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@aphearin
Created February 15, 2023 19:53
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Intro to JAX based on the Diffmah model of dark matter halo mass assembly history
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{
"cells": [
{
"cell_type": "markdown",
"id": "93acb87d",
"metadata": {},
"source": [
"# Differentiable modeling dark matter halo assembly history\n",
"\n",
"This notebook is intended to provide a few worked examples of vectorization and autodiff with JAX using the [Diffmah](https://astro.theoj.org/article/26991-a-differentiable-model-of-the-assembly-of-individual-and-populations-of-dark-matter-halos) model of dark matter halo growth. This the basic outline of what we will do in this notebook:\n",
"\n",
"\n",
"### Outline\n",
"\n",
"1. Build a simple power-law type model of $M_{\\rm halo}(t),$ the mass growth of a dark matter halo over time\n",
"2. Use `jax.grad` to compute $dM_{\\rm halo}/dt$ from $M_{\\rm halo}(t)$\n",
"3. Use `jax.vmap` to vectorize the calculation of the half-mass formation time, $t_{50\\%},$ for a population of halos at a time\n",
"4. Implement our own gradient descent loop to derive best-fitting parameters approximating $M_{\\rm halo}(t)$ of a simulated halo."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "df5e0487",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"from jax import numpy as jnp\n",
"from jax import jit as jjit\n",
"\n",
"mred = u'#d62728' \n",
"mgreen = u'#2ca02c'\n",
"mblue = u'#1f77b4' "
]
},
{
"cell_type": "markdown",
"id": "868ee138",
"metadata": {},
"source": [
"This simple sigmoid is a very useful function for building many kinds of models. We'll use it in our model of $M_{\\rm halo}(t),$ so let's take a look at how the basic underlying parameters of the sigmoid change the behavior of the function."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "bc1bda72",
"metadata": {},
"outputs": [],
"source": [
"@jjit\n",
"def _sigmoid(x, x0, k, ymin, ymax):\n",
" height_diff = ymax - ymin\n",
" return ymin + height_diff / (1.0 + jnp.exp(-k * (x - x0)))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "9c414a92",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"xlim = ax.set_xlim(-10, 10)\n",
"ylim = ax.set_ylim(-3, 3)\n",
"\n",
"xarr = np.linspace(*xlim, 100)\n",
"\n",
"# Plot a few example sigmoids\n",
"__=ax.plot(xarr, _sigmoid(xarr, 0, 1, -2, 0.5))\n",
"__=ax.plot(xarr, _sigmoid(xarr, 0, 1, -2, 2.5))\n",
"__=ax.plot(xarr, _sigmoid(xarr, -3, 1, -2, 1))\n",
"\n",
"# make black dotted lines\n",
"__=ax.plot(xarr, np.zeros_like(xarr), ':', color='k')\n",
"__=ax.plot(np.zeros_like(xarr), np.linspace(*ylim, xarr.size), ':', color='k')"
]
},
{
"cell_type": "markdown",
"id": "3b5c96df",
"metadata": {},
"source": [
"The asymptotic behavior at low- and high-$x$ is controlled by $y_{\\rm lo}$ and $y_{\\rm hi}$. The midpoint between these two asymptotic values is set by the $x_0$ parameter, and $k$ controls how quickly the sigmoid varies between the low- and high-$x$ limiting behavior."
]
},
{
"cell_type": "markdown",
"id": "a8dcba8e",
"metadata": {},
"source": [
"### Diffmah model of $M_{\\rm halo}(t)$\n",
"\n",
"In the next cell, we'll implement the Diffmah model of halo mass assembly history, $M_{\\rm halo}(t) = M_0\\cdot (t/t_0)^{\\alpha(t)},$ where the $t_0$ and $M_0$ are the present-day time and mass, and the power-law index $\\alpha(t)$ smoothly rolls in time according to a sigmoid function."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4db891e1",
"metadata": {},
"outputs": [],
"source": [
"MAH_K = 3.5\n",
"\n",
"@jjit\n",
"def _power_law_index_vs_logt(logt, logtc, k, early, late):\n",
" rolling_index = _sigmoid(logt, logtc, k, early, late)\n",
" return rolling_index\n",
"\n",
"@jjit\n",
"def _rolling_plaw_vs_logt(logt, logt0, logmp, logtc, k, early, late):\n",
" \"\"\"Kernel of the rolling power-law between halo mass and time.\"\"\"\n",
" rolling_index = _power_law_index_vs_logt(logt, logtc, k, early, late)\n",
" log_mah = rolling_index * (logt - logt0) + logmp\n",
" return log_mah"
]
},
{
"cell_type": "markdown",
"id": "063707fd",
"metadata": {},
"source": [
"Now let's use this model to look at mass assembly histories for group-mass halos $M_{0}=10^{13}M_{\\odot}$, choosing typical parameter values for halos with early, median, and late formation times. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d518d048",
"metadata": {},
"outputs": [],
"source": [
"lgm0 = 13.0\n",
"T0 = 13.8\n",
"tarr = np.linspace(0.1, T0, 100)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "117f9daa",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-3, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"\n",
"early_diffmah = -0.1, MAH_K, 2.75, 0.2\n",
"log_mah_early = _rolling_plaw_vs_logt(np.log10(tarr), np.log10(T0), lgm0, *early_diffmah)\n",
"__=ax.plot(tarr, log_mah_early, color=mred, label=r'${\\rm early}$-${\\rm forming\\ halo}$')\n",
"\n",
"med_diffmah = 0.25, MAH_K, 2.25, 1.0\n",
"log_mah_med = _rolling_plaw_vs_logt(np.log10(tarr), np.log10(T0), lgm0, *med_diffmah)\n",
"__=ax.plot(tarr, log_mah_med, color='k', label=r'${\\rm intermediate\\ formation\\ time}$')\n",
"\n",
"late_diffmah = 1.5, MAH_K, 2.0, 1.9\n",
"log_mah_late = _rolling_plaw_vs_logt(np.log10(tarr), np.log10(T0), lgm0, *late_diffmah)\n",
"__=ax.plot(tarr, log_mah_late, color=mblue, label=r'${\\rm late}$-${\\rm forming\\ halo}$')\n",
"\n",
"leg = ax.legend()\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo}\\ {\\rm [M_{\\odot}]}$')"
]
},
{
"cell_type": "markdown",
"id": "2254001f",
"metadata": {},
"source": [
"## Using `jax.grad` to calculate $dM_{\\rm halo}/dt$ \n",
"\n",
"The Diffmah model above directly parametrizes $M_{\\rm halo}(t),$ and so we can use JAX to compute the time derivative of our model, which gives the history of halo mass accretion rate.\n",
"\n",
"In the cells below, we'll use `jax.grad` to compute $dM_{\\rm halo}/dt$ in two different ways: one in which we differentiate the function above that models $\\log_{10}M_{\\rm halo}(t),$ and a second one in which we differentiate $M_{\\rm halo}(t).$ The only difference is that in the first case, we need to do a little extra calculus to account for an additional Jacobi factor of the derivative. The plot shows that these two methods agree, which just demonstrates that autodiff works as expected: when computing gradients, you can choose whether you want to propagate individual pieces of a derivative for yourself, or leave that up to autodiff."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "2414ed38",
"metadata": {},
"outputs": [],
"source": [
"from jax import grad\n",
"from jax import vmap\n",
"\n",
"\n",
"### First method in which we differentiate log10(Mh(t))\n",
"\n",
"@jjit\n",
"def _rolling_plaw_vs_t(t_gyr, logt0, logmp, logtc, k, early, late):\n",
" \"\"\"Identical to _rolling_plaw_vs_logt but written as a function of linear time\"\"\"\n",
" logt = jnp.log10(t_gyr)\n",
" return _rolling_plaw_vs_logt(logt, logt0, logmp, logtc, k, early, late)\n",
"\n",
"_d_log_mh_dt_scalar = jjit(grad(_rolling_plaw_vs_t, argnums=0))\n",
"_d_log_mh_dt = jjit(vmap(_d_log_mh_dt_scalar, in_axes=(0, *[None] * 6)))\n",
"\n",
"\n",
"@jjit\n",
"def _get_dmhdt(t_gyr, logt0, logmp, logtc, k, early, late):\n",
" \"\"\"Calculate dMh/dt in units of Msun/yr\n",
" \n",
" We use jax.grad to calculate d/dt(log10(Mh(t))) = log10(e)*(dMh/dt)/Mh\n",
" To get dMh/dt from the quantity returned by jax.grad,\n",
" we multiply by compensating factor Mh(t)/log10(e), and convert Gyr-->yr.\n",
"\n",
" \"\"\"\n",
" d_log_mh_dt = _d_log_mh_dt(t_gyr, logt0, logmp, logtc, k, early, late)\n",
" log_mah = _rolling_plaw_vs_t(t_gyr, logt0, logmp, logtc, k, early, late)\n",
" dmhdt = d_log_mh_dt * (10.0 ** (log_mah - 9.0)) / jnp.log10(jnp.e)\n",
" return dmhdt\n",
"\n",
"\n",
"### Alternate method in which we differentiate Mh(t)\n",
"\n",
"@jjit\n",
"def _mhalo_vs_t_kern(t_gyr, logt0, logmp, logtc, k, early, late):\n",
" \"\"\"Identical to _rolling_plaw_vs_logt\n",
" but written as a function of linear time and returns Mh(t) instead of log10(Mh)\"\"\"\n",
" logt = jnp.log10(t_gyr)\n",
" return 10**_rolling_plaw_vs_logt(logt, logt0, logmp, logtc, k, early, late)\n",
"\n",
"\n",
"_d_mh_dt_scalar = jjit(grad(_mhalo_vs_t_kern, argnums=0))\n",
"_d_mh_dt_vmap = jjit(vmap(_d_mh_dt_scalar, in_axes=(0, *[None] * 6)))\n",
"\n",
"\n",
"@jjit\n",
"def _get_dmhdt_alt(t_gyr, logt0, logmp, logtc, k, early, late):\n",
" \"\"\"Calculate dMh/dt in units of Msun/yr\n",
" \n",
" We use jax.grad to calculate d/dt(Mh(t))\n",
" To get dMh/dt from the quantity returned by jax.grad,\n",
" we only need to convert Gyr-->yr.\n",
"\n",
" \"\"\"\n",
" dmhdt_gyr = _d_mh_dt_vmap(t_gyr, logt0, logmp, logtc, k, early, late)\n",
" dmhdt = dmhdt_gyr/1e9\n",
" return dmhdt\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "58440924",
"metadata": {},
"outputs": [],
"source": [
"dmhdt_early = _get_dmhdt(tarr, np.log10(T0), lgm0, *early_diffmah)\n",
"dmhdt_med = _get_dmhdt(tarr, np.log10(T0), lgm0, *med_diffmah)\n",
"dmhdt_late = _get_dmhdt(tarr, np.log10(T0), lgm0, *late_diffmah)\n",
"\n",
"alt_dmhdt_early = _get_dmhdt_alt(tarr, np.log10(T0), lgm0, *early_diffmah)\n",
"alt_dmhdt_med = _get_dmhdt_alt(tarr, np.log10(T0), lgm0, *med_diffmah)\n",
"alt_dmhdt_late = _get_dmhdt_alt(tarr, np.log10(T0), lgm0, *late_diffmah)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "fde8b12f",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"yscale = ax.set_yscale('log')\n",
"ylim = ax.set_ylim(10.1, 2e4)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"__=ax.plot(tarr, dmhdt_early, color=mred, label=r'${\\rm early}$-${\\rm forming\\ halo}$')\n",
"__=ax.plot(tarr, dmhdt_med, color='k', label=r'${\\rm intermediate\\ formation\\ time}$')\n",
"__=ax.plot(tarr, dmhdt_late, color=mblue, label=r'${\\rm late}$-${\\rm forming\\ halo}$')\n",
"\n",
"# Verify that grad computed through alternate means gives identical results\n",
"# __=ax.plot(tarr, alt_dmhdt_early, ':', color=mgreen)\n",
"# __=ax.plot(tarr, alt_dmhdt_med, ':', color=mgreen)\n",
"# __=ax.plot(tarr, alt_dmhdt_late, ':', color=mgreen)\n",
"\n",
"leg = ax.legend()\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$dM_{\\rm halo}/dt\\ {\\rm [M_{\\odot}/yr]}$')"
]
},
{
"cell_type": "markdown",
"id": "84d3d857",
"metadata": {},
"source": [
"## Vectorized calculations on a population of halos\n",
"\n",
"In the previous cells, we calculated the MAH of an individual halo at a time. In our first application of `jax.vmap` to this problem, let's start from a _population_ of Diffmah parameters, and all-at-once calculate the MAHs for the population. After doing this, we'll move on to see how to vectorize other calculations based on the MAH populations."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "19c8f6f7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10000, 100)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_a = (None, None, None, 0, None, 0, 0)\n",
"_rolling_plaw_vs_logt_halopop = jjit(vmap(_rolling_plaw_vs_logt, in_axes=_a))\n",
"\n",
"n_pop = 10_000\n",
"logtc_arr = np.random.uniform(-0.25, 0.5, n_pop)\n",
"early_arr = np.random.uniform(2.0, 3.0, n_pop)\n",
"late_arr = np.random.uniform(0.1, 1.5, n_pop)\n",
"\n",
"log_mahs = _rolling_plaw_vs_logt_halopop(\n",
" np.log10(tarr), np.log10(T0), lgm0, logtc_arr, MAH_K, early_arr, late_arr)\n",
"log_mahs.shape"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cf446296",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-3, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"for ih in range(5):\n",
" __=ax.plot(tarr, log_mahs[ih, :])\n",
"\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo}\\ {\\rm [M_{\\odot}]}$')"
]
},
{
"cell_type": "markdown",
"id": "bb0f3cb1",
"metadata": {},
"source": [
"## Using DiffmahPop to generate a representative population\n",
"\n",
"Now rather than using randomly selected parameters, instead let's use the DiffmahPop to generate a population of Diffmah parameters and assembly histories. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1d5035de",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('dmhdt', 'log_mah', 'early_index', 'late_index', 'lgtc', 'mah_type')\n"
]
}
],
"source": [
"from diffmah.monte_carlo_halo_population import mc_halo_population\n",
"\n",
"# Generate assembly histories of a sample of halos of the same present-day mass\n",
"halopop = mc_halo_population(tarr, T0, lgm0+np.zeros(10_000))\n",
"\n",
"# halopop is a namedtuple with the following fields\n",
"print(halopop._fields)"
]
},
{
"cell_type": "markdown",
"id": "410c7b0b",
"metadata": {},
"source": [
"First let's just visually inspect a few different halos in the generated population."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3f9352f2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x720 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax0, ax1) = plt.subplots(2, 1, figsize=(6, 10), sharex=True)\n",
"fig.subplots_adjust(hspace=0) # smash left and right plots\n",
"\n",
"ylim = ax0.set_ylim(lgm0-2.9, lgm0+0.5)\n",
"ylim = ax1.set_ylim(40, 3_000)\n",
"xlim = ax0.set_xlim(0.1, T0)\n",
"yscale = ax1.set_yscale('log')\n",
"\n",
"for ihalo in range(4):\n",
" __=ax0.plot(tarr, halopop.log_mah[ihalo, :], lw=1, label='halo {}'.format(ihalo))\n",
" __=ax1.plot(tarr, halopop.dmhdt[ihalo, :], lw=1, label='halo {}'.format(ihalo))\n",
" \n",
"xlabel = ax1.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax0.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"ylabel = ax1.set_ylabel(r'$dM_{\\rm halo}/dt\\ [{\\rm M_{\\odot}/yr]}$')\n",
"leg = ax0.legend()\n",
"leg = ax1.legend()"
]
},
{
"cell_type": "markdown",
"id": "80a3c150",
"metadata": {},
"source": [
"### Calculating halo formation time $t_{\\rm form}$\n",
"\n",
"Now let's calculate the _formation time_, $t_{\\rm form},$ of one of the halos in our population, where we define $t_{\\rm form}$ as the time at which the halo first reaches some fraction of its present-day mass. Different choices for this fraction correspond to different definitions of halo formation time. The cell below calculates $t_{\\rm form}$ by lookup-table inversion, and \n",
"\n",
"The next plot illustrates a few different examples for the first halo in our population. After this basic illustration, then we'll use `jax.vmap` to calculate the formation time of each halo, defined as the time the halo mass first exceeds $50\\%$ of its present-day mass, so that $M_{\\rm halo}(t_{50\\%}) \\equiv \\frac{1}{2}M_0.$"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "f8c82e37",
"metadata": {},
"outputs": [],
"source": [
"@jjit\n",
"def _compute_lgtform_kern(lgtarr, lgmarr, tform_frac):\n",
" \"\"\"Calculate the time the halo reaches the input fraction of its final mass \"\"\"\n",
" lgm_form = jnp.log10(tform_frac*10**lgmarr[-1])\n",
" lgtform = jnp.interp(lgm_form, lgmarr, lgtarr)\n",
" return lgtform"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "6f15de9f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ihalo = 0\n",
"\n",
"\n",
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-2.9, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"__=ax.plot(tarr, halopop.log_mah[ihalo, :], color='k')\n",
