Utils

Utils#

pyexshalos.utils.Compute_Correlation(k: ndarray, P: ndarray, direction: str = 'pk2xi', verbose: bool = False) → dict#

Compute the correlation function given the power spectrum or the power spectrum given the correlation function.

Parameters:

  • k (numpy.ndarray) – Wavenumbers of the power spectrum or the distance of the correlation function.

  • P (numpy.ndarray) – Power spectrum or the correlation function.

  • direction (str) – Direction to compute the fftlog (“pk2xi” or “xi2pk”). Fiducial value: “pk2xi”

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

Returns:

Dictionary with keys:

  • ”R” or “k”: Ndarray with k or r

  • ”Xi” or “Pk”: Ndarray with Xi(r) or P(k)

Return type:

dict

pyexshalos.utils.Compute_High_Order_Operators(grid: ndarray, order: int = 2, nl_order: int = 0, Galileons: bool = False, Renormalized: bool = False, Lc: float = 2.0, verbose: bool = False, nthreads: int = 1) → Dict[str, ndarray]#

Compute the higher order operators up to a given order.

Parameters:

  • grid (numpy.ndarray) – Lagrangian density grid.

  • order (int) – Order to be used to compute the local operators. Fiducial value: 2

  • nl_order (int) – Order to be used to compute the non-local operators. Fiducial value: 0

  • Galileons (bool) – Whether to use the Galileons operators. Fiducial value: False

  • Renormalized (bool) – Whether to use renormalized operators. Fiducial value: False

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

Returns:

Dictionary with keys:

  • ”delta2”: Ndarray with delta^2

  • ”K2”: Ndarray with K^2 or G_2

  • ”delta3”: Ndarray with delta^3

  • ”K3”: Ndarray with K^3 or G_3

  • ”deltaK2”: Ndarray with delta*K^2 or delta*G_2

  • ”laplacian”: Ndarray with Laplacian(delta)

Return type:

dict

pyexshalos.utils.Displace_LPT(grid: ndarray, Lc: float = 2.0, Om0: float = 0.31, z: float = 0.0, k_smooth: float = 10000.0, DO_2LPT: bool = False, OUT_VEL: bool = False, Input_k: bool = False, OUT_POS: bool = True, verbose: bool = False) → Dict[str, ndarray]#

Compute the displacement of particles using Lagrangian Perturbation Theory (LPT).

Parameters:

  • grid (numpy.ndarray) – Density grid where the halos will be found.

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • Om0 (float) – Value of the matter overdensity today. Fiducial value: 0.31

  • z (float) – Redshift of the density grid and final halo catalogue. Fiducial value: 0.0

  • k_smooth (float) – Scale used to smooth the displacements. Fiducial value: 10000.0

  • DO_2LPT (bool) – Whether to use the second-order LPT. Fiducial value: False

  • OUT_VEL (bool) – Whether to output the velocities of the particles. Fiducial value: False

  • Input_k (bool) – Whether the input density grid is in real space (or Fourier). Fiducial value: False

  • OUT_POS (bool) – Whether to output the positions or just the displacements. Fiducial value: True

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

Returns:

Dictionary with keys:

  • ”pos”: Ndarray with particle positions (displacements)

  • ”vel”: Ndarray with particle velocities (if OUT_VEL is True)

Return type:

dict

pyexshalos.utils.Find_Halos_from_Grid(grid: ndarray, k: ndarray, P: ndarray, Lc: float = 2.0, Om0: float = 0.31, z: float = 0.0, delta_c: float | None = None, Nmin: int = 10, a: float = 1.0, beta: float = 0.0, alpha: float = 0.0, OUT_FLAG: bool = False, verbose: bool = False) → Dict[str, ndarray]#

Generate a halo catalogue (in Lagrangian space) given an initial density grid.

Parameters:

  • grid (numpy.ndarray) – Density grid where the halos will be found.

  • k (numpy.ndarray) – Wavenumbers of the power spectrum.

  • P (numpy.ndarray) – Power spectrum.

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • Om0 (float) – Value of the matter overdensity today. Fiducial value: 0.31

  • z (float) – Redshift of the density grid and final halo catalogue. Fiducial value: 0.0

  • delta_c (Optional[float]) – Critical density of the halo formation linearly extrapolated to z. Fiducial value: None

  • Nmin (int) – Minimum number of particles in each halo. Fiducial value: 10

  • a (float) – Parameter a of the ellipsoidal barrier. Fiducial value: 1.0

  • beta (float) – Parameter beta of the ellipsoidal barrier. Fiducial value: 0.0

  • alpha (float) – Parameter alpha of the ellipsoidal barrier. Fiducial value: 0.0

  • OUT_FLAG (bool) – Whether to output flag with the information if a cell belongs to a halo. Fiducial value: False

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

Returns:

