Utilities

class multineas.util.Stats[source]

Bases: object

Abstract class with useful routines

Attr. [HC]

calc_correlations_from_covariances()[source]

Compute the standard deviations and corresponding correlation coefficients given a set of covariance matrices.

Parameters:

Sigmas (numpy.ndarray) – Array of covariance matrices (Ngauss x Nvars x Nvars).

Returns:

  • sigmas (numpy.ndarray) – Array of standard deviations (Ngauss x Nvars).

  • rhos (numpy.ndarray) – Array of correlation coefficients (Ngauss x Nvars * (Nvars-1) / 2).

Examples

>>> Sigmas = [
...     [[1. , 0.2, 0.6],
...      [0.2, 4. , 1.8],
...      [0.6, 1.8, 9. ]]
... ]
>>> sigmas, rhos = Stats.calc_correlations_from_covariances(Sigmas)
>>> print(sigmas)
[1. 2. 3.]
>>> print(rhos)
[[0.1 0.2 0.3]]

Attr. [HC]

calc_covariance_from_correlations(rhos)[source]

Compute covariance matrices from the standard deviations and correlations (rho).

Parameters:

  • sigmas (numpy.ndarray) – Array of values of standard deviation for variables (Ngauss x Nvars).

  • rhos (numpy.ndarray) – Array with correlations (Ngauss x Nvars x (Nvars-1)/2).

Returns:

Sigmas – Array with covariance matrices corresponding to these sigmas and rhos (Ngauss x Nvars x Nvars).

Return type:

numpy.ndarray

Examples

>>> import numpy as np
>>> sigmas = np.array([[1, 2, 3]])
>>> # rho_12, rho_13, rho_23
>>> rhos = np.array([[0.1, 0.2, 0.3]])
>>> S = Stats.calc_covariance_from_correlations(sigmas, rhos)
>>> print(S)
[[[1.  0.2 0.6]
  [0.2 4.  1.8]
  [0.6 1.8 9. ]]]

This is equivalent to:

>>> rho = rhos[0]
>>> sigma = sigmas[0]
>>> R = np.eye(3)
>>> Stats.set_matrix_off_diagonal(R, rho)
>>> M = np.zeros((3, 3))
>>> for i in range(3):
...     for j in range(3):
...         M[i,j] = R[i,j] * sigma[i] * sigma[j]
>>> print(M)
[[1.  0.2 0.6]
 [0.2 4.  1.8]
 [0.6 1.8 9. ]]

Sources

Based on: https://www.visiondummy.com/2014/04/geometric-interpretation-covariance-matrix/

Attr. [HC]

calc_covariance_from_rotation(angles)[source]

Compute covariance matrices from the stds and the angles.

Parameters:

  • sigmas (numpy.ndarray) – Array of values of standard deviation for variables (Ngauss x 3).

  • angles (numpy.ndarray) – Euler angles expressing the directions of the principal axes of the distribution (Ngauss x 3).

Returns:

Sigmas – Array with covariance matrices corresponding to these sigmas and angles (Ngauss x 3 x 3). Attribution ———– [HC] This class was mostly developed by human intelligences.

Return type:

numpy.ndarray

flatten_symmetric_matrix()[source]

Given a symmetric matrix the routine returns the flatten version of the Matrix.

Parameters:

M (numpy.ndarray) – Matrix (n x n).

Returns:

F – Flatten array (nx(n+1)/2).

Return type:

numpy.ndarray

Examples

>>> M = np.array([[1, 0.2], [0.2, 3]])
>>> F = Stats.flatten_symmetric_matrix(M)
>>> print(F)
[1.  0.2 3. ]
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
gen_index()[source]

Given a set of (normalized) probabilities, randomly generate an index n following the probabilities.

For instance if we have 3 events with probabilities 0.1, 0.7, 0.2, gen_index will generate a number in the set (0,1,2) having those probabilities, ie. 1 will have 70% of probability.

Parameters:

probs (numpy.ndarray) – Probabilities (N), adimensional. NOTE: It should be normalized, ie. sum(probs)=1

Returns:

n – Index in the set [0,1,2,… len(probs)-1].

Return type:

int

Examples

>>> n = Stats.gen_index([0.1, 0.7, 0.2])
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
phi = 1.618033988749895
set_matrix_off_diagonal(off)[source]

Set a matrix with the terms of the off diagonal

Parameters:

  • M (numpy.ndarray) – Matrix (n x n).

  • off (list or numpy.ndarray) – Terms off diagonal (n x (n-1) / 2).

Returns:

Implicitly the matrix M has now the off diagonal terms.