"\n",
"tform_p = 0.5\n",
"tform_ihalo = 10**_compute_lgtform_kern(np.log10(tarr), halopop.log_mah[ihalo, :], tform_p)\n",
"lgm_at_p = jnp.log10(tform_p*10**lgm0)\n",
"__=ax.plot(np.zeros(100)+tform_ihalo, np.linspace(ylim[0], lgm_at_p, 100), '--', color=mblue)\n",
"__=ax.plot(np.linspace(xlim[0], tform_ihalo, 100), np.zeros(100)+lgm_at_p, '--', color=mblue)\n",
"\n",
"tform_p = 0.25\n",
"tform_ihalo = 10**_compute_lgtform_kern(np.log10(tarr), halopop.log_mah[ihalo, :], tform_p)\n",
"lgm_at_p = jnp.log10(tform_p*10**lgm0)\n",
"__=ax.plot(np.zeros(100)+tform_ihalo, np.linspace(ylim[0], lgm_at_p, 100), '--', color=mgreen)\n",
"__=ax.plot(np.linspace(xlim[0], tform_ihalo, 100), np.zeros(100)+lgm_at_p, '--', color=mgreen)\n",
"\n",
"tform_p = 0.04\n",
"tform_ihalo = 10**_compute_lgtform_kern(np.log10(tarr), halopop.log_mah[ihalo, :], tform_p)\n",
"lgm_at_p = jnp.log10(tform_p*10**lgm0)\n",
"__=ax.plot(np.zeros(100)+tform_ihalo, np.linspace(ylim[0], lgm_at_p, 100), '--', color=mred)\n",
"__=ax.plot(np.linspace(xlim[0], tform_ihalo, 100), np.zeros(100)+lgm_at_p, '--', color=mred)\n",
"\n",
"\n",
"a, b = 9, 11\n",
"__=ax.annotate(r'$t_{\\rm 50\\%}$', xy=(a, b), xytext=(a, b), size=25, color=mblue)\n",
"\n",
"a = 6.25\n",
"__=ax.annotate(r'$t_{\\rm 25\\%}$', xy=(a, b), xytext=(a, b), size=25, color=mgreen)\n",
"\n",
"a = 2.6\n",
"__=ax.annotate(r'$t_{\\rm 4\\%}$', xy=(a, b), xytext=(a, b), size=25, color=mred)\n",
"\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"title = ax.set_title(r'${\\rm halo\\ formation\\ time\\ definitions}$')"
]
},
{
"cell_type": "markdown",
"id": "fe0c9d4c",
"metadata": {},
"source": [
"### Calculating $t_{\\rm form}$ for a halo population with jax.vmap\n",
"\n",
"Now let's calculate $t_{\\rm form}$ for each of the mass assembly histories (MAHs) in our halo population. We could do this in a simple pure-python loop, but we can do this more efficiently by using the `jax.vmap`, which will transform `_compute_lgtform_kern` into a function that accepts a _matrix_ of MAHs, and returns an array of $t_{\\rm form}.$\n",
"\n",
"\n",
"#### Using the `in_axes` argument of `jax.vmap` to vectorize a multi-variable function\n",
"The `_compute_lgtform_kern` function accepts $N_{\\rm args}=3$ arguments: `lgtarr`, `lgmarr`, and `tform_frac`. Let's say we want to calculate $t_{50\\%}$ for every halo (so that `tform_frac=0.5`), and that we'll use the same time array `lgtarr` for the specification of every halo's MAH, so that we only want to vectorize over the second argument, `lgmarr`. We convey this information to `jax.vmap` via the `in_axes` argument, which should contain a length $N_{\\rm args}$ tuple, using `None` and `0` for non-vectorized and vectorized arguments, respectively. In the cells below, we'll use `jax.vmap` to do this form of the calculation three separate times: one each for $t_{50\\%}$, $t_{25\\%}$, and $t_{4\\%}$, and then plot a histogram of the results."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "d563ca9f",
"metadata": {},
"outputs": [],
"source": [
"from jax import vmap\n",
"\n",
"_a = (None, 0, None) # Use the same tform definition for many halos at once\n",
"_compute_lgtform_vmap_halopop = jjit(vmap(_compute_lgtform_kern, in_axes=_a))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "5a0ef8bb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tform_p50 = 10**_compute_lgtform_vmap_halopop(np.log10(tarr), halopop.log_mah, 0.5)\n",
"tform_p25 = 10**_compute_lgtform_vmap_halopop(np.log10(tarr), halopop.log_mah, 0.25)\n",
"tform_p04 = 10**_compute_lgtform_vmap_halopop(np.log10(tarr), halopop.log_mah, 0.04)\n",
"\n",
"fig, ax = plt.subplots(1, 1)\n",
"__=ax.hist(tform_p04, bins=100, density=True, alpha=0.7, color=mred, label=r'$t_{\\rm 4\\%}$')\n",
"__=ax.hist(tform_p25, bins=100, density=True, alpha=0.7, color=mgreen, label=r'$t_{\\rm 25\\%}$')\n",
"__=ax.hist(tform_p50, bins=100, density=True, alpha=0.7, color=mblue, label=r'$t_{\\rm 50\\%}$')\n",
"leg = ax.legend(fontsize=20)\n",
"\n",
"xlabel = ax.set_xlabel(r'$t_{\\rm form\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$P(t_{\\rm form}\\vert M_0)$')\n",
"title = ax.set_title(r'$M_0=10^{13}M_{\\odot}$')"
]
},
{
"cell_type": "markdown",
"id": "585c2621",
"metadata": {},
"source": [
"#### Using `jax.vmap` again to vectorize over calculations of a few different $t_{\\rm form}$ definitions\n",
"\n",
"In the code above, we created a version of `_compute_lgtform_kern` that computed some particular value of $t_{\\rm form}$ for every halo in the population. And in order to make our histogram plot of $t_{50\\%}$, $t_{25\\%}$, and $t_{4\\%}$, we repeated that calculation three separate times. This next cell shows how we can use `jax.vmap` again to create a version that accepts an array input for `tform_frac`."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "4005bca7",
"metadata": {},
"outputs": [],
"source": [
"_b = (None, None, 0) # Vectorize the tform definition\n",
"_compute_lgtform_vmap_tformdef = jjit(vmap(_compute_lgtform_vmap_halopop, in_axes=_b))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2a76dc0c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3, 10000)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tform_frac_arr = np.array((0.5, 0.25, 0.04))\n",
"tform_collection = 10**_compute_lgtform_vmap_tformdef(np.log10(tarr), halopop.log_mah, tform_frac_arr)\n",
"tform_collection.shape"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b83e2f49",
"metadata": {},
"outputs": [],
"source": [
"assert np.allclose(tform_p50, tform_collection[0, :], rtol=1e-5)\n",
"assert np.allclose(tform_p25, tform_collection[1, :], rtol=1e-5)\n",
"assert np.allclose(tform_p04, tform_collection[2, :], rtol=1e-5)"
]
},
{
"cell_type": "markdown",
"id": "dc4826c2",
"metadata": {},
"source": [
"#### More `jax.vmap` practice: calculate $t_{\\rm form}$ for every halo, where each halo gets its own individual $t_{\\rm form}$ definition\n",
"\n",
"In the code above, we vectorized `_compute_lgtform_kern` to give us a function that calculated $t_{\\rm form}$ for every halo, and for a few different values of $t_{\\rm form}.$ Let's use `jax.vmap` to give us a function that computes $t_{\\rm form}$ according to each individual halo's value of `tform_frac`. In this situation, we are vectorizing over two arguments at once, and so we set `in_axes=(None, 0, 0)`. "
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "0b4f8e8f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10000,)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_c = (None, 0, 0)\n",
"_compute_lgtform_vmap = jjit(vmap(_compute_lgtform_kern, in_axes=_c))\n",
"\n",
"n_halos = halopop.log_mah.shape[0]\n",
"tform_frac_arr = np.random.uniform(0, 1, n_halos)\n",
"tform_collection = 10**_compute_lgtform_vmap(np.log10(tarr), halopop.log_mah, tform_frac_arr)\n",
"tform_collection.shape"
]
},
{
"cell_type": "markdown",
"id": "863786be",
"metadata": {},
"source": [
"Let's verify that results with this new function agree with our previous one when passing in an array of all the same values:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "d769ee79",
"metadata": {},
"outputs": [],
"source": [
"tform_def = 0.5\n",
"tform_frac_arr = np.zeros(halopop.log_mah.shape[0]) + tform_def\n",
"t50_scalar = 10**_compute_lgtform_vmap_halopop(np.log10(tarr), halopop.log_mah, tform_def)\n",
"t50_vmap = 10**_compute_lgtform_vmap(np.log10(tarr), halopop.log_mah, tform_frac_arr)\n",
"\n",
"assert np.allclose(t50_vmap, t50_scalar, rtol=1e-5)"
]
},
{
"cell_type": "markdown",
"id": "e2193ba3",
"metadata": {},
"source": [
"## Examine the MAHs of the generated populuation\n",
"\n",
"Let's sort our MC-generated halo population according to $t_{\\rm form},$ and visually inspect the typical assembly histories of the earliest- and latest-forming halos."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "864415f2",
"metadata": {},
"outputs": [],
"source": [
"indx_sorted_tform_p50 = np.argsort(np.array(tform_p50))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "36925fae",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x792 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from matplotlib import lines as mlines\n",
"red_line=mlines.Line2D([],[],ls='-',c=mred,label=r'${\\rm early}$-${\\rm forming\\ halos}$')\n",
"blue_line=mlines.Line2D([],[],ls='-',c=mblue,label=r'${\\rm late}$-${\\rm forming\\ halos}$')\n",
"\n",
"import matplotlib.cm as cm\n",
"colors=cm.coolwarm(np.linspace(1,0,halopop.log_mah.shape[0])) # red first\n",
"\n",
"\n",
"fig, (ax0, ax1) = plt.subplots(2, 1, figsize=(6, 11), sharex=True)\n",
"fig.subplots_adjust(hspace=0) # smash left and right plots\n",
"ylim = ax0.set_ylim(lgm0-2.9, lgm0+0.25)\n",
"xlim = ax0.set_xlim(0.05, T0)\n",
"yscale = ax1.set_yscale('log')\n",
"ylim = ax1.set_ylim(1.1, 2e4)\n",
"\n",
"title = ax0.set_title(r'$M_0=10^{13}M_{\\odot}$')\n",
"ylabel = ax0.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"\n",
"n_skip = 10\n",
"for i in np.arange(halopop.log_mah.shape[0])[::n_skip]:\n",
" __=ax0.plot(tarr, halopop.log_mah[indx_sorted_tform_p50[i], :], color=colors[i], lw=0.1)\n",
"leg=ax0.legend(handles=[red_line, blue_line])\n",
"\n",
" \n",
"for i in np.arange(halopop.log_mah.shape[0])[::n_skip]:\n",
" __=ax1.plot(tarr, halopop.dmhdt[indx_sorted_tform_p50[i], :], color=colors[i], lw=0.1)\n",
"leg1=ax1.legend(handles=[red_line, blue_line])\n",
" \n",
"ylabel = ax1.set_ylabel(r'$dM_{\\rm halo}/dt\\ [{\\rm M_{\\odot}/yr]}$')\n",
"xlabel = ax1.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')"
]
},
{
"cell_type": "markdown",
"id": "a2818b41",
"metadata": {},
"source": [
"## Optimizing model parameters with gradient descent\n",
"\n",
"Let's use the parametric model defined above to approximate the MAH of a simulated halo. For simplicity, I have just dumped the MAH of a randomly selected halo of mass $M_0\\approx10^{13}M_{\\odot}$ taken from the Bolshoi-P simulation. So in the plot below let's just examine this simulated MAH against the backdrop of the range of assembly histories in our generated population."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "e20d16aa",
"metadata": {},
"outputs": [],
"source": [
"log_mah_target = np.array(\n",
" [10.9, 10.99, 11.08, 11.14, 11.43, 11.61, 11.69, 11.76, 11.8, \n",
" 11.85, 11.93, 12.01, 12.07, 12.2, 12.28, 12.38, 12.41, 12.43, \n",
" 12.44, 12.46, 12.55, 12.59, 12.61, 12.63, 12.66, 12.77, 12.81, \n",
" 12.87, 12.89, 12.9, 12.91, 12.91, 12.91, 12.93, 12.95, 12.97, 12.99])\n",
"\n",
"t_target = np.array([1.02, 1.23, 1.45, 1.69, 1.93, 2.19, 2.45, 2.72, 3.01, \n",
" 3.29, 3.59, 3.89, 4.2, 4.51, 4.83, 5.15, 5.47, 5.8, \n",
" 6.13, 6.46, 6.79, 7.13, 7.46, 7.79, 8.13, 8.46, 8.8, \n",
" 9.25, 9.74, 10.23, 10.72, 11.2, 11.67, 12.14, 12.6, 13.05, 13.5])"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "24bd08c9",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-3, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"import matplotlib.cm as cm\n",
"colors=cm.coolwarm(np.linspace(1,0,halopop.log_mah.shape[0])) # red first\n",
"\n",
"n_skip = 20\n",
"for i in np.arange(halopop.log_mah.shape[0])[::n_skip]:\n",
" __=ax.plot(tarr, halopop.log_mah[indx_sorted_tform_p50[i], :], color=colors[i], lw=0.1)\n",
"\n",
" \n",
"__=ax.plot(t_target, log_mah_target, color='k')\n",
"\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"title = ax.set_title(r'$M_0=10^{13}M_{\\odot}$')\n",
"\n",
"from matplotlib import lines as mlines\n",
"red_line=mlines.Line2D([],[],ls='-',c=mred,label=r'${\\rm early}$-${\\rm forming\\ halos}$')\n",
"blue_line=mlines.Line2D([],[],ls='-',c=mblue,label=r'${\\rm late}$-${\\rm forming\\ halos}$')\n",
"black_line=mlines.Line2D([],[],ls='-',c='k',label=r'${\\rm example\\ simulated\\ MAH}$')\n",
"\n",
"leg=ax.legend(handles=[red_line, black_line, blue_line])"
]
},
{
"cell_type": "markdown",
"id": "038a2bb7",
"metadata": {},
"source": [
"## Setting up gradient descent\n",
"\n",
"The cell below defines the loss function that we will try to minimize in order to identify a best-fitting Diffmah approximation to the simulated halo. For our loss we use the MSE of the logarithmic difference between the predicted and target MAH. In our fits, we'll hold fixed the present-day mass $M_0$ and also the `mah_k` parameter, and run a 3-parameter fit for parameters $\\theta=\\{\\log_{10}(\\tau_{\\rm c}), \\alpha_{\\rm early}, \\alpha_{\\rm late}\\}.$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "c9501582",
"metadata": {},
"outputs": [],
"source": [
"@jjit\n",
"def _mse(preds, targets):\n",
" diffs = preds - targets\n",
" return jnp.mean(diffs**2)\n",
"\n",
"@jjit\n",
"def _loss_func(params, loss_data):\n",
" t_pred, log_mah_target, lgt0, logm0, mah_k = loss_data\n",
" lgtc, early, late = params\n",
" log_mah_pred = _rolling_plaw_vs_t(t_pred, lgt0, logm0, lgtc, mah_k, early, late)\n",
" return _mse(log_mah_pred, log_mah_target)"
]
},
{
"cell_type": "markdown",
"id": "d152280c",
"metadata": {},
"source": [
"#### Choose an initial guess `p_init`\n",
"\n",
"Then collect the values that should be packed into `loss_data`, and evaluate the loss function."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "cc422e96",
"metadata": {},
"outputs": [],
"source": [
"lgtc_init, early_init, late_init = 0.25, 2.5, 0.5\n",
"p_init = jnp.array((lgtc_init, early_init, late_init))"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "3b945c98",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"DeviceArray(0.07512797, dtype=float32)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loss_data = (t_target, log_mah_target, np.log10(T0), lgm0, MAH_K)\n",
"_loss_func(p_init, loss_data)"
]
},
{
"cell_type": "markdown",
"id": "4a8fe0ee",
"metadata": {},
"source": [
"### Use value_and_grad convenience function\n",
"\n",
"The `jax.value_and_grad` is a convenient function to use in gradient descent exercises. It returns a scalar value of the loss and a length-$N_{\\rm params}$ array for the gradient of the loss w/r/t $\\theta.$ "
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "3408b6ca",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(DeviceArray(0.07512797, dtype=float32),\n",
" DeviceArray([-0.32934403, -0.07682967, -0.16427392], dtype=float32))"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from jax import value_and_grad\n",
"_loss_and_grad_func = jjit(value_and_grad(_loss_func, argnums=0))\n",
"_loss_and_grad_func(p_init, loss_data)"
]
},
{
"cell_type": "markdown",
"id": "26de332d",
"metadata": {},
"source": [
"### Descending our own gradient\n",
"\n",
"At this point we could make use of any number of very efficient optimization algorithms to identify a best-fitting set of parameters. Modern algorithms such as Adam are able to leverage accurate gradient information to optimize million-dimensional parameter spaces. [This blog post by Sebastian Ruder](https://www.ruder.io/optimizing-gradient-descent/) gives a nice summary of many different variations of gradient descent. Here we only have a three-dimensional model, and so we can get away with a very simple descent down the gradient of our loss using a fixed learning rate."
