Parameters: - rho0 – density normalization (characteristic density)
- Rs – scale radius
Returns: deflection angle at RS
-
upper_limit_default
= {'Rs': 100, 'alpha_Rs': 10, 'center_x': 100, 'center_y': 100}¶
-
static
lenstronomy.LensModel.Profiles.nfw_ellipse module¶
-
class
lenstronomy.LensModel.Profiles.nfw_ellipse.
NFW_ELLIPSE
(interpol=False, num_interp_X=1000, max_interp_X=10)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions concerning the NFW profile with an ellipticity defined in the potential parameterization of alpha_Rs and Rs is the same as for the spherical NFW profile
from Glose & Kneib: https://cds.cern.ch/record/529584/files/0112138.pdf
relation are: R_200 = c * Rs
-
density_lens
(r, Rs, alpha_Rs, e1=1, e2=0)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in the LOS projection of this quantity results in the convergence quantity.
Parameters: - r – 3d radios
- Rs – turn-over radius of NFW profile
- alpha_Rs – deflection at Rs
Returns: density rho(r)
-
derivatives
(x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function, calculated as an elliptically distorted deflection angle of the spherical NFW profile
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- Rs – turn over point in the slope of the NFW profile in angular unit
- alpha_Rs – deflection (angular units) at projected Rs
- e1 – eccentricity component in x-direction
- e2 – eccentricity component in y-direction
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: deflection in x-direction, deflection in y-direction
-
function
(x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns elliptically distorted NFW lensing potential
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- Rs – turn over point in the slope of the NFW profile in angular unit
- alpha_Rs – deflection (angular units) at projected Rs
- e1 – eccentricity component in x-direction
- e2 – eccentricity component in y-direction
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: lensing potential
-
hessian
(x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy the calculation is performed as a numerical differential from the deflection field. Analytical relations are possible
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- Rs – turn over point in the slope of the NFW profile in angular unit
- alpha_Rs – deflection (angular units) at projected Rs
- e1 – eccentricity component in x-direction
- e2 – eccentricity component in y-direction
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'Rs': 0, 'alpha_Rs': 0, 'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5}¶
-
mass_3d_lens
(R, Rs, alpha_Rs, e1=1, e2=0)[source]¶ Parameters: - R – radius (in angular units)
- Rs –
- alpha_Rs –
- e1 –
- e2 –
Returns:
-
param_names
= ['Rs', 'alpha_Rs', 'e1', 'e2', 'center_x', 'center_y']¶
-
profile_name
= 'NFW_ELLIPSE'¶
-
upper_limit_default
= {'Rs': 100, 'alpha_Rs': 10, 'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5}¶
-
lenstronomy.LensModel.Profiles.nfw_mass_concentration module¶
-
class
lenstronomy.LensModel.Profiles.nfw_mass_concentration.
NFWMC
(z_lens, z_source, cosmo=None, static=False)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions parameterises the NFW profile with log10 M200 and the concentration rs/r200 relation are: R_200 = c * Rs
ATTENTION: the parameterization is cosmology and redshift dependent! The cosmology to connect mass and deflection relations is fixed to default H0=70km/s Omega_m=0.3 flat LCDM. It is recommended to keep a given cosmology definition in the lens modeling as the observable reduced deflection angles are sensitive in this parameterization. If you do not want to impose a mass-concentration relation, it is recommended to use the default NFW lensing profile parameterized in reduced deflection angles.
-
derivatives
(x, y, logM, concentration, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function (integral of NFW)
-
function
(x, y, logM, concentration, center_x=0, center_y=0)[source]¶ Parameters: - x – angular position
- y – angular position
- Rs – angular turn over point
- alpha_Rs – deflection at Rs
- center_x – center of halo
- center_y – center of halo
Returns:
-
hessian
(x, y, logM, concentration, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'concentration': 0.01, 'logM': 0}¶
-
param_names
= ['logM', 'concentration', 'center_x', 'center_y']¶
-
set_static
(logM, concentration, center_x=0, center_y=0)[source]¶ Parameters: - logM –
- concentration –
- center_x –
- center_y –
Returns:
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'concentration': 1000, 'logM': 16}¶
-
lenstronomy.LensModel.Profiles.nfw_vir_trunc module¶
-
class
lenstronomy.LensModel.Profiles.nfw_vir_trunc.
NFWVirTrunc
(z_lens, z_source, cosmo=None)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions concerning the NFW profile that is sharply truncated at the virial radius https://arxiv.org/pdf/astro-ph/0304034.pdf
relation are: R_200 = c * Rs
lenstronomy.LensModel.Profiles.nie module¶
-
class
lenstronomy.LensModel.Profiles.nie.
NIE
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
Non-singular isothermal ellipsoid (NIE)
\[\kappa = \theta_E/2 \left[s_{scale} + qx^2 + y^2/q]−1/2\]-
density_lens
(r, theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ 3d mass density at 3d radius r. This function assumes spherical symmetry/ignoring the eccentricity.
Parameters: - r – 3d radius
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: 3d mass density at 3d radius r
-
derivatives
(x, y, theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate in image plane
- y – y-coordinate in image plane
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: alpha_x, alpha_y
-
function
(x, y, theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate in image plane
- y – y-coordinate in image plane
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: lensing potential
-
hessian
(x, y, theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate in image plane
- y – y-coordinate in image plane
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: f_xx, f_xy, f_yx, f_yy
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 's_scale': 0, 'theta_E': 0}¶
-
mass_3d_lens
(r, theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ mass enclosed a 3d radius r. This function assumes spherical symmetry/ignoring the eccentricity.
Parameters: - r – 3d radius
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: 3d mass density at 3d radius r
-
param_names
= ['theta_E', 'e1', 'e2', 's_scale', 'center_x', 'center_y']¶
-
set_static
(theta_E, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate in image plane
- y – y-coordinate in image plane
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale
- center_x – profile center
- center_y – profile center
Returns: self variables set
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 's_scale': 100, 'theta_E': 10}¶
-
-
class
lenstronomy.LensModel.Profiles.nie.
NIEMajorAxis
(diff=1e-10)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
This class contains the function and the derivatives of the non-singular isothermal ellipse. See Keeton and Kochanek 1998, https://arxiv.org/pdf/astro-ph/9705194.pdf
\[\kappa = b * (q2(s2 + x2) + y2)^{−1/2}`\]-
function
(x, y, b, s, q)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, b, s, q)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
static
kappa
(x, y, b, s, q)[source]¶ convergence
Parameters: - x – major axis coordinate
- y – minor axis coordinate
- b – normalization
- s – smoothing scale
- q – axis ratio
Returns: convergence
-
param_names
= ['b', 's', 'q', 'center_x', 'center_y']¶
-
lenstronomy.LensModel.Profiles.nie_potential module¶
-
class
lenstronomy.LensModel.Profiles.nie_potential.
NIE_POTENTIAL
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class implements the elliptical potential of Eq. (67) of LECTURES ON GRAVITATIONAL LENSING and Eq. (1) of Blandford & Kochanek 1987, mapped to Eq. (8) of Barnaka1998 to find the ellipticity bounds
-
derivatives
(x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
- theta_c – core radius (in angles)
- e1 – eccentricity component, x direction(dimensionless)
- e2 – eccentricity component, y direction (dimensionless)
Returns: deflection angle (in angles)
-
function
(x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
- theta_c – core radius (in angles)
- e1 – eccentricity component, x direction(dimensionless)
- e2 – eccentricity component, y direction (dimensionless)
Returns: lensing potential
-
hessian
(x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
- theta_c – core radius (in angles)
- e1 – eccentricity component, x direction(dimensionless)
- e2 – eccentricity component, y direction (dimensionless)
Returns: hessian matrix (in angles)
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': 0, 'e2': 0, 'theta_E': 0, 'theta_c': 0}¶
-
param_names
= ['center_x', 'center_y', 'theta_E', 'theta_c', 'e1', 'e2']¶
-
set_static
(theta_E, theta_c, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate in image plane
- y – y-coordinate in image plane
- theta_E – Einstein radius
- theta_c – core radius
- e1 – eccentricity component
- e2 – eccentricity component
- center_x – profile center
- center_y – profile center
Returns: self variables set
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.2, 'e2': 0.2, 'theta_E': 10, 'theta_c': 10}¶
-
-
class
lenstronomy.LensModel.Profiles.nie_potential.
NIEPotentialMajorAxis
(diff=1e-10)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class implements the elliptical potential of Eq. (67) of LECTURES ON GRAVITATIONAL LENSING and Eq. (1) of Blandford & Kochanek 1987, mapped to Eq. (8) of Barnaka1998 to find the ellipticity bounds
-
function
(x, y, theta_E, theta_c, eps)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, theta_E, theta_c, eps)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
param_names
= ['theta_E', 'theta_c', 'eps', 'center_x', 'center_y']¶
-
lenstronomy.LensModel.Profiles.numerical_deflections module¶
-
class
lenstronomy.LensModel.Profiles.numerical_deflections.
NumericalAlpha
(custom_class)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
This class allows one to incorporate any lens profile into the usage framework of lenstronomy. When creating the instance of LensModel with this lens profile, you must pass in numerical_alpha_class = CustomClass(), where CustomClass is a class with a call method that returns the x/y deflection angles. This allows one to numerically compute and interpolate deflection angles for potentially very complex mass profiles, and then use the results with lenstronomy without having to heavily modify the existing structure of the software.
-
derivatives
(x, y, center_x=0, center_y=0, **kwargs)[source]¶ Parameters: - x – x coordinate [arcsec]
- y – x coordinate [arcsec]
- center_x – deflector x center [arcsec]
- center_y – deflector y center [arcsec]
- kwargs – keyword arguments for the custom profile
Returns:
-
function
(x, y, center_x=0, center_y=0, **kwargs)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, center_x=0, center_y=0, **kwargs)[source]¶ Returns the components of the hessian matrix :param x: x coordinate [arcsec] :param y: y coordinate [arcsec] :param center_x: the deflector x coordinate :param center_y: the deflector y coordinate :param kwargs: keyword arguments for the profile :return: the derivatives of the deflection angles that make up the hessian matrix
-
lenstronomy.LensModel.Profiles.p_jaffe module¶
-
class
lenstronomy.LensModel.Profiles.p_jaffe.
