# 17.1.1.6. cobra.sampling¶

## 17.1.1.6.2. Package Contents¶

### 17.1.1.6.2.1. Classes¶

 HRSampler The abstract base class for hit-and-run samplers. ACHRSampler Artificial Centering Hit-and-Run sampler. OptGPSampler A parallel optimized sampler.

### 17.1.1.6.2.2. Functions¶

 shared_np_array(shape: Tuple[int, int], data: Optional[np.ndarray] = None, integer: bool = False) → np.ndarray Create a new numpy array that resides in shared memory. step(sampler: HRSampler, x: np.ndarray, delta: np.ndarray, fraction: Optional[float] = None, tries: int = 0) → np.ndarray Sample a new feasible point from the point x in direction delta. sample(model, n, method=’optgp’, thinning=100, processes=1, seed=None) Sample valid flux distributions from a cobra model.
class cobra.sampling.HRSampler(model: Model, thinning: int, nproj: Optional[int] = None, seed: Optional[int] = None, **kwargs)[source]

Bases: abc.ABC

The abstract base class for hit-and-run samplers.

New samplers should derive from this class where possible to provide a uniform interface.

Parameters
• model (cobra.Model) – The cobra model from which to generate samples.

• thinning (int) – The thinning factor of the generated sampling chain. A thinning of 10 means samples are returned every 10 steps.

• nproj (int > 0, optional) – How often to reproject the sampling point into the feasibility space. Avoids numerical issues at the cost of lower sampling. If you observe many equality constraint violations with sampler.validate you should lower this number (default None).

• seed (int > 0, optional) – Sets the random number seed. Initialized to the current time stamp if None (default None).

feasibility_tol

The tolerance used for checking equalities feasibility.

Type

float

bounds_tol

The tolerance used for checking bounds feasibility.

Type

float

n_samples

The total number of samples that have been generated by this sampler instance.

Type

int

retries

The overall of sampling retries the sampler has observed. Larger values indicate numerical instabilities.

Type

int

problem

A NamedTuple whose attributes define the entire sampling problem in matrix form.

Type

Problem

warmup

A numpy matrix with as many columns as reactions in the model and more than 3 rows containing a warmup sample in each row. None if no warmup points have been generated yet.

Type

numpy.matrix

fwd_idx

A numpy array having one entry for each reaction in the model, containing the index of the respective forward variable.

Type

numpy.array

rev_idx

A numpy array having one entry for each reaction in the model, containing the index of the respective reverse variable.

Type

numpy.array

__build_problem(self) → Problem

Build the matrix representation of the sampling problem.

Returns

The matrix representation in the form of a NamedTuple.

Return type

Problem

generate_fva_warmup(self) → None

Generate the warmup points for the sampler.

Generates warmup points by setting each flux as the sole objective and minimizing/maximizing it. Also caches the projection of the warmup points into the nullspace for non-homogeneous problems (only if necessary).

Raises

ValueError – If flux cone contains a single point or the problem is inhomogeneous.

_reproject(self, p: np.ndarray) → np.ndarray

Reproject a point into the feasibility region.

This function is guaranteed to return a new feasible point. However, no guarantee can be made in terms of proximity to the original point.

Parameters

p (numpy.array) – The current sample point.

Returns

A new feasible point. If p is feasible, it will return p.

Return type

numpy.array

_random_point(self) → np.ndarray

Find an approximately random point in the flux cone.

_is_redundant(self, matrix: np.matrix, cutoff: Optional[float] = None) → bool

Identify redundant rows in a matrix that can be removed.

_bounds_dist(self, p: np.ndarray) → np.ndarray

Get the lower and upper bound distances. Negative is bad.

abstract sample(self, n: int, fluxes: bool = True) → pd.DataFrame

Abstract sampling function.

Should be overwritten by child classes.

Parameters
• n (int) – The number of samples that are generated at once.

• fluxes (bool, optional) – Whether to return fluxes or the internal solver variables. If set to False, will return a variable for each forward and backward flux as well as all additional variables you might have defined in the model (default True).

Returns

Returns a pandas DataFrame with n rows, each containing a flux sample.

Return type

pandas.DataFrame

batch(self, batch_size: int, batch_num: int, fluxes: bool = True) → pd.DataFrame

Create a batch generator.

This is useful to generate batch_num batches of batch_size samples each.

Parameters
• batch_size (int) – The number of samples contained in each batch.

• batch_num (int) – The number of batches in the generator.

• fluxes (bool, optional) – Whether to return fluxes or the internal solver variables. If set to False, will return a variable for each forward and backward flux as well as all additional variables you might have defined in the model (default True).

Yields

pandas.DataFrame – A DataFrame with dimensions (batch_size x n_r) containing a valid flux sample for a total of n_r reactions (or variables if fluxes=False) in each row.

validate(self, samples: np.matrix) → np.ndarray

Validate a set of samples for equality and inequality feasibility.

Can be used to check whether the generated samples and warmup points are feasible.