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "8acacb4e",
"metadata": {},
"outputs": [],
"source": [
"learning_rate = 0.1\n",
"n_steps = 300\n",
"\n",
"p = np.copy(p_init)\n",
"collector = []\n",
"for istep in range(n_steps):\n",
" loss, grads = _loss_and_grad_func(p, loss_data)\n",
" p = p - learning_rate*grads\n",
" collector.append((loss, p))"
]
},
{
"cell_type": "markdown",
"id": "404cb0e1",
"metadata": {},
"source": [
"#### Inspect the loss curve"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "84f9c278",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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/eBUyUsfdfEREMRPyN1djYyNMJhMAYOPGjdBqtSgpKUFvby/UajWcTicqKysBAHl5eXj66aejU/EYmM1mNDQ0BJxTqVSQSqX+5zpVVVWQyWQBQ3FX6u7uDpi1t3nzZmzZsiUiNYeSnT4N//F1FX5h3Y9ndnagtcuNJ+9R4qqi+Al9IqLRCBk81dXVEEUxaAjNNxts8My2zs5ObN26NWKz2sbDYrFg5cqVQeeVSmXAcUVFBerr64cNnqKiInR3x36vnJTkJOhvXYSbyvLxo6Z2/MtTb+H768qgu0WB1BQuKkpEk8OwPZ4rQ6e3txctLS1BM8xKS0vh9Y7uRUeLxYKmpqZh75HJZEE9lbFqaGiAXq8POn/l8JtcLofD4ZjQ94q2G8vy8fIPV+N//uUD/MK6H395rxv1dy1FRYls5C8mIoqxkMGTk5MTdK65uRlSqRQlJSVB10b7AqlWqx22dxEugiAEvfPjdDqh0Wjg8XgCngXF43TqkcgyU/HUvUpolSfwb3/+AFXPvI17rp2Lug2LkJuZGuvyiIhCCjk+09vbG3TObDajurp6yPtH2+MJN6fTCYvFEnDON+16cLgAAwFjMBgCzjc1NQ3ZM5os1i4qhPXHq1G7Wo5m22Gs2fo6/vOtTq5uTURxK2SPx+v1or293b8Y6LZt2yAIAoxGY9C9O3bsGPJ5Sjg4HA4IguAPF6PRCLVa7X9WY7FYYLVag3pRQ61cAAz0uHw/g8vlgkajiftZbSPJSE3BT29fjLuVc/C//7oXP3txL/7w7kH82xcWY015YazLIyIKIPEO01V54IEH0NnZCZfLhc7OTphMJtx9993+6y0tLTCbzWhpaUFDQ8OU3YFUpVLBZrPFuoxR8Xq9aPnoBP7PS3vR5TqDteUF+Lc7roKiICvWpRFRggn1u3PY4PHp7OxEaWng3jC9vb1By+Rcec9UMZmCx+f8xX78dlcXft3yCc5euISvXT8f/6NyAWR8/kNEURLqd2fIobauri7/JIKhAiUnJydgAkJfX18YyqRwSU1JQs1qOb6sLMbj1v343dtd2GY/jO+sLcM3byxB+rTkWJdIRAkq5OSCsU5n9r1sSvElPysNP//yUrzyw9W4tlQGw8sfY93W1/GntsPo514/RBQDIYfakpKSxrSrqNvtHnK7hKlgMg61hbKrowf1f/sYe470YknxDPz0tsVYxVWviSgCxjzU9vDDD0MikaCioiJoWvKVvF4vezyTxCpFPv7y3Rvx4vvdML68D/c++y7WlhfgkdsXY+HM7FiXR0QJIGTw+F6+bGtrg9vthkQiGXbW2lDv/VB8SkqS4M7lxdhw9Sz8dlcXfvPaAdz6qzdQrZqLH2sWonBGeqxLJKIpbFSz2nxaWlogkUggk8n87/ckgqk01DYUz+nzeHLHAfz+nS6kJCWhdrUctavlyEzj6tdENH4Tmk49lJaWFgADK1NP9RCa6sHj86nrNIwv78NLe46iIDsNP1IvRLVqDlKSuQApEY1dqN+d4/6NUllZicrKSnR0dKCiogJbt26dUIEUe/PzMvHUV5XY/p1VmC/LwE//tAe3PfEmdnx8PGZLIhHR1DOu4Glvb8cDDzyAvLw8PProo6iurkZNTU24a6MYUc7LhfmBG/DM11biYr8X33rOhnsa38F7h8RYl0ZEU8CoB/Hb29vxwgsvwGQyIS8vD7W1tbDZbFN2tYJEJ5FIcOuSWahcXIjn3z2IX7d8gjufegtfWDYbdRvKMT8vM9YlEtEkNWzwdHV1+Xfx9Hg8qKmpQUtLC1asWBF0b19fX1xtgU3hMS05CV9fVYK7lMVofMOJxjc78coHx/DV6+bh+5ULkJ+VFusSiWiSCTnUplKpsHLlSjidTpjNZrhcLjz66KNDhg6ASb21AI0sO30afry+HDsfXoPqirn4r3cPYs1jr+PJlk9w5vzFWJdHRJNIyFltZWVl0Ov1kMlkQZu8+b5EIpHA6/WitbUVjz32GC5duhT5imMgUWa1jcWBE5/hsVc+xisfHkdhdhp+yBlwRHSFMa9coNPpRj1hYPBWCZQYygqz0HCfCrYuN+r//jF++qc9+I9/OFF36yKsv2rmqHekJaLEM+73eBIJezzD83q9eHXvcRhe/hjOk6excn4ufnr7IqycH7wRHxEljrC/x0PkI5FIsOHqWXj1h6vx8y8vxUH3Gdz99Nuo/Z0NB058FuvyiCjOMHgobFKSk3DvdfOw8+E1+IlmIXZ1uLDhV2/gke17cKLv81iXR0RxgsFDYZeRmoLvVy7AzofX4L7r58NsO4RbHnsdv3h1H059fiHW5RFRjDF4KGLystKw5UtXo+Unt6BycSGe3HEAax57Hc+91YnzF/tjXR4RxciEJxf09fVBEAS0trZCFEVIpVJUVFRArVZPmRdKObkgPN47JKL+7x/hHacb8/My8ND6ctyxbDZnwBFNUWFfnRoAtm3bBqvVCoVCEbBZnCiKcDqd0Gg0uOuuu8b78XGDwRM+Xq8Xr+87iUf//jH2HT+FZXNysOm2RVil4C6oRFPNmN/jGa1nnnkm5DXf1glEPhKJBGsXFWL1wgJsdxzG49b9uLfxXawpL8Cm2xZh0ayp0UsmotAi+oyHu5JSKMlJElSp5uK1h9Zg022LYP/Ug9ueeBM/aX4P3eLZWJdHRBE0oR6PXC5HdXU1FAoF8vLyAAAulwsA4HQ6odPpJl4hTWnp05LxwC0KfKViLp567QB+u+tTvPh+N75+w3x8Z00ZcjNTY10iEYVZWFYu2LZtG5xOp/9YLpdPqWV0+Iwneg57zuBx6378qe0IslJTULtajm/dVMptuIkmoYhMLogGURRhMpkAAK2trdBoNKitrR32a4xGI+RyOdxuNwAE3T/S9SsxeKJv37FT2PrqPlj3Hkd+Viq+t7YM91w3D2kpybEujYhGKSZL5mzfvn3Cn1FfX4+6ujrU1dXBbDbDYDD4g2goer0ecrkcWq0WtbW16OjogMViGfV1ig/ls7LR+K8qbP/OKigKsrDlxb2o/MVObHccxqX+uP63EhGNYEI9nk2bNoWcQOD1emG329Ha2jru4kRRRE1NDcxms/+c0WhEQ0MDOjo6hvya3NxceDwe/7HD4YBer4fVah3V9aGwxxNbXq8Xb3zSA+PLH+PD7j4snJmFhzcsgnpxId8BIopjEZlOrVAoAAw804kUQRDgdDr930MqlQY8TxrM4XAEnZNKpRAEYVTXKT5JJBLcsrAAN5fl428fHMUvXt2Pmt/ZoJwnRd2ti3C9PC/WJRLRGEwoeKqrq2Gz2VBZWRmuegJIpdKA3gkAWK1WqNXqIe93u92QyQKX4h98PNL1ULq7uwP+Zb1582Zs2bJlxK+j8EpKkuCOZUXYcPUsWOyH8SthP75iegerFxagbkM5lhTnxLpEIhqFCQVPTk7OsKET7kASRRGCIIR8MVUUxWG/dqTrg1dfGKyoqAjd3d1jqJQiaVpyEu65dh6+vKIYv3u7C0+91oE7nvwH7lg2Gz9ZX47S/MxYl0hEw5hUi4T6nvcolcohr0ulUv9MNZ/BxyNdp8klfVoyalcr8EbdWnxvbRlaPjoB9eM78cj2PTjWy20YiOLVmHo8Dz74IJ5++umQ1zdt2oS2tjZoNBo89NBDQ95jsVjQ1NQ07PeRyWRoaGgIOGc0GqHT6UIOs/m+7speje9YKpWOeJ0mp5zp0/DQhnL866r5eGrHATy/+yC2Ow7jG6tK8OAaBaQZfAmVKJ6MKXi0Wi0AoL29HXK5PGD16UceeQT5+fl45ZVX0NLSgu3btw+5QKhWq/V/zmhZLBYolUp/6AiCMGQAKZXKoABxu93+e0e6TpNbYXY6fnbnEtx/sxy/tO6H6U0nnn/3IL51Uym+fXMpZqRPi3WJRIRxDLWVlZVBq9WitLQUW7du9Z+3WCz+Xk5lZSXC9V6qIAhwu91QqVT+Va8Hz05zOp0B7+FUV1cHHFut1oCle0a6TpPfXFkGHt+4HC//YDVuLMvHEy2f4GbDa3jqtQM4fe5irMsjSnhjCh6HwwG73Y4DBw7A5XIhJycHfX19ABAUNOEYuhJFERqNBjqdDrm5ucjNzYVCoQh4N8hisQQMyzU0NMDpdEIQBJhMJigUioAe1kjXaeoon5WNZ+5bib9+/yasnJ+Lx17Zh9XG19D4hhOfX7gU6/KIEtaYXiDdtm1bwBpsvb29sNvtWLduHSoqKgICYceOHVi3bl14q40RvkA6NTgOevD4q/vxjwM9KMxOw3fXluEr187lMjxEERKWJXPcbjd27NiBvr4+dHV14dFHH4VKpUJvb2/Q+zahXvIkihXlvFz81/3Xoan2epTkZWLzf3+ItY+9jj/uPogLl7gVN1G0jHnJnAceeADNzc1QKBSora2FTCaDIAjQarVoa2uDVquFIAiQy+Xs8VDc8nq9+MeBHvzi1f1oPyRiniwDP6hcgH9ZUYzkJC7DQxQOUVmduq2tDQ0NDVi/fv2U2PLah8EzdXm9Xry27wR+8ep+fNjdB3lBJn6oXog7ls5GEgOIaELCGjzPPvss7HY73G43NBoN7r///rAUGa8YPFOf1+vFKx8ew+PW/dh//DMsmpWNH6oXYP1VsxhAROMUtm0R1q9fD5vNBrlc7v/QiooK/+w2oslIIpHg1iWz8fcfrMYTX1mO8xf78cB/OXD7r9/E3/YcRT+3YiAKmzG9QPrss8/CbDYjJydwMUbfZm2hVisgmiySkyS4c3kxvrB0Nl58vxtP7jiA7/zBgYUzs/D9dQtw+9LZfAZENEFj6vHk5uYGhQ4w8M5OaWlp2IoiirWU5CR8ecUcWH90C574ynL0e4Hv/7ENG371Bv7SfoSb0RFNwJiCZ7hNt7ghF01Fvh7Qqz9cjd/cuwLJEgl+8EI7NI/vxDb7YVzkNGyiMRtT8LhcLnR1dQWdb29vD7kjKNFU4NsL6O8/uBlPf1WJ1JQk/MT8Hiof34lm2yG+B0Q0BmOe1VZdXY3Ozk7/jqC+3UFHWnF6MuOsNrpSf78XwkfH8UTLJ/iwuw9zZdPx3TVluEs5B6kpk2q3EaKICet06ra2NthsNoiiCLVajRUrVoSlyHjF4KFQvF4vdnx8Ak+0fIL3D/eiWDodulvkqFbNRfo0LsVDiS3iL5Bu3bp1ys5qY/DQSLxeL17fdxK/ee0A7J96kJ+Vim/eWIr7bpjP7RgoYY05eDZs2DDqD/d6vbDb7XC5XOOvMI4xeGi0vF4vdne68dTrHXhj/0lkp6XgazfMx7duLEVBdlqsyyOKqlC/O0O+x+P1emEwGEa1vYHX68WmTZsmVCDRVCCRSHCdPA/XyfPwwZFePP16B57Z2YH/949ObKyYi5qb5Zgry4h1mUQxFbLH09bWNqZnN52dnVP2XR72eGgiOk5+hoadHfhT2xH0e4E7rynCg2sUWDAzO9alEUVUVBYJnaoYPBQOR3vPovGNTvxx90GcvXAJmqtm4jtrFFgxLzfWpRFFxJiH2ogovGbnTMe/f/EqfG9dGZ7b1YXn3uqEde9xXFcqQ83NcqxbVMgFSSkh8IUDoiiTZabix5qF2PVIJf7tC4txyH0G9//OBvUvd+KPuw9yW26a8hg8RDGSlZaC+2+WY2fdWjzxleXISE3GI9v34MZHd+AJ4RO4T5+PdYlEEcGhNqIYm5achDuXF+NL1xThHacbjW868UthP57eeQDalXPw7ZvkKM3PjHWZRGHD4CGKExKJBDco8nCDIg8HTpzCs292orn1MP7w7kFoFs9E7Wo5Vs7P5YK8NOkxeIjiUFlhNh69exl+sr4cv3+7C79751O8uvc4ls3JwTdWleALy2YjLYVL8tDkxOnUo8Dp1BRrZ85fxDbHETz3Vic6Tp5GflYq7r12Hr56/XzMnJEe6/KIhsT3eCaAwUPxwuv14h8HevDbXV1o+fgEkiUS3L50Nr6+qgTKeVIOw1Fc4Xs8RFOARCLBzQsKcPOCAnzqOo3fvf0pmm2H8N/vdWPZnBx8/YYS3HENh+EovsV9j0cURZhMJgBAa2srNBoNamtrx32/yWSC3W5HVVUVAMBsNkOv1/v3FxoKezwUz06fu4jtbcHDcPdeNx+zcjgMR7EzaXs89fX1MBgM/mOFQgEAIcNnNPc3NzfDZDJBqVSisbFx2NAhineZaSm47/r5+Np18/zDcE++dgBPvd6BykWF+Or183FzWT5XRaC4EdfBI4oinE5nwDmdTgeDwTBk8Iz2fo/HE5mCiWJo8DDcQdcZPL/7IMy2Q3h173HMlU3HPdfOQ9XKudyegWIu7lcuEAQhIEykUmlQuEzkfqKpaF5eBjbdtgi7HlmHX9+zAsXS6TC+vA+rHm3B9553YFdHD+J8lJ2msLju8Uil0qDeidVqhVqtntD9JpMJMpkMbrcbQOhhO6LJLi0lGV+6pghfuqYIB058huffPYhtjsP46/tHIS/IxL3XzsPdyjnIzUyNdamUQOJ+csFgoiiitLQULS0tUCqV47rf4XBAKpX6n+tUVVVh48aN0Gq1IT+nqKgIR48e9R9v3rwZW7ZsmdgPQxQjn1+4hJfeP4rndx+E/VMPUpOToLl6JqpVc3FTWT6S+SyIwmRKvMdTVVUFnU4XsscznvuNRiOamppgt9tD3sNZbTRVfXS0D02th/CX9iPwnLmA2TnpuFs5B9qVc1DC9eFoguImeCwWC5qamoa9RyaToaGhIeCc0WiEUqkcdeiEul8QhIBzFosFVVVVw453M3hoqjt38RJaPjoBs+0Qdu4/iX4vcG2pDNWqubh96SxkpMb1qDzFqbgJnvGwWCyQSqX+wLgyPEZ7v9PphEKhgMfjgVQq9d+r1+vR0dER8vMYPJRIjvV+jm2Ow7DYD6Oz5zQyU5Nxx7IiVKnmcJFSGpNQvzsnxaw2t9sNlUrlny7tcDj8151OJywWy6jul8vlMBgM/tABgKamJuj1+qj9PETxblZOOr67tgw7fnILzA/cgC8sm40X3++G9pm3sfqx17D1lX04cOJUrMukSSyuezyiKCI3N3g/eq1WC7