Return type:

None

Examples

>>> M = np.eye(3)
>>> off = [0.1, 0.2, 0.3]
>>> Stats.set_matrix_off_diagonal(M, off)
>>> print(M)
[[1. , 0.1, 0.2],
 [0.1, 1. , 0.3],
 [0.2, 0.3, 1. ]]
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
unflatten_symmetric_matrix(M)[source]

Given a flatten version of a matrix, returns the symmetric matrix.

Parameters:

  • F (numpy.ndarray) – Flatten array (n x (n+1)/2).

  • M (numpy.ndarray) – Matrix where the result will be stored (n x n).

Returns:

It return the results in matrix M.

Return type:

None

Examples

>>> F = [1, 0.2, 3]
>>> M = np.zeros((2, 2))
>>> Stats.unflatten_symmetric_matrix(F, M)
>>> print(M)
[[1.  0.2]
 [0.2 3. ]]
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
class multineas.util.Util[source]

Bases: object

This abstract class contains useful methods for the package.

Attr. [HC]

DTIME = -1
DUTIME = []
TIME = 1769110385.9823818
TIMESTART = 1769110385.9823813
cos = <ufunc 'cos'>
el_time(start=False)[source]

Compute the time elapsed since last call of this routine. The displayed time is preseneted in the more convenient unit, ns (nano seconds), us (micro seconds), ms (miliseconds), s (seconds), min (minutes), h (hours), d (days)

Parameters:

  • verbose (int or bool, optional) – Show the time in screen (default 1).

  • start (int or bool, optional) – Compute time from program start (default 0).

Returns:

  • dt (float) – Elapsed time in seconds.

  • dtu_unit (list) – List containing [time in units, unit string].

Examples

>>> Util.el_time() # basic usage (show output)
>>> Util.el_time(verbose=0) # no output
>>> Util.el_time(start=True) # measure elapsed time since program start
>>> print(Util.DTIME, Util.DUTIME) # show values of elapsed time
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
error_msg(msg)[source]

Add a custom message msg to an error handle.

Parameters:

  • error (Exception) – Error handle (eg. except ValueError as error).

  • msg (str) – Message to add to error. Attribution ———– [HC] This class was mostly developed by human intelligences.

exp = <ufunc 'exp'>
static f2u(x, s)[source]

Convert from a finite interval [0,s] to an unbound one [-inf,inf].

Parameters:

  • x (float or array_like) – Value in the interval [0,s].

  • s (float) – Scale (upper limit of the interval).

Returns:

  • u (float or array_like) – Unbound value.

  • Attribution

  • ———–

  • [HC] This function was mostly developed by human intelligences.

static get_data(filename)[source]

Get the full path of the filename which is one of the datafiles provided with the package.

Parameters:

filename (str) – Name of the data file.

Returns:

path – Full path to package datafile.

Return type:

str

Examples

>>> from multineas.util import Util
>>> path=Util.get_data("nea_extended.json.gz")
Attribution
-----------
[HC] This function was mostly developed by human intelligences.
log = <ufunc 'log'>
mantisa_exp()[source]

Calculate the mantisa and exponent of a number.

Parameters:

x (float) – Number.

Returns:

  • man (float) – Mantisa.

  • exp (float) – Exponent.

Examples

>>> m, e = Util.mantisa_exp(234.5)
# returns m=2.345, e=2
>>> m, e = Util.mantisa_exp(-0.000023213)
# return m=-2.3213, e=-5
    Attribution
    -----------
    [HC] This class was mostly developed by human intelligences.
sin = <ufunc 'sin'>
static t_if(p, s, f)[source]

Transform a set of parameters using a transformation function f and scales s.

This routine allows the conversion from a finite interval [0,s] to an unbound one [-inf,inf] (using f=Util.f2u) or vice versa (using f=Util.u2f).

Parameters:

  • p (list or array_like) – Parameters to transform.

  • s (list or array_like) – Scales for each parameter. If s[i] > 0, the transformation is applied. If s[i] == 0, the parameter is unchanged.

  • f (function) – Transformation function (e.g. Util.f2u or Util.u2f).

Returns:

tp – Transformed parameters.

Return type:

list

Examples

>>> scales = [0, 0, 10, 10, 1]
>>> minparams = [0.0, 0.0, 1, 1, 0.7]
>>> uparams = Util.t_if(minparams, scales, Util.f2u)
>>> print(uparams)
[0.0, 0.0, -2.197224577336219, -2.197224577336219, 0.8472978603872034]
Attribution
-----------
[HC] This function was mostly developed by human intelligences.
static u2f(t, s)[source]

Convert from an unbound interval [-inf,inf] to a finite one [0,s].

Parameters:

  • t (float or array_like) – Unbound value.

  • s (float) – Scale (upper limit of the interval).

Returns:

  • x (float or array_like) – Value in the interval [0,s].

  • Attribution

  • ———–

  • [HC] This function was mostly developed by human intelligences.