docs/examples/quickstart.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "29237420",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Quickstart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3cb2b7b8",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NVIDIA H100 PCIe\r\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "# uncomment to disable NVIDIA GPUs\n",
    "#os.environ['CUDA_VISIBLE_DEVICES'] = ''\n",
    "# or pick the device (cpu, gpu, and tpu)\n",
    "#os.environ['JAX_PLATFORMS'] = 'cpu'\n",
    "\n",
    "# change JAX GPU memory preallocation fraction\n",
    "os.environ['XLA_PYTHON_CLIENT_MEM_FRACTION'] = '.95'\n",
    "\n",
    "# you do not want this\n",
    "#os.environ['XLA_FLAGS'] = '--xla_gpu_deterministic_ops=true'\n",
    "\n",
    "import jax\n",
    "#jax.print_environment_info()\n",
    "\n",
    "!nvidia-smi --query-gpu=gpu_name --format=csv,noheader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aaaee7c1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from pmwd import (\n",
    "    Configuration,\n",
    "    Cosmology, SimpleLCDM,\n",
    "    boltzmann, linear_power, growth,\n",
    "    white_noise, linear_modes,\n",
    "    lpt,\n",
    "    nbody,\n",
    "    scatter,\n",
    ")\n",
    "from pmwd.pm_util import fftinv\n",
    "from pmwd.spec_util import powspec\n",
    "from pmwd.vis_util import simshow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6c7edc8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulate Forward"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e49bfa5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "`Configuration` stores static configuration and parameters for which we do not need derivatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e03a1c7f-3ca4-479c-8052-3bfef6fd55d1",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "if jax.default_backend() == 'gpu':\n",
    "    ptcl_spacing = 1.  # Lagrangian space Cartesian particle grid spacing, in Mpc/h by default\n",
    "    ptcl_grid_shape = (256,) * 3\n",
    "else:\n",
    "    ptcl_spacing = 4.\n",
    "    ptcl_grid_shape = (64,) * 3\n",
    "\n",
    "conf = Configuration(ptcl_spacing, ptcl_grid_shape, mesh_shape=2)  # 2x mesh shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5c0f1402",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Configuration(ptcl_spacing=1.0,\n",
      "              ptcl_grid_shape=(256, 256, 256),\n",
      "              mesh_shape=(512, 512, 512),\n",
      "              cosmo_dtype=dtype('float64'),\n",
      "              pmid_dtype=dtype('int16'),\n",
      "              float_dtype=dtype('float32'),\n",
      "              k_pivot_Mpc=0.05,\n",
      "              T_cmb=2.7255,\n",
      "              M=1.98847e+40,\n",
      "              L=3.0856775815e+22,\n",
      "              T=3.0856775815e+17,\n",
      "              transfer_fit=True,\n",
      "              transfer_fit_nowiggle=False,\n",
      "              transfer_lgk_min=-4,\n",
      "              transfer_lgk_max=3,\n",
      "              transfer_lgk_maxstep=0.0078125,\n",
      "              growth_rtol=1.4901161193847656e-08,\n",
      "              growth_atol=1.4901161193847656e-08,\n",
      "              growth_inistep=(1, None),\n",
      "              lpt_order=2,\n",
      "              a_start=0.015625,\n",
      "              a_stop=1,\n",
      "              a_lpt_maxstep=0.0078125,\n",
      "              a_nbody_maxstep=0.015625,\n",
      "              symp_splits=((0, 0.5), (1, 0.5)),\n",
      "              chunk_size=16777216)\n",
      "Simulating 16777216 particles with a (512, 512, 512) mesh for 63 time steps.\n"
     ]
    }
   ],
   "source": [
    "print(conf)  # with other default parameters\n",
    "print(f'Simulating {conf.ptcl_num} particles with a {conf.mesh_shape} mesh for {conf.a_nbody_num} time steps.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3249f227",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "`Cosmology` stores interesting parameters, whose derivatives we need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e36a1ae7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosmology(A_s_1e9=Array(2., dtype=float64),\n",
      "          n_s=Array(0.96, dtype=float64),\n",
      "          Omega_m=Array(0.3, dtype=float64),\n",
      "          Omega_b=Array(0.05, dtype=float64),\n",
      "          h=Array(0.7, dtype=float64),\n",
      "          Omega_k_=None,\n",