PZDGBgSM1qtcJqtY7q/sFB5XK5oFAoRpzVxh4PJbrT5y7i5Q+O4c/tR/DWgR70e4ElxTPwL8uL8cVrirhQKQ1pUg+1xRqDh+ifTpz6HC++dxR/aT+C9w/3IkkCrFLk487lRbh1ySxkp0+LdYkUJxg8E8DgIRpax8nP8Je2I/hzezcOus8gLSUJ6sUzccey2VhTXojpqVysNJFN2rXaiCh+KQqy8OP15fiRZiHaDon4c9sRvPT+Uby05yimT0vGusWF+MLS2VjLEKJBGDxENGESiQTKeblQzsvFv99xFXZ3uvHSnqN45cNjeOn9yyG0qBC3LZ2FdYsKOT07wbH1iSisUpKTsKosH6vK8vG/7lyCdztd+Nueo3j5g2N4ac9RpE9LwtryQty+dDbWLipEVhp/DSUatjgRRUxykgSrFPlYpcjHz760BLs73fjbnqP4+wfH8PcPjiE1OQk3KPKguWomNFfN5Oy4BMHJBaPAyQVE4XWp3wtblxvWvcdh/eg4PnWdAQAsm5MDzeKZ0Fw9E+Uzs/my6iTHWW0TwOAhihyv14sDJz7Dq3uPw7r3ONoPiQCAubLpUC8e6AlVlMgwLTnu33enK3BWGxHFJYlEggUzs7FgZja+u7YMJ059jpaPTkDYexx/ePcg/vOtLmSnpeDGsnysKS/ALeUFmJ0zPdZl0wQweIgorhRmp+Oea+fhnmvn4cz5i3hjfw927j+BnftO4uUPjwEAymdm45byAtyysACqklykpXCq9mTC4CGiuJWRmoJbl8zCrUtm+YfkXt93Ejv3n8Rzb3XB9IYTGanJWKXIwy0LC7B6YQHmyTL4bCjOMXiIaFIYPCRXs1qO0+cu4h2nCzv3n8Tr+05C+OgEAKBYOh2rFHlYVZaHVYp8zpSLQwweIpqUMtNSULl4JioXz4TX60Vnz2m81eHCrgM9sH50HGb7YQCAoiDz8pTuPFwvz+M233GAwUNEk55EIoG8IAvygizcd/189Pd78dGxPuw64MKujh5sdxzG79/5FBIJcNXsGbhBnoeKUhlU83ORl5UW6/ITDqdTjwKnUxNNbhcu9eP9w73YdaAHuzpcsB/04PzFfgADPaKKEhlUJTJcWyLDXNl0PiMKE06nJqKENS05CSvn52Ll/Fx8v3IBzl28hA+O9GJ3pwe2roHVFF5oPQQAKMxOQ0WpDBXzc6EqkWHRrGyk8B2isGLwEFHCSUtJxsr5MqycLwOgQH+/F5+c+Ay7u9ywdbnR2unGS+8fBQCkT0vC0uIcLJ8rxfK5uVg+T4qinHT2iiaAwUNECS8pSYLyWdkon5WN+66fDwA4Ip6FrcuN9kMi2g+J+O2uT9F4qRMAUJCddjmIBv4sm5PDDfDGgMFDRDSEYul0FC8vxp3LiwEA5y/246Ojff4gaj8kwrr3OABAIgFK8zJxVdEMLCnOwdVFM3B1UQ5knEE3JAYPEdEopKYk4Zq5UlwzV4qvXz4nnjmP9kMi3jvUiw+7e9F2UMRfLw/RAUBRTjquvhxES4pycHXxDMyawWE6Bg8R0ThJM1KxprwQa8oL/ec8p8/jw+4+fNjdiw+7+/BBdy+Ej47DN384LzMVi2ZnY+HMbJTPzMbCWQN/T6R9iRLnJyUiioLczFTctCAfNy3I9587fe4iPjra5w+kfcdO4YXdh3D2wiX/PcXS6f7nTOUzB8JIUZg5JdehY/AQEUVYZloKVJffFfLp7/fisOcs9h0/hf3HT2HfsYH/ffOTk7hwaaB7lJwkwTxZBuT5mZAXZA68JJs/8L/5WamTdsiOwUNEFANJSRLMy8vAvLwMaK6a6T9/4VI/unpOY9/lMOo4+RmcJ0/jHwd6cO7yS68AkJ2eAnlBFhSDQqk0PxOl+ZlInxbfvSQGDxFRHJmWnORfDPWOZf8839/vxRHxLJw9p+G8HEbOns/wttOF7W1HAj5j5ow0zJNlYK4sA/Mu/5mfN3BckJUW854Sg4eIaBJISpJg7uUwuWVhQcC1M+cvXg6i0+jqOY1D7jM46D6Dtztc+FPbEQxeGC19WpI/jHzBVCydjuLc6SiWTkfO9GkRD6a4Dx5RFGEymQAAra2t0Gg0qK2tDXm/yWSC3W5HVVUVAMBsNkOv10Mul/vvMRqNkMvlcLvdADDs5xERxbuM1BQsKc7BkuKcoGufX7iEI+JZHHSfwSH3GXzqOuP/+64OF86cvxRwf2ZqMooGBdE3byxFWWFWWOuN++Cpr6+HwWDwHysUCgDDh0VzczNMJhOUSiUaGxsDQkev16OiogJardZ/bLFY/MdERFNJ+rRkKAqyoCgIDg+v1wvX6fPoFs/iiOcsjoiX/3jOorv3LN47JKJKNTfsNcV18IiiCKfTGXBOp9PBYDAMGzwejyfkNZPJFBBkGzduhF6vZ/AQUcKRSCTIz0pDflYals2RRu37xv2Sq4IgBISPVCoNCqPRcjgcQeekUikEQRh3fURENDZx3eORSqVBvRer1Qq1Wj3s15lMJshksqBnOG63GzKZLODeK4+JiCiy4jp4riSKIgRBQEtLS8h7VCoVpFKp/7lOVVUVZDIZtFotRFEc9rOlUumQ17q7uwNmeWzevBlbtmwZz49ARJTwJlXw1NTUwGw2Q6lUhrznymsVFRWor6+HVquFVCr194J8rjweSlFREbq7u8dXNBERBYj6Mx6LxYKqqqph/+h0uqCvMxqN0Ol0Iw6zXfm8Ri6X+5/tyGSyoF6P7zhUb2ei2DOKT2yX+MR2iU/hbheJ1zv41aL4ZLFYIJVK/aEjCMKQAeR0OqFQKODxePxBYrFYoNfr0dHRAQDIzc0NeG4kCAIMBgOsVmvI7x9q3/DRkEgkmAT/iRMO2yU+sV3i03jbJdTvzkkxq83tdkOlUvmnVw+eneZ0OmGxWAAM9G4MBkNA76WpqQl6vd5/XF1d7b8fGJisMFQPi4iIIiOuezyiKCI3NzfovFarhdlsBjAwBGe1Wv09lsFB5HK5oFAogt75MRqNUCqV/mnZI61cwB7P1MN2iU9sl/gU7h5PXAdPvMjPz0dJScm4vra7uxtFRUXhLYgmjO0Sn9gu8Wm87dLV1YWenp6g8wweIiKKqrh/xkNERFMLg4eIiKKKwUNERFHF4CEioqiaVEvmTCbcbC76fJsGulyugK0vfEZqE7ZZZIxmM0e2TfSJoojm5mYA8L9gf+X/byLWLl4Ku7q6Oq/ZbA55TOFntVq9ZrPZW1tb662trQ26PlKbsM0ip66uLuBYLpd7GxoaAq6zbaKvtrbW6/F4/MdKpdJrMBj8x5FsFwZPBEil0oBju93uVavVMaomsdTV1Q0ZPCO1CdssMjwej1er1QacMxgMXrlc7j9m28SGUqkMCAqtVhvQVpFsFz7jCTNuNhd/RmoTtllkDbeZI9smdux2e8DOyw6HAxqNxv/3K4WzXfiMJ8y42Vz8GalN2GaRM9Jmjmyb+GA0GqFWq0e9aeZE24XBE2bj3WyOImekNmGbRc+VmzmybWJr8AQDhUIRcH64r5louzB4wmy8m81R5IzUJmyz6LlyM0e2TWxJpVJ/L0ej0aC1tRVmszni7cJnPGEWi83maHgjtQnbLDqG2syRbRMboijCaDQGnNNoNP6V/SPdLgyeMFMqlUH/4d1u94g7p1LkjNQmbLPIs1gsUCqVAZs5AmybWLHZbNDr9SGHzCLdLgyeCOBmc/FnpDZhm0XOSJs5sm2iT61WB22aabVaUVdX5z+OZLtwW4QIGetmczQxDocDgiCgoaEBAPxDOr5nCcDIbcI2C7/RbOYIsG1i4cpNM/Py8gKCB4hcuzB4iIgoqjjURkREUcXgISKiqGLwEBFRVDF4iIgoqhg8REQUVQweohgTRRF6vR4KhQISiSTopT7fqsG5ubmoqqoKWOmZaDLidGqiOKHX62E0GtHQ0BD0PoRvF88r37MgmozY4yGKA6IoQqFQQKvV+l+CHcxmswXsnUI0mTF4iOKAzWaDWq2GTqeDw+EIGk5zOByQy+Uxqo4ovBg8RHHAFyxqtRpyuRwGgyHWJRFFDIOHKM5otVr/5lw+3AKAphIGD1EcGBwsOp0Ooij6F3B0OBxQqVQxqowo/Bg8RDF2ZbD4htx8kwxsNlvAKttEkx2DhyjGhgoWnU4HQRBG3N/ex2KxjOo+onjA4CGKQ76p0yaTaVT3DzUFmyheMXiI4lRtbS3q6+sDekO+zbsEQYBerwcwsMOn0+lEc3NzwI6QJpMJgiDAZDL5N8rLzc2FxWKBw+GAXq8P2AmUKFpSYl0AUSITBAEymWzIazqdDiaTKWAf+4aGBuh0uoB3enxTsKurq/2TFBwOB+x2u38FBI1GA6vVCpVKBaVSCblcDqVSCYVCgY6Ojsj9gERDYPAQxYhOp0Nzc7M/RK5cmUCpVAad27hxIzQaDZRK5bD72zc1NUEqlfp7NG63239tcND57uHkBYomDrURxUhDQwM8Hg/sdnvI5XDMZnPAsVwuR0dHB3Q6HfR6fdAKB75jURRRUVEBpVIJpVIJu90+5OeH6m0RRRKDh2gS8U02UKvVMBgM/qDxDbH5ZrZVVVWhtbXV/3WDn+UMDiu3283eDkUdh9qIJhmLxQKpVAqn0+l/huN7HuR7dqNWq/0TEaRSaUDPxmazwe12w+FwBPWoiKKB2yIQJRCNRgOz2cwleCimONRGRERRxeAhShCCIMBms6G+vj7WpVCC41AbERFFFXs8REQUVQweIiKKKgYPERFFFYOHiIiiisFDRERR9f8B1PdE+ronsmkAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p_best = np.array(collector[-1][1])\n",
"lgloss_history = np.log10(np.array([x[0] for x in collector]))\n",
"\n",
"fig, ax = plt.subplots(1, 1)\n",
"__=ax.plot(lgloss_history)\n",
"\n",
"xlabel = ax.set_xlabel(r'$N_{\\rm step}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}{\\rm MSE\\ loss}$')"
]
},
{
"cell_type": "markdown",
"id": "e7bf5b2f",
"metadata": {},
"source": [
"#### Check accuracy of best-fit model"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "15189f4a",
"metadata": {},
"outputs": [],
"source": [
"log_mah_best = _rolling_plaw_vs_t(tarr, np.log10(T0), lgm0, p_best[0], MAH_K, p_best[1], p_best[2])\n",
"log_mah_init = _rolling_plaw_vs_t(tarr, np.log10(T0), lgm0, p_init[0], MAH_K, p_init[1], p_init[2])"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "49667982",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-3, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
" \n",
"__=ax.plot(tarr, log_mah_init, '--', color=mred, label=r'${\\rm initial\\ guess}$')\n",
"__=ax.plot(t_target, log_mah_target, color='k', label=r'${\\rm example\\ simulated\\ MAH}$')\n",
"__=ax.plot(tarr, log_mah_best, '--', color=mblue, label=r'${\\rm best}$-${\\rm fit\\ Diffmah}$')\n",
"leg = ax.legend()\n",
"\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"title = ax.set_title(r'$M_0=10^{13}M_{\\odot}$')"
]
},
{
"cell_type": "markdown",
"id": "ecb51d97",
"metadata": {},
"source": [
"#### Inspect how model accuracy improves over the course of the gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "8fac1b38",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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mn4/dGzto2OPA3d6Bt8tBwOdHDgR6FAcdeBJQq4gwhrNovpHrsuKZnCSSwPEkEoQgjCI+pwvXNzU4bTW4KnfjqqzFVVWL01aDZ28D4fGxRCRPRje9+y/2wrPQJU8mInkyYdESnXvrcdl2d/9V1dD41pe4qmrp2t9I2KRYtJPMqIw6FGolgU4XSnUnYVEqlGFKULRRWlvDR81NfNDcQp27E7VCwdlTJ3HZ/BS+v2AmUkwUKqMRhcGIbIgkoJfw6iVcWokOdRQOfyTNLgMNrWpqv/Gy29ZGU70Dj6sRX1c9Ab//oKeB7kphbYSGqVMi+MWPJnHqoihRHDRKiAQhCMdZwOvFVVmDc1c1Hbuqce6sxrmrGuc31XjtreimT0Y/Yxo6y1SMJ80i/kcZ6CxTiZiagEKjwdvcgnOXDeeuKpy7dtH41rs4K6vx1O0jLD6OiMnxaCQDyjA1KqOaiKRIlConsr+NgNMLLhlkLyq1Am84fB7m5r39zXywt5G2Li9atYpzZk1j5eL5XHr2YqT4BPwGE76IKNq1kXSoomj1R9Ls0tPQpmbvTh81Ve007m3B7azD1+XrnQgUCpRKBUpVd5HQaakmrl2aQFysdqS/CuEQRIIQhGPE1+GkY1tl99/2Sjp22OjYYcNdvRft5Hj0J0zHMDMZ04I5JGZ9F/3MZLST41EolciyjKe+gY4dlTh3VNL4tvVAUrAhB2R0M5KJSJqE2qgjPF5CpbfgidXSuWcv3gYXgXYtCtkHvi5UGiXGuDA0ERrC9WGo9RG8XdvAi19X8ml1Pb5AgJhIPZeecwoXnXMaZ555BqroRJxqEw3+SLZ59DR2aKnf7aem1k1dtR2no44uj6+7yWgoEdBdN6BSIUkRfOd0iaszE4k0akb6qxCOkEgQgnCU/O5OOrZV0r5lF+1f76B96zd0bP2GrqaW7iQw24JhTgpJV/4Aw+wUdDOmoQoPC73f62ilfetOGkveo2P7Ljq27cK5oxJlmAb9rBnokpNQGfVEps5GPyMR1+5q3NWVBNrrUOt1IHuh041Ko8CUpEMdpkKj1xCmN6AxHKgjMOhQGQ2g0/GH19/nL//+gBlTErn+51dwbvqFTD/xDDqQaHZG8Harkj1lXmqr22iqs+Nx1R8YJtqPHOhRUaxSoTeEc8pCE9dfkSieCMYhkSAE4TDJskzn3gbavthG2xfbaP9qB