astromodels.functions.functions_2D module

class astromodels.functions.functions_2D.Asymm_Gaussian_on_sphere(**kwargs)

Bases: Function2D

description :

A bidimensional Gaussian function on a sphere (in spherical coordinates)

see https://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function

parameters :

lon0 :

desc : Longitude of the center of the source initial value : 0.0 min : 0.0 max : 360.0

lat0 :

desc : Latitude of the center of the source initial value : 0.0 min : -90.0 max : 90.0

a :

desc : Standard deviation of the Gaussian distribution (major axis) initial value : 10 min : 0 max : 20

e :

desc : Excentricity of Gaussian ellipse initial value : 0.9 min : 0 max : 1

theta :

desc : inclination of major axis to a line of constant latitude initial value : 10. min : -90.0 max : 90.0

evaluate(x, y, lon0, lat0, a, e, theta)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

class astromodels.functions.functions_2D.Disk_on_sphere(**kwargs)

Bases: Function2D

description :

A bidimensional disk/tophat function on a sphere (in spherical coordinates)

latex : $$ f(vec{x}) = left(frac{180}{pi}right)^2 frac{1}{pi~({rm radius})^2} ~left{begin{matrix} 1 & {rm if}& {rm | vec{x} - vec{x}_0| le {rm radius}} \ 0 & {rm if}& {rm | vec{x} - vec{x}_0| > {rm radius}} end{matrix}right. $$

parameters :

lon0 :

desc : Longitude of the center of the source initial value : 0.0 min : 0.0 max : 360.0

lat0 :

desc : Latitude of the center of the source initial value : 0.0 min : -90.0 max : 90.0

radius :

desc : Radius of the disk initial value : 15 min : 0 max : 20

evaluate(x, y, lon0, lat0, radius)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

class astromodels.functions.functions_2D.Ellipse_on_sphere(**kwargs)

Bases: Function2D

description :

An ellipse function on a sphere (in spherical coordinates)

latex : $$ f(vec{x}) = left(frac{180}{pi}right)^2 frac{1}{pi~ a b} ~left{begin{matrix} 1 & {rm if}& {rm | vec{x} - vec{x}_{f1}| + | vec{x} - vec{x}_{f2}| le {rm 2a}} \ 0 & {rm if}& {rm | vec{x} - vec{x}_{f1}| + | vec{x} - vec{x}_{f2}| > {rm 2a}} end{matrix}right. $$

parameters :

lon0 :

desc : Longitude of the center of the source initial value : 0.0 min : 0.0 max : 360.0

lat0 :

desc : Latitude of the center of the source initial value : 0.0 min : -90.0 max : 90.0

a :

desc : semimajor axis of the ellipse initial value : 15. min : 0 max : 20

e :

desc : eccentricity of ellipse initial value : 0.9 min : 0 max : 1

theta :

desc : inclination of semimajoraxis to a line of constant latitude initial value : 0.0 min : -90.0 max : 90.0

calc_focal_pts(lon0, lat0, a, b, theta)

evaluate(x, y, lon0, lat0, a, e, theta)

focal_pts = False

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

lat1 = None

lat2 = None

lon1 = None

lon2 = None

class astromodels.functions.functions_2D.Gaussian_on_sphere(**kwargs)

Bases: Function2D

description :

A bidimensional Gaussian function on a sphere (in spherical coordinates)

latex : $$ f(vec{x}) = left(frac{180^circ}{pi}right)^2 frac{1}{2pi sqrt{det{Sigma}}} , {rm exp}left( -frac{1}{2} (vec{x}-vec{x}_0)^intercal cdot Sigma^{-1}cdot (vec{x}-vec{x}_0)right) \ vec{x}_0 = ({rm RA}_0,{rm Dec}_0)\ Lambda = left( begin{array}{cc} sigma^2 & 0 \ 0 & sigma^2 (1-e^2) end{array}right) \ U = left( begin{array}{cc} cos theta & -sin theta \ sin theta & cos theta end{array}right) \Sigma = ULambda U^intercal $$

parameters :

lon0 :

desc : Longitude of the center of the source initial value : 0.0 min : 0.0 max : 360.0

lat0 :

desc : Latitude of the center of the source initial value : 0.0 min : -90.0 max : 90.0

sigma :

desc : Standard deviation of the Gaussian distribution initial value : 10 min : 0 max : 20

evaluate(x, y, lon0, lat0, sigma)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

class astromodels.functions.functions_2D.Latitude_galactic_diffuse(**kwargs)

Bases: Function2D

description :

A Gaussian distribution in Galactic latitude around the Galactic plane

latex : $ K exp{left( frac{-b^2}{2 sigma_b^2} right)} $

parameters :

K :

desc : normalization initial value : 1

sigma_b :

desc : Sigma for initial value : 1

l_min :

desc : min Longtitude initial value : 10

l_max :

desc : max Longtitude initial value : 30

evaluate(x, y, K, sigma_b, l_min, l_max)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

set_frame(new_frame)

Set a new frame for the coordinates (the default is ICRS J2000)

Parameters

new_frame – a coordinate frame from astropy

Returns

(none)

class astromodels.functions.functions_2D.Power_law_on_sphere(**kwargs)

Bases: Function2D

description :

A power law function on a sphere (in spherical coordinates)

latex : $$ f(vec{x}) = left(frac{180}{pi}right)^{-1.*index} left{begin{matrix} 0.05^{index} & {rm if} & |\vec{x}-\vec{x}_0| le 0.05\ |\vec{x}-\vec{x}_0|^{index} & {\rm if} & 0.05 < |\vec{x}-\vec{x}_0| le maxr \ 0 & {rm if} & |\vec{x}-\vec{x}_0|>maxrend{matrix}right. $$

parameters :

lon0 :

desc : Longitude of the center of the source initial value : 0.0 min : 0.0 max : 360.0

lat0 :

desc : Latitude of the center of the source initial value : 0.0 min : -90.0 max : 90.0

index :

desc : power law index initial value : -2.0 min : -5.0 max : -1.0

maxr :

desc : max radius initial value : 20. fix : yes

minr :

desc : radius below which the PL is approximated as a constant initial value : 0.05 fix : yes

evaluate(x, y, lon0, lat0, index, maxr, minr)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()

class astromodels.functions.functions_2D.SpatialTemplate_2D(**kwargs)

Bases: Function2D

description :

User input Spatial Template. Expected to be normalized to 1/sr

latex : $ hi $

parameters :

K :

desc : normalization initial value : 1 fix : yes

hash :

desc: hash of model map [needed for memoization] initial value: 1 fix: yes

ihdu:

desc: header unit index of fits file initial value: 0 fix: True min: 0

properties:

fits_file:

desc: fits file to load defer: True function: _load_file

frame:

desc: coordinate frame initial value: icrs allowed values:

• icrs

• galactic

• fk5

• fk4

• fk4_no_e

evaluate(x, y, K, hash, ihdu)

get_boundaries()

Returns the boundaries of this function. By default there is no boundary, but subclasses can override this.

Returns

a tuple of tuples containing the boundaries for each coordinate (ra_min, ra_max), (dec_min, dec_max)

get_total_spatial_integral(z=None)

Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions). needs to be implemented in subclasses.

Returns

an array of values of the integral (same dimension as z).

static info()