PJaffe
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class to compute the DUAL PSEUDO ISOTHERMAL ELLIPTICAL MASS DISTRIBUTION based on Eliasdottir (2007) https://arxiv.org/pdf/0710.5636.pdf Appendix A
Module name: ‘PJAFFE’;
An alternative name is dPIED.
The 3D density distribution is
\[\rho(r) = \frac{\rho_0}{(1+r^2/Ra^2)(1+r^2/Rs^2)}\]with \(Rs > Ra\).
The projected density is
\[\Sigma(R) = \Sigma_0 \frac{Ra Rs}{Rs-Ra}\left(\frac{1}{\sqrt{Ra^2+R^2}} - \frac{1}{\sqrt{Rs^2+R^2}} \right)\]with
\[\Sigma_0 = \pi \rho_0 \frac{Ra Rs}{Rs + Ra}\]In the lensing parameterization,
\[\sigma_0 = \frac{\Sigma_0}{\Sigma_{\rm crit}}\]-
density
(r, rho0, Ra, Rs)[source]¶ computes the density
Parameters: - r – radial distance from the center (in 3D)
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: density at r
-
density_2d
(x, y, rho0, Ra, Rs, center_x=0, center_y=0)[source]¶ projected density
Parameters: - x – projected coordinate on the sky
- y – projected coordinate on the sky
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
- center_x – center of profile
- center_y – center of profile
Returns: projected density
-
derivatives
(x, y, sigma0, Ra, Rs, center_x=0, center_y=0)[source]¶ deflection angles
Parameters: - x – projected coordinate on the sky
- y – projected coordinate on the sky
- sigma0 – sigma0/sigma_crit (see class documentation above)
- Ra – core radius (see class documentation above)
- Rs – transition radius from logarithmic slope -2 to -4 (see class documentation above)
- center_x – center of profile
- center_y – center of profile
Returns: f_x, f_y
-
function
(x, y, sigma0, Ra, Rs, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – projected coordinate on the sky
- y – projected coordinate on the sky
- sigma0 – sigma0/sigma_crit (see class documentation above)
- Ra – core radius (see class documentation above)
- Rs – transition radius from logarithmic slope -2 to -4 (see class documentation above)
- center_x – center of profile
- center_y – center of profile
Returns: lensing potential
-
grav_pot
(r, rho0, Ra, Rs)[source]¶ gravitational potential (modulo 4 pi G and rho0 in appropriate units)
Parameters: - r – radial distance from the center (in 3D)
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: gravitational potential (modulo 4 pi G and rho0 in appropriate units)
-
hessian
(x, y, sigma0, Ra, Rs, center_x=0, center_y=0)[source]¶ Hessian of lensing potential
Parameters: - x – projected coordinate on the sky
- y – projected coordinate on the sky
- sigma0 – sigma0/sigma_crit (see class documentation above)
- Ra – core radius (see class documentation above)
- Rs – transition radius from logarithmic slope -2 to -4 (see class documentation above)
- center_x – center of profile
- center_y – center of profile
Returns: f_xx, f_xy, f_yx, f_yy
-
lower_limit_default
= {'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100, 'sigma0': 0}¶
-
mass_2d
(r, rho0, Ra, Rs)[source]¶ mass enclosed projected 2d sphere of radius r
Parameters: - r – radial distance from the center in projection
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: Sigma(<r)
-
mass_3d
(r, rho0, Ra, Rs)[source]¶ mass enclosed a 3d sphere or radius r
Parameters: - r – radial distance from the center (in 3D)
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: M(<r)
-
mass_3d_lens
(r, sigma0, Ra, Rs)[source]¶ mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
Parameters: - r – radial distance from the center (in 3D)
- rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: M(<r) in angular units (modulo critical mass density)
-
mass_tot
(rho0, Ra, Rs)[source]¶ total mass within the profile
Parameters: - rho0 – density normalization (see class documentation above)
- Ra – core radius
- Rs – transition radius from logarithmic slope -2 to -4
Returns: total mass
-
param_names
= ['sigma0', 'Ra', 'Rs', 'center_x', 'center_y']¶
-
rho2sigma
(rho0, Ra, Rs)[source]¶ converts 3d density into 2d projected density parameter, Equation A4 in Eliasdottir (2007)
Parameters: - rho0 – density normalization
- Ra – core radius (see class documentation above)
- Rs – transition radius from logarithmic slope -2 to -4 (see class documentation above)
Returns: projected density normalization
-
sigma2rho
(sigma0, Ra, Rs)[source]¶ inverse of rho2sigma()
Parameters: - sigma0 – projected density normalization
- Ra – core radius (see class documentation above)
- Rs – transition radius from logarithmic slope -2 to -4 (see class documentation above)
Returns: 3D density normalization
-
upper_limit_default
= {'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100, 'sigma0': 10}¶
-
lenstronomy.LensModel.Profiles.p_jaffe_ellipse module¶
-
class
lenstronomy.LensModel.Profiles.p_jaffe_ellipse.
PJaffe_Ellipse
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions concerning the NFW profile
relation are: R_200 = c * Rs
-
derivatives
(x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function (integral of NFW)
-
function
(x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns double integral of NFW profile
-
hessian
(x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'sigma0': 0}¶
-
mass_3d_lens
(r, sigma0, Ra, Rs, e1=0, e2=0)[source]¶ Parameters: - r –
- sigma0 –
- Ra –
- Rs –
- q –
- phi_G –
Returns:
-
param_names
= ['sigma0', 'Ra', 'Rs', 'e1', 'e2', 'center_x', 'center_y']¶
-
upper_limit_default
= {'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'sigma0': 10}¶
-
lenstronomy.LensModel.Profiles.pemd module¶
-
class
lenstronomy.LensModel.Profiles.pemd.
PEMD
(suppress_fastell=False)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for power law ellipse mass density profile. This class effectively calls the class SPEMD_SMOOTH with a fixed and very small central smoothing scale to perform the numerical integral using the FASTELL code by Renan Barkana.
\[\kappa(x, y) = \frac{3-\gamma}{2} \left(\frac{\theta_{E}}{\sqrt{q x^2 + y^2/q}} \right)^{\gamma-1}\]with \(\theta_{E}\) is the (circularized) Einstein radius, \(\gamma\) is the negative power-law slope of the 3D mass distributions, \(q\) is the minor/major axis ratio, and \(x\) and \(y\) are defined in a coordinate system aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
\[\kappa(r) = \frac{3-\gamma}{2} \left(\frac{\theta'_{E}}{r \sqrt{1 − e*\cos(2*\phi)}} \right)^{\gamma-1}\]with \(\epsilon\) is the ellipticity defined as
\[\epsilon = \frac{1-q^2}{1+q^2}\]And an Einstein radius \(\theta'_{\rm E}\) related to the definition used is
\[\left(\frac{\theta'_{\rm E}}{\theta_{\rm E}}\right)^{2} = \frac{2q}{1+q^2}.\]-
density_lens
(r, theta_E, gamma, e1=None, e2=None)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in the LOS projection of this quantity results in the convergence quantity.
Parameters: - r – radius within the mass is computed
- theta_E – Einstein radius
- gamma – power-law slope
- e1 – eccentricity component (not used)
- e2 – eccentricity component (not used)
Returns: mass enclosed a 3D radius r
-
derivatives
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: deflection angles alpha_x, alpha_y
-
function
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: lensing potential
-
hessian
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: Hessian components f_xx, f_xy, f_yx, f_yy
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'gamma': 1.5, 'theta_E': 0}¶
-
mass_3d_lens
(r, theta_E, gamma, e1=None, e2=None)[source]¶ computes the spherical power-law mass enclosed (with SPP routine) :param r: radius within the mass is computed :param theta_E: Einstein radius :param gamma: power-law slope :param e1: eccentricity component (not used) :param e2: eccentricity component (not used) :return: mass enclosed a 3D radius r
-
param_names
= ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']¶
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'gamma': 2.5, 'theta_E': 100}¶
-
lenstronomy.LensModel.Profiles.point_mass module¶
-
class
lenstronomy.LensModel.Profiles.point_mass.
PointMass
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class to compute the physical deflection angle of a point mass, given as an Einstein radius
-
derivatives
(x, y, theta_E, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
Returns: deflection angle (in angles)
-
function
(x, y, theta_E, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
Returns: lensing potential
-
hessian
(x, y, theta_E, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coord (in angles)
- y – y-coord (in angles)
- theta_E – Einstein radius (in angles)
Returns: hessian matrix (in angles)
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'theta_E': 0}¶
-
param_names
= ['theta_E', 'center_x', 'center_y']¶
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'theta_E': 100}¶
-
lenstronomy.LensModel.Profiles.sersic module¶
-
class
lenstronomy.LensModel.Profiles.sersic.
Sersic
(smoothing=1e-05, sersic_major_axis=False)[source]¶ Bases:
lenstronomy.LensModel.Profiles.sersic_utils.SersicUtil
,lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions to evaluate a Sersic mass profile: https://arxiv.org/pdf/astro-ph/0311559.pdf
-
derivatives
(x, y, n_sersic, R_sersic, k_eff, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function
-
function
(x, y, n_sersic, R_sersic, k_eff, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate
- y – y-coordinate
- n_sersic – Sersic index
- R_sersic – half light radius
- k_eff – convergence at half light radius
- center_x – x-center
- center_y – y-center
Returns:
-
hessian
(x, y, n_sersic, R_sersic, k_eff, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'R_sersic': 0, 'center_x': -100, 'center_y': -100, 'k_eff': 0, 'n_sersic': 0.5}¶
-
param_names
= ['k_eff', 'R_sersic', 'n_sersic', 'center_x', 'center_y']¶
-
upper_limit_default
= {'R_sersic': 100, 'center_x': 100, 'center_y': 100, 'k_eff': 10, 'n_sersic': 8}¶
-
lenstronomy.LensModel.Profiles.sersic_ellipse_kappa module¶
-
class
lenstronomy.LensModel.Profiles.sersic_ellipse_kappa.
SersicEllipseKappa
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains the function and the derivatives of an elliptical sersic profile with the ellipticity introduced in the convergence (not the potential).
