{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# HST WFC3 Chemically Consistent Transmission/Transit Tutorial \n", "\n", "Welcome to the transmission spectrum model/retrieval tutorial!\n", "\n", "For this particular setup, the atmosphere is parameterized within the \"chemically-consistent\" framework as described in Kreidberg et al. 2015. The atmospheric composition is parameterized with only a metalicity and carbon-to-oxygen ratio assumed to be in thermochemical equilibrium along the temperature-pressure profile. Originally this code would compute the gas and condensate phase mixing ratios by calling the NASA CEA routine. However, in order to remove fortran dependencies, a finely sampled pre-computed, interpolateable chemistry grid was instead produced with CEA as a function of temperature (T from 400K - 3400K in 100K increments), pressure ($log_{10}(P)$ from -7.0 (0.1$\\mu$bar) - 2.4 (316 bar) in 0.1 increments), metallicity ($[M/H]$ from -2.0 (0.01$\\times$) to 3.0 (1000$\\times$)), and C/O ($log_{10}(C/O)$ from -2.0 (0.01) to 0.3 (2) awkwardly spaced to better sample the transition about C/O=1). All elemental abundances are scaled with respect to the Lodders 2009 solar abundance pattern. A pseudo-hack rainout approximation is made to the gas phase abundances of TiO, VO, Na, K, and FeH. In this hack, these species are set to 0 abundance at levels above where they first fall below some critical value ($10^{-8}$). This is to mimic the loss of these species from the gas phase into the condensate phase. In no case are we accounting for the loss of elemental abundances.\n", "\n", "The 3-parameter temperature profile parameterization utilizes the Guillot 2010/Parmentier et al. 2014 analytic formulism (see Line et al. 2013a for implementation details). \n", "\n", "The transmission spectrum routine closely follows the equations (and figure) in Tinetti et al. 2012 (as described in the tutorial text). Instead of using line-by-line, or \"sampled\" cross-sections, this implementation uses the \"correlated-K\" method (see Lacis & Oinas 1990, or more recently Amundsen et al. 2017). Correlated-K is advantageous as it preserves the wavelength bin\"integrated\" precision as line-by-line but with far less demanding computation. We include as correlated-K line opacites H2O, CH4, CO, CO2, NH3, HCN, H2S, C2H2, Na, K, TiO, VO, FeH and as continuum gas opacities H2-H2, H2-He CIA, and the H- bound free and free free (e.g., Arcangeli et al. 2018). See the \"opacity\" tutorial for more details on correlated-K. \n", "\n", "To handle the effects of disequilibrium chemistry due to vertical mixing, we apply the \"quench-pressure\" approximation. We include a quench pressure parameter for the carbon-system and one for the nitrogen system (as in Morley et al. 2017 for GJ436b, and Kreidberg et al. 2018 for WASP-107b). The carbon quench pressure fixes the H2O, CO, and CH4 abundances above the quench pressure level to their abundances at the quench pressure level. Similarly, the nitrogen quench pressure fixes the N2, NH3, and HCN abundances above the quench pressure to their values at the quench pressure level. This is indeed a kludge, and a better implementation would be to use the timescale/eddy mixing prescription described in Zahnle & Marley 2015. Regardless, any non-full kinetics approach is a kludge anyway (not to mention the 1D nature of the problem...). \n", "\n", "There are two different cloud prescriptions built in. The first is the Ackerman & Marley 2001 \"eddy-sed\" approach that self-consistently computes the vertical particle size distribution given a sedimentation factor, $f_{sed}$ and an eddy mixing factor (K$_{zz}$) from some cloud base pressure and intrinsic condensate mixing ratio. The classic \"power-law haze\" and \"grey cloud\" prescripton is also included.\n", "\n", "Finally, if one doesn't like the \"chemically-consistent\" concept, they can use the \"gas_scale\" array to switch off or scale the abundances each opacity source. \n", "\n", "This specific notebook goes through the steps to generate the forward model, and illustrate how to actually perform the retrieval. However, the retrievals are bust run on a compute cluster or a node with more than 4 cores. We will use the \"benchmark\" system, WASP-43b as our example utilizing the HST WFC3 data presented in Kreidberg et al. 2014b.