Dictionay with keys:

  • ”posh”: Ndarray with halo positions

  • ”Mh”: Ndarray with halo masses

  • ”flag”: Ndarray with flags for each cell

Return type:

dict

pyexshalos.utils.Fit_Barrier(k: ndarray, P: ndarray, M: ndarray, dndlnM: ndarray, dn_err: ndarray | None = None, grid: ndarray | None = None, R_max: float = 100000.0, Mmin: float | None = None, Mmax: float | None = None, Nm: int = 25, nd: int = 256, Lc: float = 2.0, Om0: float = 0.31, z: float = 0.0, delta_c: float | None = None, Nmin: int = 10, seed: int = 12345, x0: ndarray | None = None, verbose: bool = False, nthreads: int = 1, Max_iter: int = 100, tol: float | None = None) → ndarray#

Fit the parameters of the barrier given a mass function.

Parameters:

  • k (numpy.ndarray) – Wavenumbers of the power spectrum

  • P (numpy.ndarray) – Power spectrum

  • M (numpy.ndarray) – Mass of the mass function to be approximated.

  • dndlnM (numpy.ndarray) – Differential mass function to be approximated.

  • dn_err (Optional[numpy.ndarray]) – Errors on the mass function. Fiducial value: None

  • grid (Optional[numpy.ndarray]) – Pre-computed Gaussian density grid. Fiducial value: None

  • R_max (float) – Maximum size used to compute the correlation function in Mpc/h. Fiducial value: 100000.0

  • Mmin (Optional[float]) – Minimum mass used to construct the mass bins. Fiducial value: None

  • Mmax (Optional[float]) – Maximum mass used to construct the mass bins. Fiducial value: None

  • Nm (int) – Number of mass bins. Fiducial value: 25

  • nd (int) – Number of cells in each direction. Fiducial value: 256

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • Om0 (float) – Value of the matter overdensity today. Fiducial value: 0.31

  • z (float) – Redshift of the density grid and final halo catalogue. Fiducial value: 0.0

  • delta_c (Optional[float]) – Critical density, for the halo formation, linearly extrapolated to z. Fiducial value: None

  • Nmin (int) – Minimum number of particles in each halo. Fiducial value: 10

  • seed (int) – Seed used to generate the random numbers. Fiducial value: 12345

  • x0 (Optional[numpy.ndarray]) – Initial guess for the parameters of the barrier. Fiducial value: None

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

  • Max_iter (int) – Maximum number of iterations used in the minimization. Fiducial value: 100

  • tol (Optional[float]) – Tolerance for the minimization. Fiducial value: None

Returns:

Best fit of the values of the parameters of the ellipsoidal barrier.

Return type:

numpy.ndarray

pyexshalos.utils.Fit_HOD(k: ndarray, P: ndarray, nbar: float | None = None, posh: ndarray | None = None, Mh: ndarray | None = None, velh: ndarray | None = None, Ch: ndarray | None = None, nd: int = 256, ndx: int | None = None, ndy: int | None = None, ndz: int | None = None, Lc: float = 2.0, Om0: float = 0.31, z: float = 0.0, x0: ndarray | None = None, sigma: float = 0.5, Deltah: float = -1.0, seed: int = 12345, USE_VEL: bool = False, l_max: int = 0, direction: str = 'z', window: str | int = 'cic', R: float = 4.0, R_times: float = 5.0, interlacing: bool = True, Nk: int = 25, k_min: float | None = None, k_max: float | None = None, verbose: bool = False, nthreads: int = 1, Max_inter: int = 100, tol: float | None = None) → ndarray#

Fit the parameters of the Halo Occupation Distribution (HOD).

Parameters:

  • k (numpy.ndarray) – Wavenumbers of the galaxy power spectrum.

  • P (numpy.ndarray) – Galaxy power spectrum.

  • nbar (Optional[float]) – Mean number density of galaxies. Fiducial value: None

  • posh (Optional[numpy.ndarray]) – Positions of the halos. Fiducial value: None

  • Mh (Optional[numpy.ndarray]) – Mass of the halos. Fiducial value: None

  • velh (Optional[numpy.ndarray]) – Velocities of the halos. Fiducial value: None

  • Ch (Optional[numpy.ndarray]) – Concentration of the halos. Fiducial value: None

  • nd (int) – Number of cells in each direction. Fiducial value: 256

  • ndx (Optional[int]) – Number of cells in the x direction. Fiducial value: None

  • ndy (Optional[int]) – Number of cells in the y direction. Fiducial value: None

  • ndz (Optional[int]) – Number of cells in the z direction. Fiducial value: None

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • Om0 (float) – Value of the matter overdensity today. Fiducial value: 0.31

  • z (float) – Redshift of the density grid and final halo catalogue. Fiducial value: 0.0