This requires the use of numerical integrals (Keeton 2004)
-
derivatives
(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0)[source]¶ deflection angles
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
function
(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'R_sersic': 0, 'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'k_eff': 0, 'n_sersic': 0.5}¶
-
param_names
= ['k_eff', 'R_sersic', 'n_sersic', 'e1', 'e2', 'center_x', 'center_y']¶
-
upper_limit_default
= {'R_sersic': 100, 'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'k_eff': 10, 'n_sersic': 8}¶
-
lenstronomy.LensModel.Profiles.sersic_ellipse_potential module¶
-
class
lenstronomy.LensModel.Profiles.sersic_ellipse_potential.
SersicEllipse
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions to evaluate a Sersic mass profile: https://arxiv.org/pdf/astro-ph/0311559.pdf
-
derivatives
(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function
-
hessian
(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'R_sersic': 0, 'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'k_eff': 0, 'n_sersic': 0.5}¶
-
param_names
= ['k_eff', 'R_sersic', 'n_sersic', 'e1', 'e2', 'center_x', 'center_y']¶
-
upper_limit_default
= {'R_sersic': 100, 'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'k_eff': 10, 'n_sersic': 8}¶
-
lenstronomy.LensModel.Profiles.sersic_utils module¶
-
class
lenstronomy.LensModel.Profiles.sersic_utils.
SersicUtil
(smoothing=1e-05, sersic_major_axis=False)[source]¶ Bases:
object
-
alpha_abs
(x, y, n_sersic, r_eff, k_eff, center_x=0, center_y=0)[source]¶ Parameters: - x –
- y –
- n_sersic –
- r_eff –
- k_eff –
- center_x –
- center_y –
Returns:
-
static
b_n
(n)[source]¶ b(n) computation. This is the approximation of the exact solution to the relation, 2*incomplete_gamma_function(2n; b_n) = Gamma_function(2*n). :param n: the sersic index :return:
-
d_alpha_dr
(x, y, n_sersic, r_eff, k_eff, center_x=0, center_y=0)[source]¶ Parameters: - x –
- y –
- n_sersic –
- r_eff –
- k_eff –
- center_x –
- center_y –
Returns:
-
density
(x, y, n_sersic, r_eff, k_eff, center_x=0, center_y=0)[source]¶ de-projection of the Sersic profile based on Prugniel & Simien (1997) :return:
-
get_distance_from_center
(x, y, e1, e2, center_x, center_y)[source]¶ Get the distance from the center of Sersic, accounting for orientation and axis ratio :param x: :param y: :param e1: eccentricity :param e2: eccentricity :param center_x: center x of sersic :param center_y: center y of sersic
-
k_bn
(n, Re)[source]¶ returns normalisation of the sersic profile such that Re is the half light radius given n_sersic slope
-
total_flux
(amp, R_sersic, n_sersic, e1=0, e2=0, **kwargs)[source]¶ computes analytical integral to compute total flux of the Sersic profile
Parameters: - amp – amplitude parameter in Sersic function (surface brightness at R_sersic
- R_sersic – half-light radius in semi-major axis
- n_sersic – Sersic index
- e1 – eccentricity
- e2 – eccentricity
Returns: Analytic integral of the total flux of the Sersic profile
-
lenstronomy.LensModel.Profiles.shapelet_pot_cartesian module¶
-
class
lenstronomy.LensModel.Profiles.shapelet_pot_cartesian.
CartShapelets
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains the function and the derivatives of the cartesian shapelets
-
H_n
(n, x)[source]¶ constructs the Hermite polynomial of order n at position x (dimensionless)
Parameters: - n – The n’the basis function.
- x – 1-dim position (dimensionless)
Returns: array– H_n(x).
Raises: AttributeError, KeyError
-
derivatives
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function
-
function
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'beta': 0, 'center_x': -100, 'center_y': -100, 'coeffs': [0]}¶
-
param_names
= ['coeffs', 'beta', 'center_x', 'center_y']¶
-
phi_n
(n, x)[source]¶ constructs the 1-dim basis function (formula (1) in Refregier et al. 2001)
Parameters: - n – The n’the basis function.
- x – 1-dim position (dimensionless)
Returns: array– phi_n(x).
Raises: AttributeError, KeyError
-
pre_calc
(x, y, beta, n_order, center_x, center_y)[source]¶ calculates the H_n(x) and H_n(y) for a given x-array and y-array :param x: :param y: :param amp: :param beta: :param n_order: :param center_x: :param center_y: :return: list of H_n(x) and H_n(y)
-
upper_limit_default
= {'beta': 100, 'center_x': 100, 'center_y': 100, 'coeffs': [100]}¶
-
lenstronomy.LensModel.Profiles.shapelet_pot_polar module¶
-
class
lenstronomy.LensModel.Profiles.shapelet_pot_polar.
PolarShapelets
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains the function and the derivatives of the Singular Isothermal Sphere
-
derivatives
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function
-
function
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, coeffs, beta, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'beta': 0, 'center_x': -100, 'center_y': -100, 'coeffs': [0]}¶
-
param_names
= ['coeffs', 'beta', 'center_x', 'center_y']¶
-
upper_limit_default
= {'beta': 100, 'center_x': 100, 'center_y': 100, 'coeffs': [100]}¶
-
lenstronomy.LensModel.Profiles.shear module¶
-
class
lenstronomy.LensModel.Profiles.shear.
Shear
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for external shear gamma1, gamma2 expression
-
derivatives
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: deflection angles
-
function
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: lensing potential
-
hessian
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: f_xx, f_xy, f_yx, f_yy
-
lower_limit_default
= {'dec_0': -100, 'gamma1': -0.5, 'gamma2': -0.5, 'ra_0': -100}¶
-
param_names
= ['gamma1', 'gamma2', 'ra_0', 'dec_0']¶
-
upper_limit_default
= {'dec_0': 100, 'gamma1': 0.5, 'gamma2': 0.5, 'ra_0': 100}¶
-
-
class
lenstronomy.LensModel.Profiles.shear.
ShearGammaPsi
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class to model a shear field with shear strength and direction. The translation ot the cartesian shear distortions is as follow:
\[\gamma_1 = \gamma_{ext} \cos(2 \phi_{ext} \gamma_2 = \gamma_{ext} \sin(2 \phi_{ext}\]-
derivatives
(x, y, gamma_ext, psi_ext, ra_0=0, dec_0=0)[source]¶ deflection angles
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
static
function
(x, y, gamma_ext, psi_ext, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma_ext – shear strength
- psi_ext – shear angle (radian)
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns:
-
hessian
(x, y, gamma_ext, psi_ext, ra_0=0, dec_0=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
lower_limit_default
= {'dec_0': -100, 'gamma_ext': 0, 'psi_ext': -3.141592653589793, 'ra_0': -100}¶
-
param_names
= ['gamma_ext', 'psi_ext', 'ra_0', 'dec_0']¶
-
upper_limit_default
= {'dec_0': 100, 'gamma_ext': 1, 'psi_ext': 3.141592653589793, 'ra_0': 100}¶
-
-
class
lenstronomy.LensModel.Profiles.shear.
ShearReduced
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
reduced shear distortions \(\gamma' = \gamma / (1-\kappa)\). This distortion keeps the magnification as unity and, thus, does not change the size of apparent objects. To keep the magnification at unity, it requires
\[(1-\kappa)^2 - \gamma_1^2 - \gamma_2^ = 1\]Thus, for given pair of reduced shear \((\gamma'_1, \gamma'_2)\), an additional convergence term is calculated and added to the lensing distortions.
-
derivatives
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: deflection angles
-
function
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: lensing potential
-
hessian
(x, y, gamma1, gamma2, ra_0=0, dec_0=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y0-coordinate (angle)
- gamma1 – shear component
- gamma2 – shear component
- ra_0 – x/ra position where shear deflection is 0
- dec_0 – y/dec position where shear deflection is 0
Returns: f_xx, f_xy, f_yx, f_yy
-
lower_limit_default
= {'dec_0': -100, 'gamma1': -0.5, 'gamma2': -0.5, 'ra_0': -100}¶
-
param_names
= ['gamma1', 'gamma2', 'ra_0', 'dec_0']¶
-
upper_limit_default
= {'dec_0': 100, 'gamma1': 0.5, 'gamma2': 0.5, 'ra_0': 100}¶
-
lenstronomy.LensModel.Profiles.sie module¶
-
class
lenstronomy.LensModel.Profiles.sie.
SIE
(NIE=True)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for singular isothermal ellipsoid (SIS with ellipticity)
\[\kappa(x, y) = \frac{1}{2} \left(\frac{\theta_{E}}{\sqrt{q x^2 + y^2/q}} \right)\]with \(\theta_{E}\) is the (circularized) Einstein radius, \(q\) is the minor/major axis ratio, and \(x\) and \(y\) are defined in a coordinate sys- tem aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
\[\kappa(r) = \frac{1}{2} \left(\frac{\theta'_{E}}{r \sqrt{1 − e*\cos(2*\phi)}} \right)\]with \(\epsilon\) is the ellipticity defined as
\[\epsilon = \frac{1-q^2}{1+q^2}\]And an Einstein radius \(\theta'_{\rm E}\) related to the definition used is
\[\left(\frac{\theta'_{\rm E}}{\theta_{\rm E}}\right)^{2} = \frac{2q}{1+q^2}.\]-
static
density
(r, rho0, e1=0, e2=0)[source]¶ computes the density :param r: radius in angles :param rho0: density at angle=1 :return: density at r
-
static
density_2d
(x, y, rho0, e1=0, e2=0, center_x=0, center_y=0)[source]¶ projected density :param x: :param y: :param rho0: :param center_x: :param center_y: :return:
-
density_lens
(r, theta_E, e1=0, e2=0)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in the LOS projection of this quantity results in the convergence quantity.