\n", "\n", "Note, this particular version does not include marginilzation over spots (e.g., Iyer & Line 2019). However, this can be trivially implemented in the fx_trans rouutine in fm.py. Simply add in the \"rackham\" formula along with a grid of stellar spectral models, say, drawn from pysynphot (or whatever your favorite stellar model generator is). Interpolate over this grid of stellar models using standard built in python linear interpolators.\n", "\n", "\n", "Software Requirements: This runs in the python 3 anaconda environment. It is also crucial that anaconda numba is installed as many of the routines are optimized using numba's \"@jit\" decorator (http://numba.pydata.org/). \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Routines\n", "\n", "This first segment loads in the routines from fm.py and the correlated-K coefficients. There are two sets of correlated-K coefficients (which I've called \"xsecs\" here). There are ones taylored for HST WFC3+STIS (xsects_HST function in fm.py) and JWST (xsects_JWST in fm.py). The WFC3+STIS correlated-K coefficients are generated at an R=200 longwards of 1 $\\mu$m (up to 5$\\mu$m and R=500 from 0.3 - 1 $\\mu$m. Note...these *are not sampled cross-sections* so each resolution element at that R is correctly computed and matches line-by-line when binned to that same R.\n", "\n", "Note that the \"core\" set of routines are all in fm.py. If you want to know more about what is in the sausage, look into fm.py. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/michaelline/anaconda3/lib/python3.6/site-packages/numpy/core/fromnumeric.py:2957: RuntimeWarning: Mean of empty slice.\n", " out=out, **kwargs)\n", "/Users/michaelline/anaconda3/lib/python3.6/site-packages/numpy/core/_methods.py:80: RuntimeWarning: invalid value encountered in double_scalars\n", " ret = ret.dtype.type(ret / rcount)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Cross-sections Loaded\n" ] } ], "source": [ "#import all of the functions in fm, namely, the CK-coefficients (may take a minute)\n", "from chimera import *\n", "%matplotlib notebook\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load Opacities, Make Star" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\n", "stellar_file = 'sum_star.h5'\n", "temp = 5000\n", "logmh = 0 \n", "logg = 4.0\n", "stellar_db = 'phoenix'\n", "make_stellar(temp,logmh,logg,stellar_db,stellar_file)\n", "\n", "#preload CK-coeffs--a giant array/variable to be passed--inputs are lower wavenumber, upper wavenumber\n", "#between 2000 and 30000 cm-1 for HST--R=200 > 1 um, then R=500 < 1 um \n", "#to convert between microns and wavenumbers-- wavelength [um] = 10,000/wavenumber [cm-1]\n", "#make sure xsec wavenumber/wavelength range is *larger* than data wavelength range\n", "\n", "wnomin = 2000\n", "wnomax = 25000\n", "observatory='HST'\n", "directory = os.path.join(os.getcwd(),'..','..','ABSCOEFF_CK')\n", "xsecs=xsects(wnomin, wnomax, observatory, directory,stellar_file=stellar_file)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup Atmospheric Parameters to Generate a Spectrum\n", "\n", "This segement defines the various atmospheric quantities and assignes them values for the generation of a simple transmission spectrum. A description of each parameter along with a reasonable range of values is given as a comment following the assigned value. All of the parameters are then put into the parameter \"state-vector\" array, x." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#setup \"input\" parameters. We are defining our 1D atmosphere with these\n", "#the parameters\n", "#planet/star system params--xRp is the \"Rp\" free parameter, M right now is fixed, but could be free param\n", "Rp=1.036 #Planet radius in Jupiter Radii--this will be forced to be 10 bar radius--arbitrary (scaling to this is free par)\n", "Rstar=0.667 # #Stellar Radius in Solar Radii\n", "M =2.034 #Mass in Jupiter Masses\n", "D=0.01526 #semimajor axis in AU\n", "\n", "#TP profile params (3--Guillot 2010, Parmentier & Guillot 2013--see Line et al. 2013a for implementation)\n", "Tirr=1400 #Irradiation temperature as