      "          w_0_=None,\n",
      "          w_a_=None,\n",
      "          transfer=None,\n",
      "          growth=None,\n",
      "          varlin=None)\n"
     ]
    }
   ],
   "source": [
    "cosmo = Cosmology(conf, A_s_1e9=2.0, n_s=0.96, Omega_m=0.3, Omega_b=0.05, h=0.7)\n",
    "# or simply use the predefined SimpleLCDM\n",
    "#cosmo = SimpleLCDM(conf)\n",
    "\n",
    "print(cosmo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf4e3d4f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "``boltzmann`` computes the transfer and growth functions and caches them in ``Cosmology``.\n",
    "\n",
    "The first run is slower because it includes the **JIT compilation** time. JAX uses **asynchronous dispatch** to hide Python overheads. To measure the true cost, use ``jax.block_until_ready()`` to wait for the computation to complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8c5e7168",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.14 s, sys: 212 ms, total: 2.35 s\n",
      "Wall time: 2 s\n",
      "14.2 ms ± 21.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%time cosmo = jax.block_until_ready(boltzmann(cosmo, conf))\n",
    "%timeit jax.block_until_ready(boltzmann(cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf681169",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Generate a white noise field, and scale it with the linear power spectrum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "daaa93ce",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "seed = 0\n",
    "modes = white_noise(seed, conf)\n",
    "\n",
    "modes = linear_modes(modes, cosmo, conf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "737cfc42",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Solve LPT at some early time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "db10419a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.37 s, sys: 41.1 ms, total: 1.42 s\n",
      "Wall time: 821 ms\n",
      "8.93 ms ± 4.89 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(Array(0.105, dtype=float32), Array(0.007, dtype=float32))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time ptcl, obsvbl = jax.block_until_ready(lpt(modes, cosmo, conf))\n",
    "%timeit jax.block_until_ready(lpt(modes, cosmo, conf))\n",
    "ptcl.disp.std(), ptcl.vel.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f9435ac",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, N-body time integration from the LPT initial conditions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "440cab3f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.31 s, sys: 618 ms, total: 3.93 s\n",
      "Wall time: 3.56 s\n",
      "CPU times: user 689 ms, sys: 543 ms, total: 1.23 s\n",
      "Wall time: 1.4 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(Array(5.318, dtype=float32), Array(3.286, dtype=float32))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time jax.block_until_ready(nbody(ptcl, obsvbl, cosmo, conf))\n",
    "%time ptcl, obsvbl = jax.block_until_ready(nbody(ptcl, obsvbl, cosmo, conf))\n",
    "ptcl.disp.std(), ptcl.vel.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4b6c54",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Scatter the particles to mesh to get the density field, and plot a slab's 2D projection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ac0a4dcf",
   "metadata": {
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dens = scatter(ptcl, conf)\n",
    "simshow(dens[:16].mean(axis=0), norm='CosmicWebNorm');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dbd7441-3cef-4721-be9f-1dffe9d07543",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Measure and plot the matter density power spectra:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7f424b83-c1d4-425a-a0a0-feadf1918d68",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "text/plain": [
       "<Figure size 480x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k, P, _, _ = powspec(dens, conf.cell_size)\n",
    "\n",
    "dens_lin = fftinv(modes, shape=conf.ptcl_grid_shape, norm=conf.ptcl_spacing)\n",
    "dens_lin *= growth(conf.a_stop, cosmo, conf)\n",
    "k_lin, P_lin, _, _ = powspec(dens_lin, conf.ptcl_spacing)\n",
    "\n",
    "P_linth = linear_power(k, conf.a_stop, cosmo, conf)\n",
    "\n",
    "plt.figure(figsize=(4, 3), dpi=120)\n",
    "plt.loglog(k, P_linth, ls='--', label='linear theory')\n",
    "plt.loglog(k_lin, P_lin, ls=':', label='linear')\n",