Parameters: - r – radius in angles
- theta_E – Einstein radius
- e1 – eccentricity component
- e2 – eccentricity component
Returns: density
-
derivatives
(x, y, theta_E, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x –
- y –
- theta_E –
- q –
- phi_G –
- center_x –
- center_y –
Returns:
-
function
(x, y, theta_E, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x –
- y –
- theta_E –
- q –
- phi_G –
- center_x –
- center_y –
Returns:
-
grav_pot
(x, y, rho0, e1=0, e2=0, center_x=0, center_y=0)[source]¶ gravitational potential (modulo 4 pi G and rho0 in appropriate units) :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return:
-
hessian
(x, y, theta_E, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x –
- y –
- theta_E –
- q –
- phi_G –
- center_x –
- center_y –
Returns:
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'theta_E': 0}¶
-
mass_2d
(r, rho0, e1=0, e2=0)[source]¶ mass enclosed projected 2d sphere of radius r :param r: :param rho0: :param a: :param s: :return:
-
static
mass_3d
(r, rho0, e1=0, e2=0)[source]¶ mass enclosed a 3d sphere or radius r :param r: radius in angular units :param rho0: density at angle=1 :return: mass in angular units
-
mass_3d_lens
(r, theta_E, e1=0, e2=0)[source]¶ mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
Parameters: - r – radius in angular units
- theta_E – Einstein radius
Returns: mass in angular units
-
param_names
= ['theta_E', 'e1', 'e2', 'center_x', 'center_y']¶
-
static
theta2rho
(theta_E)[source]¶ converts projected density parameter (in units of deflection) into 3d density parameter :param theta_E: :return:
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'theta_E': 100}¶
-
static
lenstronomy.LensModel.Profiles.sis module¶
-
class
lenstronomy.LensModel.Profiles.sis.
SIS
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains the function and the derivatives of the Singular Isothermal Sphere
\[\kappa(x, y) = \frac{1}{2} \left(\frac{\theta_{E}}{\sqrt{x^2 + y^2}} \right)\]with \(\theta_{E}\) is the Einstein radius,
-
static
density
(r, rho0)[source]¶ computes the density :param r: radius in angles :param rho0: density at angle=1 :return: density at r
-
static
density_2d
(x, y, rho0, center_x=0, center_y=0)[source]¶ projected density :param x: :param y: :param rho0: :param center_x: :param center_y: :return:
-
density_lens
(r, theta_E)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in projected in units of angles (i.e. arc seconds) results in the convergence quantity.
Parameters: - r – 3d radius
- theta_E – Einstein radius
Returns: density(r)
-
function
(x, y, theta_E, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
grav_pot
(x, y, rho0, center_x=0, center_y=0)[source]¶ gravitational potential (modulo 4 pi G and rho0 in appropriate units) :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return:
-
hessian
(x, y, theta_E, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'theta_E': 0}¶
-
mass_2d
(r, rho0)[source]¶ mass enclosed projected 2d sphere of radius r :param r: :param rho0: :param a: :param s: :return:
-
mass_2d_lens
(r, theta_E)[source]¶ Parameters: - r – radius
- theta_E – Einstein radius
Returns: mass within a radius in projection
-
static
mass_3d
(r, rho0)[source]¶ mass enclosed a 3d sphere or radius r :param r: radius in angular units :param rho0: density at angle=1 :return: mass in angular units
-
mass_3d_lens
(r, theta_E)[source]¶ mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
Parameters: - r – radius in angular units
- theta_E – Einstein radius
Returns: mass in angular units
-
param_names
= ['theta_E', 'center_x', 'center_y']¶
-
static
rho2theta
(rho0)[source]¶ converts 3d density into 2d projected density parameter :param rho0: :param gamma: :return:
-
static
theta2rho
(theta_E)[source]¶ converts projected density parameter (in units of deflection) into 3d density parameter :param theta_E: :return:
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'theta_E': 100}¶
-
static
lenstronomy.LensModel.Profiles.sis_truncate module¶
-
class
lenstronomy.LensModel.Profiles.sis_truncate.
SIS_truncate
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains the function and the derivatives of the Singular Isothermal Sphere
-
derivatives
(x, y, theta_E, r_trunc, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function
-
function
(x, y, theta_E, r_trunc, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, theta_E, r_trunc, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'r_trunc': 0, 'theta_E': 0}¶
-
param_names
= ['theta_E', 'r_trunc', 'center_x', 'center_y']¶
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'r_trunc': 100, 'theta_E': 100}¶
-
lenstronomy.LensModel.Profiles.spemd module¶
-
class
lenstronomy.LensModel.Profiles.spemd.
SPEMD
(suppress_fastell=False)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for smooth power law ellipse mass density profile. This class effectively performs the FASTELL calculations by Renan Barkana. The parameters are changed and represent a spherically averaged Einstein radius an a logarithmic 3D mass profile slope.
The Einstein ring parameter converts to the definition used by GRAVLENS as follow: (theta_E / theta_E_gravlens) = sqrt[ (1+q^2) / (2 q) ]
FASTELL has the following defintions: The parameters are position (x1,x2), overall factor (q), power (gam), axis ratio (arat) which is <=1, core radius squared (s2), and the output potential (phi). The projected mass density distribution, in units of the critical density, is kappa(x1,x2)=q [u2+s2]^(-gam), where u2=[x1^2+x2^2/(arat^2)].
-
static
convert_params
(theta_E, gamma, q, s_scale)[source]¶ converts parameter defintions into quantities used by the FASTELL fortran library
Parameters: - theta_E – Einstein radius
- gamma – 3D power-law slope of mass profile
- q – axis ratio minor/major
- s_scale – float, smoothing scale in the core
Returns: pre-factors to SPEMP profile for FASTELL
-
derivatives
(x, y, theta_E, gamma, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale in the center of the profile
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: deflection angles alpha_x, alpha_y
-
function
(x, y, theta_E, gamma, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale in the center of the profile (angle)
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: lensing potential
-
hessian
(x, y, theta_E, gamma, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale in the center of the profile
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: Hessian components f_xx, f_xy, f_yx, f_yy
-
static
is_not_empty
(x1, x2)[source]¶ Check if float or not an empty array :return: True if x1 and x2 are either floats/ints or an non-empty array, False if e.g. objects are [] :rtype: bool
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'gamma': 0, 's_scale': 0, 'theta_E': 0}¶
-
param_names
= ['theta_E', 'gamma', 'e1', 'e2', 's_scale', 'center_x', 'center_y']¶
-
param_transform
(x, y, theta_E, gamma, e1, e2, s_scale, center_x=0, center_y=0)[source]¶ transforms parameters in the format of fastell4py
Parameters: - x – x-coordinate (angle)
- y – y-coordinate (angle)
- theta_E – Einstein radius (angle), pay attention to specific definition!
- gamma – logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
- e1 – eccentricity component
- e2 – eccentricity component
- s_scale – smoothing scale in the center of the profile
- center_x – x-position of lens center
- center_y – y-position of lens center
Returns: x-rotated, y-rotated, q_fastell, gam, s2, q, phi_G
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'gamma': 100, 's_scale': 100, 'theta_E': 100}¶
-
static
lenstronomy.LensModel.Profiles.spep module¶
-
class
lenstronomy.LensModel.Profiles.spep.
SPEP
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for Softened power-law elliptical potential (SPEP)
-
density_lens
(r, theta_E, gamma, e1=0, e2=0)[source]¶ Parameters: - r –
- theta_E –
- gamma –
- e1 –
- e2 –
Returns:
-
derivatives
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ deflection angles
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
function
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ Parameters: - x (array of size (n)) – set of x-coordinates
- theta_E (float.) – Einstein radius of lense
- gamma (<2 float) – power law slope of mass profifle
- q (0<phi_G<pi/2) – Axis ratio
- phi_G – position angel of SES
Returns: function
Raises: AttributeError, KeyError
-
hessian
(x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'e1': -0.5, 'e2': -0.5, 'gamma': 0, 'theta_E': 0}¶
-
mass_3d_lens
(r, theta_E, gamma, e1=0, e2=0)[source]¶ computes the spherical power-law mass enclosed (with SPP routiune) :param r: :param theta_E: :param gamma: :param q: :param phi_G: :return:
-
param_names
= ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']¶
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'e1': 0.5, 'e2': 0.5, 'gamma': 100, 'theta_E': 100}¶
-
lenstronomy.LensModel.Profiles.splcore module¶
-
class
lenstronomy.LensModel.Profiles.splcore.
SPLCORE
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
This lens profile corresponds to a spherical power law (SPL) mass distribution with logarithmic slope gamma and a 3D core radius r_core
\[\]holeft(r, ho_0, r_c, gamma ight) = ho_0 rac{{r_c}^gamma}{left(r^2 + r_c^2 ight)^{ rac{gamma}{2}}}
The difference between this and EPL is that this model contains a core radius, is circular, and is also defined for gamma=3.
With respect to SPEMD, this model is different in that it is also defined for gamma = 3, is circular, and is defined in terms of a physical density parameter rho0, or the central density at r=0 divided by the critical density for lensing such that rho0 has units 1/arcsec.
