Generate profiles from two non-negative matrices (X,C), whose product approximates the non-negative matrix Q of observed metals in quasar spectra. These profiles can be used to generate large libraries of realistic metal absorption profiles

Parameters
----------
NMF_dct: Dictionary containing the information about the non-negative matrices (X,C).
    X : NMF_dct['X'] ndarray of shape n x m, where m is the number of reduced features in the NMF space
    C : NMF_dct['C'] ndarray of shape m x u and represents the coeffcient matrix of the m reduced features

nsim: int, default = 1
    Number of profiles to be generated.

ion_family: {'moderate', 'low', 'user'}, default='moderate'.
    Ions families to be considered.
    Valid options:
    
    - 'moderate': If 'moderate' the profiles will follow a DeltaV_90 distribution typical of moderate ions transitions.
    
    - 'low': If 'low' the profiles will follow a DeltaV_90 distribution typical of low ions transitions
    
    - 'user': If 'user' the profiles will follow a DeltaV_90 distribution provided by the user with filename_ion_familiy
    
filename_ion_familiy: str, default=None
    User filename for DeltaV_90 pdf if ion_family = 'user'

ion_logN: ndarray of shape (nsim,), default=[14.0]
    log Ion Column Density in cm^-2

ion: str, default=['CIV']
    Ion transition to be simulated

trans_wl: float, default=[1548.2040]
    Ion transition wavelength in Angstrom
    
filename_ion_list: str, default=None
    User filename for lines' physical parameters

convolved: Boolean, default = False
    Allow for the generated profile to be convolved with a Gaussian kernel

res: float, default = 8
    Resolution of the generated profiles in km/s. Needs to set convolved True to take effect
    
px_scale = float, default = None
    Sampling of the generated profiles in km/s
    
SN = ndarray of shape (nsim,), default = [None]
    Signal-to-Noise ratio of the continuum signal used to compute the gaussian noise to be added
    
sigma_sky = int, default = None
    RMS value of the sky signal. If not None the sky noise is computed as a random distribution centred on 0 
    and with dispersion sigma_sky

doublet: Boolean, default = False
    Enables creation of doublets (e.g. MgII, CIV etc...)

dbl_fratio: float, default = 0
    If doublet True, create a second line with oscillator strengh 
    f_line_2 = dbl_fratio * f_line_1


dbl_dvel: float, default = 0
    If doublet True, create a second line with center shifted in velocity by dbl_dvel [km/s]

seed: int, default = None
    Allow selection of seed
    
verbosity = int, defalut = 0
    Print (1) or not (0) info to terminal


Attributes
----------

flux = nsim synthetic spectra, with noise if so desired
flux_nonoise = nsim synthetic spectra, no noise
noise = associated noise values 
wave =  wavelength values for the nsim synthetic spectra
ew   =  E.W. (A) distribution of the profiles (intergates on doublet if present)
wave_native = original wave before resampling/convolution
flux_native = original flux before resampling/convolution


Authors
----------
A. Longobardi
"""

Examples
----------

import numpy as np
from nmfpm.nmf_profile_maker import NMFPM



- Example 1: Generate 10^3 CIV1548.204 absorbers (no doublet), at infinite S/N, 
         with a resolution of 8 km/s and a pixel sampling of 1 km/s
  


nsim_=1000
ion_=['CIV'] *nsim_
trans_wl_ = [1548.2040]*nsim_
ion_logN_ = np.random.uniform(12,15,nsim_)

nmf_pm_spc = NMFPM(nsim=nsim_,ion_family='moderate',ion_logN = ion_logN_, ion = ion_, trans_wl =trans_wl_)
simulated = nmf_pm_spc.simulation() # nsim simulated Optical Depth profiles (not convolved nor rebinned)
fluxes = nmf_pm_spc.flux  # nsim fluxes 

- Example 2: Generate 10^5 MgII absorbers with doublet, at S/N varying in range 2.5 <= S/N <= 15
         at a resolution of 60 km/s and a pixel sampling of 16 km/s.
         Anable to print NMF-PM additional logs.


nsim_=1000000
ion_=['MgII']*nsim_
trans_wl_ = [2796.3543]*nsim_
ion_logN_ = np.random.uniform(13,15.5,nsim_)
SN_= np.random.uniform(2.5,15,nsim_)
px_scale=16
res=60
doublet=True
dbl_fratio = [2.01]*nsim
dbl_dvel = [770]*nsim

nmf_pm_spc = NMFPM(nsim=nsim_,ion_family='low',ion_logN=ion_logN_, ion=ion_, trans_wl = trans_wl_,\
                   res=res,convolved=True,px_scale=px_scale,SN=SN_\,
                   doublet=doublet,dbl_fratio=dbl_fratio_,dbl_dvel=dbl_dvel_,verbosity=1)

simulated = nmf_pm_spc.simulation() # nsim simulated optical Depth profiles (not convolved nor rebinned)
fluxes = nmf_pm_spc.flux  # nsim fluxes (with noise, convolved and rebinned as required)