Generate random numbers that obey normal distribution

1.matlab in normrnd function
function ： Generating random numbers that obey normal distribution

grammar ：

R＝normrnd(MU,SIGMA)
R＝normrnd(MU,SIGMA,m)
R＝normrnd(MU,SIGMA,m,n)

say bright ：

• R＝normrnd(MU,SIGMA)： The generation follows a normal distribution (MU The parameter represents the mean value ,SIGMA The parameter represents the standard deviation ) The random number . Input vector or matrix MU and SIGMA Must be in the same form , Output R Also in the same form as them . The scalar input will be expanded into a matrix with the same dimension as other inputs .
• R＝norrmrnd(MU,SIGMA,m)： The generation follows a normal distribution (MU The parameter represents the mean value ,SIGMA The parameter represents the standard deviation ) Of
  Random number matrix , The form of the matrix is determined by m Definition .m It's a 1×2 vector , Two of these elements represent the return value R The dimension of rows and columns in .
• R＝normrnd(MU,SIGMA,m,n)： Generate m×n A matrix of random numbers in the form of normal distribution .

2.python in np.random.multivariate_normal
Definition ：def multivariate_normal(mean, cov, size=None, check_valid=None, tol=None)

• mean： Dimension of multivariate normal distribution ;n Mean value of dimensional distribution ;

• cov： Covariance matrix of multivariate normal distribution , Be careful ： The covariance matrix must be symmetric and positive semidefinite （ Shape is (N,N) Two dimensional array of ）;

• size： Specify the dimension of the generated normal distribution matrix （ example ： if size=(1, 1, 2), Then... Of the output matrix shape That is, the shape is
  1X1X2XN（N by mean The length of ））.

• check_valid： This parameter is used to determine when cov That is, the processing method of the program when the covariance matrix is not a positive semi definite matrix , It has three values ：warn,raise as well as ignore（igore: Ignore the problem that the covariance matrix is not a positive semidefinite matrix , Generating arrays .warn: Output warning , But the array will still be generated .raise: Application error , And will not generate an array ）.

• tol： Tolerance when checking singular value of covariance matrix ,float type .

import numpy as np

x = np.random.multivariate_normal(10, 2, (2, 3), 'raise')

3.python Create normal distribution number
（1） Generate an array of random normal distributions

np.random.normal(loc =0.0 , scale= 1.0,size = (5,4))    

• loc：float type , Represents the mean value of this normal distribution （ Corresponding to the whole distribution center ）;
• scale：float type , Represents the standard deviation of this normal distribution （ Corresponding to the density of the distribution ,scale The bigger, the fatter , The more scattered the data ;scale Smaller, thinner and taller , More centralized data ）
• size： Output shape,size=(k,m,n)
  Indicative output k dimension ,m That's ok ,n Number of columns , The default is None, Output only one value ,size=100, Indicative output 100 It's worth
  （2） Generate an array of standard normal distributions

np.random.standard_normal(size = (5,4))   # Returns an array of standard normal distributions of a specified shape 

The following is the equivalent statement ：
python in ：

print(np.random.normal(loc =0.0 , scale= 1.0,size = (2,1)))
print(np.random.standard_normal(size = (2,1)))

matlab in ：normrnd(0,1,2,1)