Cara menggunakan np.random.multivariate_normal python

The multivariate normal, multinormal or Gaussian distribution is a generalisation of the one-dimensional normal distribution to higher dimensions.

Such a distribution is specified by its mean and covariance matrix, which are analogous to the mean (average or “centre”) and variance (standard deviation squared or “width”) of the one-dimensional normal distribution.

Parameters:

mean : (N,) ndarray

Mean of the N-dimensional distribution.

cov : (N,N) ndarray

Covariance matrix of the distribution.

size : tuple of ints, optional

Given a shape of, for example, (m,n,k), m*n*k samples are generated, and packed in an m-by-n-by-k arrangement. Because each sample is N-dimensional, the output shape is (m,n,k,N). If no shape is specified, a single sample is returned.

Returns:

out : ndarray

The drawn samples, arranged according to size. If the shape given is (m,n,...), then the shape of out is is (m,n,...,N).

In other words, each entry out[i,j,...,:] is an N-dimensional value drawn from the distribution.

Notes

The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution.

def _new_recombination2(self, X, trials=100): print(" * Trying to reboot...") from numpy import average, identity, cov, logspace from numpy.random import multivariate_normal from matplotlib.pyplot import scatter, show, xlim, ylim, subplots, legend #fig, ax = subplots(1,1, figsize=(5,5)) best_solutions = self._get_best_solutions(int(self.numberofparticles/3)) all_sols = [] for sol in best_solutions: all_sols.append(sol.X) all_sols = array(all_sols).T #print (all_sols) com = [average( x, weights=logspace(0,-2,self.numberofparticles/3) ) for x in all_sols] cova = cov(all_sols) res = multivariate_normal(com, cova, trials) if False: scatter(all_sols[0], all_sols[1], label="all selected solutions") scatter(com[0], com[1], label="weighted average") scatter(res.T[0], res.T[1], alpha=0.5, s=10, label="new samples") scatter(all_sols[0][0], all_sols[1][0], label="best individual") xlim(-100,100) ylim(-100,100) legend() show() ; exit() for r in res: for d in range(len(r)): if r[d]>self.Boundaries[d][1]: r[d] = self.Boundaries[d][1] elif r[d]

With the help of np.multivariate_normal() method, we can get the array of multivariate normal values by using np.multivariate_normal() method.

Syntax : np.multivariate_normal(mean, matrix, size)
Return : Return the array of multivariate normal values.

Example #1 :
In this example we can see that by using np.multivariate_normal() method, we are able to get the array of multivariate normal values by using this method.

# import numpy

import numpy as np

  

mean= np.multivariate_normal()0np.multivariate_normal()1np.multivariate_normal()2np.multivariate_normal()3np.multivariate_normal()4

np.multivariate_normal()5= np.multivariate_normal()7np.multivariate_normal()1np.multivariate_normal()2np.multivariate_normal(mean, matrix, size)0np.multivariate_normal()2np.multivariate_normal(mean, matrix, size)0np.multivariate_normal(mean, matrix, size)1np.multivariate_normal(mean, matrix, size)0np.multivariate_normal()2np.multivariate_normal()1np.multivariate_normal()2np.multivariate_normal(mean, matrix, size)0np.multivariate_normal(mean, matrix, size)1np.multivariate_normal(mean, matrix, size)0np.multivariate_normal()2np.multivariate_normal(mean, matrix, size)0np.multivariate_normal()2np.multivariate_normal()1np.multivariate_normal(mean, matrix, size)5

.T transposes a matrix. So in your case, if n=2, your code will work (or at least, will run without error) without the transpose, because a matrix such as:

>>> np.random.multivariate_normal(mean, cov, size = 2)
array([[ 1.4594626 , -0.55863612],
       [-1.17139735, -0.36484634]])

Can be split into 2 arrays (x will be [ 1.4594626 , -1.17139735] and y will be [-0.55863612, -0.36484634]). Note that this is not necessarily what you are looking for, and you might end up plotting the wrong thing (depending what you're trying to do).

But for anything bigger (or smaller), it won't:

>>> np.random.multivariate_normal(mean, cov, size = 5)
array([[-0.34091962,  2.2368088 ],
       [-1.11081547,  0.93089064],
       [ 1.45452483, -0.40007311],
       [ 0.96038401,  0.26206106],
       [ 0.3079481 ,  0.66869094]])

Because that is essentially 5 arrays that you are trying to unpack into 2 variables (hence the error). However when you transpose it:

>>> np.random.multivariate_normal(mean, cov, size = 5).T
array([[ 0.04466423,  0.88384196,  0.09108559, -2.30473587,  1.58497064],
       [ 0.66190894,  0.90202853,  0.31090378,  0.95697681, -0.61557393]])

You're good to go. Your x array will be the first "row":

>>> np.random.multivariate_normal(mean, cov, size = 5)
array([[-0.34091962,  2.2368088 ],
       [-1.11081547,  0.93089064],
       [ 1.45452483, -0.40007311],
       [ 0.96038401,  0.26206106],
       [ 0.3079481 ,  0.66869094]])

0 and y will be your second:

>>> np.random.multivariate_normal(mean, cov, size = 5)
array([[-0.34091962,  2.2368088 ],
       [-1.11081547,  0.93089064],
       [ 1.45452483, -0.40007311],
       [ 0.96038401,  0.26206106],
       [ 0.3079481 ,  0.66869094]])

2