Source code for astroML.lumfunc

import numpy as np


def _sorted_interpolate(x, y, x_eval):
    """utility function for binned_Cminus"""
    # note that x should be sorted
    N = len(x)
    ind = x.searchsorted(x_eval)
    ind[ind == N] = N - 1

    y_eval = np.zeros(x_eval.shape)

    # find perfect matches
    match = (x[ind] == x_eval) | (x_eval > x[-1]) | (x_eval < x[0])
    y_eval[match] = y[ind[match]]

    ind = ind[~match]

    # take care of extrapolation
    ind[ind == 0] = 1

    x_lo = x[ind - 1]
    x_up = x[ind]

    y_lo = y[ind - 1]
    y_up = y[ind]

    # take care of places where x_lo = x_up

    y_eval[~match] = (y_lo + (x_eval[~match] - x_lo)
                      * (y_up - y_lo) / (x_up - x_lo))

    return y_eval


[docs]def Cminus(x, y, xmax, ymax): """Lynden-Bell's C-minus method Parameters ---------- x : array_like array of x values y : array_like array of y values xmax : array_like array of maximum x values for each y value ymax : array_like array of maximum y values for each x value Returns ------- Nx, Ny, cuml_x, cuml_y: ndarrays Nx and cuml_x are in the order of the sorted x array Ny and cuml_y are in the order of the sorted y array """ # make copies of input x, y, xmax, ymax = map(np.array, (x, y, xmax, ymax)) Nall = len(x) cuml_x = np.zeros(x.shape) cuml_y = np.zeros(y.shape) Nx = np.zeros(x.shape) Ny = np.zeros(y.shape) # first the y direction. i_sort = np.argsort(y) x = x[i_sort] y = y[i_sort] xmax = xmax[i_sort] ymax = ymax[i_sort] for j in range(1, Nall): Ny[j] = np.sum(x[:j] < xmax[j]) Ny[0] = np.inf cuml_y = np.cumprod(1. + 1. / Ny) Ny[0] = 0 # renormalize cuml_y *= Nall / cuml_y[-1] #now the x direction i_sort = np.argsort(x) x = x[i_sort] y = y[i_sort] xmax = xmax[i_sort] ymax = ymax[i_sort] for i in range(1, Nall): Nx[i] = np.sum(y[:i] < ymax[i]) Nx[0] = np.inf cuml_x = np.cumprod(1. + 1. / Nx) Nx[0] = 0 # renormalize cuml_x *= Nall / cuml_x[-1] return Nx, Ny, cuml_x, cuml_y
[docs]def binned_Cminus(x, y, xmax, ymax, xbins, ybins, normalize=False): """Compute the binned distributions using the Cminus method Parameters ---------- x : array_like array of x values y : array_like array of y values xmax : array_like array of maximum x values for each y value ymax : array_like array of maximum y values for each x value xbins : array_like array of bin edges for the x function: size=Nbins_x + 1 ybins : array_like array of bin edges for the y function: size=Nbins_y + 1 normalize : boolean if true, then returned distributions are normalized. Default is False. Returns ------- dist_x, dist_y : ndarrays distributions of size Nbins_x and Nbins_y """ Nx, Ny, cuml_x, cuml_y = Cminus(x, y, xmax, ymax) # simple linear interpolation using a binary search # interpolate the cumulative distributions x_sort = np.sort(x) y_sort = np.sort(y) Ix_edges = _sorted_interpolate(x_sort, cuml_x, xbins) Iy_edges = _sorted_interpolate(y_sort, cuml_y, ybins) if xbins[0] < x_sort[0]: Ix_edges[0] = cuml_x[0] if xbins[-1] > x_sort[-1]: Ix_edges[-1] = cuml_x[-1] if ybins[0] < y_sort[0]: Iy_edges[0] = cuml_y[0] if ybins[-1] > y_sort[-1]: Iy_edges[-1] = cuml_y[-1] x_dist = np.diff(Ix_edges) / np.diff(xbins) y_dist = np.diff(Iy_edges) / np.diff(ybins) if normalize: x_dist /= len(x) y_dist /= len(y) return x_dist, y_dist
[docs]def bootstrap_Cminus(x, y, xmax, ymax, xbins, ybins, Nbootstraps=10, normalize=False): """ Compute the binned distributions using the Cminus method, with bootstrapped estimates of the errors Parameters ---------- x : array_like array of x values y : array_like array of y values xmax : array_like array of maximum x values for each y value ymax : array_like array of maximum y values for each x value xbins : array_like array of bin edges for the x function: size=Nbins_x + 1 ybins : array_like array of bin edges for the y function: size=Nbins_y + 1 Nbootstraps : int number of bootstrap resamplings to perform normalize : boolean if true, then returned distributions are normalized. Default is False. Returns ------- dist_x, err_x, dist_y, err_y : ndarrays distributions of size Nbins_x and Nbins_y """ x, y, xmax, ymax = map(np.asarray, (x, y, xmax, ymax)) x_dist = np.zeros((Nbootstraps, len(xbins) - 1)) y_dist = np.zeros((Nbootstraps, len(ybins) - 1)) for i in range(Nbootstraps): ind = np.random.randint(0, len(x), len(x)) x_dist[i], y_dist[i] = binned_Cminus(x[ind], y[ind], xmax[ind], ymax[ind], xbins, ybins, normalize=normalize) return (x_dist.mean(0), x_dist.std(0, ddof=1), y_dist.mean(0), y_dist.std(0, ddof=1))