Numpy random numbers
1. Numpy random number overview
The random number generation functions included in Numpy are shown in the following table:
| function | function |
|---|---|
| rand (d0, d1,…, dn) | Returns the matrix corresponding to the dimension of the input array |
| randn(d0, d1, …, dn) | Returns the matrix of the input array dimension corresponding to the standard normal distribution |
| randint(low[, high, size, dtype]) | Returns integer random data in the range [low, high) |
| random_integers(low[, high, size]) | Returns a random integer between [low, high] |
| random_sample([size]) | Returns a floating point random number between [0.0, 1.0) |
| random([size]) | Returns a floating point random number from the range [0.0, 1.0) |
| ranf([size]) | Returns a floating point random number from the range [0.0, 1.0) |
| sample([size]) | Returns a floating point random number from the range [0.0, 1.0) |
| choice(a[, size, replace, p]) | Generate random samples from the given 1D array |
| bytes(length) | return random bytes |
2. Random number generation example
2.1 rand (d0, d1,…, dn)
This function returns a random matrix of the specified dimension, and the random numbers are derived from samples that follow the [1,0) distribution.
Example:
np.random.rand(3, 4)
[[ 0.9453398 0.15785589 0.14297825 0.40554182]
[ 0.58353036 0.16330881 0.79096958 0.29872379]
[ 0.30474484 0.85217927 0.06831362 0.61730196]]2.2 randn(d0, d1, …, dn)
This function returns a random matrix of the specified dimension, and the random numbers are derived from samples that obey the (0,1) standard normal distribution. This function is similar to random.standard_normal, and the corresponding normal distribution N(mu, sigma^2) can be obtained by the following formula:
sigma * np.random.randn(…) + mu
Example:
np.random.randn(3, 4)
[[-2.30951289 -1.05847819 -0.06452076 -0.82147271]
[ 0.324241 -0.51254897 0.51067497 0.66082303]
[-0.0982416 0.78864197 -0.80479118 2.2884627 ]]2.3 randint(low[, high, size, dtype])
This function returns a matrix of random numbers from a [low, high) discrete uniform distribution. If the high parameter is not specified, the range will be limited to [0, low)
Example:
np.random.randint(0, 3, (3, 4))
[[1 0 2 0]
[0 2 0 2]
[2 2 2 1]]2.4 random_integers(low[, high, size])
This function is similar to the previous one, except that it returns a random number matrix that obeys the [low, high] discrete uniform distribution. If the high parameter is not specified, the range will be limited to [1, low]
Example:
np.random.random_integers(0, 3, (3, 4))
[[2 2 0 3]
[2 0 1 2]
[3 3 2 0]]Generate N uniform integers between a and b:
a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)
2.5 random_sample([size]),random([size]),ranf([size]),sample([size])
This function returns the continuous mean floating point number distribution in the range [0.0, 1.0). If the range of the numbers to be generated is [a,b), then:
(b - a) * random_sample() + a
Example:
np.random.random_sample((3, 4))
[[ 0.12439296 0.44063728 0.65585181 0.29929493]
[ 0.93312505 0.61461946 0.15346194 0.11332448]
[ 0.35118524 0.31794849 0.69337822 0.73912451]]2.6 choice(a, size=None, replace=True, p=None)
The function returns the decimation matrix in the one-dimensional array a. If a is a number, the one-dimensional number is np.arange(a).
Example:
a = [2, 4, 6, 8, 10]
np.random.choice(a, (3, 4))
[[ 2 2 6 2]
[ 4 10 2 8]
[ 8 10 6 2]]2.7 bytes(length)
Returns random bytes
Example :
np.random.bytes(5)
l�;�Common distribution functions
1. Distribution functions included in Numpy
| function | specific distribution |
|---|---|
| beta(a, b[, size]) | Draw samples from a Beta distribution. |
| binomial(n, p[, size]) | Draw samples from a binomial distribution. |
| chisquare(df[, size]) | Draw samples from a chi-square distribution. |
| dirichlet(alpha[, size]) | Draw samples from the Dirichlet distribution. |
| exponential([scale, size]) | Draw samples from an exponential distribution. |
| f(dfnum, dfden[, size]) | Draw samples from an F distribution. |
| gamma(shape[, scale, size]) | Draw samples from a Gamma distribution. |
| geometric(p[, size]) | Draw samples from the geometric distribution. |
| gumbel([loc, scale, size]) | Draw samples from a Gumbel distribution. |
| hypergeometric(ngood, nbad, nsample[, size]) | Draw samples from a Hypergeometric distribution. |
| laplace([loc, scale, size]) | Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). |
| logistic([loc, scale, size]) | Draw samples from a logistic distribution. |
| lognormal([mean, sigma, size]) | Draw samples from a log-normal distribution. |
| logseries(p[, size]) | Draw samples from a logarithmic series distribution. |
| multinomial(n, pvals[, size]) | Draw samples from a multinomial distribution. |
| multivariate_normal(mean, cov[, size, …) | Draw random samples from a multivariate normal distribution. |
| negative_binomial(n, p[, size]) | Draw samples from a negative binomial distribution. |
| noncentral_chisquare (df, nonc [, size]) | Draw samples from a noncentral chi-square distribution. |
| noncentral_f(dfnum, dfden, nonc[, size]) | Draw samples from the noncentral F distribution. |
| normal([loc, scale, size]) | Draw random samples from a normal (Gaussian) distribution. |
| pareto(a[, size]) | Draw samples from a Pareto II or Lomax distribution with specified shape. |
| poisson([lam, size]) | Draw samples from a Poisson distribution. |
| power(a[, size]) | Draws samples in [0, 1] from a power distribution with positive exponent a - 1. |
| rayleigh([scale, size]) | Draw samples from a Rayleigh distribution. |
| standard_cauchy([size]) | Draw samples from a standard Cauchy distribution with mode = 0. |
| standard_exponential([size]) | Draw samples from the standard exponential distribution. |
| standard_gamma(shape[, size]) | Draw samples from a standard Gamma distribution. |
| standard_normal([size]) | Draw samples from a standard Normal distribution(mean=0, stdev=1). |
| standard_t(df[, size]) | Draw samples from a standard Student’s t distribution with df degrees of freedom. |
| triangular(left, mode, right[, size]) | Draw samples from the triangular distribution over the interval [left, right]. |
| uniform([low, high, size]) | Draw samples from a uniform distribution. |
| vonmises(mu, kappa[, size]) | Draw samples from a von Mises distribution. |
| wald(mean, scale[, size]) | Draw samples from a Wald, or inverse Gaussian, distribution. |
| weibull(a[, size]) | Draw samples from a Weibull distribution. |
| zipf(a[, size]) | Draw samples from a Zipf distribution. |
2. 函数使用
这里就是用最常用的高斯分布作为示例进行讲解，其它分的使用也是类似的。
mu = 50
sigma = 10.0
a = np.linspace(0, 100, 1000)
y = 1/(sigma * np.sqrt(2 * np.pi))*np.exp(-(a - mu)**2 / (2 * sigma**2))
data = np.random.normal(mu, sigma, 1000)
plt.figure()
plt.hist(data, 50, normed=True)
plt.plot(a, y, 'r-')
plt.show()