21f7cC9uw79jGkY55+Acf4JTMv+MYa5M9ElJ6Ho0ZNWDgRwVdfS9M7/aP96O+1bdtCxbSfe1nYMs2egnz2T8EnRxCScStSS+bhraujYtg3Pnu2Emc0o1QoCnR3g7cI4SYdKrUAT4UOjC0djkAgzRqDR61AZ9agNhgP1BEYChkh8ERJ2RQS/ujuPN98u4ZLMa7jyV4/S2Kbm871dFL9kp7WxDo/bg9/r+7bCWNHdYkgTpmLKNAPXLYvn1FRRRzBRiJ7UgtAPWZZxVdbQumkLrRVbaNu0ldbNW1EolUQumEvkSbOIPGk2xhNnYZhtQanpXYwi+/04d9po+3IrbV9upf2rbbR/vR2NWcI4bzaGeScQFm2CgA9PQwMdW7fh3LETtUGPJsoEspdAexsK/Ki1GlQq0Og0hOnD0Oi1hBl1qPU61EY9KoMBpcFIwGjErzPh10l0ak041VG0y0YcXXoq9zhZteJyqrZ9xoJzVhI//cd4PV34vd8WESkUCpQqJRE6DUsWmrjhJ0nExoingvFO9KQWhEPorGvAsfFLHKVf0lr+NY7yr1Eb9ZhS52FaOJfkm3+OaeFcwuNj+9w9y7KMq7qG1oqvadv0FW2bv6b96+2Ex8dhPGkuxpPmIC06kYDXg6uqivavvqZ+zYtoJAlNlAlFwIff0YzWpEEdIaPyt6COUKORjIQZtGgMEYQZdagMetRGQ/egcoZIAvpIfHoTLm0UrrBIOmSJFq8eu1PLvhoFe/d5qa1uZff2Dyl9+wY8rkbmLLmPSPO5uNucB/oRhHPhOdH8IjMBvU7UFQi9iQQhTDh+TxdtFVto+WwzLZ9twrHxC/zuTqRTTkZafBLTb/kFptR5hE+K6ff9vg4nreVfHvjbTGvFVyi14ZgWnkjkwhOZ9qtrUapknDu/oe2LL6l/8XlQq4hImAQqBX5HM+EGNZpwH0rXftRaFZqECMIMWsKCdQaRelQGPUq9EYzdxUR+nQmXVsKlNeFEotVvxO6OYP9+NfWNPmqrO9hXuw9Xmwtfl5eAP4CjcRNbPl+JQqHitO8WkHXZOVz34ySRDITDIhKEMO55W1qxf7qJlo/LsX9URtsX29HPTCbqtIXEX5rO7PtvQ2eZMmC5eufeelo+34RjYwWOjZtw2WqIPHE2prSTSbzyMix33ISnppbWTZux/+9d9vyjmohpU9GYjARcHajDAqi0KhTO/agUAbQGDZpJUvdwEwYdGqMOtUHXXVRkjAw9HXh1Jjq1Ei6NRFsgklavnianln17YG+9lxqbHcf+3vUGAEqVkrBwNRH+j/n085WkTJ/Om2++icViOZ6nXRgHRIIQxh2vo43mDzZif38jze9vxFm5G2nxSZjPTOOEe25GOuUk1AZ9v++VZRn37j20fFLa/fdZBX6XC+mUhUhLUom//GLCzCbaNn9Ba2kZ1Q8/jN/pIsIyDZUuHIXCR5heg7KrFRrtaNQQER9BmD6cMKOWMIO+OxlE6lEbjSj03z4ddOokOiOi6FBG0uqPxOHRs785jH3NfmprXdRVNdJub8fb5e3ueXyg3kClVpGYqCPnJ0ksnKNh48aNvPHGGzz66KOcc845vPrqq5jN5uP8LQjjgUgQwpjn7/TQ8kkFTdaPadrwKR07bESdupDo7yxh3qN3I6XNRxkWNuD7O+sbsH/4GfYPP6fl440EfH7Mpy8m6vQ0km++DpVBR+tnn+P4vIx9a18m4PNjmDEdZUQ4GkkH3nZo30fA4SVMrUSXqD+QELrrDtQH6g5UkQYUeiN+g4mAzoRLL+EOl3AqJFoDRuxuHY0NGur2+6ip6aC+eg+uVmd3QvAHuiuSlUrCtWpOWWzmlmsn42xr4OOPP+aTTz7h1us/5ssvvyQQCKBQKLj66qt56qmnCA8PP47fhjCeiFZMwpgjyzLOXdU0vvU+jSUfYf+4HOO8E4hJP52Y805DWrKgVz+Dg/mcLlo+KaX5vU+wv/8JXU12os44BfNZSzCfuYSwSTG0fl5Ky8ef0vLZRnyOVgxzZ6E26OhqasRTu5swyYjC34VKJaPRqtHowwg7UJmsMeq7nxAMkSiMRgIGI36dRJcuik6tRIfCdCAh6Gls704Iu6s7qN/djKs1WH/QPWeCUqVEbwjje+caWTynncrKnWzbto0tW7bw6aefUldXB4DBYODUU0/l9NNP54wzzuDUU08lMjLyuHwfwtg22HVTJAhhTAh0ddH8QSn7//M/9r/9Pn53J3EXnk3sRWcTc+6p3U1DB9CdUGw0b/iIJuuHtFZ8SeTJ84j+zumYzzkN4/zZOHfswv7hR9g/+gTnth0Y5s0mPC4Gf0c7zh3b0ejCUalk8HehidAQptOg0WsJN+pQR+q7B6szGlEE6xAMJrw6Cbc2ig6VRHsgEnunnsaOMOr2dxcZ7bU109FyoMjoQCc0v68VAnWcaLETrqxj584dbNu2jd27d4eOR6lUMn36dJYsWRJKCPPnz0etFgUCwtCJBCGMSb72Dva/+T77/m2l8d2PMJwwnUmXnEfcd7+D8aRZg3bWCnR5afm0jMZ336Pp3feR/T6izz+LmPPOwnzWEhQKBS2ffEbze+9j/+BjlHodxnmzUWlUuGyV+Jr2EyYZkTs7UIerUYcrCTdo0RgjCDfqURv1qCMNqIzBeQxM+HRRdOqicIWZaA9I2Lv0NDkj2Ncks2dvF7srm3Dsb6XL7cHZVoOrrQq3swZvZy1a1V6aGmy0tLSEjkGn0zFr1ixmz57NnDlzmD17NrNnz2bmzJlotaJ/gjA8RIIQxgyvo42Gf6+n/tV3sH+wkagzFhF/aQZxF5+LNj520Pf6Opw0rf+Q/W+up/l/H6NPSSbmgnOIvfBcDHNm4m1qpmnDezSv/x+tFZsxzJ+DbuoUAq4O2jZvQq0NQ6WRoasTjVbT/aRgDCfcoENjMqCONBx4SjARiOyuWPbquuc16FBIOPxGmp06Ghxq9jb42G1rpaG2kc6OTrxdnTj2b8K+7yPs+z7G7awLxR0fHx+6+Pf8mzJlyriZ1lIYvURHOWFU8zld7P/P/6hb+1+a3/uc6O8sIXHp91jwzwfRmIyDv7e9g8Z3/kfDv9/F/vFGpMULiPve+cz64wrCJ8XSuXcvje9Y+eZP9+GyVSGdegoR05JQhqvo+HIztDeh8LrQ6kAd7iNcF0ZYZAxhRj2ayANJIfLARDcGCa9BojPCjDNc6n5K8BhotGupb5LZXdtJ7Td7aWtqw+vx0uV2YN//GfaGj3E0fEaXpx2tVktGRgbf+95dLFiwgNmzZyNJ0nE5z4IwVCJBCCNC9vtpfu9z9rz4Og3/2UDUkpNJXHYxJ/8975BJwe9y01jyPvtefRP7R58TdeoiJl16IfMe+zMaUySde+toeOM/NL1TQufeesxnn45p4UloJAMdm0vxTYpBdrWji9KiUbnRmLqnwAwz6dBEGg8UHZmQI034DSY69WbcEVG0q6NpDxhpchvY36RhT4Of3VVt1FfV4upw4/d6kQMyzfs+pqG6iJb9m/D7fcTFxfHTq5bygx/8gPT0dHQ6MemNMDYcUYJ45plnaG1tPaxtZVmmrKyMNWvWHMlHCeOMy1ZL7T/Xsef51wiLjWbyT37AnAduH7DXcpDs92P/6HPqi96g8d33iVwwj/gffY95j96HxhRJl93O/v+8yf7/voWrajfR3zkL8xmn4vxmF62ffkhEfBwBZyu6qAg0ONHERRBujCDc9O1TgsrU/ZQQMEq49QeKjlQSLT4TTU4d9S1q9tR5qa6007SnubuDms8HMqjD1Jw4J4zW3Y/zwafPMWPGDJavuJ0f/OAHnHLKKaKoSBiTjihBmM1mli9fftjbr1u37kg+RhgnAl4vDa9b2f3MGtq/3E7iFZew+N+FRJ4465DvdX5TRd0r/0f9uv8QFhtNYuYlzLz7t4THxRDweGja8B4N//4vreUVmM86A/OZp6GbkoDjkw/wxMdBZ/eTgirQRni0lnBTBGEmffeTgimyOykYu5OCSx+NO8JMmyKKFl8kjW066u0KavZ0Ub2rgZZ9LXR1dhHw+1EoFGgjNPwkaxpXXZ7Ixo0b+clPlmGz2Vi5ciX33nsvYYP0vRCEsUBUUgvHTOfeBnYXvkztP4rRz0hmWs4VTPphxqB9FKC7CKnhP++y96VXcVVWk5B1CYlLL8UwZyayLNOxZSv71v0f+996F8Oc2USdthhfi51mqxVNpB6lSgZ3B+owJWG6MMIitYSbDISZDAeSgnSg+MhMl9GMOyL626TQoaPOrmB3jYeqnY20NrSEOqoplEqkqHBW/jKZJQujAPD5fKxatYo//OEPJCUl8cILL3D22Wcfj9MrCMPiuFdSb9q0CYCWlhbS0tJEh50JxlH6JVWP/pPGdz4k8ccXs+Stf2CcN/OQ73PuslH73Br2rfsPpkUnMS3np8RknINSo8HX3s7el16hvuhV/B0dxF38PaZe9zOa33+P/a+uJTzGjEbjQ40LjVqJNtFIeKQBjWRAI0WiNpmQIyX8kVF06qNx6aJpV0fR4pNobNOxt1nJ7toubDv20trQQpfHixzoTgoJ8Truu91CyjRDr3irqqq46qqr+OSTT7jyyit54oknRIWzMK4Me4LYsGED5513Xuj1pk2biIqKIjk5ebg/ShhF5ECA/W+9T2V+IZ17G0i+8SrmP3YPGmnwmwPZ76fxnfeoffZfdOz4hqSfXM4SazERkxMAaN+ylbqXi2gqsRJ1+qkkLrsc166d7H99HRGJ8SicDsJ1SlQeO7p4A9pIHeGSsTspSJEoTFH4jVF4jGY69TG0qaNx+E00ugzstaup2ePFtqOB5rpmvJ6u0JPC5CQ9D9xhYXJC3zGbZFnm+eef51e/+hUKhYKXXnqJK6+88picV0EYScOaIFpbW4mK6n70bmtrIzIykoULF7JhwwaRIMapgM9H3Zr/YntwNQq1ipTblxN/+YUoD9Gr19fewd5/vUbt6pfQREcxdflVTLo4A2V4GIEuL/v/+xZ7X3wZT0MjCZk/ZPqtN9L45pvUv/BPwmIlwnVKlJ12wg0qwow6tFHG7iIkyYRKiiIQGYUvMgqPPo72CDNtATP73Qb27Q9nd52Pb3a2sH93Ix5XZ3edglJJ/KQIHlg5g+TJ3yYFt9vNrl272LZtG9u3b2f79u18/fXXfP3115x11lm88MILTJs27VifZkEYEcOaIGw2GwsXLgQgNTUVq9VKcnIy46iaQzgg4PNR9/J/2HX/k2gT4piTv4KYjDMPORWlp6GRmsIX2PvSOsxnncr8p/KQ0k4Guudm3vPPF9j70itEJE8jIfMyPHV7aHi1GO2kGBRdLjThAVTOJnSxOrSSnvAoIxpTJBpzFLJJwm8y4zbE4NLF0ao0Y/dGUt+ko6YhwDe72tizqxp3u4uuTie+rla04S6uuESHSeemqamJfzzzKk1NTVRXV7Nt2zaqq6tD/34VCgXJycnMnj2b6667jptuuglVjylFBWG8GdYEsXDhQjZv3syCBQv45ptvhnPXwighBwLUrfkvu/70OOHxsZz09J+IPmfJId/nqq6h+rG/0/DGuyRcfjFL3llDxLTJAHTu3cue516k4Y3/Ev2ds5lx5+04PvmE3Y//Df30aYRpQelpRaOW0Zq7m6aGRUWiiYpEFWUmEGnGGxmD2xhDe3g0LX4z+51GqhtkvijfyZayz2ms3UqHw4arfTfujhq8Xd82037/9W/jVCgUREdHk5SUxJIlS/j5z38eGuZi5syZREREDPs5FYTRatjrIGRZDhUvAaxfv56UlJTh/hhhBDSWfMT2lQ+hDNMw//F7iT731EM+MTgrq6n62zM0lbzP5J8v44xP/kNYTPfcBM5vKql95h80v/8h8Zk/Ytaf72H/66+z+69/QTslgXCdCkVrPXpJQ7ipu24h3ByJOioKZZQZvxRNpyEGpz6WFkU0ZVv38eHHVio+/5CaXV/Q2mxDDnhDseiNMSxaOI+5c89gypQpxMbGEhsbS0xMTOgvKipKPBUIwgHDniAWLlxIVVUVlZWVtLS0cP755w/3RwjHWdtXO9h2+wO4a+uY9affEP+jCw6ZGNy791D50JM0WT9gynU/4YzP3kRj6r5p6Nixk91PFNBasYnEq67ghPPOov6VNTg+2EB4jAlNWABFSx2GaC3aKB3aqEg0UVJ3MVJUNH5TNO26aDbubuH9dzby2edlfFXxCR1tTQCERcRiMJ3A5BlpTEqYyV23nc1ZZywI1Y8JgnB4jjhBBIuS+jN9+nQ2b97cqzWTMPZ0Nbew895HqV/3NjN/fxNTly9FqRl8LmPP/iaqHi5g32tvMuWaKzjj87fQRHYPndGxcxe7nyigrWIzSdf8jLiLL6Tu+RdoKXGiMerQKDpRtnYSER2O1mxAG2VCY45CbTYTkKLxSrE4tGbu/tvfWbeuGGdHOwDGqGlExp5O0swTiTSfhCFqGj/PSuLnmZOP+TkShPHsiBNEbm4uWVlZA64vKirinXfeOdLdCyNIDgSofbaIHfc8QkLmdznnqzcJix787tvvdFH91HPUrn6JhKWXcvpHb4SKkty1e6h+7ElaPvmMyVf/jPhLv8+eZ5/F7nGjNkSg8DtRdnQQERWO1mxEG20iLFpCZY7BHxWDxxSHUx/HLruCW679FV9t+oT5py5DZzoFTfgsVOooFCiIj9fx+B9nExMtZlAThOFwxAlClmXKy8sHnAhdtFwam9q/3slXv7wbOSCz5O1/EHnS7EG3l/1+6tb+m8q8x5GWpLLk3bVETE0CoKvZzu6nCtn/n7dI+ukVxP/wEvb8/e80/ed1wqOM+J0dKNvbiZDCiYiORBvT/cSgio7BHxWLW4qjXR+PPRDLh+U27v3Nj+lobWbBuflIMWcT8PlRqVX84IJJ3HLttEMWewmCMDRHnCDeffddqqqqcDgcAKHmrUHp6elHFZhwfPk9XXzz5yeoeWYNJ9x7C1OXL0NxiAHmWiu+YvvK+1Co1Zz87MOYFp0EQMDjYc8L/2LP358n7uKLmP/036j75/M0v/UfIpLiCfg7ULQ60UthaM2RRMRKaGLMqMwx+MxxuEzxtOnjafZHs7fVRPErr/DK4zegCZc46eynMETOJDxcRd69szl57sAzyQmCcHSOqpJ6+vTpof8PDq+hUChYsGBBn4QhjF6tm7fxxdUr0FmmcFbFv9EmxA26fVeTnV1/foSm9R8y865fk5B5CQqFAlmWaXrXiu2hR9DPmsm8p/5G05tvsuO3t2GYPQMVHuSmWvRSOBExRrTREmExZlQxsfjMcThN8bTpE9jvi2Wv3cjO3T5efORWtn1egClmAXNPuY/pKVMouH8OBsPgdSGCIBy9YWvFFEwIVVVVLFu2jMWLF3PbbbcN1+6FYyDg81GZV0D1Ey8yJz+XpJ9cOmgxjSzL1K/9N7v++BfiL/s+p3/071AFtMtWxa77HsDbbGfmH+6is9rGjt/8BuOcEwjTKZEbdqOXNESYDUTERBEWZ0YVHYcvJg6nKeFAYoijptHIzt1+yj/Zxoev3oB932ckWi7jp9f9kftz54hhswXhOBq2BPHMM89QUFCAQqEgOzubpUuXDteuhWPAXVPHpp/+FpUugjM3vkbE5PhBt3dV17Dttj/idbSy8OWniTxpLgB+t5vdTz1DfdGrTLv+OgyzZlD117