    "plt.loglog(k, P, ls='-', label='nonlinear')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48748218",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can combine all steps together:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "07ff8ab8",
   "metadata": {
    "cell_style": "center",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 16777216 particles with a (512, 512, 512) mesh for 63 time steps.\n",
      "CPU times: user 711 ms, sys: 545 ms, total: 1.26 s\n",
      "Wall time: 1.43 s\n"
     ]
    }
   ],
   "source": [
    "cosmo = SimpleLCDM(conf)\n",
    "modes = white_noise(seed, conf)\n",
    "\n",
    "def model(modes, cosmo, conf):\n",
    "    cosmo = boltzmann(cosmo, conf)\n",
    "    modes = linear_modes(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = lpt(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf)\n",
    "    return ptcl, obsvbl\n",
    "\n",
    "print(f'Simulating {conf.ptcl_num} particles with a {conf.mesh_shape} mesh for {conf.a_nbody_num} time steps.')\n",
    "%time jax.block_until_ready(model(modes, cosmo, conf));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8adba199",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulate Forward and Differentiate Backward"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3aaa69a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For the gradient, we use the same ``Configuration`` and ``Cosmology`` as before, but different white noise ``modes``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9a1e9378",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "seed = 1  # change the seed for a different realization, to be compared to the previous one in the objective\n",
    "modes = white_noise(seed, conf, real=True)  # this time we want real modes to look at their gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33099d1d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Define a simple MSE objective function between this and the previous realizations of density fields, and differentiate it with respect to the modes and cosmological parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a8119a3f-3900-4d13-bfe7-e6d747dfb563",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 16777216 particles with a (512, 512, 512) mesh for 63 time steps, and then differentiating backward.\n",
      "CPU times: user 20.4 s, sys: 2.32 s, total: 22.7 s\n",
      "Wall time: 19.3 s\n",
      "CPU times: user 3.39 s, sys: 1.9 s, total: 5.29 s\n",
      "Wall time: 5.27 s\n"
     ]
    }
   ],
   "source": [
    "def obj(tgt_dens, modes, cosmo, conf):\n",
    "    cosmo = boltzmann(cosmo, conf)\n",
    "    modes = linear_modes(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = lpt(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf)\n",
    "    dens = scatter(ptcl, conf)\n",
    "    return (dens - tgt_dens).var()\n",
    "\n",
    "obj_grad = jax.grad(obj, argnums=(1, 2))\n",
    "\n",
    "print(f'Simulating {conf.ptcl_num} particles with a {conf.mesh_shape} mesh for {conf.a_nbody_num} time steps, '\n",
    "      'and then differentiating backward.')\n",
    "%time jax.block_until_ready(obj_grad(dens, modes, cosmo, conf))\n",
    "%time modes_grad, cosmo_grad = jax.block_until_ready(obj_grad(dens, modes, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5767210d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "A slice of the mode gradients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d7393d2b",
   "metadata": {
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simshow(modes_grad[..., 0], cmap='RdBu_r', vmin=-0.04, vmax=0.04);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c39ebbe8",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Cosmological parameter gradients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "65e1656e",
   "metadata": {
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosmology(A_s_1e9=Array(51.601, dtype=float64),\n",
      "          n_s=Array(121.798, dtype=float64),\n",
      "          Omega_m=Array(569.083, dtype=float64),\n",
      "          Omega_b=Array(-1422.57, dtype=float64),\n",
      "          h=Array(361.472, dtype=float64),\n",
      "          Omega_k_=None,\n",
      "          w_0_=None,\n",
      "          w_a_=None,\n",
      "          transfer=None,\n",
      "          growth=None,\n",
      "          varlin=None)\n"
     ]
    }
   ],
   "source": [
    "print(cosmo_grad)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}