This class is defined for all gamma > 1
-
alpha
(r, sigma0, r_core, gamma)[source]¶ Returns the deflection angle at r :param r: radius [arcsec] :param sigma0: convergence at r=0 :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: deflection angle at r
-
density
(r, rho0, r_core, gamma)[source]¶ Returns the 3D density at r :param r: radius [arcsec] :param sigma0: convergence at r=0 :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: density at r
-
density_2d
(x, y, rho0, r_core, gamma)[source]¶ Returns the convergence at radius r :param x: x position [arcsec] :param y: y position [arcsec] :param sigma0: convergence at r=0 :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: convergence at r
-
density_lens
(r, sigma0, r_core, gamma)[source]¶ Returns the 3D density at r :param r: radius [arcsec] :param sigma0: convergence at r=0 :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: density at r
-
derivatives
(x, y, sigma0, r_core, gamma, center_x=0, center_y=0)[source]¶ Parameters: - x – projected x position at which to evaluate function [arcsec]
- y – projected y position at which to evaluate function [arcsec]
- sigma0 – convergence at r = 0
- r_core – core radius [arcsec]
- gamma – logarithmic slope at r -> infinity
- center_x – x coordinate center of lens model [arcsec]
- center_y – y coordinate center of lens model [arcsec]
Returns: deflection angle alpha in x and y directions
-
function
(x, y, sigma0, r_core, gamma, center_x=0, center_y=0)[source]¶ lensing potential
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
hessian
(x, y, sigma0, r_core, gamma, center_x=0, center_y=0)[source]¶ Parameters: - x – projected x position at which to evaluate function [arcsec]
- y – projected y position at which to evaluate function [arcsec]
- sigma0 – convergence at r = 0
- r_core – core radius [arcsec]
- gamma – logarithmic slope at r -> infinity
- center_x – x coordinate center of lens model [arcsec]
- center_y – y coordinate center of lens model [arcsec]
Returns: hessian elements
alpha_(x/y) = alpha_r * cos/sin(x/y / r)
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'gamma': 1.000001, 'r_core': 1e-06, 'sigma0': 0}¶
-
mass_2d
(r, rho0, r_core, gamma)[source]¶ mass enclosed projected 2d disk of radius r :param r: radius [arcsec] :param rho0: density at r = 0 in units [rho_0_physical / sigma_crit] (which should be equal to [1/arcsec]) where rho_0_physical is a physical density normalization and sigma_crit is the critical density for lensing :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: projected mass inside disk of radius r
-
mass_2d_lens
(r, sigma0, r_core, gamma)[source]¶ mass enclosed projected 2d disk of radius r :param r: radius [arcsec] :param sigma0: convergence at r = 0 where rho_0_physical is a physical density normalization and sigma_crit is the critical density for lensing :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: projected mass inside disk of radius r
-
mass_3d
(r, rho0, r_core, gamma)[source]¶ mass enclosed a 3d sphere or radius r :param r: radius [arcsec] :param rho0: density at r = 0 in units [rho_0_physical / sigma_crit] (which should be equal to [arcsec]) where rho_0_physical is a physical density normalization and sigma_crit is the critical density for lensing :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: mass inside radius r
-
mass_3d_lens
(r, sigma0, r_core, gamma)[source]¶ mass enclosed a 3d sphere or radius r :param r: radius [arcsec] :param sigma0: convergence at r = 0 :param r_core: core radius [arcsec] :param gamma: logarithmic slope at r -> infinity :return: mass inside radius r
-
param_names
= ['sigma0', 'center_x', 'center_y', 'r_core', 'gamma']¶
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'gamma': 5.0, 'r_core': 100, 'sigma0':<PHONE_NUMBER>000.0}¶
-
lenstronomy.LensModel.Profiles.spp module¶
-
class
lenstronomy.LensModel.Profiles.spp.
SPP
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
class for circular power-law mass distribution
-
static
density
(r, rho0, gamma)[source]¶ computes the density :param x: :param y: :param rho0: :param a: :param s: :return:
-
static
density_2d
(x, y, rho0, gamma, center_x=0, center_y=0)[source]¶ projected density :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return:
-
density_lens
(r, theta_E, gamma)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in projected in units of angles (i.e. arc seconds) results in the convergence quantity.
-
derivatives
(x, y, theta_E, gamma, center_x=0.0, center_y=0.0)[source]¶ deflection angles
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
function
(x, y, theta_E, gamma, center_x=0, center_y=0)[source]¶ Parameters: - x (array of size (n)) – set of x-coordinates
- theta_E (float.) – Einstein radius of lens
- gamma (<2 float) – power law slope of mass profile
Returns: function
Raises: AttributeError, KeyError
-
grav_pot
(x, y, rho0, gamma, center_x=0, center_y=0)[source]¶ gravitational potential (modulo 4 pi G and rho0 in appropriate units) :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return:
-
hessian
(x, y, theta_E, gamma, center_x=0.0, center_y=0.0)[source]¶ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
Parameters: - x – x-coordinate
- y – y-coordinate
- kwargs – keywords of the profile
Returns: raise as definition is not defined
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'gamma': 1.5, 'theta_E': 0}¶
-
mass_2d
(r, rho0, gamma)[source]¶ mass enclosed projected 2d sphere of radius r :param r: :param rho0: :param a: :param s: :return:
-
mass_2d_lens
(r, theta_E, gamma)[source]¶ Parameters: - r – projected radius
- theta_E – Einstein radius
- gamma – power-law slope
Returns: 2d projected radius enclosed
-
static
mass_3d
(r, rho0, gamma)[source]¶ mass enclosed a 3d sphere or radius r :param r: :param a: :param s: :return:
-
param_names
= ['theta_E', 'gamma', 'center_x', 'center_y']¶
-
static
rho2theta
(rho0, gamma)[source]¶ converts 3d density into 2d projected density parameter :param rho0: :param gamma: :return:
-
static
theta2rho
(theta_E, gamma)[source]¶ converts projected density parameter (in units of deflection) into 3d density parameter :param theta_E: :param gamma: :return:
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'gamma': 2.5, 'theta_E': 100}¶
-
static
lenstronomy.LensModel.Profiles.tnfw module¶
-
class
lenstronomy.LensModel.Profiles.tnfw.
TNFW
[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
this class contains functions concerning the truncated NFW profile with a truncation function (r_trunc^2)*(r^2+r_trunc^2)
relation are: R_200 = c * Rs
-
static
alpha2rho0
(alpha_Rs, Rs)[source]¶ convert angle at Rs into rho0; neglects the truncation
Parameters: - alpha_Rs – deflection angle at RS
- Rs – scale radius
Returns: density normalization (characteristic density)
-
static
density
(r, Rs, rho0, r_trunc)[source]¶ three dimensional truncated NFW profile
Parameters: - r (float/numpy array) – radius of interest
- Rs (float > 0) – scale radius
- r_trunc (float > 0) – truncation radius (angular units)
Returns: rho(r) density
-
density_2d
(x, y, Rs, rho0, r_trunc, center_x=0, center_y=0)[source]¶ projected two dimensional NFW profile (kappa*Sigma_crit)
Parameters: - R (float/numpy array) – projected radius of interest
- Rs (float) – scale radius
- rho0 (float) – density normalization (characteristic density)
- r_trunc (float > 0) – truncation radius (angular units)
Returns: Epsilon(R) projected density at radius R
-
derivatives
(x, y, Rs, alpha_Rs, r_trunc, center_x=0, center_y=0)[source]¶ returns df/dx and df/dy of the function (integral of TNFW), which are the deflection angles
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- Rs – turn over point in the slope of the NFW profile in angular unit
- alpha_Rs – deflection (angular units) at projected Rs
- r_trunc – truncation radius (angular units)
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: deflection angle in x, deflection angle in y
-
function
(x, y, Rs, alpha_Rs, r_trunc, center_x=0, center_y=0)[source]¶ Parameters: - x – angular position
- y – angular position
- Rs – angular turn over point
- alpha_Rs – deflection at Rs
- r_trunc – truncation radius
- center_x – center of halo
- center_y – center of halo
Returns: lensing potential
-
hessian
(x, y, Rs, alpha_Rs, r_trunc, center_x=0, center_y=0)[source]¶ returns d^2f/dx^2, d^2f/dxdy, d^2f/dydx, d^2f/dy^2 of the TNFW potential f
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- Rs – turn over point in the slope of the NFW profile in angular unit
- alpha_Rs – deflection (angular units) at projected Rs
- r_trunc – truncation radius (angular units)
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
-
lower_limit_default
= {'Rs': 0, 'alpha_Rs': 0, 'center_x': -100, 'center_y': -100, 'r_trunc': 0}¶
-
mass_2d
(R, Rs, rho0, r_trunc)[source]¶ analytic solution of the projection integral (convergence)
Parameters: - R – projected radius
- Rs – scale radius
- rho0 – density normalization (characteristic density)
- r_trunc – truncation radius (angular units)
Returns: mass enclosed 2d projected cylinder
-
mass_3d
(r, Rs, rho0, r_trunc)[source]¶ mass enclosed a 3d sphere or radius r
Parameters: - r – 3d radius
- Rs – scale radius
- rho0 – density normalization (characteristic density)
- r_trunc – truncation radius (angular units)
Returns: M(<r)
-
nfwAlpha
(R, Rs, rho0, r_trunc, ax_x, ax_y)[source]¶ deflection angel of NFW profile along the projection to coordinate axis
Parameters: - R (float/numpy array) – radius of interest
- Rs (float) – scale radius
- rho0 (float) – density normalization (characteristic density)
- r_trunc (float > 0) – truncation radius (angular units)
- axis (same as R) – projection to either x- or y-axis
Returns:
-
nfwGamma
(R, Rs, rho0, r_trunc, ax_x, ax_y)[source]¶ shear gamma of NFW profile (times Sigma_crit) along the projection to coordinate ‘axis’
Parameters: - R (float/numpy array) – radius of interest
- Rs (float) – scale radius
- rho0 (float) – density normalization (characteristic density)
- r_trunc (float > 0) – truncation radius (angular units)
- axis (same as R) – projection to either x- or y-axis
Returns:
-
nfwPot
(R, Rs, rho0, r_trunc)[source]¶ lensing potential of truncated NFW profile
Parameters: - R (float/numpy array) – radius of interest
- Rs (float) – scale radius
- rho0 (float) – density normalization (characteristic density)
- r_trunc (float > 0) – truncation radius (angular units)
Returns: lensing potential
-
param_names
= ['Rs', 'alpha_Rs', 'r_trunc', 'center_x', 'center_y']¶
-
profile_name
= 'TNFW'¶
-
static
rho02alpha
(rho0, Rs)[source]¶ convert rho0 to angle at Rs; neglects the truncation
Parameters: - rho0 – density normalization (characteristic density)
- Rs – scale radius
Returns: deflection angle at RS
-
upper_limit_default
= {'Rs': 100, 'alpha_Rs': 10, 'center_x': 100, 'center_y': 100, 'r_trunc': 100}¶
-
static
lenstronomy.LensModel.Profiles.uldm module¶
-
class
lenstronomy.LensModel.Profiles.uldm.