defined in Guillot 2010\n", "logKir=-1.5 #TP profile IR opacity (log there-of) controlls the \"vertical\" location of the gradient\n", "logg1=-0.7 #single channel Vis/IR (log) opacity. Controls the delta T between deep T and TOA T\n", "Tint=200 #interior temperature...this would be the \"effective temperature\" if object were not irradiated\n", "\n", "#Composition parameters---assumes \"chemically consistent model\" described in Kreidberg et al. 2015\n", "logMet=0.0 #. #Metallicity relative to solar log--solar is 0, 10x=1, 0.1x = -1: valid range is -1.5 - 3.0\n", "logCtoO=-0.26 #log C-to-O ratio: log solar is -0.26: valid range is -1.0 - 0.3 \n", "logPQCarbon=-5.5 #CH4, CO, H2O Qunech pressure--forces CH4, CO, and H2O to constant value at quench pressure value: valid range -6.0 - 1.5\n", "logPQNitrogen=-5.5 #N2, NH3 Quench pressure--forces N2 and NH3 to \"\" \n", "\n", "#Ackerman & Marley 2001 Cloud parameters--physically motivated with Mie particles\n", "logKzz=7 #log Kzz (cm2/s)--valid range: 2 - 11 -- higher values make larger particles\n", "fsed=2.0 #sediminetation efficiency--valid range: 0.5 - 5--lower values make \"puffier\" more extended cloud \n", "logPbase=-1.0 #cloud base pressure--valid range: -6.0 - 1.5\n", "logCldVMR=-5.5 #cloud condensate base mixing ratio (e.g, see Fortney 2005)--valid range: -15 - -2.0\n", "\n", "#simple 'grey+rayleigh' parameters just in case you don't want to use a physically motivated cloud\n", "#(most are just made up anyway since we don't really understand all of the micro-physics.....)\n", "logKcld = -40 #uniform in altitude and in wavelength \"grey\" opacity (it's a cross-section)--valid range: -50 - -10 \n", "logRayAmp = -30 #power-law haze amplitude (log) as defined in des Etangs 2008 \"0\" would be like H2/He scat--valid range: -30 - 3 \n", "RaySlope = 0 #power law index 4 for Rayleigh, 0 for \"gray\". Valid range: 0 - 6\n", "\n", "#10 bar radiuss scaling param (only used in transmission)\n", "xRp=0.991\n", "\n", "#stuffing all variables into state vector array\n", "x=np.array([Tirr, logKir,logg1,Tint, logMet, logCtoO, logPQCarbon,logPQNitrogen, Rp*xRp, Rstar, M, logKzz, fsed,logPbase,logCldVMR, logKcld, logRayAmp, RaySlope])\n", "#gas scaling factors to mess with turning on various species\n", "#set to \"0\" to turn off a gas. Otherwise keep set at 1\n", "#thermochemical gas profile scaling factors\n", "# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21\n", "#H2O CH4 CO CO2 NH3 N2 HCN H2S PH3 C2H2 C2H6 Na K TiO VO FeH H H2 He e- h- mmw\n", "gas_scale=np.array([1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1., 1., 1.]) #can be made free params if desired (won't affect mmw)#can be made free params if desired (won't affect mmw)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load in Transmission Data Set \n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#WASP43b transmission spectrum from kreidberg et al. 2014...a 3 column ascii file\n", "wlgrid, y_meas, err=np.loadtxt('w43b_trans.txt').T\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate Model Atmosphere & Transmission Spectrum \n", "\n", "Here we call the forward model routine \"fx\" (think F(x)) from fm.py. fx controls the input values and calls the relevent functions to compute the transmission spectrum. The inputs into fx are the parameter state vector, \"x\", the data wavelength grid, \"wlgrid\", the gas scaling factors (for turning off particular gases), \"gas_scale\", and the correlated-K tables, \"xsects\". Fx then returns the simulated model spectrum ($(R_p/R_{\\star})^2$) at the native CK-table resolution, \"y_mod\", the native wavenumber grid, \"wno\", the data wavelength grid binned model spectrum, \"y_binned\". The \"atm\" array contains the generated temperature-pressure profile and gas mixing ratio profiles generated under the chemically consistent assumption. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DONE\n" ] } ], "source": [ "#calling forward model, fx. This will produce the (Rp/Rstar)^2 spectrum....\n", "y_binned,y_mod,wno,atm=fx_trans(x,wlgrid,gas_scale, xsecs) #returns binned model spectrum, higher res model spectrum, wavenumber grid, and vertical abundance profiles from chemistry\n", "print('DONE')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting the Model Atmosphere & Transmission Spectrum \n", "\n", "Self-explanatory...