Utility Functions

Function Reference

qinfer.utils.binomial_pdf(N, n, p)[source]

Returns the PDF of the binomial distribution \(\operatorname{Bin}(N, p)\) evaluated at \(n\).


Returns the outer product of a vector \(v\) with itself, \(v v^\T\).

qinfer.utils.particle_meanfn(weights, locations, fn=None)[source]

Returns the mean of a function \(f\) over model parameters.

  • weights (numpy.ndarray) – Weights of each particle.
  • locations (numpy.ndarray) – Locations of each particle.
  • fn (callable) – Function of model parameters to take the mean of. If None, the identity function is assumed.
qinfer.utils.particle_covariance_mtx(weights, locations)[source]

Returns an estimate of the covariance of a distribution represented by a given set of SMC particle.

  • weights – An array containing the weights of each particle.
  • location – An array containing the locations of each particle.
Return type:

numpy.ndarray, shape (n_modelparams, n_modelparams).


An array containing the estimated covariance matrix.

qinfer.utils.in_ellipsoid(x, A, c)[source]

Determines which of the points x are in the closed ellipsoid with shape matrix A centered at c. For a single point x, this is computed as

\[(c-x)^T\cdot A^{-1}\cdot (c-x) \leq 1\]
  • x (np.ndarray) – Shape (n_points, dim) or n_points.
  • A (np.ndarray) – Shape (dim, dim), positive definite
  • c (np.ndarray) – Shape (dim)

bool or array of bools of length n_points

qinfer.utils.ellipsoid_volume(A=None, invA=None)[source]

Returns the volume of an ellipsoid given either its matrix or the inverse of its matrix.

qinfer.utils.mvee(points, tol=0.001)[source]

Returns the minimum-volume enclosing ellipse (MVEE) of a set of points, using the Khachiyan algorithm.


Returns the unique elements of a sequence seq.

qinfer.utils.format_uncertainty(value, uncertianty, scinotn_break=4)[source]

Given a value and its uncertianty, format as a LaTeX string for pretty-printing.

Parameters:scinotn_break (int) – How many decimal points to print before breaking into scientific notation.

Interprets the last index of y as stick breaking fractions in logit space and returns a non-negative array of the same shape where the last dimension always sums to unity.

A unit simplex is a list of non-negative numbers \((x_1,...,x_K)\) that sum to one, \(\sum_{k=1}^K x_k=1\), for example, the probabilities of an K-sided die. It is sometimes desireable to parameterize this object with variables that are unconstrained and “decorrelated”. To this end, we imagine \(\vec{x}\) as a partition of the unit stick \([0,1]\) with \(K-1\) break points between \(K\) successive intervals of respective lengths \((x_1,...,x_K)\). Instead of storing the interval lengths, we start from the left-most break point and iteratively store the breaking fractions, \(z_k\), of the remaining stick. This gives the formula \(z_k=x_k / (1-\sum_{k'=1}^{k-1}x_k)\) with the convention \(x_0:=0\), which has an inverse formula \(x_k = z_k(1-z_{k-1})\cdots(1-z_1)\). Note that \(z_K=1\) since the last stick is not broken; this is the result of the redundant information imposed by \(\sum_{k=1}^K x_k=1\). To unbound the parameters \(z_k\) into the real line, we pass through the logit function, \(\operatorname{logit}(p)=\log\frac{p}{1-p}\), to end up with the parameterization \(y_k=\operatorname{logit}(z_k)+\log(K-k)\), with the convention \(y_K=0\). The shift by \(\log(K-k)\) is largely asthetic and causes the uniform simplex \(\vec{x}=(1/K,1/K,...,1/K)\) to be mapped to \(\vec{x}=(0,0,...,0)\).

Inverse to from_simplex().

Parameters:np.ndarray – Array of logit space stick breaking fractions along the last index.
Return type:np.ndarray

Inteprets the last index of x as unit simplices and returns a real array of the sampe shape in logit space.

Inverse to to_simplex() ; see that function for more details.

Parameters:np.ndarray – Array of unit simplices along the last index.
Return type:np.ndarray