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model

photXclus.model

NFW_r(r, rx, integr_c)

Evaluate the Navarro-Frank-White (NFW) model at given physical radii

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
rx float

Scale radius of the model

 required
integr_c float

Integral of the model

 required

Returns:

Name Type Description
NFW_model array_like

Array of the Navarro-Frank-White model evaluated at the input physical radii
Source code in photXclus/model.py 
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@nb.njit()
def NFW_r(r, rx, integr_c):
    """
    Evaluate the Navarro-Frank-White (NFW) model at given physical radii

    Parameters
    ----------
    r : array_like
        Array of physical radii
    rx : float
        Scale radius of the model
    integr_c : float
        Integral of the model

    Returns
    -------
    NFW_model : array_like
        Array of the Navarro-Frank-White model evaluated at the input physical radii
    """
    rs = rx/3.
    return integr_c * psi_r_cut(r, rs)

clus_field_zr(z, r, ngal_c, muz_c, bin_zc, sigz_z, ngal_f, binz_ampl_f, bin_z, C_Omega, rx, deltac)

Evaluate the total model at given redshifts and physical radii

Parameters:

Name Type Description Default
z array_like

Array of redshifts

 required
r array_like

Array of physical radii

 required
ngal_c float

Number of galaxies in the cluster

 required
muz_c float

Mean of the cluster redshift distribution

 required
bin_zc array_like

Array of redshift bins

 required
sigz_z array_like

Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

 required
ngal_f float

Number density of galaxies in the field in degrees^-2

 required
binz_ampl_f array_like

Amplitude of the field model at each redshift bin

 required
bin_z array_like

Array of redshift bins

 required
C_Omega float

Area of the field of view in degrees^-2

 required
rx float

Scale radius of the cluster model

 required
deltac float

Delta parameter for the field model

 required

Returns:

Name Type Description
total_model array_like

Array of the total model evaluated at the input redshifts and physical radii
Source code in photXclus/model.py 
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@nb.njit()
def clus_field_zr(z, r, ngal_c, 
                  muz_c, bin_zc, sigz_z, 
                  ngal_f, 
                  binz_ampl_f, bin_z, C_Omega, rx, deltac):
    """
    Evaluate the total model at given redshifts and physical radii

    Parameters
    ----------
    z : array_like
        Array of redshifts
    r : array_like
        Array of physical radii
    ngal_c : float
        Number of galaxies in the cluster
    muz_c : float
        Mean of the cluster redshift distribution
    bin_zc : array_like
        Array of redshift bins
    sigz_z : array_like
        Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))
    ngal_f : float
        Number density of galaxies in the field in degrees^-2
    binz_ampl_f : array_like
        Amplitude of the field model at each redshift bin
    bin_z : array_like
        Array of redshift bins
    C_Omega : float
        Area of the field of view in degrees^-2
    rx : float
        Scale radius of the cluster model
    deltac : float
        Delta parameter for the field model

    Returns
    -------
    total_model : array_like
        Array of the total model evaluated at the input redshifts and physical radii
    """
    if deltac == 1:
        pclus = clus_z(z, muz_c, bin_zc, sigz_z) * clus_r(r, rx)
        pfield = field_z(z, binz_ampl_f, bin_z, sigz_z) * field_r(r, C_Omega)
        ptot = ngal_c * pclus + C_Omega * ngal_f * pfield
    else:
        pfield = field_z(z, binz_ampl_f, bin_z, sigz_z)
        ptot = C_Omega * ngal_f * pfield
    return ptot

clus_r(r, rx, integr_c=1.0, model='Plummer')

Evaluate the cluster radial model at given physical radii

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
rx float

Scale radius of the cluster model

 required
integr_c float

Integral of the cluster model, used for the NFW model

 1.0
model str

Model to be used, either 'Plum' or 'NFW'

 'Plummer'

Returns:

Name Type Description
clus_model array_like

Array of the cluster model evaluated at the input physical radii
Source code in photXclus/model.py 
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@nb.njit()
def clus_r(r, rx, integr_c = 1., model='Plummer'):
    """
    Evaluate the cluster radial model at given physical radii

    Parameters
    ----------
    r : array_like
        Array of physical radii
    rx : float
        Scale radius of the cluster model
    integr_c : float, optional
        Integral of the cluster model, used for the NFW model
    model : str, optional
        Model to be used, either 'Plum' or 'NFW'

    Returns
    -------
    clus_model : array_like
        Array of the cluster model evaluated at the input physical radii
    """
    if model == 'Plummer':
        return plum_r(r, rx)
    elif model == 'NFW':
        return NFW_r(r, rx, integr_c)
    else:
        raise NotImplementedError(f"{model} radial model not implemented")

clus_z(z, muz_c, z_binc, sigz_z)

Evaluate the cluster redshift model at given redshifts

Parameters:

Name Type Description Default
z array_like

Array of redshifts

 required
muz_c float

Mean of the cluster redshift distribution

 required
z_binc array_like

Array of redshift bins

 required
sigz_z array_like

Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

 required

Returns:

Name Type Description
clus_model array_like

Array of the cluster model evaluated at the input redshifts
Source code in photXclus/model.py 
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@nb.njit()
def clus_z(z, muz_c, z_binc, sigz_z ):
    """
    Evaluate the cluster redshift model at given redshifts

    Parameters
    ----------
    z : array_like
        Array of redshifts
    muz_c : float
        Mean of the cluster redshift distribution
    z_binc : array_like
        Array of redshift bins
    sigz_z : array_like
        Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

