Machine learning deep learning -- Vectorization

To quantify

Whenever possible, avoid explicit for-loops.

Why vectorization

Speed up the operation , This requires a powerful toolkit numpy
Go directly to the code to see the comparison between non vectorization and vectorization Calculation The inner product of two vectors , You can see , The result of vectorization is 300 times faster than that of non vectorization

More examples of vectorization

A matrix is multiplied by a vector

Calculate the exponent of a vector

Apply vectorization to logistic In the regression

Non vectorization logistic Regression gradient descent code ：
In this code There are two cycles , Part of the green indication , In the calculation dw When , If we have multiple eigenvalues , You have to calculate multiple dw, here n=2,dw Just count two , Most of the time, it is necessary to use a cycle to solve , But in order not to cycle , Change the following code to a vector

take dw1,dw2 … Change it to a vector dw Express , initialization dw by n_x That's ok 1 Column 0 that will do

To quantify logistic Return to

In the vectorization above , It simplifies the intermediate requirements dw The cycle of , here , take for i=1 to m Also simplified , To quantify
Here's how ：
First ask for z1,z2 etc. , from z = wTx + b You know , Should first w,x and b To quantify ,x Is the number of input eigenvalues , Write it down as nx, Each sample corresponds to a different input , altogether m Samples , So there is m Column , therefore x yes R(nx,m) Matrix , and w I already know it is a R(nx,1) Matrix ,w*x The resulting matrix is R(1*m) Of , therefore b It's also R(1*m) Of , Last z = np.dot(w.t, X) + b
And then calculate a1,a2 etc. ,a Is a pair of activation functions z Obtained , When z Have worked out , You can directly put the vector into the activation function to find the vector a, Last A = σ(Z)

To quantify logistic Gradient output of regression

And then there's the calculation dz,db,dw

Last , Apply vectorization to logistic The gradient output of regression goes