\n", "\n", "## Plot Model Atmosphere \n", "\n", "Spaghetti plot of the model atmosphere." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#finally doing some plotting\n", "#and the usual matplotlib shenanigans\n", "ymin=np.min(y_binned)*1E2*0.99\n", "ymax=np.max(y_binned)*1E2*1.01\n", "fig1, ax=subplots()\n", "xlabel('$\\lambda$ ($\\mu$m)',fontsize=18)\n", "ylabel('(R$_{p}$/R$_{*}$)$^{2} \\%$',fontsize=18)\n", "minorticks_on()\n", "errorbar(wlgrid, y_meas*100, yerr=err*100, xerr=None, fmt='Dk', label='Data')\n", "plot(wlgrid, y_binned*1E2,'ob',label='Binned Model')\n", "plot(1E4/wno, y_mod*1E2, label='Model')\n", "ax.set_xscale('log')\n", "ax.set_xticks([0.3, 0.5,0.8,1,1.4, 2, 3, 4, 5])\n", "ax.axis([0.3,5,ymin,ymax])\n", "ax.get_xaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n", "ax.tick_params(length=10,width=1,labelsize='large',which='major')\n", "legend(frameon=False)\n", "savefig('./plots/transmission_spectrum_WFC3_CC.pdf',fmt='pdf')\n", "show()\n", "#close()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Play around with Transmission Spectrum " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Explore cloud contribution" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DONE\n", "DONE\n" ] }, { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " if (mpl.ratio != 1) {\n", " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", " }\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " fig.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '
');\n", " var titletext = $(\n", " '
');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", " nav_element.append(button);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('
');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.pyplot import *\n", "from matplotlib.ticker import FormatStrFormatter\n", "\n", "#NOTE; Will use whatever \"cloud properties\" from above\n", "\n", "##generating \"complete\" spectrum (same as above)\n", "# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21\n", "#H2O CH4 CO CO2 NH3 N2 HCN H2S PH3 C2H2 C2H6 Na K TiO VO FeH H H2 He e- h- mmw\n", "gas_scale=np.array([1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1., 1., 1.]) #can be made free params if desired (won't affect mmw)#can be made free params if desired (won't affect mmw)\n", "#calling forward model, fx. This will produce the (Rp/Rstar)^2 spectrum....\n", "y_binned_0,y_mod_0,wno_0,atm_0=fx_trans(x,wlgrid,gas_scale, xsecs) #returns binned model spectrum, higher res model spectrum, wavenumber grid, and vertical abundance profiles from chemistry\n", "print('DONE')\n", "\n", "##generating cloud component only\n", "#gas_scale[11]=0. #Na #shutting off a single gas (use the index map above)\n", "#gas_scale[12]=0. #K #shutting off a single gas (use the index map above)\n", "gas_scale[0]=0. #H2O #shutting off a single gas (use the index map above)\n", "\n", "y_binned_1,y_mod_1,wno_1,atm_1=fx_trans(x,wlgrid,gas_scale, xsecs) #returns binned model spectrum, higher res model spectrum, wavenumber grid, and vertical abundance profiles from chemistry\n", "print('DONE')\n", "\n", "#feel free to remove more gases and add to plotting...\n", "\n", "ymin=np.min(y_binned_0)*1E2*0.99\n", "ymax=np.max(y_binned_0)*1E2*1.01\n", "fig1, ax=subplots()\n", "xlabel('$\\lambda$ ($\\mu$m)',fontsize=18)\n", "ylabel('(R$_{p}$/R$_{*}$)$^{2} \\%$',fontsize=18)\n", "minorticks_on()\n", "errorbar(wlgrid, y_meas*100, yerr=err*100, xerr=None, fmt='Dk', label='Data')\n", "plot(wlgrid, y_binned_0*1E2,'ob',label='Binned Full Model')\n", "plot(1E4/wno, y_mod_0*1E2, label='Full Model')\n", "plot(1E4/wno, y_mod_1*1E2, label='Removing A Gas', color='red')\n", "\n", "ax.set_xscale('log')\n", "ax.set_xticks([0.3, 0.5,0.8,1,1.4, 2, 3, 4, 5])\n", "ax.axis([0.3,5,ymin,ymax])\n", "ax.get_xaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n", "ax.tick_params(length=10,width=1,labelsize='large',which='major')\n", "legend(frameon=False)\n", "show()\n", "#close()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time to Get to the \"Retrieval\" \n", "\n", "The \"retrieval\" is performed using the DYNESTY (https://dynesty.readthedocs.io/en/latest/index.html) nested sampling suite. It's basically like all of the others (e.g., multinest, pymultnest, nestle etc.), though it's more flexible in terms of sampling methods optimized for certain numbers of parameters. This example just uses \"generic\" settings." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/michaelline/anaconda3/lib/python3.6/site-packages/numpy/core/fromnumeric.py:2957: RuntimeWarning: Mean of empty slice.\n", " out=out, **kwargs)\n", "/Users/michaelline/anaconda3/lib/python3.6/site-packages/numpy/core/_methods.py:80: RuntimeWarning: invalid value encountered in double_scalars\n", " ret = ret.dtype.type(ret / rcount)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Cross-sections Loaded\n" ] } ], "source": [ "#set up a \"dynest\" nested sampling run--see https://dynesty.readthedocs.io/en/latest/index.html\n", "#a super cool useful comparision of all MCMC/Multinests out there...\n", "#http://mattpitkin.github.io/samplers-demo/pages/samplers-samplers-everywhere/\n", "#(feel free to mix and match samplers--probably not a bad idea...)\n", "#for safty, just reloading everything again\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import dynesty\n", "from multiprocessing import Pool\n", "from fm import *\n", "import pickle\n", "#load crosssections between wnomin and wnomax\n", "xsecs=xsects_HST(6000,9400) #make sure this range is *larger* than the data wavelength grid (but not by too much)\n", "#6000 cm-1 (1.68 um) to 9400 cm-1 (1.06 um)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining log-likelihood function\n", "This computes \"chi-square\" log-likelihood function. The input value is \"theta\" which is the same as \"x\"--the parameter state vector, though just for the parameters we care about. These can be a sub-set of the full \"x\" defined above. The first block defines a bunch of parameters--same as what gets passed into fx--to a generic default value. Thes parameter values get overridden with the values in the \"theta (parameters to retrieve) vector. In this particular example only Tirr, logMet, logCtoO, logKzz, fsed ,logPbase,logCldVMR,xRp are retrieved. All other values passed into fx are assigned the other values. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "#defining log-likelihood function\n", "# log-likelihood\n", "def loglike(theta):\n", "\n", " #setting default parameters---will be fixed to these values unless replaced with 'theta'\n", " #planet/star system params--xRp is the \"Rp\" free parameter, M right now is fixed, but could be free param\n", " Rp= 1.036#0.930#*x[4]# Planet radius in Jupiter Radii--this will be forced to be 10 bar radius--arbitrary (scaling to this is free par)\n", " Rstar=0.667#0.598 #Stellar Radius in Solar Radii\n", " M =2.034#1.78 #Mass in Jupiter Masses\n", "\n", " #TP profile params (3--Guillot 2010, Parmentier & Guillot 2013--see Line et al. 2013a for implementation)\n", " Tirr=1400#1500#x[0]#544.54 #terminator **isothermal** temperature--if full redistribution this is equilibrium temp\n", " logKir=-1.5 #TP profile IR opacity controlls the \"vertical\" location of the gradient\n", " logg1=-0.7 #single channel Vis/IR opacity. Controls the delta T between deep T and TOA T\n", " Tint=200.\n", " \n", " #Composition parameters---assumes \"chemically consistnat model\" described in Kreidberg et al. 2015\n", " logMet=0.0#x[1]#1.5742E-2 #. #Metallicity relative to solar log--solar is 0, 10x=1, 0.1x = -1 used -1.01*log10(M)+0.6\n", " logCtoO=-0.26#x[2]#-1.97 #log C-to-O ratio: log solar is -0.26\n", " logPQCarbon=-5.5 #CH4, CO, H2O Qunech pressure--forces CH4, CO, and H2O to constant value at quench pressure value\n", " logPQNitrogen=-5.5 #N2, NH3 Quench pressure--forces N2 and NH3 to \"\" --ad hoc for chemical kinetics--reasonable assumption\n", " #A&M Cloud parameters--includes full multiple scattering (for realzz) in both reflected and emitted light\n", " logKzz=7 #log Rayleigh Haze Amplitude (relative to H2)\n", " fsed=3.0 #haze slope--4 is Rayeigh, 0 is \"gray\" or flat. \n", " logPbase=-1.0 #gray \"large particle\" cloud opacity (-35 - -25)\n", " logCldVMR=-25.0 #cloud fraction\n", " #simple 'grey+rayleigh' parameters--non scattering--just pure extinction\n", " logKcld = -40\n", " logRayAmp = -30\n", " RaySlope = 0\n", "\n", " #unpacking parameters to retrieve (these override the fixed values above)\n", " Tirr, logMet, logCtoO, logKzz, fsed ,logPbase,logCldVMR,xRp=theta\n", " \n", " ##all values required by forward model go here--even if they are fixed\n", " x=np.array([Tirr, logKir,logg1, Tint,logMet, logCtoO, logPQCarbon,logPQNitrogen, Rp*xRp, Rstar, M, logKzz, fsed,logPbase,logCldVMR, logKcld, logRayAmp, RaySlope])\n", " gas_scale=np.array([1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1., 1., 1.]) #can be made free params if desired (won't affect mmw)#can be made free\n", " foo=fx_trans(x,wlgrid,gas_scale,xsecs)\n", " y_binned=foo[0]\n", " \n", " loglikelihood=-0.5*np.sum((y_meas-y_binned)**2/err**2) #your typical \"quadratic\" or \"chi-square\"\n", " \n", " return loglikelihood\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Prior Function\n", "Nested samplers use this \"cube\" concept whereby all of the parameter values are transformed on the interval [0,1]. This makes the sampling more-or-less scale indepenent. The prior_transform function maps those back onto the actual parameter value ranges we want. In this case, the prior ranges are all uniform over the range as defined here. Live points will be drawn from this hypercube uniformly. These \"live point\" parameter values are then assesed by the log-likelihood function. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "#defining prior cube (cube is a standard multi-nest way of doing priors)\n", "def prior_transform(utheta):\n", " Tirr, logMet, logCtoO, logKzz, fsed ,logPbase,logCldVMR,xRp=utheta\n", " #uniform prior ranges--each \"variable\", say Tirr is sampled over the interval [0,1]--the numbers here transform that\n", " Tirr = 1400 * Tirr + 400 #Tirr uniform from 400 - 3000K (add the lower value to the multiplier to get upper bound)\n", " logMet= 5.*logMet-2 #[M/H] from -1.5 - 3.0 (0.03x - 1000x)\n", " logCtoO=2.3*logCtoO-2\n", " logKzz=6*logKzz+5\n", " fsed=5.5*fsed+0.5\n", " logPbase=7.5*logPbase-6.0\n", " logCldVMR=13*logCldVMR-15\n", " xRp=1*xRp+0.5\n", "\n", " return Tirr, logMet, logCtoO, logKzz, fsed ,logPbase,logCldVMR,xRp\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading in Data and Setting up Nested Sampling Parameters\n", "This segment first loads in the \"3 column\" data file...Here it is just a pickle, but this could be replaced with a 3-column ascii file read in--wavelength grid, data values, error bars. The other knobs are self-explanatory. The number of live points is \"problem dependent\". Some problems can get away with less. I wouldn't go below 100. It's safer to use more (e.g., just like walkers in emcee). For \"real science\" I prefer 1000+ live points to make sure the posterior is well sampled and no modes are missed. Of course, this takes longer to run, but no sense in getting the the wrong answer faster!" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "#setting up other dynesty run params and loading in the data\n", "#WASP43b transmission spectrum...a 3 column ascii file\n", "wlgrid, y_meas, err=np.loadtxt('w43b_trans.txt').T\n", "outname='./OUTPUT/dyn_trans_WFC3_CC.pic' #dynesty output file name (saved as a pickle)\n", "Nparam=8 #number of parameters--make sure it is the same as what is in prior and loglike\n", "Nproc=4 #number of processors for multi processing--best if you can run on a 12 core+ node or something\n", "Nlive=500 #number of nested sampling live points\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running Nested Sampler\n", "This calls the Nested Sampler function to compute the posterior. This may take a few hours depending on the number of parameters and number of live points." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#running the \"standard\" nested sampler. Again, see https://dynesty.readthedocs.io/en/latest/index.html for details\n", "#depending on the number of live points (I like lots, usually 1000+, but I'm paranoid), number of params, and number of\n", "#processors on your computer, this could take some time. -- your computer will make loud noises..1-2 hours with 4 cores\n", "#in real life, you should probably run this on a multi-core machine (8+)\n", "#in really real life, you should probably use pymultinest...it tends to \"converge\" faster with fewer likelihood\n", "#evaluations than does dynest, even with the same number of live points (see: https://mattpitkin.github.io/samplers-demo/pages/samplers-samplers-everywhere/)\n", "#e.g., when I ran this with 56 cores (2x28 core nodes) with multinest it took ~20 min.