    Returns
    -------
    clus_model : array_like
        Array of the cluster model evaluated at the input redshifts
    """
    sigz_c = np.interp(muz_c, z_binc, sigz_z)
    res =  (1./(sigz_c * np.sqrt(2 * np.pi))) * np.exp(-0.5*((z-muz_c)/sigz_c)**2)
    return res

clus_zr(z, r, muz_c, bin_zc, sigz_z, rx)

Evaluate the cluster model at given redshifts and physical radii

Parameters:

Name Type Description Default
z array_like

Array of redshifts

 required
r array_like

Array of physical radii

 required
muz_c float

Mean of the cluster redshift distribution

 required
bin_zc array_like

Array of redshift bins

 required
sigz_z array_like

Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

 required
rx float

Scale radius of the cluster model

 required

Returns:

Name Type Description
clus_model array_like

Array of the cluster model evaluated at the input redshifts and physical radii
Source code in photXclus/model.py 
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@nb.njit()
def clus_zr(z, r, muz_c, bin_zc, sigz_z, rx):
    """
    Evaluate the cluster model at given redshifts and physical radii

    Parameters
    ----------
    z : array_like
        Array of redshifts
    r : array_like
        Array of physical radii
    muz_c : float
        Mean of the cluster redshift distribution
    bin_zc : array_like
        Array of redshift bins
    sigz_z : array_like
        Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))
    rx : float
        Scale radius of the cluster model

    Returns
    -------
    clus_model : array_like
        Array of the cluster model evaluated at the input redshifts and physical radii
    """
    res = clus_z(z, muz_c, bin_zc, sigz_z) * clus_r(r, rx)
    return res

field_r(r, C_Omega)

Evaluate the field radial model at given physical radii

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
C_Omega float

Area of the field of view in degrees^-2

 required

Returns:

Name Type Description
field_model array_like

Array of the field model evaluated at the input physical radii
Source code in photXclus/model.py 
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@nb.njit()
def field_r(r, C_Omega):
    """
    Evaluate the field radial model at given physical radii

    Parameters
    ----------
    r : array_like
        Array of physical radii
    C_Omega : float
        Area of the field of view in degrees^-2

    Returns
    -------
    field_model : array_like
        Array of the field model evaluated at the input physical radii
    """
    return 2*np.pi*r / C_Omega

field_z(z, binz_ampl_f, bin_z, sigz_z)

Evaluate the field redshift model at given redshifts

Parameters:

Name Type Description Default
z array_like

Array of redshifts

 required
binz_ampl_f array_like

Amplitude of the field model at each redshift bin

 required
bin_z array_like

Array of redshift bins

 required
sigz_z array_like

Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

 required

Returns:

Name Type Description
field_model array_like

Array of the field model evaluated at the input redshifts
Source code in photXclus/model.py 
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@nb.njit()
def field_z(z, binz_ampl_f, bin_z, sigz_z):
    """
    Evaluate the field redshift model at given redshifts

    Parameters
    ----------
    z : array_like
        Array of redshifts
    binz_ampl_f : array_like
        Amplitude of the field model at each redshift bin
    bin_z : array_like
        Array of redshift bins
    sigz_z : array_like
        Array of standard deviation of the galaxy photometric redshift (sigma_zphot(z))

    Returns
    -------
    field_model : array_like
        Array of the field model evaluated at the input redshifts
    """
    iz = np.digitize(z,bin_z)-1
    return binz_ampl_f[iz]

plum_r(r, rx)

Evaluate the Plum model at given physical radii

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
rx float

Scale radius of the model

 required

Returns:

Name Type Description
plum_model array_like

Array of the Plum model evaluated at the input physical radii
Source code in photXclus/model.py 
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@nb.njit()
def plum_r(r, rx):
    """
    Evaluate the Plum model at given physical radii

    Parameters
    ----------
    r : array_like
        Array of physical radii
    rx : float
        Scale radius of the model

    Returns
    -------
    plum_model : array_like
        Array of the Plum model evaluated at the input physical radii
    """
    rs = rx/10.
    res =  ( 1 / np.sqrt(1 + (r/rs)**2) ) - (1 / np.sqrt(1 + (10)**2))
    return res

psi_r(r, rs)

Evaluate the dimensionless potential at given physical radii

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
rs float

Scale radius of the potential

 required

Returns:

Name Type Description
psi array_like

Array of the dimensionless potential evaluated at the input physical radii
Source code in photXclus/model.py 
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@nb.njit()
def psi_r(r, rs):    
    """
    Evaluate the dimensionless potential at given physical radii

    Parameters
    ----------
    r : array_like
        Array of physical radii
    rs : float
        Scale radius of the potential

    Returns
    -------
    psi : array_like
        Array of the dimensionless potential evaluated at the input physical radii
    """
    denom = r/rs * (1 + r/rs)**2
    return 1. / denom

psi_r_cut(r, rs)

Evaluate the dimensionless potential at given physical radii, cut off at a certain radius

Parameters:

Name Type Description Default
r array_like

Array of physical radii

 required
rs float

Scale radius of the potential

 required

Returns:

Name Type Description
psi array_like

Array of the dimensionless potential evaluated at the input physical radii, cut off at a certain radius
Source code in photXclus/model.py 
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@nb.njit()
def psi_r_cut(r, rs):    
    """
    Evaluate the dimensionless potential at given physical radii, cut off at a certain radius

    Parameters
    ----------
    r : array_like
        Array of physical radii
    rs : float
        Scale radius of the potential

    Returns
    -------
    psi : array_like
        Array of the dimensionless potential evaluated at the input physical radii, cut off at a certain radius
    """
    rcut = 0.01*3*rs
    sigma0 = psi_r(rcut, rs) / (2*np.pi*rcut)
    res = psi_r(r, rs)
    i = 0
    while r[i] < rcut:
        res[i] = 2*np.pi*r[i]*sigma0
        i += 1
    return res