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“cell_type”: “markdown”, “id”: “4e960e91”, “metadata”: {}, “source”: [
“# Custom distributions and populationsn”, “n”, “Custom populations can be created either by piecing together existing populations (spatial and luminosity populations) or building them from scratch with distributions.n”, “n”, “popsynth comes loaded with many combinations of typical population distributions. However, we demonstrate here how to create your own.”]
}, {
“cell_type”: “markdown”, “id”: “f194e86c”, “metadata”: {}, “source”: [
“## Creating distributionsn”, “n”, “The population samplers rely on distributions. Each population has an internal spatial and luminosity distribution. For example, lets look at a simple spatial distribution:n”]
}, {
“cell_type”: “code”, “execution_count”: 1, “id”: “cb1a3c83”, “metadata”: {
- “execution”: {
- “iopub.execute_input”: “2022-02-09T16:32:32.946777Z”, “iopub.status.busy”: “2022-02-09T16:32:32.946123Z”, “iopub.status.idle”: “2022-02-09T16:32:36.700551Z”, “shell.execute_reply”: “2022-02-09T16:32:36.699391Z”
}
}, “outputs”: [], “source”: [
“%matplotlib inlinen”, “n”, “import numpy as npn”, “import matplotlib.pyplot as pltn”, “from jupyterthemes import jtplotn”, “n”, “jtplot.style(context=”notebook”, fscale=1, grid=False)n”, “purple = “#B833FF”n”, “yellow = “#F6EF5B”n”, “n”, “n”, “import popsynthn”, “n”, “popsynth.update_logging_level(“INFO”)n”, “import warningsn”, “n”, “warnings.simplefilter(“ignore”)”]
}, {
“cell_type”: “code”, “execution_count”: 2, “id”: “e908ebe6”, “metadata”: {
- “execution”: {
- “iopub.execute_input”: “2022-02-09T16:32:36.706958Z”, “iopub.status.busy”: “2022-02-09T16:32:36.706407Z”, “iopub.status.idle”: “2022-02-09T16:32:36.709785Z”, “shell.execute_reply”: “2022-02-09T16:32:36.709332Z”
}
}, “outputs”: [], “source”: [
“from popsynth.distribution import SpatialDistributionn”, “n”, “n”, “class MySphericalDistribution(SpatialDistribution):n”, “n”, ” # we need this property to register the classn”, “n”, ” _distribution_name = “MySphericalDistribution”n”, “n”, ” def __init__(n”, ” self,n”, ” seed=1234,n”, ” form=None,n”, ” ):n”, “n”, ” # the latex formula for the ditributionn”, ” form = r”4 \pi r2”n”, “n”, ” # we do not need a “truth” dict here becausen”, ” # there are no parametersn”, “n”, ” super(MySphericalDistribution, self).__init__(n”, ” seed=seed,n”, ” name=”sphere”,n”, ” form=form,n”, ” )n”, “n”, ” def differential_volume(self, r):n”, “n”, ” # the differential volume of a spheren”, ” return 4 * np.pi * r * rn”, “n”, ” def transform(self, L, r):n”, “n”, ” # luminosity to fluxn”, ” return L / (4.0 * np.pi * r * r)n”, “n”, ” def dNdV(self, r):n”, “n”, ” # define some crazy change in the number/volume for funn”, “n”, ” return 10.0 / (r + 1) ** 2”]
}, {
“cell_type”: “markdown”, “id”: “0c8d532f”, “metadata”: {}, “source”: [
“We simply define the differential volume and how luminosity is transformed to flux in the metric. Here, we have a simple sphere out to some r_max. We can of course subclass this object and add a normalization.n”, “n”, “n”, “Now we define a luminosity distribution.”]
