documents/tutorials/voigt_function.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Voigt profile"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from exojax.spec import voigt\n",
"import jax.numpy as jnp\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's compute the Voigt function $V(\\nu, \\beta, \\gamma_L)$ using exojax!\n",
"$V(\\nu, \\beta, \\gamma_L)$ is a convolution of a Gaussian with a STD of $\\beta$ and a Lorentian with a gamma parameter of $\\gamma_L$. \n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7faaf9d64358>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nu=jnp.linspace(-10,10,100)\n",
"plt.plot(nu, voigt(nu,1.0,2.0)) #beta=1.0, gamma_L=2.0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function \"voigt\" is vmapped for nu (input=0), therefore a bit hard to handle when you want to differentiate. Instead, you can use \"voigtone\", which is not vmapped for all of the input arguments. \n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from exojax.spec import voigtone \n",
"from jax import grad, vmap\n",
"\n",
"dvoigt_nu=vmap(grad(voigtone,argnums=0),(0,None,None),0) #derivative by nu\n",
"dvoigt_beta=vmap(grad(voigtone,argnums=1),(0,None,None),0) #derivative by beta"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7faaf9b45c50>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(nu, voigt(nu,1.0,2.0),label=\"$V(\\\\nu,\\\\beta=1,\\\\gamma_L=2)$\")\n",
"plt.plot(nu, dvoigt_nu(nu,1.0,2.0),label=\"$\\\\partial_\\\\nu V(\\\\nu,\\\\beta=1,\\\\gamma_L=2)$\")\n",
"plt.plot(nu, dvoigt_beta(nu,1.0,2.0),label=\"$\\\\partial_\\\\beta V(\\\\nu,\\\\beta=1,\\\\gamma_L=2)$\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## HMC-NUTS of a simple absorption model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we try to fit a simple absorption model to mock data.\n",
"The absorption model is \n",
"\n",
"$ e^{-a V(\\nu,\\beta,\\gamma_L)}$\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def absmodel(nu,a,beta,gamma_L):\n",
" return jnp.exp(-a*voigt(nu,beta,gamma_L))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Adding a noise...\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7faaf97f9710>]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy.random import normal\n",
"data=absmodel(nu,2.0,1.0,2.0)+normal(0.0,0.01,len(nu))\n",
"plt.plot(nu,data,\".\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then, let's perfomr a HMC-NUTS."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"import arviz\n",
"import numpyro.distributions as dist\n",
"import numpyro\n",
"from numpyro.infer import MCMC, NUTS\n",
"from numpyro.infer import Predictive\n",
"from numpyro.diagnostics import hpdi"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def model_c(nu,y):\n",
" sigma = numpyro.sample('sigma', dist.Exponential(1.0))\n",
" a = numpyro.sample('a', dist.Exponential(1.0))\n",
" beta = numpyro.sample('beta', dist.Exponential(1.0))\n",
" gamma_L = numpyro.sample('gammaL', dist.Exponential(1.0))\n",
" mu=absmodel(nu,a,beta,gamma_L)\n",
" numpyro.sample('y', dist.Normal(mu, sigma), obs=y)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"from jax import random\n",
"rng_key = random.PRNGKey(0)\n",
"rng_key, rng_key_ = random.split(rng_key)\n",
"num_warmup, num_samples = 1000, 2000"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"sample: 100%|██████████| 3000/3000 [00:48<00:00, 65.47it/s, 15 steps of size 1.93e-01. acc. prob=0.95]\n"
]
}
],
"source": [
"kernel = NUTS(model_c,forward_mode_differentiation=True)\n",
"mcmc = MCMC(kernel, num_warmup, num_samples)\n",
"mcmc.run(rng_key_, nu=nu, y=data)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"\n",
"posterior_sample = mcmc.get_samples()\n",
"pred = Predictive(model_c,posterior_sample)\n",
"predictions = pred(rng_key_,nu=nu,y=None)\n",
" \n",
"median_mu = jnp.median(predictions[\"y\"],axis=0)\n",
"hpdi_mu = hpdi(predictions[\"y\"], 0.9)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7faa2408aa20>"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(nrows=1, ncols=1) \n",
"ax.plot(nu,median_mu,color=\"C0\")\n",
"ax.plot(nu,data,\"+\",color=\"C1\",label=\"data\")\n",
"ax.fill_between(nu, hpdi_mu[0], hpdi_mu[1], alpha=0.3, interpolate=True,color=\"C0\",\n",
" label=\"90% area\")\n",
"plt.xlabel(\"$\\\\nu$\",fontsize=16)\n",
"plt.legend()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We got a posterior sampling."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1987.2x1324.8 with 10 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"refs={};refs[\"sigma\"]=0.01;refs[\"a\"]=2.0;refs[\"beta\"]=1.0;refs[\"gammaL\"]=2.0\n",
"arviz.plot_pair(arviz.from_numpyro(mcmc),kind='kde',\\\n",
" divergences=False,marginals=True,reference_values=refs,\\\n",
" reference_values_kwargs={'color':\"red\", \"marker\":\"o\", \"markersize\":12})\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## curve of growth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As an application, we consider the curve of growth.\n",
"The curve of growth is the equivalent width evolution as a function of the absorption sterngth. Here, it corresponds to $a$. Let's see, the growth of absorption feature as"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nu=jnp.linspace(-100,100,10000)\n",
"aarr=jnp.logspace(-3,3,10)\n",
"for a in aarr:\n",
" plt.plot(nu,absmodel(nu,a,0.1,0.1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us define the equivalent width by a simple summation of the absorption."
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [],
"source": [
"def EW(a):\n",
" return jnp.sum(1-absmodel(nu,a,0.1,0.1))\n",
"vEW=vmap(EW,0,0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is the curve of growth. As you see, when the absorption is weak, the power of the curve is proportional to unity (linear region). But, as increasing the absorption sterength, the power converges to 1/2. "
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"aarr=jnp.logspace(-3,3,100)\n",
"plt.plot(aarr,vEW(aarr))\n",
"plt.yscale(\"log\")\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"a\")\n",
"plt.ylabel(\"equivalent width\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have auto-diff for the Voigt. So, we can directly compute the power as a function of $a$.\n",
"\n",
"$power = \\frac{\\partial}{\\partial \\log_{10} a } \\log_{10} ( EW ) $"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {},
"outputs": [],
"source": [
"def logEW(loga):\n",
" return jnp.log10(jnp.sum(1-absmodel(nu,10**(loga),0.1,0.1)))"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [],
"source": [
"dlogEW=grad(logEW)\n",
"vlogdEW=vmap(dlogEW,0,0)"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"logaarr=jnp.linspace(-3,3,100)\n",
"plt.plot(10**(logaarr),vlogdEW(logaarr))\n",
"plt.axhline(1.0,label=\"linear limit\",color=\"gray\",ls=\"dashed\")\n",
"plt.axhline(0.5,label=\"damped limit\",color=\"gray\",ls=\"dotted\")\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"a\")\n",
"plt.ylabel(\"power\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
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