Uldm
(*args, **kwargs)[source]¶ Bases:
lenstronomy.LensModel.Profiles.base_profile.LensProfileBase
This class contains functions concerning the ULDM soliton density profile, whose good approximation is (see for example https://arxiv.org/pdf/1406.6586.pdf )
\[\rho = \rho_0 (1 + a(\theta/\theta_c)^2)^{-\beta}\]where \(\theta_c\) is the core radius, corresponding to the radius where the density drops by half its central value, :math: beta is the slope (called just slope in the parameters of this model), :math: rho_0 = kappa_0 Sigma_c/D_lens, and :math: a is a parameter, dependent on :math: beta, chosen such that :math: theta_c indeed corresponds to the radius where the density drops by half (simple math gives :math: a = 0.5^{-1/beta} - 1 ). For an ULDM soliton profile without contributions to background potential, it turns out that :math: beta = 8, a = 0.091. We allow :math: beta to be different from 8 to model solitons which feel the influence of background potential (see 2105.10873) The profile has, as parameters: :param kappa_0: central convergence :param theta_c: core radius (in arcseconds) :param slope: exponent entering the profile, default value is 8
-
alpha_radial
(r, kappa_0, theta_c, slope=8)[source]¶ returns the radial part of the deflection angle
Parameters: - kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
- r – radius where the deflection angle is computed
Returns: radial deflection angle
-
density
(R, kappa_0, theta_c, slope=8)[source]¶ three dimensional ULDM profile in angular units (rho0_physical = rho0_angular Sigma_crit / D_lens) :param R: radius of interest :param kappa_0: central convergence of profile :param theta_c: core radius (in arcsec) :param slope: exponent entering the profile :return: rho(R) density in angular units
-
density_2d
(x, y, kappa_0, theta_c, center_x=0, center_y=0, slope=8)[source]¶ projected two dimensional ULDM profile (convergence * Sigma_crit), but given our units convention for rho0, it is basically the convergence
Parameters: - R – radius of interest
- kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
Returns: Epsilon(R) projected density at radius R
-
density_lens
(r, kappa_0, theta_c, slope=8)[source]¶ computes the density at 3d radius r given lens model parameterization. The integral in the LOS projection of this quantity results in the convergence quantity.
Parameters: - r – 3d radius
- kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
Returns: density rho(r)
-
derivatives
(x, y, kappa_0, theta_c, center_x=0, center_y=0, slope=8)[source]¶ returns df/dx and df/dy of the function (lensing potential), which are the deflection angles
Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: deflection angle in x, deflection angle in y
-
function
(x, y, kappa_0, theta_c, center_x=0, center_y=0, slope=8)[source]¶ Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: lensing potential (in arcsec^2)
-
hessian
(x, y, kappa_0, theta_c, center_x=0, center_y=0, slope=8)[source]¶ Parameters: - x – angular position (normally in units of arc seconds)
- y – angular position (normally in units of arc seconds)
- kappa_0 – central convergence of profile
- theta_c – core radius (in arcsec)
- slope – exponent entering the profile
- center_x – center of halo (in angular units)
- center_y – center of halo (in angular units)
Returns: Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
-
kappa_r
(R, kappa_0, theta_c, slope=8)[source]¶ convergence of the cored density profile. This routine is also for testing
Parameters: - R – radius (angular scale)
- kappa_0 – convergence in the core
- theta_c – core radius
- slope – exponent entering the profile
Returns: convergence at r
-
lower_limit_default
= {'center_x': -100, 'center_y': -100, 'kappa_0': 0, 'slope': 3.5, 'theta_c': 0}¶
-
mass_2d
(R, kappa_0, theta_c, slope=8)[source]¶ mass enclosed a 2d sphere or radius r :param R: radius over which the mass is computed :param kappa_0: central convergence of profile :param theta_c: core radius (in arcsec) :param slope: exponent entering the profile :return: mass enclosed in 2d sphere
-
mass_3d
(R, kappa_0, theta_c, slope=8)[source]¶ mass enclosed a 3d sphere or radius r :param R: radius in arcseconds :param kappa_0: central convergence of profile :param theta_c: core radius (in arcsec) :param slope: exponent entering the profile :return: mass of soliton in angular units
-
mass_3d_lens
(r, kappa_0, theta_c, slope=8)[source]¶ mass enclosed a 3d sphere or radius r :param r: radius over which the mass is computed :param kappa_0: central convergence of profile :param theta_c: core radius (in arcsec) :param slope: exponent entering the profile :return: mass enclosed in 3D ball
-
param_names
= ['kappa_0', 'theta_c', 'slope', 'center_x', 'center_y']¶
-
rhotilde
(kappa_0, theta_c, slope=8)[source]¶ Computes the central density in angular units :param kappa_0: central convergence of profile :param theta_c: core radius (in arcsec) :param slope: exponent entering the profile :return: central density in 1/arcsec
-
upper_limit_default
= {'center_x': 100, 'center_y': 100, 'kappa_0': 1.0, 'slope': 10, 'theta_c': 100}¶
-


Police seize £10m of cocaine hidden in frozen fish cargo
by PA MediaDrug haul discovered in refrigerated van as it came off ferry at Newhaven, East Sussex
A driver has been charged after £10m worth of cocaine was found hidden in a load of frozen fish.
The haul was discovered in the back of a refrigerated van when the vehicle was searched as it came off a ferry at Newhaven port, in East Sussex, in the early hours of Saturday morning.
Officers found 97 packages, each containing around 1kg of cocaine.
The National Crime Agency said the drugs could have been sold for about £10m at street value.
James Satterley, 50, from Cookham, Maidenhead, has been charged with importing class A drugs. He was remanded in custody and is due to appear before Brighton magistrates on Monday.
Paul Morris, the NCA senior investigating officer, said: “NCA officers are working alongside Border Force, Sussex police, Thames Valley police and the south-east regional organised crime unit to investigate this seizure and the circumstances around it.
“Working with partners, we are determined to do all we can to disrupt the organised crime groups involved in the large-scale importation of class A drugs, which fuel serious violence and impact some of the most vulnerable members of our society.
“Making seizures like this is an important part of that work.”


Harshvardhan Uppaluru
I am a Ph.D. candidate in the Scalable Move And Resilient Transversability (SMART) Lab
at University of Arizona, advised by
Prof. Hossein Rastgoftar.
SMART Lab is associated with Aerospace & Mechanical Engineering Department and College of Engineering.
I am minoring in Systems and Industrial Engineering advised by
Prof. Erfan Yazdandoost Hamedani.
Prior to pursuing Ph.D., I completed my Masters in Robotics Engineering from
University of Maryland - College Park.
I have a Bachelors degree in Mechatronics Engineering from
SRM University (Currently SRM Institute of Science & Technology).
Apart from research, I play cricket and watch soccer on weekends. Arsenal is my favorite soccer team.
In addition, I completed four levels of cricket umpiring: USACUA Preliminary, USACUA Final, WICUA Final, and WICUA Oral & Practical.
I have umpired in various leagues such as Minor League Cricket (MiLC), Washington Cricket League (WCL), Arizona Cricket Association (ACA) and Washington Youth Cricket League (WYCL).
Email /
GitHub /
Google Scholar /
LinkedIn /
Twitter
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This module implements those functions that replace aspects of the scipy.fftpack module. This module provides the entire documented namespace of scipy.fftpack, but those functions that are not included here are imported directly from scipy.fftpack.
The exceptions raised by each of these functions are mostly as per their equivalents in scipy.fftpack, though there are some corner cases in which this may not be true.
It is notable that unlike scipy.fftpack, these functions will generally return an output array with the same precision as the input array, and the transform that is chosen is chosen based on the precision of the input array. That is, if the input array is 32-bit floating point, then the transform will be 32-bit floating point and so will the returned array. If any type conversion is required, the default will be double precision.
Some corner (mis)usages of scipy.fftpack may not transfer neatly. For example, using scipy.fftpack.fft2() with a non 1D array and a 2D shape argument will return without exception whereas pyfftw.interfaces.scipy_fftpack.fft2() will raise a ValueError.
Perform a 1D FFT.
The first three arguments are as per scipy.fftpack.fft(); the rest of the arguments are documented in the additional argument docs.
Perform a 1D inverse FFT.
The first three arguments are as per scipy.fftpack.ifft(); the rest of the arguments are documented in the additional argument docs.
Perform an n-D FFT.
The first three arguments are as per scipy.fftpack.fftn(); the rest of the arguments are documented in the additional argument docs.
Perform an n-D inverse FFT.
The first three arguments are as per scipy.fftpack.ifftn(); the rest of the arguments are documented in the additional argument docs.
Perform a 1D real FFT.
The first three arguments are as per scipy.fftpack.rfft(); the rest of the arguments are documented in the additional argument docs.
Perform a 1D real inverse FFT.
The first three arguments are as per scipy.fftpack.irfft(); the rest of the arguments are documented in the additional argument docs.
Perform a 2D FFT.
The first three arguments are as per scipy.fftpack.fft2(); the rest of the arguments are documented in the additional argument docs.
Perform a 2D inverse FFT.
The first three arguments are as per scipy.fftpack.ifft2(); the rest of the arguments are documented in the additional argument docs.


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Fabric8 uses the following extensions for
file names:
*.AZI
= horizontally distributed
orientation
data with polarity, 0° to
359°, type: azimuth,
*.BMP = Windows Bitmap Format for
graphic files,
*.DXF =
Drawing Exchange Format for graphic files,
*.EMF = Enhanced Metafile (Windows)
for graphic
files,
*.FLI = data for a Flinn or Hsü diagram
*.FOU =
Fourier-coefficients, type:
vergency,x1,y1 x2,y2 x3,y3,
*.FRN = data file for the
enhanced Fry method,
*.FRY
= data file for the conventional Fry method,
*.GIF = Graphic
Interchange Format for graphic
files,
*.JPG = Jpeg format for
compressed graphic files,
*.LAZ = horizantally
distributed orientation data with polarity and magnitudes,
*.LIN =
three-dimensionally distributed linear orientation data, type:
azimuth
of
dip / angle
of dip,
*.LI2 = Files with
pairs of lineations for the
calculation of planes, angles, and normals,
*.LST = horizontally
distributed bipolar orientation data with magnitudes,
type:
fotolineation,
*.MAP = files for structural maps (Coordinates and
compass measures),
*.PCH
= Planes
(dip azimuth/dip angle) and clockwise
Pitch angle,
*.PLA = three-dimensionally
distributed planar
orientation data, type: azimuth
of
dip / angle
of dip,
*.PLB = three-dimensionally
distributed planar
orientation data, type: strike,dip,
direction of dip,
*.PLI = Planes
(dip
azimuth/dip angle) and lineation (dip azimuth/dip angle)
in the plane,
*.PLT = Hewlett
Packard Graphic Language for
vectorgraphic,
*.PL2 = Files with pairs
of planar data for
calculation of intersection lines or
angles,
*.POL = X-y-coordinates of
Corner points of polygons for the Panozzo method,
*.RFI = Data for the
Rf/Phi
method,
*.RGD =
Data for R%-G%-diagramms, type: R%,G%,
*SCI = files for small circles,
*.SLI =
Slickensides with striations with polarity,
type: azimuth of dip /+ or - angle of dip,
*.STR = horizontally
distributed bipolar orientation data, type: strike lines,
*.TAL = distances of isogons for the
T’alpha/alpha
method,
*.TIF
= Tagged Image Format for graphic
files,
*.TLI = Linears
(stretching or compression) for
the Talbot method,
*.WMF = Windows Metafile for graphic files,
*.WOO = Files with eigenvalues, type: E1,E2,E3.