\n", "import time\n", "pool = Pool(processes=Nproc)\n", "dsampler = dynesty.NestedSampler(loglike, prior_transform, ndim=Nparam,\n", " bound='multi', sample='auto', nlive=Nlive,\n", " update_interval=3., pool=pool, queue_size=Nproc)\n", "#this executes and runs it\n", "t1=time.time()\n", "dsampler.run_nested()\n", "t2=time.time()\n", "print(\"Run Time:\", t2-t1)\n", "#extracting results from sampler object\n", "dres = dsampler.results\n", "#dumping as a pickle\n", "pickle.dump(dres,open(outname,'wb')) \n", "#some real time dynesty output/status will pop up down here (this one took 57961 lnL calls over 16350s = 4.5 hrs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting Corner Plot\n", "Plots the corner plots and spectral fit plot. Note: All of the plotting below can be used for a \"previously\" generated run. Just start here and load in the sampler output." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ln(Z)= -25.7512456861343\n" ] }, { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wlgrid, y_meas, err, y_binned_array, wno, y_mod_array=pickle.load(open('./OUTPUT/spectral_samples_trans_dyn_wfc3_CC.pic','rb'))\n", "y_median=np.zeros(wno.shape[0])\n", "y_high_1sig=np.zeros(wno.shape[0])\n", "y_high_2sig=np.zeros(wno.shape[0])\n", "y_low_1sig=np.zeros(wno.shape[0])\n", "y_low_2sig=np.zeros(wno.shape[0])\n", "\n", "for i in range(wno.shape[0]):\n", " percentiles=np.percentile(y_mod_array[i,:],[4.55, 15.9, 50, 84.1, 95.45])\n", " y_low_2sig[i]=percentiles[0]\n", " y_low_1sig[i]=percentiles[1]\n", " y_median[i]=percentiles[2]\n", " y_high_1sig[i]=percentiles[3]\n", " y_high_2sig[i]=percentiles[4]\n", " \n", " \n", "from matplotlib.pyplot import *\n", "from matplotlib.ticker import FormatStrFormatter\n", "\n", "ymin=np.min(y_meas)*1E2*0.995\n", "ymax=np.max(y_meas)*1E2*1.005\n", "fig1, ax=subplots()\n", "xlabel('$\\lambda$ ($\\mu$m)',fontsize=14)\n", "ylabel('(R$_{p}$/R$_{*}$)$^{2} \\%$',fontsize=14)\n", "minorticks_on()\n", "\n", "\n", "#for i in range(20): plot(wlgrid, y_binned_array[:,i]*100.,alpha=0.5,color='red')\n", "#for i in range(20): plot(1E4/wno, y_mod_array[:,i]*100.,alpha=0.5,color='red')\n", "\n", "fill_between(1E4/wno[::-1],y_low_2sig[::-1]*100,y_high_2sig[::-1]*100,facecolor='r',alpha=0.5,edgecolor='None') \n", "fill_between(1E4/wno[::-1],y_low_1sig[::-1]*100,y_high_1sig[::-1]*100,facecolor='r',alpha=1.,edgecolor='None') \n", "\n", "\n", "errorbar(wlgrid, y_meas*100, yerr=err*100, xerr=None, fmt='Dk')\n", "plot(1E4/wno, y_median*1E2)\n", "ax.set_xscale('log')\n", "ax.set_xticks([0.3, 0.5,0.8,1,1.4, 2, 3, 4, 5])\n", "ax.axis([0.3,5.0,ymin,ymax])\n", "ax.get_xaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n", "ax.tick_params(length=5,width=1,labelsize='small',which='major')\n", "savefig('./plots/transmission_spectrum_fits_WFC3_CC.pdf',fmt='pdf')\n", "show()\n", "#close()\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Doing all of that again, but with PyMultiNest \n", "\n", "PyMultiNest (a python wrapper for MultiNest): Buchner et al. 2014
\n", "Paper: https://ui.adsabs.harvard.edu/abs/2014A%26A...564A.125B/abstract)
\n", "GitHub: https://johannesbuchner.github.io/PyMultiNest/

\n", "MultiNest: Feroz & Hobson 2008
\n", "Paper: https://ui.adsabs.harvard.edu/abs/2009MNRAS.398.1601F/abstract
\n", "GitHub:https://github.com/farhanferoz/MultiNest

