greedy.sampler.SteepestDescentSolver.sample

SteepestDescentSolver.sample(bqm, num_reads=None, initial_states=None, initial_states_generator='random', seed=None, large_sparse_opt=False, **kwargs)

Sample from a binary quadratic model.

Starts from initial_states, and converges to local minima using discrete steepest-descent method.

Parameters

• bqm (BinaryQuadraticModel) – The binary quadratic model to be sampled.

• num_reads (int, optional, default=len(initial_states) or 1) – Number of reads. Each read is generated by one run of the steepest descent algorithm. If num_reads is not explicitly given, it is selected to match the number of initial states given. If initial states are not provided, only one read is performed.

• initial_states (samples-like, optional, default=None) – One or more samples, each defining an initial state for all the problem variables. Initial states are given one per read, but if fewer than num_reads initial states are defined, additional values are generated as specified by initial_states_generator. See dimod.as_samples() for a description of “samples-like”.

• initial_states_generator ({'none', 'tile', 'random'}, optional, default='random') –

  Defines the expansion of initial_states if fewer than num_reads are specified:

  • ”none”:

    If the number of initial states specified is smaller than num_reads, raises ValueError.

  • ”tile”:

    Reuses the specified initial states if fewer than num_reads or truncates if greater.

  • ”random”:

    Expands the specified initial states with randomly generated states if fewer than num_reads or truncates if greater.

• seed (int (32-bit unsigned integer), optional) – Seed to use for the PRNG. Specifying a particular seed with a constant set of parameters produces identical results. If not provided, a random seed is chosen.

• large_sparse_opt (bool, optional, default=False) – Use optimizations for large and sparse problems (search tree for next descent variable instead of linear array).

Returns

A dimod SampleSet object.

Number of descends (single variable flips) taken to reach the local minimum for each sample is stored in a data vector called num_steps.

Return type

dimod.SampleSet

Examples

This example samples a simple two-variable Ising model.

>>> import dimod
>>> bqm = dimod.BQM.from_ising({}, {'ab': 1})
...
>>> import greedy
>>> sampler = greedy.SteepestDescentSampler()
...
>>> samples = sampler.sample(bqm)
>>> samples.first.energy
-1.0

Run steepest descent one million times (takes ~150ms on an average laptop), converging to local minima, each time starting from a random state:

>>> bqm = dimod.BQM.from_ising({}, {'ab': 1})
>>> sampler = greedy.SteepestDescentSampler()
...
>>> samples = sampler.sample(bqm, num_reads=10**6)
>>> print(samples.aggregate())      
   a  b energy num_oc. num_st.
0 -1 +1   -1.0  500115       1
1 +1 -1   -1.0  499885       1
['SPIN', 2 rows, 1000000 samples, 2 variables]

Use a combination of one fixed initial state and two randomly generated ones to sample from a simple convex Ising problem with global minimum at (-1,-1):

>>> bqm = dimod.BQM.from_ising({'x': 2, 'y': 2}, {'xy': -1})
>>> sampler = greedy.SteepestDescentSampler()
...
>>> samples = sampler.sample(bqm, initial_states=([1, 1], 'xy'), num_reads=3)
>>> print(samples)      
   x  y energy num_oc. num_st.
0 -1 -1   -5.0       1       2
1 -1 -1   -5.0       1       1
2 -1 -1   -5.0       1       2
['SPIN', 3 rows, 3 samples, 2 variables]

Notice it required 2 variable flips (num_steps field in the last column) to reach the minimum state, (-1, -1), from the initial state, (1, 1).