How BBNaija Mike Edwards bite more than he could chew
by Temisan AmoyeBBNaija Mike is so much loved that the gangling dude could get away with just about anything but on a certain occasion last week the first runner-up of the Season 4 of the Big Brother Naija got on the wrong side of people by assuming some sort of authority to speak about faithfulness in marriage.
Mike was so highly celebrated for his fidelity in the Big Brother House but people think that hasn’t earned him some right to give out tips on faithfulness in marriage.
ALSO READ: Eddie Murphy says women find It ‘sexy’ that he has 10 kids
Their argument was simple – he has only been married a year!
“ Can someone tell him that one year in marriage is not enough to give tips on how to be faithful.
I need to revisit this issue with him 10 years from now and see if he still has the same energy on teaching, “How to be faithful”,” an Instagram based platform ‘Inside Life ng’ responded.
ALSO READ: The ghost and the house of truth mirroring a decrepit society
The reality TV star had been rather smug dishing out tips on how to stay faithful in a marriage on his Instagram page, saying he had been asked the question, “How do you stay faithful?” too many times.
Inside Life Ng and many people wouldn’t have it as they believe the question is beyond him to answer.


{% extends "base.html" %} {% block title %}Plan your trip{% endblock %} {% block content %}
For trans-Atlantic flights the best airport to fly into is London Heathrow (LHR). It has direct coach (bus) connection with Bath via National Express, and has express train service to London Paddington via Heathrow Express. London Paddington is located in central London, ideal for tourist destinations and is also the station for direct rail service to Bath Spa for the convention.
From European destinations we recommend flying into Bristol International Airport (BRS) if you will not be visiting London on your trip. Bristol Airport has direct coach service to Bath via Air Decker at a rate of £20 return (round trip) and is less than half the journey time of travelling from Heathrow.
London Gatwick (LGW) also provides coach service to Bath via National Express but tickets are generally more expensive than those from Heathrow. Additionally, the Gatwick Express train service travels to London Victoria, requiring a tube journey to London Paddington for connecting trains to Bath Spa.
Bath Spa rail station is located in central Bath right next to the coach (bus) station and is on the main Great Western Main line which runs from London Paddington to Bristol and on to south Wales. The train operator between London and Bath is First Great Western but we recommend purchasing tickets and planning your journey through the trainline website and mobile app (iOS | Android) or through Red Spotted Hanky.
Please Note: We recommend planning and purchasing rail travel as far in advance as possible for the lowest fares. Purchasing tickets 2 months in advance will usually result in fares half price or lower.
Bus service from central Bristol to Bath Bus Station is via FirstBus, and bus service from the centre of Bath to the University runs every 15-20 minutes throughout the day via FirstBus 18 or Wessex Uniconnect U18.
On-site accommodation booking is available separately through Bath University: click this Accommodation Booking link to book your convention accommodation.
For guests who have additional needs, or for those wanting double beds, rooms are available in Woodland Court. All rooms are ensuite, with doubles and large showers available as well as flat screens and VOIP phones.
Additional accommodation is also available at the YHA Hostel on Bathwick Hill. Located just 10 minutes walk from the University, this grand hostel features stunning architecture, gardens and views over Bath with shared dorms starting at just £21.50 pp/night.
At the Thermae Bath Spa, visitors can soak in the same naturally warm and mineral rich waters that the Celts and Romans did over 2000 years ago.
First discovered in 863 BC, the source of the water remains somewhat in mystery but it is believed to have fallen as rain water about 10,000 years ago before passing through carboniferous limestone to a depth of 2km. There the water is heated by high temperature rock before rising back up into one of three hot springs in the centre of the city. There is also a rooftop pool with stunning views across the city and beyond.
Remember to bring your sports kit! The convention venue is home to a renowned £30 million Sports Training Village (STV) on campus which houses sport, fitness, coaching, physio and sport science facilities all largely under one roof. The STV has indoor and outdoor facilities to accommodate more than 50 sports and regularly hosts major international competitions as well as being a world-class multi-sport training environment. Visit the TEAM BATH website and see the Sports facility timetable & price list, or alternatively call Sports Training Village reception on +44 (0)1225 386339.


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@(title: String, registrationForm: Form[forms.RegistrationForm], courts: List[Court]) @import bootstrap3._ @import utils.Tags._ @scripts = { } @Main(title, scripts) { @if(Secured.isLoggedIn(ctx())) {
| @game.getName |
You aren't following any courts
Find courts here
} else { @for(court <- courts) { } }The HIHoops site is designed to make it easy for players to connect with players of a similar skill level, location, and even gender.
Looking for a court to play at? Our gyms page can locate gyms & courts near you!
Find other b-ballers to play with and check their sportsmanship rating!
Search for teams to join based on skill level and position!
Advertise, create, and manage your league! Or search for leagues that your team can play in!
Hawaii Hoops Network isn't one of those mainland websites that tries to cater to basketball players on the islands. Hawaii Hoops Network was created by a group of local students who have a passion for amateur basketball.


Ambiguous Codes
问题描述 :
The very first thing needed to establish any kind of communication is a common code. A code is a way of changing the form of a piece of information into some other form, in general to make it possible to convey that piece of information from one place to another. Flag codes used by boats and the Morse code used in telegraphy are examples of codes for translating letters into different forms to enable communication over different media.
More formally, a code is a set of strings composed of symbols from one alphabet. Each string defined in the code is called a code word. A message is then composed concatenating a set of code words to convey the information needed. For example, in Morse code the alphabet is composed of the symbols hyphen and dot; letter “S” is represented by the code word “…”, letter “O” is represented by the code word “—”, and therefore the distress message “SOS” in Morse code is “…—…”.
Codes for communication can have many desirable and undesirable properties such as ambiguity, entropy, redundancy, and many more. In this problem we will focus on ambiguity as a key property.
A code is ambiguous when there exists a message using that code that can be partitioned into different sequences of code words. In other words, in an ambiguous code a message may have more than one meaning. For example, consider the binary alphabet, composed of symbols {0,1}. For the code composed of the words {10, 01, 101} the message 10101 can be understood as 10-101 or 101-01 and therefore the code is ambiguous. On the other hand, for the code composed of the words {01, 10, 011} no ambiguous message exists and therefore the code is unambiguous.
As a part of the computer science community, you are required to develop a tester that checks if codes are ambiguous. In case a code is indeed ambiguous, you are also required to report the length (i.e. the number of symbols) of the shortest ambiguous message for that code.
输入:
Input is terminated by N = 0.
输出:
Input is terminated by N = 0.
样例输入:
3 10 01 101 3 AB BA ABB 0
样例输出:
5 -1
题意大概是这样的
就是让我们去早这么一个字符串，是由前面给的字符串拼成的，然后如果这个拼成的字符能够拆成另外的由前面给出的字符串的话就是Ambiguous ，让我们输出长度最短的Ambiguous 的长度，如果没有就输出-1
如输入
01
10
101
可以找到最短的10101
它可以看成是101 01组成
也可以看成10 101组成
所以就输出10101的长度5
#include <cstdio> #include <iostream> #include <cstring> #include <cmath> #include <algorithm> #define maxn 100+5 #define maxlen 50+5 int n; char str[maxn][maxlen]; int toX[maxn][maxlen][maxn]; int toY[maxn][maxlen][maxn]; int need[maxn][maxlen][maxn]; int len[maxn]; using namespace std; void check(){ for(int i = 0; i < n; i++){ len[i] = strlen(str[i]); } for (int i = 0; i < n; i++){ for (int j = 1; j <= len[i]; j++){ for (int k = 0; k < n; k++){ if(j == len[i] && i == k){//如果str[k]就是str[i]本身 toX[i][j][k] = -1; } else if(memcmp(str[i] + len[i] - j, str[k], min(j, len[k])) == 0){ toX[i][j][k] = j > len[k] ? i : k; toY[i][j][k] = fabs(j - len[k]); need[i][j][k] = j > len[k] ? 0 : len[k] - j; } else toX[i][j][k] = -1; } } } } const int maxq = (maxn) * (maxlen) * 10; int q[maxq],begin,end; int dis[maxn][maxlen]; bool inq[maxn][maxlen]; void spa(){ begin = 0; end = 0; memset(dis, 0x3f, (sizeof(dis))); memset(inq, 0, sizeof(inq)); for(int i = 0; i < n; i++){ q[end++] = i; q[end++] = len[i]; dis[i][len[i]] = len[i]; inq[i][len[i]] = true; } while(begin != end){ int x = q[begin++]; int y = q[begin++]; if (begin == maxq) begin = 0; inq[x][y] = false; for(int i = 0; i < n; i++){ if(toX[x][y][i] != -1){ int xx = toX[x][y][i]; int yy = toY[x][y][i]; int ll = need[x][y][i]; if(dis[xx][yy] > dis[x][y] + ll){//如果dis[xx][yy]还没有求出来 dis[xx][yy] = dis[x][y] + ll; if(!inq[xx][yy]){ q[end++] = xx; q[end++] = yy; if(end == maxq){ end = 0; } inq[xx][yy] = true;//标记inq[xx][yy]在队列中 } } } } } } void output(){ int ans = 0x3f000000; for(int i = 0; i < n; i++){ if(ans > dis[i][0]){ ans = dis[i][0]; } } printf("%d\n", ans >= 0x30000000 ? -1 : ans); } int main(){ while(scanf("%d", &n), n){ for (int i = 0; i < n; i++){ scanf("%s", str[i]); } /*判断每一个字符串的最后的每一位可以用哪一个字符串的前几位接上，记下最后的几位是属于哪个 字符串（toX来储存），相对多出了几位（用toY来储存）， 需要在当前的字符串后面加上几位才能、 得到新串（need来储存）*/ check(); /*枚举出所有在末尾加字符串后的结果*/ spa(); output(); } }
有没有捉妖记高清的
看似简单，还是不少坑的
对，还是这种实现比较好理解。虽然效率有点低
第一题是不是可以这样想，生了n孩子的家庭等价于n个家庭各生了一个1个孩子，这样最后男女的比例还是1:1
您没有考虑 树的根节点是负数的情况， 若树的根节点是个很大的负数，那么就要考虑过不过另外一边子树了
在第 18行的，while(scanf("%d %dn", &n, &c), n)，这句有错吧
能不能说一下tmp数组和solve都是干嘛的？
额，不对应吧
辛苦了，顶
第一题还是比较考验智商~
顺利测试通过了，多谢
此网站甚是喜欢，潜力巨大，请问站长，如何加入开发团队~
好的，多谢指出
Good task for the group. Hold it up for every yeara??s winner. This is a excellent oppotunity for a lot more enhancement. Indeed, obtaining far better and much better is constantly the crucial. Just like my pal suggests on the truth about ab muscles, he just keeps obtaining much better.
