>>> np.random.rand(3,2)
array([[ 0.14022471,  0.96360618],  #random
       [ 0.37601032,  0.25528411],  #random
       [ 0.49313049,  0.94909878]]) #random

Notes

For random samples from , use:

sigma * np.random.randn(...) + mu

Examples

>>> np.random.randn()
2.1923875335537315 #random

Two-by-four array of samples from N(3, 6.25):

>>> 2.5 * np.random.randn(2, 4) + 3
array([[-4.49401501,  4.00950034, -1.81814867,  7.29718677],  #random
       [ 0.39924804,  4.68456316,  4.99394529,  4.84057254]]) #random

>>> np.random.randint(2, size=10)
array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0])
>>> np.random.randint(1, size=10)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

Generate a 2 x 4 array of ints between 0 and 4, inclusive:

>>> np.random.randint(5, size=(2, 4))
array([[4, 0, 2, 1],
       [3, 2, 2, 0]])

Notes

To sample from N evenly spaced floating-point numbers between a and b, use:

a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)

Examples

>>> np.random.random_integers(5)
4
>>> type(np.random.random_integers(5))
<type ‘int‘>
>>> np.random.random_integers(5, size=(3.,2.))
array([[5, 4],
       [3, 3],
       [4, 5]])

Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (i.e., from the set ):

>>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4.
array([ 0.625,  1.25 ,  0.625,  0.625,  2.5  ])

Roll two six sided dice 1000 times and sum the results:

>>> d1 = np.random.random_integers(1, 6, 1000)
>>> d2 = np.random.random_integers(1, 6, 1000)
>>> dsums = d1 + d2

Display results as a histogram:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(dsums, 11, normed=True)
>>> plt.show()

To sample multiply the output of random_sample by (b-a) and add a:

(b - a) * random_sample() + a

Examples

>>> np.random.random_sample()
0.47108547995356098
>>> type(np.random.random_sample())
<type ‘float‘>
>>> np.random.random_sample((5,))
array([ 0.30220482,  0.86820401,  0.1654503 ,  0.11659149,  0.54323428])

Three-by-two array of random numbers from [-5, 0):

>>> 5 * np.random.random_sample((3, 2)) - 5
array([[-3.99149989, -0.52338984],
       [-2.99091858, -0.79479508],
       [-1.23204345, -1.75224494]])

（官网例子与random_sample完全一样）

（官网例子与random_sample完全一样）

（官网例子与random_sample完全一样）

Examples

Generate a uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3)
array([0, 3, 4])
>>> #This is equivalent to np.random.randint(0,5,3)

Generate a non-uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])
array([3, 3, 0])

Generate a uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False)
array([3,1,0])
>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]

Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])
array([2, 3, 0])

Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:

>>> aa_milne_arr = [‘pooh‘, ‘rabbit‘, ‘piglet‘, ‘Christopher‘]
>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])
array([‘pooh‘, ‘pooh‘, ‘pooh‘, ‘Christopher‘, ‘piglet‘],
      dtype=‘|S11‘)

>>> np.random.bytes(10)
‘ eh\x85\x022SZ\xbf\xa4‘ #random

>>> arr = np.arange(10)
>>> np.random.shuffle(arr)
>>> arr
[1 7 5 2 9 4 3 6 0 8]

This function only shuffles the array along the first index of a multi-dimensional array:

>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.shuffle(arr)
>>> arr
array([[3, 4, 5],
       [6, 7, 8],
       [0, 1, 2]])

>>> np.random.permutation(10)
array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6])

>>> np.random.permutation([1, 4, 9, 12, 15])
array([15,  1,  9,  4, 12])

>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.permutation(arr)
array([[6, 7, 8],
       [0, 1, 2],
       [3, 4, 5]])

>>> mean = [0,0]
>>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis

>>> import matplotlib.pyplot as plt
>>> x, y = np.random.multivariate_normal(mean, cov, 5000).T
>>> plt.plot(x, y, ‘x‘); plt.axis(‘equal‘); plt.show()

Notes

The probability density for the Gaussian distribution is

where is the mean and the standard deviation. The square of the standard deviation, , is called the variance.

The function has its peak at the mean, and its “spread” increases with the standard deviation (the function reaches 0.607 times its maximum at and [R217]).

Examples

Draw samples from the distribution:

>>> mu, sigma = 0, 0.1 # mean and standard deviation
>>> s = np.random.normal(mu, sigma, 1000)

Verify the mean and the variance:

>>> abs(mu - np.mean(s)) < 0.01
True
>>> abs(sigma - np.std(s, ddof=1)) < 0.01
True

Display the histogram of the samples, along with the probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 30, normed=True)
>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *
...                np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
...          linewidth=2, color=‘r‘)
>>> plt.show()