normal

random.normal(shape, mean, standard_deviation, seed=None, *, name=None)

Create a sample of normally distributed random numbers.

Parameters:

shape (tuple[int, ...]) – The shape of the sampled random numbers.
mean (float) – The mean of the normal distribution.
standard_deviation (float) – The standard deviation of the normal distribution.
seed (int or None, optional) – A seed for the random number generator. Defaults to None, in which case a random value for the seed is used.
name (str or None, optional) – The name of the node.

Returns:

A tensor containing a sample of normally distributed random numbers with shape shape.

Return type:

Tensor

See also

Graph.random.choices: Create random samples from the data that you provide.
Graph.random.uniform: Create a sample of uniformly distributed random numbers.
boulderopal.run_stochastic_optimization: Function to find the minimum of generic stochastic functions.

Examples

Create a random tensor by sampling from a Gaussian distribution.

>>> samples = graph.random.normal(
...     shape=(3, 1), mean=0.0, standard_deviation=0.05, seed=0, name="samples"
... )
>>> result = bo.execute_graph(graph=graph, output_node_names="samples")
>>> result["output"]["samples"]["value"]
array([[-0.03171833], [0.00816805], [-0.06874011]])

Create a batch of noise signals to construct a PWC Hamiltonian. The signal is defined as \(a \cos(\omega t)\), where \(a\) follows a normal distribution and \(\omega\) follows a uniform distribution.

>>> seed = 0
>>> batch_size = 3
>>> sigma_x = np.array([[0, 1], [1, 0]])
>>> sample_times = np.array([0.1, 0.2])
>>> a = graph.random.normal((batch_size, 1), mean=0.0, standard_deviation=0.05, seed=seed)
>>> omega = graph.random.uniform(
...     shape=(batch_size, 1), lower_bound=np.pi, upper_bound=2 * np.pi, seed=seed
... )
>>> sampled_signal = a * graph.cos(omega * sample_times[None])
>>> hamiltonian = graph.pwc_signal(sampled_signal, duration=0.2) * sigma_x
>>> hamiltonian.name = "hamiltonian"
>>> result = bo.execute_graph(graph=graph, output_node_names="hamiltonian")
>>> result["output"]["hamiltonian"]
{
    'durations': array([0.1, 0.1]),
    'values': array([
        [
            [[-0.        , -0.02674376], [-0.02674376, -0.        ]],
            [[-0.        , -0.01338043], [-0.01338043, -0.        ]]
        ],
        [
            [[ 0.        ,  0.00691007], [ 0.00691007,  0.        ]],
            [[ 0.        ,  0.00352363], [ 0.00352363,  0.        ]]],
        [
            [[-0.        , -0.06230612], [-0.06230612, -0.        ]],
            [[-0.        , -0.04420857], [-0.04420857, -0.        ]]
        ]
    ]),
    'time_dimension': 1
}

See more examples in the How to optimize controls robust to strong noise sources user guide.