astromodels.functions.priors module

class astromodels.functions.priors.Beta(**kwargs)

Bases: Function1D

description :

A beta distribution function

latex : $ f(x, a, b)=frac{Gamma(a+b) x^{a-1}(1-x)^{b-1}}{Gamma(a) Gamma(b)}$

parameters :

a :

desc : first shape parameter initial value : 0.5 min: 0.

b :

desc : second shape parameter initial value : 0.5 min: 0.

evaluate(x, a, b)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Cauchy(**kwargs)

Bases: Function1D

description :

The Cauchy distribution

latex : $ K frac{1}{ gamma pi} left[ frac{gamma^2}{(x-x_0)^2 + gamma^2} right] $

parameters :

K :

desc : Integral between -inf and +inf. Fix this to 1 to obtain a Cauchy distribution initial value : 1

x0 :

desc : Central value initial value : 0.0

gamma :

desc : standard deviation initial value : 1.0 min : 1e-12

tests :

• { x : 0.0, function value: 0.3989422804014327, tolerance: 1e-10}

• { x : -1.0, function value: 0.24197072451914337, tolerance: 1e-9}

evaluate(x, K, x0, gamma)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Cosine_Prior(**kwargs)

Bases: Function1D

description :

A function which is constant on the interval angular interval of cosine

latex : $cos(x)$

parameters :

lower_bound :

desc : Lower bound for the interval initial value : -90 min : -np.inf max : np.inf

upper_bound :

desc : Upper bound for the interval initial value : 90 min : -np.inf max : np.inf

value :

desc : Value in the interval initial value : 1.0

evaluate(x, lower_bound, upper_bound, value)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

has_fixed_units()

Returns True if this function cannot change units, which is the case only for very specific functions (like models from foreign libraries like Xspec)

Returns:

True or False

static info()

class astromodels.functions.priors.Exponential(**kwargs)

Bases: Function1D

description :

An exponential distribution function

latex : $ f(x, alpha) = alphaexp(-alpha x)$

parameters :

alpha :

desc : first shape parameter initial value : 1 min: 0.

evaluate(x, alpha)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Gamma(**kwargs)

Bases: Function1D

description :

A gamma distribution function

latex : $ f(x, alpha, beta)=frac{beta^alpha x^{alpha-1} e^{-beta x}}{Gamma(alpha)}$

parameters :

alpha :

desc : first shape parameter initial value : 0.5 min: 0.

beta :

desc : second shape parameter initial value : 1. min: 0.

evaluate(x, alpha, beta)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Gaussian(**kwargs)

Bases: Function1D

description :

A Gaussian function

latex : $ K frac{1}{sigma sqrt{2 pi}}exp{frac{(x-mu)^2}{2~(sigma)^2}} $

parameters :

F :

desc : Integral between -inf and +inf. Fix this to 1 to obtain a Normal distribution initial value : 1

mu :

desc : Central value initial value : 0.0

sigma :

desc : standard deviation initial value : 1.0 min : 1e-12

tests :

• { x : 0.0, function value: 0.3989422804014327, tolerance: 1e-10}

• { x : -1.0, function value: 0.24197072451914337, tolerance: 1e-9}

evaluate(x, F, mu, sigma)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Log_normal(**kwargs)

Bases: Function1D

description :

A log normal function

latex : $ K frac{1}{ x sigma sqrt{2 pi}}exp{frac{(log x/piv - mu/piv)^2}{2~(sigma)^2}} $

parameters :

F :

desc : Integral between 0and +inf. Fix this to 1 to obtain a log Normal distribution initial value : 1

mu :

desc : Central value initial value : 0.0

sigma :

desc : standard deviation initial value : 1.0 min : 1e-12

piv :

desc : pivot. Leave this to 1 for a proper log normal distribution initial value : 1.0 fix : yes

tests :