}, {
“cell_type”: “code”, “execution_count”: 3, “id”: “4f244eea”, “metadata”: {
- “execution”: {
- “iopub.execute_input”: “2022-02-09T16:32:36.716469Z”, “iopub.status.busy”: “2022-02-09T16:32:36.715966Z”, “iopub.status.idle”: “2022-02-09T16:32:36.719283Z”, “shell.execute_reply”: “2022-02-09T16:32:36.718758Z”
}, “lines_to_next_cell”: 2
}, “outputs”: [], “source”: [
“from popsynth.distribution import LuminosityDistribution, DistributionParametern”, “n”, “n”, “class MyParetoDistribution(LuminosityDistribution):n”, ” _distribution_name = “MyParetoDistribution”n”, “n”, ” Lmin = DistributionParameter(default=1, vmin=0)n”, ” alpha = DistributionParameter(default=2)n”, “n”, ” def __init__(self, seed=1234, name=”pareto”):n”, “n”, ” # the latex formula for the ditributionn”, ” lf_form = r”\frac{\alpha L_{\rm min}^{\alpha}}{L^{\alpha+1}}”n”, “n”, ” super(MyParetoDistribution, self).__init__(n”, ” seed=seed,n”, ” name=”pareto”,n”, ” form=lf_form,n”, ” )n”, “n”, ” def phi(self, L):n”, “n”, ” # the actual function, only for plottingn”, “n”, ” out = np.zeros_like(L)n”, “n”, ” idx = L >= self.Lminn”, “n”, ” out[idx] = self.alpha * self.Lmin ** self.alpha / L[idx] ** (self.alpha + 1)n”, “n”, ” return outn”, “n”, ” def draw_luminosity(self, size=1):n”, ” # how to sample the latent parametersn”, ” return (np.random.pareto(self.alpha, size) + 1) * self.Lmin”]
}, {
“cell_type”: “markdown”, “id”: “ab4f0cef”, “metadata”: {}, “source”: [
“<div class=”alert alert-info”>n”, “n”, “Note: If you want to create a cosmological distribution, inherit from from ComologicalDistribution class!n”, “n”, “</div>n”, “n”, “## Creating a population synthesizern”, “n”, “Now that we have defined our distributions, we can create a population synthesizer that encapsulated them”]
}, {
“cell_type”: “code”, “execution_count”: 4, “id”: “ee47db3c”, “metadata”: {
- “execution”: {
- “iopub.execute_input”: “2022-02-09T16:32:36.725785Z”, “iopub.status.busy”: “2022-02-09T16:32:36.724480Z”, “iopub.status.idle”: “2022-02-09T16:32:36.726369Z”, “shell.execute_reply”: “2022-02-09T16:32:36.726788Z”
}
}, “outputs”: [], “source”: [
“from popsynth.population_synth import PopulationSynthn”, “n”, “n”, “class MyPopulation(PopulationSynth):n”, ” def __init__(self, Lmin, alpha, r_max=5, seed=1234):n”, “n”, ” # instantiate the distributionsn”, ” luminosity_distribution = MyParetoDistribution(seed=seed)n”, “n”, ” luminosity_distribution.alpha = alphan”, ” luminosity_distribution.Lmin = Lminn”, “n”, ” spatial_distribution = MySphericalDistribution(seed=seed)n”, ” spatial_distribution.r_max = r_maxn”, “n”, ” # pass to the super classn”, ” super(MyPopulation, self).__init__(n”, ” spatial_distribution=spatial_distribution,n”, ” luminosity_distribution=luminosity_distribution,n”, ” seed=seed,n”, ” )”]
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“u001b[32mu001b[1m INFO u001b[0m| u001b[32mu001b[1m The volume integral is 768.219980 u001b[0mn”]
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“u001b[32mu001b[1m INFO u001b[0m| u001b[32mu001b[1m Expecting 741 total objects u001b[0mn”]
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“u001b[32mu001b[1m INFO u001b[0m| u001b[32mu001b[1m applying selection to fluxes u001b[0mn”]
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“name”: “stdout”, “output_type”: “stream”, “text”: [
“u001b[32mu001b[1m INFO u001b[0m| u001b[32mu001b[1m Detected 258 distances u001b[0mn”]
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“name”: “stdout”, “output_type”: “stream”, “text”: [
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“my_pop_gen = MyPopulation(Lmin=1, alpha=1, r_max=10)n”, “n”, “flux_selector = popsynth.HardFluxSelection()n”, “flux_selector.boundary = 1e-2n”, “n”, “my_pop_gen.set_flux_selection(flux_selector)n”, “n”, “population = my_pop_gen.draw_survey()”]
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