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20.3 Examples

20.3 Examples

Some example uses of the numarray.random_array module. Note: Naturally the exact output of running these examples will be different each time!

```>>> from numarray.random_array import *
>>> seed() # Set seed based on current time
>>> print get_seed() # Find out what seeds were used
(897800491, 192000)
>>> print random()
0.0528018975065
>>> print random((5,2))
[[ 0.14833829 0.99031458]
[ 0.7526806 0.09601787]
[ 0.1895229 0.97674777]
[ 0.46134511 0.25420982]
[ 0.66132009 0.24864472]]
>>> print uniform(-1,1,(10,))
[ 0.72168852 -0.75374185 -0.73590945 0.50488248 -0.74462822 0.09293685
-0.65898308 0.9718067 -0.03252475 0.99611011]
>>> print randint(0,100, (12,))
[28 5 96 19 1 32 69 40 56 69 53 44]
>>> print permutation(10)
[4 2 8 9 1 7 3 6 5 0]
>>> seed(897800491, 192000) # resetting the same seeds
>>> print random() # yields the same numbers
0.0528018975065
```
Most of the functions in this package take zero or more distribution specific parameters plus an optional shape parameter. The shape parameter gives the shape of the output array:
```>>> from numarray.random_array import *
>>> print standard_normal()
-0.435568600893
>>> print standard_normal(5)
[-1.36134553 0.78617644 -0.45038718 0.18508556 0.05941355]
>>> print standard_normal((5,2))
[[ 1.33448863 -0.10125473]
[ 0.66838062 0.24691346]
[-0.95092064 0.94168913]
[-0.23919107 1.89288616]
[ 0.87651485 0.96400219]]
>>> print normal(7., 4., (5,2)) #mean=7, std. dev.=4
[[ 2.66997623 11.65832615]
[ 6.73916003 6.58162862]
[ 8.47180378 4.30354905]
[ 1.35531998 -2.80886841]
[ 7.07408469 11.39024973]]
>>> print exponential(10., 5) #mean=10
[ 18.03347754 7.11702306 9.8587961 32.49231603 28.55408891]
>>> print beta(3.1, 9.1, 5) # alpha=3.1, beta=9.1
[ 0.1175056 0.17504358 0.3517828 0.06965593 0.43898219]
>>> print chi_square(7, 5) # 7 degrees of freedom (dfs)
[ 11.99046516 3.00741053 4.72235727 6.17056274 8.50756836]
>>> print noncentral_chi_square(7, 3, 5) # 7 dfs, noncentrality 3
[ 18.28332138 4.07550335 16.0425396 9.51192093 9.80156231]
>>> F(5, 7, 5) # 5 and 7 dfs
array([ 0.24693671, 3.76726145, 0.66883826, 0.59169068, 1.90763224])
>>> noncentral_F(5, 7, 3., 5) # 5 and 7 dfs, noncentrality 3
array([ 1.17992553, 0.7500126 , 0.77389943, 9.26798989, 1.35719634])
>>> binomial(32, .5, 5) # 32 trials, prob of an event = .5
array([12, 20, 21, 19, 17])
>>> negative_binomial(32, .5, 5) # 32 trials: prob of an event = .5
array([21, 38, 29, 32, 36])
```
Two functions that return generate multivariate random numbers (that is, random vectors with some known relationship between the elements of each vector, defined by the distribution). They are multivariate_normal and multinomial. For these two functions, the lengths of the leading axes of the output may be specified. The length of the last axis is determined by the length of some other parameter.
```>>> multivariate_normal([1,2], [[1,2],[2,1]], [2,3])
array([[[ 0.14157988, 1.46232224],
[-1.11820295, -0.82796288],
[ 1.35251635, -0.2575901 ]],
[[-0.61142141, 1.0230465 ],
[-1.08280948, -0.55567217],
[ 2.49873002, 3.28136372]]])
>>> x = multivariate_normal([10,100], [[1,2],[2,1]], 10000)
>>> x_mean = sum(x)/10000
>>> print x_mean
[ 9.98599893 100.00032416]
>>> x_minus_mean = x - x_mean
>>> cov = matrixmultiply(transpose(x_minus_mean), x_minus_mean) / 9999.
>>> cov
array([[ 2.01737122, 1.00474408],
[ 1.00474408, 2.0009806 ]])
```
The a priori probabilities for a multinomial distribution must sum to one. The prior probability argument to multinomial doesn't give the prior probability of the last event: it is computed to be one minus the sum of the others.
```>>> multinomial(16, [.1, .4, .2]) # prior probabilities [.1, .4, .2, .3]
array([2, 7, 1, 6])
>>> multinomial(16, [.1, .4, .2], [2,3]) # output shape [2,3,4]
array([[[ 1, 9, 1, 5],
[ 0, 10, 3, 3],
[ 4, 9, 3, 0]],
[[ 1, 6, 1, 8],
[ 3, 4, 5, 4],
[ 1, 5, 2, 8]]])
```
Many of the functions accept arrays or sequences for the distribution arguments. If no shape argument is given, then the shape of the output is determined by the shape of the parameter argument. For instance:
```>>> beta([5.0, 50.0], [10.0, 100.])
array([ 0.54379648,  0.35352072])
```
Broadcasting rules apply if two or more arguments are arrays:
```>>> beta([5.0, 50.0], [[10.0, 100.], [20.0, 200.0]])
array([[ 0.30204576,  0.32154009],
[ 0.10851908,  0.19207685]])
```
The shape argument can still be used to specify the output shape. Any array argument will be broadcasted to have the given shape:
```>>> beta(5.0, [10.0, 100.0], shape = (3, 2))
array([[ 0.49521708,  0.02218186],
[ 0.21000148,  0.04366644],
[ 0.43169656,  0.05285903]])
```
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