clmm.support.sampler module

@file.py sampler.py Functions for sampling (output either peak or full distribution)

clmm.support.sampler.basinhopping(model_to_shear_profile, logm_0, **kwargs)

Uses basinhopping, a scipy global optimization function, to find the minimum.

Parameters:

• model_to_shear_profile (callable) -- The objective function to be minimized. model_to_shear_profile(x, *args) -> float where x is an 1-D array with shape (n,) and args is a tuple of the fixed parameters needed to completely specify the function.

• logm_0 (array_like) -- Initial guess. Array of real elements of size (n,), where 'n' is the number of independent variables.

• kwargs -- Other optional keyword arguments passed to basinhopping. Please check the scipy documentaion for information on default values and methods.

Returns:

• x (array)

• The solution of the optimization

clmm.support.sampler.scicurve_fit(profile_model, radius, profile, err_profile, absolute_sigma=True, **kwargs)

Uses scipy.optimize.curve_fit to find best fit parameters

Parameters:

• profile_model (callable) -- The model function, f(x, ...). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.

• radius (array_like or object) -- The independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object.

• profile (array_like) -- The dependent data, a length M array - nominally f(xdata, ...).

• err_profile (M-length sequence or MxM array) -- Determines the uncertainty in ydata. If we define residuals as r = ydata - f(xdata, *popt), then the interpretation of sigma depends on its number of dimensions: - A 1-D sigma should contain values of standard deviations of errors in ydata. In this case, the optimized function is chisq = sum((r / sigma) ** 2). - A 2-D sigma should contain the covariance matrix of errors in ydata. In this case, the optimized function is chisq = r.T @ inv(sigma) @ r.

• absolute_sigma (bool, optional) -- If True (default), sigma is used in an absolute sense and the estimated parameter covariance pcov reflects these absolute values. If False, only the relative magnitudes of the sigma values matter. The returned parameter covariance matrix pcov is based on scaling sigma by a constant factor. This constant is set by demanding that the reduced chisq for the optimal parameters popt when using the scaled sigma equals unity. In other words, sigma is scaled to match the sample variance of the residuals after the fit. Default is True. Mathematically, pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)

• kwargs -- Other optional keyword arguments passed to curve_fit Please check the scipy documentaion for information on default values and methods.

Returns:

p --

contains :

p[0]array

Optimal values for the parameters so that the sum of the squared residuals of f(xdata, *popt) - ydata is minimized.

p[1]2-D array

The estimated covariance of popt. The diagonals provide the variance of the parameter estimate. To compute one standard deviation errors on the parameters use perr = np.sqrt(np.diag(pcov)). How the sigma parameter affects the estimated covariance depends on absolute_sigma argument, as described above.

Return type:

list

clmm.support.sampler.sciopt(model_to_shear_profile, logm_0, **kwargs)

Uses scipy optimize minimize to output the peak

Parameters:

• model_to_shear_profile (callable) -- The objective function to be minimized. model_to_shear_profile(x, *args) -> float where x is an 1-D array with shape (n,) and args is a tuple of the fixed parameters needed to completely specify the function.

• logm_0 (ndarray, shape (n,)) -- Initial guess. Array of real elements of size (n,), where 'n' is the number of independent variables.

• kwargs -- Other optional keyword arguments passed to minimize. Please check the scipy documentaion for information on default values and methods.

Returns:

• x (array)

• The solution of the optimization