+i0kWgjY3E37CbCIOKiCg9uliJsLho1DGx+GPicUUl0KpPpMEbR81+I9tsPrZU1FCz/XO++vgOPK59/Gx5Hv8sXHE8TokgCAc5qgSxYcMGnn76aTZt2kRmZiZFRUWhYqe2trZhCVAYfvv+r4SvbrwHy6+vxvKbaweta5ADAWr//jK2vzxF8q+uZWr2T0PjLLV88hk7772PyJPmc/JzhdS9+AINa18mYloSvroa1BqZCFMEujgJbVw0mrg4/LFxdEYl4TBOpsEXx+79kWy1+fi6bDf2+gaqvn6W2p0vIElmrO+8xxlnnHG8TosgCAc54gQxc+ZM0tPTWblyZb/1DatWrWLVqlVHFZwwvAJeL9tW5NHw3/+R9upTRC05edDt3bV1bLnl9wQ6PSz+z4voU5IB8LY4qMz/C46NZcy4ayU+exNbb7wR49xZqJRdyA270ZnC0MVGEhFnJmxSHHJsAp7oRNoik2gIxFPVJLH1Gz9fl+2mpaGFlobN7Nz8AK62Kn7605/y8MMPEx0dfRzOiiAIAzniBLFw4UIyMzOx2+1s2LAB6C6jDlZWlpeXD1uQwtHzNDRRccWtqAw6ztr42iGH4a4r+jc773mQadf/nOQbr0ZxYPiJpv+9z6577iP2onROfOpRqh56CH9HG7rEGPx1NiIMGnTROnTx0YRNikMZl4A3JoEOaQr7FUnsdkSxpVpm02c13TO0uduo2f4se75Zw5QpUyhY8xYXXXTR8TglgiAcwhEniLy8vF6tmA42UP8I4fhzbPyS8h/fzOSf/YgT7v7VoEVKvg4n23P/RNsXW1i09hmM82cfWN5B5aoHcWwsY3b+n3HbvmHL9dcTedJc/PuaUGoUaKN06CdJaBPi0EyahC82iXbzFBo1k9ndEcvWagXlG+tpqm3C1+Wl1V5Gw86H2Fdfy0033cT999+P0Wg8XqdFEIRDOKImIQ899NCgyQF6N4F96KGHjuRjhGFQX/wWpZdmM+/h3zPr3lsGTQ5tX27l84ylKMPDWfLOmlByaK3YRNmlWSg0GuY/9Tf2PruaxrfeJCI+Ct/eSiIiNZimRhN1wmSMs2aiPGEOLssC6ial8bX/RN77ZhJrX7fz7qtb2FdZj9fTTpj7Mb54/xZMkTo+/PBDHnvsMZEcBGGUOaIniIULF/Lggw8eVs9VWZZpbm4+ko8RjoIsy9j+sprqJ15kydvPEXny4D2i9760jl1//huz719J/A+/270Pv5+agmfZ+/IaZv7hLmS3iy05B54aGqpQhSnQmXXoE2LQJk5CmZBEV9wUWkzTqPMnsW2PgdLyVqq+3oXH5UGpUnJV5iReeTab/73/PnfeeSd33XUXWq32eJwSQRCG6IgSxPnnny9GaR3FAj4fW27+I47Pv+D0D9cM2oTV3+lhx53349hYweLXn0M/s7to0NPQwLbb70ShVLLg+dXUFj6Dc+d29FPi8e3pfmrQx5rQJU0iPCkBX/xUWmOm06Cayi57NKVfePi6dAfuNicAZ54Wyx9/Y2Hp0qVs2LCBF154gauuuuq4nA9BEI7MsA/3LYwsv6eLTVf9hoDLzWnvvYTaaBhw2876Br74xS1oJydwytuvoDZ0T7XZ8nkp22+/k8QrlmI+63S23fprdNMmo/J2QIcTvRSBISkGbVI8isSpuOOn06hPpsqZSMUuKPuoGsf+FgL+AEmTDbzw8HyUyu7+Ma+++ioPP/ywSA6CMAaIBDGO+JwuyjNvQm0ykPbaUyjDwgbctu2LLWz+xc1M+cWPSb75ulDrs9pnn2PPP19k9gP34dlTy7ZbbiFy3gl07akkXKfCMMmEfko84UmJeBOn0RYzkz3yVL7cbeCjj5qo+6YeX5cXbUQYL/5tPrEx3cVHd955J6tXr+Z3v/sdt95663E6I4IgHA2RIMYJr6ON0h9ko585nRML/hTqzNaf/W9a2XrbH5jz4N1M+n4G0D1c9/aVd+FpaODk559lT2Ehbltld0V0XTW6SBXGpBgipiahTJqGK2E6+3Qz2NGSwMflHraUbqOzw41SpeSuX88k/azY0Of99a9/ZdWqVeTk5PCnP/3pmJ8LQRCGh0gQ44C3tZ3PL7qaqFMXMvevdw7aUqn6qeeoKXyB1JefJvLkeQB01tXz9Y23YJw7h+m/vomdd95JmFlC4W5BFaZAH2PAOHUS2uQpeBOTaY6bRbXPQunWMD7eUENLgx1Zlllwspm/3dO7Mvz555/nt7/9LZmZmTzxxBNiSG5BGENEghjjfB1OSi9ZjrRkAXMf/t2AF2A5EGDXn/5K0/oPOeU/L6JNSgCgddMXbL3lNiZf/VMMc05gS3YOxhPn0mXbRrhOhTFBwjB9MqrkZNwJM6nTncBXTQm891ELtq++wevpIkIXztqnTiTS2LtI64033uCaa67h/PPP58UXXxRzPQvCGCMSxBjmd7kp/eH1GObMYN4gySHg9bL1N/fgsu1m8evPo4nqnkOh8e132fWnVcz68x/wNjXyzd13o58xDV/NTnSRGiKnxqGzTCEw1YIjfi6VgRl89KWGT9bvoqOlHYVCwS+vTmbZJYl9PvPDDz9k6dKlpKam8tprrxEeLmZ5E4SxZtgSxPr16ykuLgYgIyODyy677JDvcTgcFBYW0tzcTF5eXr/rAEpLS8nIyCA7O3u4wh3zAl1dlGXeRERSPCc++YcBi5X8nR6+vO43IAdYVLQalS4CgD0v/IvaZ5/jxMInaHrnHVo+eB9ttBG5cQ/6qDBMyYloLdPxTJtFvTSPL5qmULK+mertu/B7fcTG6Vn75Il9ht/evXs3999/P3//+99JSUnhzTffFB3gBGGMGpYEsW7dOmw2G5mZmQBUVFSwevVqrrvuugHfY7VacTgcVFZW9rt+1apVvZJGSkoKgEgSdHeC+3L571BFhHPSs6tC4yQdzO/u5Itf3Iw60sj8Jx9AqdEgBwLY/vI37O99wEnPPk3NE0/gbW5CRScqbwBjvAnjjKmoUmbQPnkelerZfPCVjg/f3UmHowOlUsH9d87ijLTeA+nV1NSEEoNCoSAnJ4e77rqLmJiY43FKBEE4BoYlQUiSxO233x56ff7557N+/fpB3xOckrS0tDQ0bWmQw+HAZrP1WpaTk0NeXp5IEMCOux/BWVnDqe8+N2BrJb/Lzeaf/Yqw2GjmPfZnlGo1ss/Hjrv+gHt3DfOf/Bu77r0XtU6LbK8nPEKJaVoc+pSpyDNm05R4Ml+2zeQ//3VQ+dVW/F4fiUlG/vXo/F5FWTU1NaxatYpnn30WhULB8uXLueOOO5gyZcrxOh2CIBwjw5Ig+iv7bm1tPap9Wq1WbDZbaNA/SZL6JI2JaHfhK9QXv8XpH7wSKi46mN/pYtNVN6KdnMC8R/6EQqUi0OVle+6d+No7mLXqj2y//Ta08XF4d+9Ca1QhTU/AMDuFLss8ak0n80FlHO/8p4q2pjaUCgX3/24WZyz69qlh3759/PGPf2T16tUAXHfddaxcuVIkBkEYR4YlQbS0tLBy5UoWL14MdD8VBIuEjoQkSbS0tPRaVlJSEnrqmKj2v/0+u/70OKe99y/CY839bhPwdLH56lvQTklk3sN/7E4OHg9bbr0dhVJJyorfsPWXN2I4wUJX9U50kgYpJQntnBNwWhayXX0y/35fxeaPtuH1dGEy6/i/wpN61TWsW7eOnJwc2trauPbaa1m5ciVTp049XqdBEITjZFgSxOWXX47FYmHNmjUALFu2rN9JhI6Uw+HAarUestiqrq6u19PMPffcw7333jtscYwk565qvrjmDhYVP4E+pf+LccDn46vrb0cdaQwlB39nJ1tuvBW1ycTU7KvZ+qtfYZwzA2/NLgzmMKQTpqGZOxf79MVsdMyl6LV6GnY3gixz3c+n8dNLk0L7dzgc3HzzzbzwwgssWrSIF154gTlz5hyvUyAIwnF2xAmiurq61+uoqCiuv/760OuVK1cO24xyy5cvp6ioiNTU1EG3S0xMpK6ublg+czTxtXdQlnkjJ9x7C+bT+z8HciDA1lvvwt/pYcE/HztQrNTFlpt/iyZKYsq1P2fbzbdgmDkdb20lBrOWqHnTUcw9mT2JS3hnVxLvvL4LV5sTTbiG11efjF7/bb+GDRs28Itf/IK6ujruvvtufv/736PRaI7XKRAEYQQccYJIT09n0aJFyLIcWha8e5dlmU2bNg1LgsjPzycnJ2fCFi/JgQCbr7mDqNNSmZb94wG323l3Pu7aOlJffhplmKa778OvV6CKiGDyL65i2823oJ+ZjH/fbiIn6ZDmzyQwP42dptN5eUMEX3y8Db/Xx6xZZgpXfdsb2u12c+edd/LII49wwgkn8Mknn3DKKaccj0MXBGGEHXGCKCgoGHTI702bNh3prkOKi4tJTU0NJQer1TrhEsU3eQV49jWx8MW/DrhNTeELNH/wGYvfeB6VLgLZ52P7ijtBlpm6/Gq2//rXGGZOw99QiynRiHTyLLrmn0aZ5jT+8UIL+6p3Awru+u1M0s/4dgyliooKrrrqKrZt28ZNN91EXl4eOp3uOBy1IAijwRHNKAcMmhw2b95MVVXVke4a6E4GdrudtLS0ULPXioqKo9rnWGP/qIzdT77EojV/QxXe/8is+99cT/UT/2DhS0+iMUUiyzI77/0zvrZ2pt96I9t/8xv0KVPwN+xBmmIkKu0kOhaez1vOs3n0yT3U2/ah1qh5+6VFoeTg8/m47777WLJkCa2trbzzzjs89thjIjkIwgQzLJXUVVVV5OTk0NLSEipyOlRv6oqKCqxWa6j3dX5+Punp6aSmpuJwOMjI6B5lNCcnJ/SeYEe8icDb0srmn9/OiQX3oU2c1O82rRVfsfW2e1n4r6eImNI93EX1o0/i3LmTWffdy7Zbb0GfMpXA/lqkKVGYFp9M04nns2bLDEre2IG300N8UiRrHpsf2ueuXbv42c9+xmeffcYVV1zB448/jtncf4spQRDGt2FJEAUFBRQUFACELiaH6rOQmppKamoqK1as6LNOkqRedRsTjSzLfHn9XUy6NJ1J3/tOv9t07q3ni6tvYd7Df8K0oPsCv/dfa2h86x3mPvoQ23/7W/TTp+LfV03UVDPGUxdSN+d7PP5uDF9/vhM5EODSi5P4zTXTQp/59NNPc9tttxEeHs4rr7zCsmXLjtchC4IwCg1Lgli2bBnTp08H4NVXX+Wyyy7r049BOHy1q9fi+mY3C55/qN/1/k4PX1zza6Yuv4rYC78DQOO7VmoKVnNiwePsuutuIqYl4a+vQpoaheHMJVSlXEz+v1Ts3WVDoVTwVN485syIBLqbB1977bW8/fbbXHjhhTz77LMkJSX1+9mCIEwcw5Ig7HY7ixcvprS0lI0bN4aGzzjvvPOGY/cTSsfOKnbc/TCnbnip33oHWZbZnvsnIqYmMe3GqwFo/3oLu+79M/OeepTqRx4hTDLi31tF1FQJwzmn8+WUy/lLQSstDS2owzW8/fxCNBo1siyzdu1afvnLX+J2u3niiSe44YYbxJwNgiAAw5Qgzj//fEpLSwF44IEHWLdu3SH7LAh9yYEAXy6/kxm/uxHjnP57ou95bg1tm7ew+M2XUCgUeBoa2PKr3zDz3t/RsHYNssdFoLmeqOQoDOeezcfxS3nssb2425zoTTre/McCfD4fL7/8Mvn5+WzevJklS5bw/PPPc8IJJxznIxYEYTQ74lZMg7n88svFXegRqH7yJQCSf/mTftc7NlZge+hJTn7ub6j1OvxuN1/f+GsSr1yGa8c23FWVBJrqkKaaMJx3Dm8as3j40d2425wkp5gpfuIEHn/8cWbOnMmVV15JZ2cnq1ev5qOPPhLJQRCEPoblCaK6upqioiLsdjvQXQyyfv360FOFcGiuqlp23fc4p7//cr9zO3hbWvnqhlzm/vWP6KZPRZZldtx5N/oUC9qEOGqffhqVwoMpwYAh4zu8FMjitcIqfD4/py7WofeuZdq0x2hqauK0007jkUce4ZJLLukzn4MgCELQsCSIBx54gIyMjF7FSgcP4S0MTJZlvrrhblJuuw7DLEu/67f8+i7ivnt+qFJ6zz+ep7OunpQVv2ZH7h1ojRp0Ji2mC87lsaYfs+G/W2mu/xiD6mP+9ocSPB4Pl1xyCStWrODMM888zkcoCMJYNCwJIicnp8/gfGlpacOx6wlhz3Pr8DramH7r1QOsX0PnnnpOKuhu1eTYWEbtP55n/hOPsHPFCiImSYTjJOqis7nx4ym8//q1NO7ZgM/bTlxcHDk5OWRnZzNv3rzjeViCIIxxR5wg2traQv/f0tLChg0bQnM3QHffiOEarG8887a0suOuh1n8xjP9Tv7TvmU7lQ8+weI3XkAZHoZnfyPbbl/JCX+8C1teHhGTJ+Gy1/J8QKbghr/R7tiLUqXlsh/9kGuv/Tnp6emoB5hUSBAEYTADXjna2tqIjIwc8I2pqal9BuvrabgG6xvvdtz7KJMuTce0cG6fdf5OD1/dkMsJ996GPiWZgNfLtt/kkrA0E8fHH6HUKCjdsYU/bK+kuslB1KQlzFmSzYb/u4H4+Nh+Pk0QBOHwDZggVq1aNegF/ngM1jfetX21g/ritzjny//2u9724JPoZ0wnIesHAFQ//hTKCC0RUxL55r+v89T2r3mpqpbIqGmcfPafiU5I4+0XFohhuAVBGBYDJoji4mIuuOACzj333H7XD5YcgGGdMGg8kmWZLbfexwl33URYdFSf9a3lX1K35v847X+volAocGwspeG1N5jz1wcoysnhTzu2Uut0M2fxzzEn/Aytzoj15cUjcCSCIIxXAyaIpqam0NDawSG3MzIySEtL67fo6VBFUkJv9UVv4XO0MXV53/GO/J0ettzyO2b9eSVhsdF4W9vYfsddJN1+K7+64gpe+mYXSUYdF/30X7icyWjC1CI5CIIw7AZMEMHRVs1mMzabjZKSEvLy8lAoFFgsllDCSE1NJTk5+ZBFUsK3/O5Ott2Rz8LnH0KhUvVZX5n/OIY5JxB/6UXIssyue/+EK/UkLrjuGnbs38+yGVOIWPoWtu1tIjkIgnDMDJggpk+fzvLly1m/fj0Wi4V3330X6E4c5eXllJSUcN1119Ha2ookSQAiQRym3U//C9PCuZjP7NsUuHXTV9QXvcFp/3sVgIb/+zfrP/2Uu7d8QcDj4YlTF2C7rJiyz/aL5CAIwjGlkA9zXO1169aRkpLCggULei2vqqqipKSEBx98kF27dh2LGA9bWloaZWVlIxrDoXjbOnhvzgWc+u4/Mc6b2Wud7Pfz+XevYOryq0jM+gHuunp+e9qZFOypxqLT8fDik/jiB09T8mEHKo2K9a+IqT8FQTg6g103D3uchcsvvxyTycSrr77aqw/E9OnTyc7O5vLLLz/6SCeAqof/TuwFZ/VJDgC1z61BrdeRkHkJ7e3tXHrmWTxVY+OC5GRe/G46ey5aSclHHSjVKv6e1/9gfoIgCMNlSD2opk+fzvTp01m/fj2tra29ZozrOfOb0D9Po53qJ1/izM/X9V3X0IjtL0+R9tpzVFZWcvF557OrtobfLV1KZsBLlTaaVzbGoFQqyLt3KtOmRY/AEQiCMJEcURfbYBPXdevWERUVxXnnnReaMEgYWOUDT5P444vRJU/us27nPQ+SdOVluM2RnDp7Nt62NtasymPqu2/j1