\n", "It is highly advised that you read the relevant sections of these papers and online documentation\n", "\n", "### First have to install MultiNest (a bunch of Fortran, C) and PyMultiNest\n", "While dynesty is easy to install and use, it's not quite as an efficient as a sampler as MultiNest/PyMultiNest (at least that I have found). Here we will re-do the above retrieval, but with the PyMultiNest package. The MultiNest package is readily parallelizeble on any compute cluster or multicore desktop/laptop (using mpi). Be forewarned, installing PyMultiNest can be a challenge as it is a combination of python, c, and fortran codes. Most compute cluster admins are able to install this package (both within slurm and torque). Below I outline the steps that I took on my 2016 MacBook Pro with High Sierra (10.13.6) based on a combination of https://www.astrobetter.com/wiki/MultiNest+Installation+Notes and https://exoai.github.io/software/taurex/installation.\n", "\n", "Assuming you have some version of MacPorts, execute the following in this order from a terminal command line (note this can take several hours):\n", "1. sudo port install gcc5\n", "2. sudo port select --set gcc mp-gcc5\n", "3. sudo port install cmake\n", "4. sudo port install openblas +gcc5\n", "5. sudo port install openmpi +gcc5\n", "6. sudo port select --set mpi openmpi-mp-fortran\n", "7. git clone https://github.com/JohannesBuchner/MultiNest.git\n", "8. cd MultiNest/build/\n", "9. cmake ..\n", "10. make\n", "11. sudo make install\n", "12. git clone https://github.com/JohannesBuchner/PyMultiNest.git \n", "13. cd PyMultiNest \n", "14. python setup.py install\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time To Run It\n", "OK, time to run. Sorry, you will have to leave the comfort and safety of this notebook, but I'll walk you through it here. We will be using \"mpirun\" to run on your multiple processors on your laptop which I have not figured out how to do from a jupyter notebook (maybe you can use spawn or whatever, if your ambitious). \n", "\n", "### STEP 1\n", " Open the routine \"call_pymultinest_transmission.py\". Have a look, digest it, read the comments, etc. It should look farily similar to the above dynesty fundtions (e.g., a loglikelihood, prior cube, etc.). No need to modify anything for this. However, you would modify this script if you wanted to add/remove particular parameters or change the wavelength/wavenumber ranch of the run. \n", " \n", "### STEP 2 (really a pseudostep)\n", "Go to the folder (in terminal) where you have downloaded the CHIMERA code (mainly, where \"call_pymultinest_transmission.py\" lives). To run using one CPU, simpley type the following:\n", "\n", "python call_pymultinest_transmission_wfc3_CC.py\n", "\n", "Wait a minute. You should see some useless unimportant error messages pop out followed by \"Cross-sections Loaded\" followed shortely there after by\n", "\n", "\n", "$*************************$
\n", "MultiNest v3.10
\n", "Copyright Farhan Feroz & Mike Hobson
\n", "Release Jul 2015

\n", "no. of live points = 500
\n", "dimensionality = 8
\n", "$*************************$
\n", "Starting MultiNest
\n", "generating live points\n", "\n", "\n", "\n", "$------------------$\n", "\n", "Eventually (a few minutes) you whould see more output:\n", "\n", " live points generated, starting sampling\n", "
\n", "Acceptance Rate: 0.998185
\n", "Replacements: 550
\n", "Total Samples: 551
\n", "Nested Sampling ln(Z): $**************$
\n", "Acceptance Rate: 0.977199
\n", "Replacements: 600
\n", "Total Samples: 614
\n", "Nested Sampling ln(Z): $**************$
\n", "Acceptance Rate: 0.965825
\n", "Replacements: 650
\n", "Total Samples: 673
\n", "Nested Sampling ln(Z): $**************$
\n", "Acceptance Rate: 0.939597
\n", "Replacements: 700
\n", "Total Samples: 745
\n", "Nested Sampling ln(Z): $**************$
\n", "\n", "\n", "\n", "Do not be alarmed by the $*****$. It just means that there are too many digits to print out for the inital ln(Z) values. Eventually normalish looking numbers (usually negative) print out here. Ok, feel free to kill this now, because we will use mpi to make it faster.\n", "\n", "### STEP 3\n", "To do mpi, if everything installed correctly, you just need to type the following into the same command line:

\n", "mpirun -np 4 python call_pymultinest_transmission_wfc3_CC.py

\n", "Note, you can use more than 4 cpu's/cores if your computer has them. Use as many as you have. Now, just wait. You should see similar output as for the single cpu, ubt at a faster rate. For the default setup, with 4 cpu's, this takes $\\sim$1hr 10 min (15452 calls). When it is done it will print out this:
\n", "\n", " ln(ev)= -25.249086782326863 +/- 0.12562433089471531 \n", " Total Likelihood Evaluations: 15452
\n", " