tensiometer.utilities

This file contains some utilities that are used in the tensiometer package.

tensiometer.utilities.KL_decomposition(matrix_a, matrix_b)

Computes the Karhunen–Loeve (KL) decomposition of the matrix A and B.

Notice that B has to be real, symmetric and positive.

The algorithm is taken from this link. The algorithm is NOT optimized for speed but for precision.

Parameters:

• matrix_a – the first matrix.
• matrix_b – the second matrix.

Returns:

the KL eigenvalues and the KL eigenvectors.

tensiometer.utilities.QR_inverse(matrix)

Invert a matrix with the QR decomposition. This is much slower than standard inversion but has better accuracy for matrices with higher condition number.

Parameters:matrix – the input matrix. Returns:the inverse of the matrix.

tensiometer.utilities.bernoulli_thin(chain, temperature=1, num_repeats=1)

Function that thins a chain with a Bernoulli process.

Parameters:

• chain – MCSamples the input chain.
• temperature – temperature of the Bernoulli process. If T=1 then this produces a unit weight chain.
• num_repeats – number of repetitions of the Bernoulli process.

Returns:

a MCSamples chain with the reweighted chain.

tensiometer.utilities.clopper_pearson_binomial_trial(k, n, alpha=0.32)

http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval alpha confidence intervals for a binomial distribution of k expected successes on n trials.

Parameters:

• k – number of success.
• n – total number of trials.
• alpha – (optional) confidence level.

Returns:

lower and upper bound.

tensiometer.utilities.from_chi2_to_sigma(val, dofs, exact_threshold=6)

Computes the effective number of standard deviations for a chi squared variable. This matches the probability computed from the chi squared variable to the number of standard deviations that an event with the same probability would have had in a Gaussian distribution as in Eq. (G1) of (Raveri and Hu 18).

\[n_{\sigma}^{\rm eff}(x, {\rm dofs}) \equiv \sqrt{2} {\rm Erf}^{-1}({\rm CDF}(\chi^2_{\rm dofs}(x)))\]

For very high statistical significant events this function switches from the direct formula to an accurate asyntotic expansion.

Parameters:

• val – value of the chi2 variable
• dofs – number of degrees of freedom of the chi2 variable
• exact_threshold – (default 6) threshold of value/dofs to switch to the asyntotic formula.

Returns:

the effective number of standard deviations.

tensiometer.utilities.from_confidence_to_sigma(P)

Transforms a probability to effective number of sigmas. This matches the input probability with the number of standard deviations that an event with the same probability would have had in a Gaussian distribution as in Eq. (G1) of (Raveri and Hu 18).

\[n_{\sigma}^{\rm eff}(P) \equiv \sqrt{2} {\rm Erf}^{-1}(P)\]

Parameters:P – the input probability. Returns:the effective number of standard deviations.

tensiometer.utilities.from_sigma_to_confidence(nsigma)

Gives the probability of an event at a given number of standard deviations in a Gaussian distribution.

Parameters:nsigma – the input number of standard deviations. Returns:the probability to exceed the number of standard deviations.

tensiometer.utilities.get_separate_mcsamples(chain)

Function that returns separate MCSamples for each sampler chain.

Parameters:chain – MCSamples the input chain. Returns:list of MCSamples with the separate chains.

tensiometer.utilities.make_list(elements)

Checks if elements is a list. If yes returns elements without modifying it. If not creates and return a list with elements inside.

Parameters:elements – an element or a list of elements Returns:a list containing elements.

tensiometer.utilities.random_samples_reshuffle(chain)

Performs a coherent random reshuffle of the samples.

Parameters:chain – MCSamples the input chain. Returns:a MCSamples chain with the reshuffled chain.