it5lFwUyORcHcfiOfEjEL0gCBPNEQ/l2dbWRkpKCjabjWXLllFdXT2MYY0/7po69rz4OjPvvKHPuuYPPsNRthnLb67nnnvuwdHSwiu3/paZ27ehjYrg97r7kQMBzr0wiWXfFYlYEITjY9ChNmw2W+ivsrKy12vo7uwlSRIWi0WMvXQIlX95linXZBI+KabXctnvZ+ddecz64wp27q6msKCAH01J5qT5c2l8Ywe3hf8Rn6eLeYsmc/fyKSMUvSAIE9GACUKSJBQKBZIkMX36dCwWCwsXLiQzMxOLxYLFYhHFSofJs7+Zupff4Ox+htTY+6/XUEeZiP3u+Vzz/e+jVSi59/4/s/fZZ/hD8sN0OZxMnjGJJ+8UyUEQhONrwARhsVjIyclBkiTS09NFMjgKVY89T0LWd9EeNICer8NJ5YNPsOD5x/jf//7Hf996i1+feQ6BD97n0RMeoGO/E1OcicdWiB7qgiAcfwMmiMzMTG6//Xage+C91atXh9ZZLBbOO++8Xtu/+uqrvVo1Cd28bR3UPPMKZ35S3Gdd9eN/J/qsJRhPmstvTvoxk8LCuenaX/Diei+1Th9ag45Hl9VgjhHzOAiCcPwddke5nqqqqrBarTgcDhQKBSaTifz8fNFRrh+VDxbS9uUOFr7wl17LO+v28dl5l7PEWswa6ztcffXV/O2a60iqdfOY8UZUGjW//6WZc88W/R0EQTh2BrtuHlEz1+AwHEEVFRU0NzcfWXTjmN/dSdWjz3PKm8/2WffNA4+R9NMsZLOJO2+/nblSFBcmT+f6tvNRIPPDZdM49+y4EYhaEASh27DMWJ+amkp2dvZw7Gpc2fPPVzEtmk/kibN6Le/YUUmT9UOm33wdf3nwQeqbmrjv17/mVzsuJBAIcOKSaVwVXzFCUQuCIHQblgQB8MADDwzXrsYFORCg6rF/knLbdX3W2R56kuRf/oImZwcPrFrFeckWXtmdjsflIW5yNHec/CFRp100AlELgiB8a9gShNBb0/pPUIaHE3XGol7L27fupOXTMqZc/WPuWrkST1cXZ3wvl30tMjqTntyrlCRmLB2hqAVBEL4lEsQxsvupl0j+5VUoFIpey21/eYppN17Njt3V/P2f/yRr4Sl80HAi6jANP/vpNGY1bhyhiAVBEHoTCeIYcFXvwf5xBYlXXNxrefvX23GUbmbKz5dR8MjfUAF7pv4JUHBG+gwy2l/B+L0rRyRmQRCEgx1RKyZhcDWFrzD5pz9Erdf1Wl754JNMv+kalBFa1q1ZQ8zk01Aq9CSmTOIXi3YQOecXIxOwIAhCP446QbS1tWG1WiktLcXhcCBJEosXLyY9PX1CzlHt7/RQ+9w6Tn//5V7L277cStsXWzjx6Xw+ee3/2NvWysyUs9Gb9CxfasBU9i/CFp46QlELgiD0dVQJYt26dZSUlJCSkoLFYgktr6yspKSkhIyMjAnXu7p+7ZuYUuehn5nca3n1Y88y7fqfoYrQ8s/78wAlcVO+ww+yLJy07xWil/9uROIVBEEYyFE/QTz99NMDrlu/fv3R7n7MqX7qJWb+/sZey1zVtdg/+py5D/+R9q3b+dc3jZhiTibt3DQuStpCmFP0lhYEYfQ5ppXUra2tx3L3o07r5m107W8m7qKzey2vKXiepKsyURv03HHXmzhbbUyd/V2WfacL6ZM3MJ5+3gB7FARBGDlH9QRhsVhYunQpKSkpREd3T4EZHHLDZrNNuGlI977wGklXXYpCpQot62puof7V/3L6B6+zr/wr3trxDQC/+OXPmdX8PyKuun2kwhUEQRjUUT1BLFy4kLVr15KWloYsy8iyjNlsJi0tjTVr1vQZ8XU8C3i97H3lP0z+6Y96La/9x8tM+n4G4ZNiueohN0117xM/LZUfznfiKysl3CiNTMCCIAiHMCzNXC+//PLh2M2Y1vj2B+hnTEM/Y1pomd/lpvbvr7D49ef4/Z++oL1lL+0tW/nxVb8jesf7mHIfHsGIBUEQBndM6yBeffXVY7n7UWXPC//X5+mhbs3rSIsXQNJkPtrsorX5UwCuPjOZrn2O4x+kIAjCEBzVE8Qdd9wxYEW0LMuUl5dPiGauXc0tNK3/hJOeuT+0TA4EqHnmReb+5V4uy/4SFOBq/YyUlBnMa99D5E33jlzAgiAIh+GoEkRKSnfzzJ59ICaiulf+S9z3voPGZAwts3/4OcowDW/tT6DTtRu9pGRv5cf8+sof0KWJGcFoBUEQDs9RJYilS5dSVlbG+eefP1zxjEl7XniNWX+8tfey514h8ec/ZuULtWjCw5AMZQQCAS6eZCDmZzeNTKCCIAhDcFR1ECaTadDkMBESR/uWXXTW7yfm/NNDyzrr9mH/pJTffDYLZBnLiVPY/cU6psRFc9K5l45gtIIgCIdPjOZ6lPa+8h+SrrikV9+HPS8U4/nuUpoaXeijDJy2SEXZp+/z/RMmY/5+5ghGKwiCcPiGlCBuuOGGQdffcccdXHjhhTz00ENHFdRYIcsy+9a9TULmd0PLAl1e9r5YzIP1p6NUqzjlnOk0f/UyXV4vP/jRj0cwWkEQhKEZUoLIzOy++928eTNtbW291q1cuZKYmBjeeecdFi5cOCGauLZ/vZNAlxfTovmhZfvftPL+7J/g8/qITYrmlDnw8TtFxBoiuOAW0WtaEISxY8hFTDNmzCAzM5Pp06f3elIoLi7mtttuA7rrHmRZHr4oR6l9r75D/GUX9po1rua5NWyQ56PRhnPGd5KYotqF9aONfPe0U1H1KIYSBEEY7YaUICoqKigvL+ebb76hubkZk8kUepI4OCFIkjRsQY5W9a++Q8JlF4ZeO3fZeEj9Y2QZkuckEa3YyvXX/JSOTg8/yxXDeQuCMLYMKUFYLBZMJlPodbCZK0BUVFSvbQ+ei3m8ad/6Db62DqRTTgot2/r8f2kIRKLVh9Na8w+uW3oGX++s5OFrfzIhWnQJgjC+DClB2O12NmzYQFtbG9XV1TzwwAOkpaXR2tpKS0tLr21tNtuwBjra7HvtHeJ/dAEKZfcplP1+7tqVhrOtki/eu5bi1XeSfsrJfHRjFreufnGEoxUEQRi6ISWI5cuXs3btWpKTk8nKysJisVBSUsIdd9xBQUEBDz30ENXV1axevXrc966uX9e7eKl03ads21xIxYZrcHfU8cRf83j5l5cTM3nWCEYpCIJw5BTyMNYmb9q0iYKCAi644IIRGYMpLS0tVOR1LHXsrOKz9J9yfvUHKJRKZFlmyszL2Vv5GvNPu4K/Pvh7FsvbCHz8P8y5jx/zeAThYBUVFSxfvpz09HTy8vJGOhxhFBvsunlEHeVWr17NDTfcwLJly1i9enVo+cKFC3n66acPOzk4HA7y8/PJzc09ovUjZd9r7xL/wwtCyeHKK3/J3srXmJm6nLse/AdzJDeaumqcjq6RDlUYIVlZWRQWFh7V9v29/3D3m5qaOuEm7BKG35DHYrrggguwWCykpKRgsVgoKyujoKCA9evXExkZedj7sVqtOBwOKisrj2j9SNr36jvMzlsBwP33388rrzxNUsrlXHHzw0yXWjDYq/HW7iH+rkdGNlBhxOTk5AypmPXg7W02Gw6H46j2azabR+XvRxg7hpQgVq9eTVFRUa+WTNB9p19YWBjqB3E40tPTASgtLe33h3Co9SOlc18jrqo9mM9M47HHHuP3v/89cVMu4rRLVjF/ppp4RR2afbux1zYg6XQjHa4wQoL/fo90+7y8vNBoyUez3yPhcDgmRDN14dCGlCCioqL6JAfo7vMwffr0YQtqNGt850Nizj+N5198kZtvvpmYxLOZe+rdnLx4MskmB8aWGrx1ezHfdNdIhzqu7Lv/fjzbto/IZ4fPmU38nXce9vYHl/9brVZyc3NZtmxZ6O6/pKSE3NxcLBZLv9vbbDZsNhuSJGGxWEhPT++3XqGiogLofuIoKSkhLy9vSBf3iooKrFZrqMFJRkYGpaWlZGRkkJubS1paGgUFBVRUVITiLSgoCH1mcXExFouF0tJSVq5cGfrswsJCLBYLDoeDkpKS0HsGWi6MTkNKEIP1bRgN/R7q6up6xXHPPfdw7733DutnNL79PuWxWq6/9lpOWnAWkVP/wKRpCcyermSSsh51Uy2tNftImjFnWD9XGDuC5f/B4p309HRycnIoKiqipKQE6G4yXlBQQF5eXr/bBy/82dnZA+4XuuskioqKQsPg5ObmDumie/7551NVVYUkSZSWlmK320PJJycnh/Ly8l6fvWbNmtB7MzIyQrGkpqaSlZVFSUkJ+fn5pKenk5qaCnzb5H2g5cLoNaQE0dzcTHV1NcnJyb2Wb968eVSUdSYmJlJXV3fM9h/wetnw1jv8vrOaU045hbCEP6IO0zM/dRJTIx0YW/cSqKsj/MyLj1kME9VQ7uBHg/7K/3ve2ZvN5lCyGGj7w9lveXl5aL8Wi+WILro94zrc33FhYWHoQh/87GBLGIvFwvLly8nJyWHp0qWhJDfQcmH0GlKCWL58OUuXLqWqqir0qGyz2bBYLL3uLMarj18q5g8dNpJnWPjNHf/g8X/aiU6MZtY0JTGqBjTNdbj27CPuhlUjHaowCpnN5mOy39zcXBYvXozdbsdutw/pvUuXLqW4uDj01FJUVHRY76usrMThcGC1WkPLgu8NPs0UFBSQk5NDdnY2BQUFAy4XRq8ht2Jau3YtmzZtoqysDIfDwR133MHChQuPRWyjSk1NDVk334BOp+Odd97hmhUNqDUa5i2MZ4qpDam9Dhr24vaFjXSowjhTXFwcurj25HA4WLRoUegpoqKiInTBPdyGHYsWLSI1NZWysrJeTzT96Zl8Fi9eTEVFRb+V5larlczMzFDMixYtCtWp9Ld8vHeqHcuOqB/EwoULWb58ObfffnsoOYznOSDsdjsXXXQRTpeTdU8UUNNgwOf1ETUpihOmaYhVN6Kx1+PZ10Di7x8c6XCFUcButw+p9d3B21ssFpqbmwfdrqysDEmSQkVEweKl4MX4cGIoLy8PVYIfzGKx9EoKPRNIZmZmn/0H+2eUlJT0KuoK7nug5cLoNeATxIUXXjjQqj5kWaa8vHxIzVzHCpfLxcUXX4zNZuM+4wzOuDKTjJ+Uo9KombMwkclRTiKd9SibG3DW2Yk2Hn5fEGF8ChbV2Gw2rFYrZrO5z+uCgoJerYB6rk9PTyczM5M1a9aEWv30t9/09HTS0tJC26SmppKWlhYqMjp42/5IkhRqTmu320OtloJJo6ioiOLiYoBQy6bCwkKys7MpKipi1apVLF68GPj2gp+SkhJqGeVwOFi8eHGo71R/y4XRa8ChNi644ILDbjInyzJ33HEHa9euPewPDjavCz4S5+Tk9GrhcKj1/TkWQ21ceeWVvPLKKzx5/a9Z0g66e+8l+/avMCfF8MMfTWdJYg2JdZ8R2FyG94Qzib348mH9fEE4VoqLi7Hb7b0qi4PNWQ9V3CSMH4NdNwdMEJs2bRpS3UJVVdWI94U4FgmitLSUL7/8kpPf3kT8penklEzB5fJxSsY8LjglwDzlV0Tu3Ijj83ISHxSjtgpjR35+PqmpqX2eLjIyMkSCmECOKEGMRcdqsL5AVxcliaezpOK/XHprJQZzJD9aOoslU+uZ2lSG4usy7N/sJ/mh1YfemSCMIoWFhTgcjlB9g8PhIDs7W/SknkAGu24OuRXTRNTy2Wb0M6bx28caUSgVJM9OZHK0lyh/IypHA+6GRlE5LYxJoi+CMJgjasU00TS/vxHzd06l0tZOuE7LzJl6Jula0Tv3o7A34d7fQpgUdegdCYIgjCEiQRyG5vc/59/hZyAjE588iamTQFI2o27dj7epmbDU74x0iIIgCMNOFDEdgr/TQ2vZ17wTpUQTpuaEOWYmGZ0YnI2oHM04G+3E3frLkQ5TEARh2IkniENwbPyCuoXpBPwBouLNTE1UY1Y7CG9vwm9vxm13oVSK0ygIwvgjniAOofn9jayNvxyVX0HK3EkkmDoxeZtRtTfS2WQnMvOakQ5REAThmBC3voew/72NuD0BIow6pk0NIzq8nQhXE9jtdDa1EJ3xvZEOURAE4ZgQCWIQ/k4PL8pnolAoSJoxiaQoP5KyBXVbM74WO50ecfqEsauiooJFixaNujnfB3O8Y7ZarYf8PJvNRm5uLgqFgvz8/AG3iYqKIiMjIzR0ycGysrIOuf+srKzQCLpWq5WsrKzQ5x6L+TXEFW4Qjs83syP6JNRhGiwpJmL0TvSdzajamulqbmXSr1aOdIiCcMSCkwANt6ysrNDAfcPtSGI+mliCkz0NxmKxkJeXN+jw5cFRa3Nzc/sdmddqtVJcXNzvRT64f4CVK1eGer4HY5MkiRUrVhyTca1EghjE5je/JOAPYIqTSJqkIkrdSnhHM7KjBXeTA8OcE0c6REE4KsdijorguGnHylBittlsx21O+4yMDODbaWCHwmazkZ6ePurmxxAJYhCPVM9GqVIxffYk4iM9GP0OVB3NeB0OfLrokQ5PEEal9PT0UTNKa/DO+3gJjsLbk81mIy0t7ZDvzcrKGrD4aaSIVkwD8Lk7afOpiTBqmZoUTlS4nQh3M8pWB132VpJuu3+kQ5xQbr31VjZv3jwin71gwQIeeeSRIb2n51DepaWlrFy5EkmSKC4uZtWqVTgcDsrLy7Hb7aSkpJCdnU1ubi4WiyV0B2qz2SgpKQmNqmy1WsnNzWXZsmVYLBYkSaKoqIjc3NzQe0pKSkL7CW6flpYWurvtuX4ocfcnOMy4w+GgpKSEgoICKioqWL58Oenp6eTl5R1VzMH9BdcNdHc92PkKzo0hSVKveS8GO06Hw9FrGPOhTKeck5PDokWLeiWmQ02KFByO3Ww2k5OTQ0VFxaCjVh9PIkEM4Mm/fQHITJoaS0IMmFRtaDoc+FsddDa3ERefMNIhCqNYRkZG6MKSmppKVlYWJSUlZGZmkp6ezqJFiwBCc0P0HBMpKyuLoqKiUFl1bm4uBQUFoTLnoqKi0GirNpuNrKwsysvLQ+/Py8sLbb9s2TJKS0tD+wp+9kAXvYHiPlh+fn6v4feDZefBOoLgPo4k5pycnNC64P4Gm9J4sPMVTB4Hjzk12HGef/75rF+/PpQwSktLB/zsg1ksllCiO9xitp4z86Wnp7NmzZoBE0RBQUHo3w7Q6xweCyJBDOD1TaDWaEhOiSJG34ne60DVYafL0YpXYxzp8Cacod7Bj6TCwsJeP3CLxdJrtExJksjLyyMrK4usrKw+F6/gFKLB9x5ccdnzjt5sNvcqk5ckqc/2Pe9eg3fSwUl/hhL3wftcvnw5OTk5LF26tNe+zGZznwQ01JiH4lDn62CDHWewhVDPeFNSUob0FLFs2TKKiopCCepQxUs9PysnJ4fc3NwBi8ZycnJ6xW61Woc0D89QiQTRj85OHz6vH1NcJEkJGqQwBxHtdhRtDrocbcT/6o6RDlEYxSorK3E4HKGLDUBRUVGvbTIzMwetkMzNzWXx4sXY7fZe035C30raoQ7NbbFY+r3gHU7cQcG79YKCAnJycgZtwTMcMR/KYOfrYIMdZ0VFxVHXn2RnZzN9+nQKCgqw2+2DFhdZrVYcDkeopZXD4cBms42aYiaRIPrxwJPVKBQKJltiiZP8RKpaUbta8Le14rG3M2nm7JEOURjFFi9e3KvYoD/BsvVgi5/gRcnhcLBo0aLQXXFFRUXowjtcrXGCRTxHEneQ1WolMzMzlCgWLVp0yLL2IzXYBX8o56u4uJjMzMxBjzM1NXXQ4qzDIUlSaOrXQyVCm83GihUrei0rKSkZtJjpeBKtmPrx4efNqMM0TJlmJEbXic7jQNnhwNfaTpccNtLhCaNcZmZmaPKdoJ5t8R0OB2VlZaFmjT0v1mVlZUiSFLqwBItLgpWtR6Ln+4J3qMEioZ5xHirunkpKSnrtt+fF9uB9DFVw8qKen9VTz/0f6nxZLBaam5t7vX+w4wweR8915eXlh3U8PWPOysoiNze313npbx/9LcvJyTlm/UiGSjxBHMR1oHhJioskPkaFUd2Ott2Boq0VT0s7sdf8aqRDFMaAoqKiXi1hgheK/Px8CgoKQnfeZrOZiooKsrKyQp2g0tLSQi2EUlNTQ3ej6enpFBUVYbPZsFqtoQruYIuc1NRUCgoKKCsr61PHEGw+WVpaGrrgVlRU9NpfcP/9xX2wlJQUrFZrqBXT4sWLQy2wDo5xqDEH4wjGnJGRQW5uLoWFhaSlpfWJeaDztWLFitATQXD9ob4fgPXr17Nq1apQy69g67PgE8jBgj2de1aIZ2dnh4rxgkVINputV91Cbm4uDoejT2X/mjVrcDgc5OTkhDrCBZ+KVq1aFXrqtFqt5OXl4XA4yM/PJzMzc9if4MSUowe568GdfPhZM3OXzOS75xqYF2kjtv4L2PEV9k07mPb0umGKVhCOvfz8fJqbm497fwBh7BjsuimKmA7ycVkL6jANk6caMevc6LtaUTrb8LV14Oka6egEQRCOH5EgenC5ffi9fvSSkUnRKoyqDsI6HSg62vC2tmNeJob2FsYOq9XKmjVrKC4u7tViRxAOl6iD6OG+x2wolAoSp0cTY/JhVLShdjoItLfhaelg8gViaG9h7EhPTz/mHamE8U08QfTwWVkLao2GpMkGzBEedJ5WlM52fO3tdHZ4UCgUIx2iIAjCcSMSxAGuTh9+nx9DlJG4GDWRmg7CPG0oXO34Wp2EzV106J0IgiCMIyJBHPDYszUoFAoSkqOJNQXQKzpQuVoJtLfjaXOS9Mtfj3SIgiAIx5VIEAes/7gZlUZNQpIBSduJzteOytWOv70dj6MDtTFypEMUBEE4rkSCOMDj8REeEc6kGDWRYW7CPK0oOtrxtXfgU0eMdHiCIAjHnUgQQNkXLSDLmJPMmCMDGFQdhLnbkJ3teNtcxFyZfeidCIIgjDMiQQB/KaxBqVKSNEXCrOsiwt+O0tWO3+mks81J1DnnjXSIwhgSnOh+oAnsj4eKigry8/MpLi4mPz//uE27KYwvIkEA+/a7UYdpmDRJQ2SYmwhPG0p3O752J13tXaJ5qzAkwYl6joXDGcQtODbQihUryMzMpLKyss+cAaNlMDhhdJvwHeVcbh8BfwCj2UiMpEKv7EDT1QbODnwdTjQz5490iIIAdF/4D+dJwGq1hgaaA0JTcA51P4Iw4Z8gHv37bhQKBZOmmDHrfehxonK1E3A66Wpzknjjb0Y6REEAOOwB9w6++B88J4EYuE84XBP+CWLDx3ZUGjXxCQZMWg/arnaUbie+DieeNjfhsXEjHaIA/OGNLWytaxuRz56bGMk9l8wb8vsqKytDk8ZUVFT0Go45ONy1xWKhtLSUlStXhi7kwaGpHQ4HJSUlFBQUYLVaQ3McBKcN7W8obqvVGhrOW5IkHA4Ha9asIT09nby8vMPejyCASBB4PD70Jj2x0Sr0ajcaZwcKVwc+pxOfmBxIOAp2uz00f0B6enqvuY0zMjJC/5+amkpWVhYlJSXk5+f3mR8g+P6e8w0MpL/tJEkKfdbh7kcQYIIniM83dTdvjYqPItoEepULdWc7uJx4O9wYz71opEMUDjiSO/iRdvDkLRaLJVQ53HM6SYvFEhqP32KxsHz5cnJycli6dKm4iAsjakIniL/9vRalSknCZAkpwkdEoB1lZzt+ZwfedheJV/x0pEMUxhGLxdJrlrGeQ3AXFRUBhJ44CgoKyMnJITs7OzSb2MEyMjJ6TfsZ3LcgDJcJnSD2NbhRazTExYVjCO8gvKsdpctJl9OFp92NKlw70iEK44jdbmfRokWhaUYHqkPIzMwMJYpFixaF5lbuqbi4uM9czUdioGk0BQEmeCsmv89PuF5LtKTCoHIT5ukAdwc+Zyd+WTPS4QljXM+7++Dr7OxsMjMzsdvtvVobBYueSkpKer2vZxKxWCw0NzcfdVzDtR9h/JuwTxBfbetuEWNOMGE2+IlQuFB1diC7XPg6XOjPFL2nhSMXbB1UXFwMQGlpaagYCbqLlFatWsXixYuBbxNBSkoKVqs11Ipp8eLFoaeHzMxM1qxZE2rl1J/gLHLQXc9hNpspKirCZrORkZFBenr6Ye1HEAAUsizLIx3EcBls8u2D3fC7LWzb0c7i9PlceCrMCv+GqD2bCezYimOrjcQH/4larz/GEQuCIIyswa6bE7aIaZfNhUqjJi42DEOYB21XB0q3C7/TjafdLZKDIAgT3oRNEL4uH2HaMKIilehUbtRdHdDpwu9y45MnbMmbIAhCyIRMEI3NnciyjCnGiGQIoFc4UXmcyC4nXqcb/eKzRjpEQRCEETchE8RTL+xBoVQQmyhh0nrR+lwoOzvwu9x0Od3E/+K6kQ5REARhxE3IBPFpuQOlSkVcXASG8E7CvB0o3c7uBNHeSZhJGukQBUEQRtyETBButxdNeBjmKBV6pRtNlxM6O/G7OvEGVCMdniAIwqgw4RKEx+NHDsgYJD1RBgVahRulxwkuJz6nC92CU0Y6REEQhFFhwiWINf+uB4WCmAQJU4QPrexC2enE73bjdXpIuOb6kQ5REARhVJhwCeK1dxtRqpTExBnQh3sI73Ki7HQRcLvpcnYSHhM70iEKgiCMChMuQTgcHtQaNTExKvQaDxqvEzpd+FydeF1dIx2eIAjCqDGiPcIcDgeFhYU0Nzf3Ow1ifn4+FosFu90ODM8EJwF/AK1ei2RQoVN2ouo8UEHt7oTI6KPevyAIwngxYk8QVqsVq9VKZWVlvxOo5+bmYrFYyMzMJDs7OzR949FobO4EwBQbiUnvR6twofS6CLhdeF0eTOd976j2f7zce++9Ix3CcSeOeeKYiMc9Wo95xAfry83NxeFw9JkUJSoqipaWltDriooKcnNzBx0D/1CD9T2yuor/e2sfC78zl++eoWaudgdRNRX4dm6nZUslkx9+CbVOd/QHdYwpFArG0RiLh0Uc88QxEY97JI95zA3WF5wztydJknrNwHUkPtjYikKlJDomHIO2i3CvE0Wnm4C7E6/TMyaSgyAIwvEyKhOE3W7HbDb3Wnbw6yPR2tqFSqXCLKmIUHpQd7m/7SDXFTjq/QuCIIwno3LY0v7qJHqukySp33Vbt25FoVCEXickJJCYmNhnu7/fBX/vbwdpaUMLdIQkJCSQNkZiHS7imCeOiXjcI3nM1dXVA64blQlCkqRQy6Wgg1/3x+VyHauQBEEQJpxRWcRkNpv7PEUEXw/09CAIgiAMr1GZIFJTU/skArvd3msCd0EQBOHYGpUJAmDp0qW9+j2UlJSQk5MzghEJgiBMLCPWD6KiogKr1Rrq/5CTk0N6ejqpqamhbfLz80lNTcVmswHD05NaEARBODwj3lFO6C04/AhAaWkpGRkZgybGwsJCysvLycrKAqCoqCjUC32sOJJjOBbDsBxvWVlZ5OTkYLFY+jTj7q+ubSx+18M9nM5Y+N4HO+Yx9/uWhVFlxYoVvV5bLBa5oKBgwO0LCgpkSZJkQE5NTZXLy8uPdYjDbqjHsGLFCrmoqGjA12OFxWKRgT5/Ax3LWPuuS0pK5KKiIjk7O1vOzs7us36o3+NY+N4P55h7Gu2/b5EgRpGWlhY5MzOz17K8vDzZYrEM+J7B/nGNFUM9BkmSer0uLy+X09PThzOk4yIvL++wlgWN1e96xYoV/V4sh/o9jqXvvb9jHou/71FbST1RWa3WUJ0LdBc19Hw90R2rYVhGwsFFC/n5+axYsWKEojm+hvo9jpfvfaz9vkdlR7mJSpKkXgMUQnfrrUM17y0sLMRsNo/qctlDOdxjOFbDsIyEnvUMVqv1sJpxj4fvGob+PY6H730s/r5FghjFHA4HVquV9evXD7hNWloakiSFKq2ysrIwm81kZmYerzCP2lCO4UiHYRntioqK+oxofLDx8F0HDfV7HI/f+1j4fYsiplFs+fLlFBUV9Wr6e7DU1NReLRoWL17MqlWrjkd4w2Yox3Ckw7CMZsXFxSxatOiQ242H7zpoqN/jePzex8LvWySIUSo/Pz/UN2QwB5fBWiyWfstrR7OhHMN4HIaloKDgsJotjofvOmio3+N4+97Hyu9bJIhRqLi4mNTU1NA/noEq4mw2GxkZGX1+OKO5XfzBhnoM43EYFqvVesjy9PHwXfc01O9xPH3vY+n3LRLEKGO1WrHb7aSlpeFwOLDZbL3uGGw2W2gIEovFQl5eXq8fzpo1a8jNzT3eYR+xwzmGnscM42sYlsHugsfbd32wQ32P4/F7H2u/b9GTehRxOBxERUX1WZ6ZmUlRURHQ/WhaUlISmnq15z+o5uZmUlJSxlzLlkMdw8HHHFw2HoZhcTgcLFq0iPLy8j5JYqx/10c7nM5Y/N4HO+ax+PsWCUIQBEHolyhiEgRBEPolEoQgCILQL5EgBEEQhH6JBCEIgiD0SyQIQRAEoV8iQQjCOORwOMjJySEnJ+e4jxYa7CXcs8+CMDaJwfoEYZySJGnAWdyam5uJjo5GkqTQ4G/FxcWkp6cf9dAVK1aswOFwsGrVqjE5kKDwLZEghAkpNzcXh8NxyBFUD0d/o4kO5/6Hi8PhCE1z2nPeieA0mHl5eZSXl49ghMJoIxKEMCEtW7Zs2Pa1du3aPr1bh3P/w+X8888nLy+vz/hFkiSxdOnSMTdshXDsiToIYUJKTU0ddJjloeg5FMSx2P9wCE46M9DgdpIkieIgoQ+RIAThKASLkka7goICsrKyBt1mND71CCNLFDEJx1XwTha6h2vuWTRzqHXBYY4dDkdoRMzc3FwkSWLlypXY7XYcDgelpaXk5eWFhlGuqKjAYrGE7pBtNluoOKXn3f9gn9+f4uLi0Iic+fn5QPfgcXa7vdf+KyoqjijOoOAAdcHjPpLB2oL7HkzPzw3WSUiSRFFRUei9GRkZ2O12nnnmGaB70pu0tDSysrKw2WyUlJSEBp4TxgFZEI6TFStWyAUFBaHXlZWVodeZmZlyZWVlaF1LS4ucnp4uy7IsFxQU9Fm3YsUKWZZluaSkRE5NTe21PjMzM7Q+SJKkXq/Ly8tD+z9UbIM5eD8DLT/SODMzM+Xy8vJecRYVFR0yrp7nqLKyUgZ67edwFBQUyNnZ2b2WFRUVyS0tLaHXPY+rpaVFzsvL6/P5wtglipiE4yLYUqbn3W9xcTGVlZVUVFRgs9l63eEG5+EtLCwE6NUaSJKkUHFIcKaxnu/t70754BnJerY6Giy2I3Vwq6YjiTM4V0DPuoxly5YNuWXUkU4wk52dzdq1a/ss73lsPY9LkqReraOEsU8kCOG4sFqtfS5UK1asIC8vj7Kysn4vYikpKZSXl5OdnY3NZkOhUJCRkUFhYWGvi2Z/7fajo6OHJbbhNNQ4rVYrkiRhtVpDfzab7Yg6vlksFsrKyvosdzgcoY5tCoWiT8e69PT0UIe3/przBvctjE8iQQgjbrBK3mB5fVFRES0tLeTm5lJUVNSrSWZ/03WO1DzFg128hxpn8M48PT099JeZmXlETzY9J6U5+PN7JsPc3NxeF/yVK1eGnlisVmu/raDG4pzQwuERCUI4LnrOAtaTw+EgPT2933WVlZVkZGSwatUqoPtClJ6eTklJybAOHzFYbEM1nBPKDxTXkcjLy+szvWV/Dk5iwRiO93AdwuggEoRwXFgsFpYuXRqqUwiyWq2kpqZisVh6XbwcDgdlZWWheoGD39fzLtdut/f5vKFc3AeL7XDe2/PiOdjd9FDjTE9Px2w297moHxzn4SopKSE3N7ffMZLWrl07YFFRcEyngfp1jIVmvsIRGulacmFiycvLkwsKCuSSkpI+rXHy8vLkoqIiuaioSM7Lywu1lsnLy5NLSkpCf0VFRXJlZaVcXl4uZ2ZmypIkhVrPFBUVyRaLRU5NTZVLSkpC7wfk7OxsubKyUq6srAy9r2dLpcFiO5xjCr7n4P0faZz97f9w4xqsFVFeXp68YsWK0PkOthIrLy/v1UKp574GaqnV87h6vle0YhofxJzUgjAOBQfLG66K9uLi4iH1tB7uzxdGhihiEgRhUFarVQzDMUGJBCEIQh85OTmhug9RxzBxiQQhCEIfWVlZ2O32IRctCeOLGItJEMYpm81GVlYWeXl5Q+7MNtCor4cjPz+f0tJSMfjfOCAqqQVBEIR+iSImQRAEoV8iQQiCIAj9EglCEARB6JdIEIIgCEK/RIIQBEEQ+vX/avM4Wrk7QwUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.cm as cm\n",
"\n",
"colors=cm.coolwarm(np.linspace(1, 0, n_steps)) # red first\n",
"\n",
"\n",
"fig, ax = plt.subplots(1, 1)\n",
"ylim = ax.set_ylim(lgm0-3, lgm0+0.5)\n",
"xlim = ax.set_xlim(0.1, T0)\n",
"\n",
"n_skip = 5\n",
"for ip, (loss, p) in enumerate(collector[::n_skip]):\n",
" log_mah_pred = _rolling_plaw_vs_t(tarr, np.log10(T0), lgm0, p[0], MAH_K, p[1], p[2])\n",
" __=ax.plot(tarr, log_mah_pred, color=colors[::n_skip][ip], lw=1)\n",
"\n",
"__=ax.plot(t_target, log_mah_target, '-', color='k')\n",
"xlabel = ax.set_xlabel(r'${\\rm cosmic\\ time\\ [Gyr]}$')\n",
"ylabel = ax.set_ylabel(r'$\\log_{10}M_{\\rm halo\\ [M_{\\odot}]}$')\n",
"title = ax.set_title(r'$M_0=10^{13}M_{\\odot}$')\n",
"\n",
"red_line=mlines.Line2D([],[],ls='-',c=mred,label=r'${\\rm initial\\ guess}$')\n",
"blue_line=mlines.Line2D([],[],ls='-',c=mblue,label=r'${\\rm best}$-${\\rm fit}$')\n",
"leg=ax.legend(handles=[red_line, black_line, blue_line])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "35e4d1b1",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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