为什么for循环找到的i一定是素数叻，而且约数定理说的是n=p1^a1*p2^a2*p3^a3*…*pk^ak，而你每次取余都用的是原来的m，也就是n


|
Standard Reference Data Program |
Data Gateway |
Chemistry WebBook |
Go To: Top, Constants of diatomic molecules, References, Notes / Error Report
Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A. All rights reserved.
Data compiled by: J.E. Bartmess
View reactions leading to GeH+ (ion structure unspecified)
| Quantity | Value | Units | Method | Reference | Comment |
|---|---|---|---|---|---|
| ΔrH° | 1457. ± 21. | kJ/mol | D-EA | Scheer, Bilodeau, et al., 1998 | gas phase; Given: 1.232712(15) eV |
Go To: Top, Gas phase ion energetics data, References, Notes / Error Report
Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A. All rights reserved.
Data compiled by: K.P. Huber and G. Herzberg
| State | Te | ωe | ωexe | ωeye | Be | αe | γe | De | βe | re | Trans. | ν00 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B (2Σ) | [41074] 1 | B ← X R | 39686 H | |||||||||
| Barrow, Drummond, et al., 1953 | ||||||||||||
| B ← X R | 40573 H | |||||||||||
| Barrow, Drummond, et al., 1953 | ||||||||||||
| A 2Δ | 25454 2 | [1185.15] Z | (127) 3 | 6.535 4 | 0.6196 | [0.000571] 5 | 1.611 | A ↔ X R | 25197.0 Z | |||
| missing citation; missing citation; Veseth, 1973 | ||||||||||||
| a 4Σ(-) | [16747] 6 | [6.7654] 6 | [0.000460] | [1.5834] | a → X V | 15802.8 Z | ||||||
| Kleman and Werhagen, 1953; Klynning, 1966 | ||||||||||||
| State | Te | ωe | ωexe | ωeye | Be | αe | γe | De | βe | re | Trans. | ν00 |
| X 2Πr | 0 7 | [1833.77] Z | (37) 3 | 6.7259 8 | 0.1916 | [0.000326] 9 | 1.5880 |
| 1 | Incompletely resolved bands. |
| 2 | A0 = 10.3, A1 = 6.1; moderate J dependence. For a more detailed theoretical discussion of this 2Δ state see Veseth, 1971. |
| 3 | Estimated from isotope shifts Klynning and Lindgren, 1966. |
| 4 | Spin-doubling constants γ = 0.473 (v=0) and γ= 0.362 (v=1). Broadening of absorption lines due to predissociation above 27000 cm-1. |
| 5 | D1 = 8.01E-4; also higher order constants. |
| 6 | Spin-splitting constants 13= 6.52, γ1 = 0.037, γ2 = 0.048. Note that the definitions of 13, γ1 and γ2 used in Klynning, 1966 are those of Hougen Hougen, 1962 and differ from those used by Martin and Merer [see ref. Klynning and Lindgren, 1966 of GeF). The B0 value in the abstract of Klynning, 1966 and quoted in DONNSPEC is clearly wrong. |
| 7 | A0 = 892.52 Klynning and Lindgren, 1966, A1 = 896.12 Klynning and Lindgren, 1966; small J dependence. See also Veseth, 1973. |
| 8 | Λ-type doubling, Δv(2Π1/2) = 0.496(J+1/2)-...; v=0 |
| 9 | D1 = 3.40E-4. |
| 10 | From the predissociation in A 2Δ Klynning and Lindgren, 1966; thermochemical data give the same value Barrow and Deutsch, 1960. |
| 11 | From the value for GeH. |
| 12 | A0 = 14.4, A1 = 9.9, A2 = 7.2; moderate J dependence. |
| 13 | Spin-doubling constants γ= 0.300 (v=0), γ= 0.281 (v=1), γ= 0.22 (v=2). Predissociation, see 4 . |
| 14 | D1 = 1.65E-4, D2 = 1.7E-4; also higher order constants. |
| 15 | A0 = 891.86 Klynning and Lindgren, 1966, A1 = 894.35 Klynning and Lindgren, 1966; small J dependence. See also Veseth, 1973. |
| 16 | Λ-type doubling; in Δv(2Π1/2) = 0.2506(J+1/2) - ...; v=0 |
| 17 | D1 = 0.824E-4. |
Go To: Top, Gas phase ion energetics data, Constants of diatomic molecules, Notes / Error Report
Data compilation copyright by the U.S. Secretary of Commerce on behalf of the U.S.A. All rights reserved.
Scheer, Bilodeau, et al., 1998
Scheer, M.; Bilodeau, R.C.; Brodie, C.A.; Haugen, H.K.,
Systematic study of the stable states of C-, Si-, Ge-, and Sn- via infrared laser spectroscopy,
Phys. Rev. A, 1998, 58, 2844-2856. [all data]
Barrow, Drummond, et al., 1953
Barrow, R.F.; Drummond, G.; Garton, W.R.S.,
Ultra-violet bands associated with germanium,
Proc. Phys. Soc. London Sect. A, 1953, 66, 191. [all data]
Veseth, 1973
Veseth, L.,
Some anomalies in the electronic spectra of GeH, GeD, SnH, and SnD related to Hund's coupling case (c),
J. Mol. Spectrosc., 1973, 48, 283. [all data]
Kleman and Werhagen, 1953
Kleman, B.; Werhagen, E.,
A 4Σ--2Π-system in germanium hydride (GeH),
Ark. Fys., 1953, 6, 399. [all data]
Klynning, 1966
Klynning, L.,
On the 4Σ state of GeH,
Ark. Fys., 1966, 32, 563. [all data]
Veseth, 1971
Veseth, L.,
Second-order spin-orbit splitting in 2Δ states of diatomic molecules,
Physica (Amsterdam), 1971, 56, 286. [all data]
Klynning and Lindgren, 1966
Klynning, L.; Lindgren, B.,
Rotational analysis of the 2Δ-2Π band system of GeH and of GeD,
Ark. Fys., 1966, 32, 575. [all data]
Hougen, 1962
Hougen, J.T.,
The rotational energy levels of diatomic molecules in 4Σ electronic states,
Can. J. Phys., 1962, 40, 598. [all data]
Barrow and Deutsch, 1960
Barrow, R.F.; Deutsch, J.L.,
Gaseous SiH and GeH,
Proc. Chem. Soc. London, 1960, 122. [all data]
Go To: Top, Gas phase ion energetics data, Constants of diatomic molecules, References
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I needed an application which whould show me
all my tasks and tasks which I should do today.
I also needed history of work
(what I have been doing what day), times of tasks and total times of my work.
I am looking for partner(s) which would help me improve and propagate this app.
Write me on:
I wanted to do this app commercial, but it's impossible without a good team.
One day @markusgattol wrote me that
he likes TodoToday and asked if i could open source it.
I had to think about it and i have decided to make it opensource.
Now you can contact me and together we can make the best TODO application ever!
Github repo: https://github.com/Elfoslav/todotoday/


words:
play, tennis, piano, ride, club, term, board, well, all, worry, teach, then, monitor, start, ready, promise, fast, fit, just, ball, game, team, best, score, tidy, sure, everybody, beautiful, fly, kite, swim,
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We're passionate about cloud computing...
GDG Cloud Melbourne DevFest is an event for the Google Cloud community. It's a chance for Google Cloud enthusiasts to share, learn and generally geek out!
We'll be covering a diverse range of topics including IoT, ML, Serverless, Kubernetes and Culture
Explore presentations here
DevFests are large, community-run developer events happening around the globe focused on community building and learning about Google’s technologies. There are two DevFests happening right here in Melbourne!
GDG Cloud Melbourne are running this one, which is specifically focused on Google Cloud content. There is another DevFest being run by our friends from the Melbourne Android GDG group, and they'll be focussing on Mobile & Web technologies (not Google Cloud). For more info on their DevFest swing over here


Drop an MP3 file to play it, or switch to the mic input. When a beat is detected the volume bar flashes white. Requires Chrome.
View Blog Post. Built by @felixturner
Music: "Cissy Strut" by The Meters


Part of nukebox2000.NukeBoxServer View In Hierarchy
NukeBox 2000 Protocol Class
| Method | __init__ | Protocol Constructor |
| Method | connectionMade | Server receives a new connection |
| Method | connectionLost | Server loses a connection |
| Method | lineReceived | Incoming Line Data |
| Method | rawDataReceived | Raw File data |
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I have written the preceding material to provide an introduction to pointers for newcomers to C. In C, the more one understands about pointers the greater flexibility one has in the writing of code. The above expands on my first effort at this which was entitled ptr_help.txt and found in an early version of Bob Stout's collection of C code SNIPPETS. The content in this version has been updated from that in PTRTUTOT.ZIP included in SNIP9510.ZIP.
I am always ready to accept constructive criticism on this material,
or review requests for the addition of other relevant material.
Therefore, if you have questions, comments, criticisms, etc. concerning
that which has been presented, I would greatly appreciate your
contacting me via email me at tjensen@ix.netcom.com.