Parameters

samples (numpy.matrix) – Must be of dimension (samples x n_reactions). Contains the samples to be validated. Samples must be from fluxes.

Returns

A one-dimensional numpy array containing a code of 1 to 3 letters denoting the validation result: - ‘v’ means feasible in bounds and equality constraints - ‘l’ means a lower bound violation - ‘u’ means a lower bound validation - ‘e’ means and equality constraint violation

Return type

numpy.array

Raises

ValueError – If wrong number of columns.

cobra.sampling.shared_np_array(shape: Tuple[int, int], data: Optional[np.ndarray] = None, integer: bool = False) → np.ndarray[source]

Create a new numpy array that resides in shared memory.

Parameters
• shape (tuple of int) – The shape of the new array.

• data (numpy.array, optional) – Data to copy to the new array. Has to have the same shape (default None).

• integer (bool, optional) – Whether to use an integer array. By default, float array is used (default False).

Returns

The newly created shared numpy array.

Return type

numpy.array

Raises

ValueError – If the input data (if provided) size is not equal to the created array.

cobra.sampling.step(sampler: HRSampler, x: np.ndarray, delta: np.ndarray, fraction: Optional[float] = None, tries: int = 0) → np.ndarray[source]

Sample a new feasible point from the point x in direction delta.

class cobra.sampling.ACHRSampler(model: Model, thinning: int = 100, nproj: Optional[int] = None, seed: Optional[int] = None, **kwargs)[source]

Artificial Centering Hit-and-Run sampler.

A sampler with low memory footprint and good convergence.

Parameters
• model (cobra.Model) – The cobra model from which to generate samples.

• thinning (int, optional) – The thinning factor of the generated sampling chain. A thinning of 10 means samples are returned every 10 steps (default 100).

• nproj (int > 0, optional) – How often to reproject the sampling point into the feasibility space. Avoids numerical issues at the cost of lower sampling. If you observe many equality constraint violations with sampler.validate you should lower this number (default None).

• seed (int > 0, optional) – Sets the random number seed. Initialized to the current time stamp if None (default None).

n_samples

The total number of samples that have been generated by this sampler instance.

Type

int

problem

A NamedTuple whose attributes define the entire sampling problem in matrix form.

Type

typing.NamedTuple

warmup

A numpy matrix with as many columns as reactions in the model and more than 3 rows containing a warmup sample in each row. None if no warmup points have been generated yet.

Type

numpy.matrix

retries

The overall of sampling retries the sampler has observed. Larger values indicate numerical instabilities.

Type

int

fwd_idx

A numpy array having one entry for each reaction in the model, containing the index of the respective forward variable.

Type

numpy.array

rev_idx

A numpy array having one entry for each reaction in the model, containing the index of the respective reverse variable.

Type

numpy.array

prev

The current/last flux sample generated.

Type

numpy.array

center

The center of the sampling space as estimated by the mean of all previously generated samples.

Type

numpy.array

Notes

ACHR generates samples by choosing new directions from the sampling space’s center and the warmup points. The implementation used here is the same as in the MATLAB COBRA Toolbox [2]_ and uses only the initial warmup points to generate new directions and not any other previous iterations. This usually gives better mixing, since the startup points are chosen to span the space in a wide manner. This also makes the generated sampling chain quasi-Markovian since the center converges rapidly.

Memory usage is roughly in the order of (2 * number of reactions) ^ 2 due to the required nullspace matrices and warmup points. So, large models easily take up a few GBs of RAM.

References

1

Direction Choice for Accelerated Convergence in Hit-and-Run Sampling David E. Kaufman, Robert L. Smith Operations Research 199846:1 , 84-95 https://doi.org/10.1287/opre.46.1.84

2

https://github.com/opencobra/cobratoolbox

__single_iteration(self) → None

Run a single iteration of the sampling.

sample(self, n: int, fluxes: bool = True) → pd.DataFrame

Generate a set of samples.

This is the basic sampling function for all hit-and-run samplers.

Parameters
• n (int) – The number of samples that are generated at once.

• fluxes (bool, optional) – Whether to return fluxes or the internal solver variables. If set to False, will return a variable for each forward and backward flux as well as all additional variables you might have defined in the model (default True).

Returns

Returns a pandas DataFrame with n rows, each containing a flux sample.

Return type

pandas.DataFrame

Notes

Performance of this function linearly depends on the number of reactions in your model and the thinning factor.

class cobra.sampling.OptGPSampler(model, processes=None, thinning=100, nproj=None, seed=None)[source]

A parallel optimized sampler.

A parallel sampler with fast convergence and parallel execution. See [1]_ for details.

Parameters
• model (cobra.Model) – The cobra model from which to generate samples.

• processes (int, optional (default Configuration.processes)) – The number of processes used during sampling.

• thinning (int, optional) – The thinning factor of the generated sampling chain. A thinning of 10 means samples are returned every 10 steps.