• { x : 0.0, function value: 0.3989422804014327, tolerance: 1e-10}

• { x : -1.0, function value: 0.24197072451914337, tolerance: 1e-9}

evaluate(x, F, mu, sigma, piv)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Log_uniform_prior(**kwargs)

Bases: Function1D

description :

A function which is K/x on the interval lower_bound - upper_bound and 0 outside the interval. The extremes of the interval are NOT counted as part of the interval. Lower_bound must be >= 0.

latex : $ f(x)=K~begin{cases}0 & x le text{lower_bound} \frac{1}{x} & text{lower_bound} < x < text{upper_bound} \ 0 & x ge text{upper_bound} end{cases}$

parameters :

lower_bound :

desc : Lower bound for the interval initial value : 1e-20 min : 1e-30 max : np.inf

upper_bound :

desc : Upper bound for the interval initial value : 100 min : 1e-30 max : np.inf

K :

desc : Normalization initial value : 1 fix : yes

evaluate(x, lower_bound, upper_bound, K)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Powerlaw_Prior(**kwargs)

Bases: Function1D

description :

An power law distribution function between a-b

latex : $ f(x, alpha) = alpha x^{alpha-1)$

parameters :

alpha :

desc : slope parameter initial value : 1 min: 0.

a :

desc: lower bound of distribution initial value : 0. min: 0.

b:

desc: upper bound of distribution initial value: 1 min: 0.

evaluate(x, alpha, a, b)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()

class astromodels.functions.priors.Truncated_gaussian(**kwargs)

Bases: Function1D

description :

A truncated Gaussian function defined on the interval between the lower_bound (a) and upper_bound (b)

latex : $begin{split}f(x;mu,sigma,a,b)=frac{frac{1}{sigma} phileft( frac{x-mu}{sigma} right)}{Phileft( frac{b-mu}{sigma} right) - Phileft( frac{a-mu}{sigma} right)}\phileft(zright)=frac{1}{sqrt{2 pi}}expleft(-frac{1}{2}z^2right)\Phileft(zright)=frac{1}{2}left(1+erfleft(frac{z}{sqrt(2)}right)right)end{split}$

parameters :

F :

desc : Integral between -inf and +inf. Fix this to 1 to obtain a Normal distribution initial value : 1

mu :

desc : Central value initial value : 0.0

sigma :

desc : standard deviation initial value : 1.0 min : 1e-12

lower_bound :

desc: lower bound of gaussian, setting to -np.inf results in half normal distribution initial value : -1.

upper_bound :

desc: upper bound of gaussian setting to np.inf results in half normal distribution initial value : 1.

tests :

• { x : 0.0, function value: 0.3989422804014327, tolerance: 1e-10}

• { x : -1.0, function value: 0.24197072451914337, tolerance: 1e-9}

evaluate(x, F, mu, sigma, lower_bound, upper_bound)

from_unit_cube(x)

static info()

class astromodels.functions.priors.Uniform_prior(**kwargs)

Bases: Function1D

description :

A function which is constant on the interval lower_bound - upper_bound and 0 outside the interval. The extremes of the interval are counted as part of the interval.

latex : $ f(x)=begin{cases}0 & x < text{lower_bound} \text{value} & text{lower_bound} le x le text{upper_bound} \ 0 & x > text{upper_bound} end{cases}$

parameters :

lower_bound :

desc : Lower bound for the interval initial value : 0 min : -np.inf max : np.inf

upper_bound :

desc : Upper bound for the interval initial value : 1 min : -np.inf max : np.inf

value :

desc : Value in the interval initial value : 1.0

tests :

• { x : 0.5, function value: 1.0, tolerance: 1e-20}

• { x : -0.5, function value: 0, tolerance: 1e-20}

evaluate(x, lower_bound, upper_bound, value)

from_unit_cube(x)

Used by multinest

Parameters:

• x – 0 < x < 1

• lower_bound –

• upper_bound –

Returns:

static info()