrix([[1, 2, 3, 4], [5, 6, 7, 8]])
b = numpy.reshape(a, -1)

output:

matrix([[1, 2, 3, 4, 5, 6, 7, 8]])

this can be explained more precisely with another example:

b = np.arange(10).reshape((-1,1))

output:(is a 1 dimensional columnar array)

array([[0],
       [1],
       [2],
       [3],
       [4],
       [5],
       [6],
       [7],
       [8],
       [9]])

or

b = np.arange(10).reshape((1,-1))

output:(is a 1 dimensional row array)

array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])

Solution 5

The -1 stands for "unknown dimension" which can be inferred from another dimension. In this case, if you set your matrix like this:

a = numpy.matrix([[1, 2, 3, 4], [5, 6, 7, 8]])

Modify your matrix like this:

b = numpy.reshape(a, -1)

It will call some default operations to the matrix a, which will return a 1-d numpy array/matrix.

However, I don't think it is a good idea to use code like this. Why not try:

b = a.reshape(1, -1)

It will give you the same result and it's more clear for readers to understand: Set b as another shape of a. For a, we don't how many columns it should have (set it to -1!), but we want a 1-dimension array (set the first parameter to 1!).

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