• nproj (int > 0, optional) – How often to reproject the sampling point into the feasibility space. Avoids numerical issues at the cost of lower sampling. If you observe many equality constraint violations with sampler.validate you should lower this number.

• seed (int > 0, optional) – Sets the random number seed. Initialized to the current time stamp if None.

model

The cobra model from which the samples get generated.

Type

cobra.Model

thinning

The currently used thinning factor.

Type

int

n_samples

The total number of samples that have been generated by this sampler instance.

Type

int

problem

A python object whose attributes define the entire sampling problem in matrix form. See docstring of Problem.

Type

collections.namedtuple

warmup

A matrix of with as many columns as reactions in the model and more than 3 rows containing a warmup sample in each row. None if no warmup points have been generated yet.

Type

numpy.matrix

retries

The overall of sampling retries the sampler has observed. Larger values indicate numerical instabilities.

Type

int

seed

Sets the random number seed. Initialized to the current time stamp if None.

Type

int > 0, optional

nproj

How often to reproject the sampling point into the feasibility space.

Type

int

fwd_idx

Has one entry for each reaction in the model containing the index of the respective forward variable.

Type

numpy.array

rev_idx

Has one entry for each reaction in the model containing the index of the respective reverse variable.

Type

numpy.array

prev

The current/last flux sample generated.

Type

numpy.array

center

The center of the sampling space as estimated by the mean of all previously generated samples.

Type

numpy.array

Notes

The sampler is very similar to artificial centering where each process samples its own chain. Initial points are chosen randomly from the warmup points followed by a linear transformation that pulls the points a little bit towards the center of the sampling space.

If the number of processes used is larger than the one requested, number of samples is adjusted to the smallest multiple of the number of processes larger than the requested sample number. For instance, if you have 3 processes and request 8 samples you will receive 9.

Memory usage is roughly in the order of (2 * number reactions)^2 due to the required nullspace matrices and warmup points. So large models easily take up a few GB of RAM. However, most of the large matrices are kept in shared memory. So the RAM usage is independent of the number of processes.

References

1

Megchelenbrink W, Huynen M, Marchiori E (2014) optGpSampler: An Improved Tool for Uniformly Sampling the Solution-Space of Genome-Scale Metabolic Networks. PLoS ONE 9(2): e86587. https://doi.org/10.1371/journal.pone.0086587

sample(self, n, fluxes=True)

Generate a set of samples.

This is the basic sampling function for all hit-and-run samplers.

Parameters
• n (int) – The minimum number of samples that are generated at once (see Notes).

• fluxes (boolean) – Whether to return fluxes or the internal solver variables. If set to False will return a variable for each forward and backward flux as well as all additional variables you might have defined in the model.

Returns

Returns a matrix with n rows, each containing a flux sample.

Return type

numpy.matrix

Notes

Performance of this function linearly depends on the number of reactions in your model and the thinning factor.

If the number of processes is larger than one, computation is split across as the CPUs of your machine. This may shorten computation time. However, there is also overhead in setting up parallel computation so we recommend to calculate large numbers of samples at once (n > 1000).

__getstate__(self)

Return the object for serialization.

cobra.sampling.sample(model, n, method='optgp', thinning=100, processes=1, seed=None)[source]

Sample valid flux distributions from a cobra model.

The function samples valid flux distributions from a cobra model. Currently we support two methods:

1. ‘optgp’ (default) which uses the OptGPSampler that supports parallel

sampling [1]_. Requires large numbers of samples to be performant (n < 1000). For smaller samples ‘achr’ might be better suited.

or

1. ‘achr’ which uses artificial centering hit-and-run. This is a single process method with good convergence [2]_.

Parameters
• model (cobra.Model) – The model from which to sample flux distributions.

• n (int) – The number of samples to obtain. When using ‘optgp’ this must be a multiple of processes, otherwise a larger number of samples will be returned.

• method (str, optional) – The sampling algorithm to use.

• thinning (int, optional) – The thinning factor of the generated sampling chain. A thinning of 10 means samples are returned every 10 steps. Defaults to 100 which in benchmarks gives approximately uncorrelated samples. If set to one will return all iterates.

• processes (int, optional) – Only used for ‘optgp’. The number of processes used to generate samples.

• seed (int > 0, optional) – The random number seed to be used. Initialized to current time stamp if None.

Returns

The generated flux samples. Each row corresponds to a sample of the fluxes and the columns are the reactions.

Return type

pandas.DataFrame

Notes

The samplers have a correction method to ensure equality feasibility for long-running chains, however this will only work for homogeneous models, meaning models with no non-zero fixed variables or constraints ( right-hand side of the equalities are zero).

References

1

Megchelenbrink W, Huynen M, Marchiori E (2014) optGpSampler: An Improved Tool for Uniformly Sampling the Solution-Space of Genome-Scale Metabolic Networks. PLoS ONE 9(2): e86587.

2

Direction Choice for Accelerated Convergence in Hit-and-Run Sampling David E. Kaufman Robert L. Smith Operations Research 199846:1 , 84-95