Detailed ufunc function in numpy

• What is the universal function

A universal function (or ufunc for short ) is a function that operates on ndarrays in an element-by-element fashion, supporting array broadcasting, type casting, and several other standard features. That is, a ufunc is a "vectorized" wrapper for a function that Takes a Fi xed Number of the speci Fi C Inputs and Produces a Fi xed Number of the speci Fi C Outputs
- source: numpy.org
Briefly, universal function is defined operation on ndarray is element - computing element
numpy there a important concepts: broadcast (broadcast), broadcasting means, such that the shape can be different with the array involved in computing, reference: broadcasting

• ufunc some simple properties

1. nin number of input data:
2. nout number of output:
3. nargs: The number of arguments. Data attribute containing the number of arguments the ufunc takes, including optional ones.
4. ntypes: The number of numerical NumPy types - of which there are 18 total - on which the ufunc can operate
5. types: Returns a list with types grouped input->output. Data attribute listing the data-type “Domain-Range” groupings the ufunc can deliver. The data-types are given using the character codes
6. identity: Data attribute containing the identity element for the ufunc, if it has one. If it does not, the attribute value is None.
7. Signature : Determines How at The Signature at The Dimensions of the each the INPUT / Array are the Output Split Core and Loop Dimensions INTO
   Tip: Call ufunc .__ doc__ can view the documentation of the function

E.g

print(np.multiply.__doc__)

• ufunc method (method):
  Below we function as an example to explain to add.reduce

1. ufunc.reduce
   Usage: reduce (a, axis, initial , keepdims)
   See the reduce
   A is a matrix of the input
   axis dimension is involved in computing (default is 0)
   , for example:

import numpy as np
a=np.arange(9).reshape(3,3)
print(a)
# [[0 1 2]
#  [3 4 5]
#  [6 7 8]]
#如果我们想把矩阵按行(axis=0)进行划分，把各行相加
b=np.add.reduce(a,axis=0)
print(b)
# [ 9 12 15]

Our view b of shape, the result is (3), visible after completion of the operation, axis = 0 has been removed (reduce), of course, if we want to change before and after the operation ndim, that is not the axis = 0 to reduce off keepdims = 1 can be achieved

b=np.add.reduce(a,axis=0,keepdims=1)

If we want to obtain a final solution if the bias, so that each element is the result of both a plus 5, you can call this initial parameter

b=np.add.reduce(a,axis=0,keepdims=1,initial=5)
print(b)
#[[14 17 20]]

Similarly, multiply.reduce and add.reduce are very similar, the only difference is the "sum" into multiplied to reduce other functions, is similar.

2. ufunc.accumulate
   Similarly, we add.accumulate for example
   what if we put a matrix of rows (axis = 0) to be divided, we look at the results obtained are add.accumulate

import numpy as np
a=np.arange(9).reshape(3,3)
print(a)
# [[0 1 2]
#  [3 4 5]
#  [6 7 8]]
#如果我们想吧矩阵按行(axis=0)进行划分，把各行相加
b=np.add.accumulate(a,axis=0)
print(b)
# [[ 0  1  2]
#  [ 3  5  7]第一行+第二行
#  [ 9 12 15]]第一行+第二行+第三行

3. ufunc.outer
   We add.outer A Case Study

import numpy as np
a=np.array([1,2,3])
b=np.array([4,5,6])
print(np.add.outer(a,b))
# [[5 6 7]
#  [6 7 8]
#  [7 8 9]]

We have found, in the A 1 + 1 is replaced with [4,5,6], 2 + 2 has been replaced with [4,5,6], is replaced by 3 3+ [4,5,6]
summary: add.outer (a, b) is equivalent to a replacement of each element to the element Shape and b and, as a result of (a.shape, b.shape)