  • x0 (Optional[numpy.ndarray]) – Initial guess for the best fit parameters of the HOD. Fiducial value: None

  • sigma (float) – Parameter of the exclusion term of the halo density profile. Fiducial value: 0.5

  • Deltah (Optional[float]) – Overdensity of the halos. Fiducial value: None

  • seed (int) – Seed used to generate the density field. Fiducial value: 12345

  • USE_VEL (bool) – Whether to use the power spectrum in redshift space. Fiducial value: False

  • l_max (int) – Maximum multipole to consider. Fiducial value: 0

  • direction (str) – Direction for redshift space distortions. Fiducial value: “z”

  • window (Union[str, int]) – Type of window function to use. Fiducial value: “cic”

  • R (float) – Smoothing radius. Fiducial value: 4.0

  • R_times (float) – Smoothing factor for the radius. Fiducial value: 5.0

  • interlacing (bool) – Whether to use interlacing to reduce aliasing effects. Fiducial value: True

  • Nk (int) – Number of bins in k for the power spectrum. Fiducial value: 25

  • k_min (Optional[float]) – Minimum wavenumber for the power spectrum. Fiducial value: None

  • k_max (Optional[float]) – Maximum wavenumber for the power spectrum. Fiducial value: None

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

  • Max_inter (int) – Maximum number of iterations used in the minimization. Fiducial value: 100

  • tol (Optional[float]) – Tolerance for the minimization. Fiducial value: None

Returns:

The best fit parameters of the HOD.

Return type:

numpy.ndarray

pyexshalos.utils.Generate_Density_Grid(k: ndarray, P: ndarray, R_max: float = 100000.0, nd: int = 256, ndx: int | None = None, ndy: int | None = None, ndz: int | None = None, Lc: float = 2.0, outk: bool = False, seed: int = 12345, fixed: bool = False, phase: float = 0.0, k_smooth: float = 100000.0, verbose: bool = False, nthreads: int = 1) → ndarray#

Compute the Gaussian density grid given the power spectrum.

Parameters:

  • k (numpy.ndarray) – Wavenumbers of the power spectrum.

  • P (numpy.ndarray) – Power spectrum.

  • R_max (float) – Maximum size used to compute the correlation function in Mpc/h. Fiducial value: 100000.0

  • nd (int) – Number of cells per dimension. Fiducial value: 256

  • ndx (Optional[int]) – Number of cells in the x direction. Fiducial value: None

  • ndy (Optional[int]) – Number of cells in the y direction. Fiducial value: None

  • ndz (Optional[int]) – Number of cells in the z direction. Fiducial value: None

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • outk (bool) – Whether to return the density field in Fourier space. Fiducial value: False

  • seed (int) – Seed used to generate the random numbers. Fiducial value: 12345

  • fixed (bool) – Whether to use fixed amplitudes. Fiducial value: False

  • phase (float) – Phase of the density field. Fiducial value: 0.0

  • k_smooth (float) – Smoothing scale in k-space. Fiducial value: 100000.0

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

Returns:

The 3D density grid in real space (and in Fourier space if outk is True).

Return type:

numpy.ndarray

pyexshalos.utils.Smooth_Fields(grid: ndarray, Lc: float = 2.0, k_smooth: float = 10000.0, Input_k: bool = False, Nfields: int = 1, verbose: bool = False, nthreads: int = 1) → ndarray#

Smooth a given field (or fields) on a given scale.

Parameters:

  • grid (numpy.ndarray) – Lagrangian density grid.

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • k_smooth (float) – Scale used to smooth the fields. Fiducial value: 10000.0

  • Input_k (bool) – Whether the density grid is in real or Fourier space. Fiducial value: False

  • Nfields (int) – Number of fields. Fiducial value: 1

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

Returns:

A dictionary with all fields (excluding the linear) up to the given order or a single smoothed field.

Return type:

np.ndarray

pyexshalos.utils.Smooth_and_Reduce_Fields(grid: ndarray, Lc: float = 2.0, k_smooth: float = 10000.0, Input_k: bool = False, Nfields: int = 1, verbose: bool = False, nthreads: int = 1) → ndarray#

Smooth a given field (or fields) on a given scale and reduce it.

Parameters:

  • grid (numpy.ndarray) – Lagrangian density grid.

  • Lc (float) – Size of each cell in Mpc/h. Fiducial value: 2.0

  • k_smooth (float) – Scale used to smooth the fields. Fiducial value: 10000.0

  • Input_k (bool) – Whether the density grid is in real or Fourier space. Fiducial value: False

  • Nfields (int) – Number of fields. Fiducial value: 1

  • verbose (bool) – Whether to output information in the C code. Fiducial value: False

  • nthreads (int) – Number of threads used by OpenMP. Fiducial value: 1

Returns:

Smoothed and reduced fields.

Return type:

numpy.ndarray

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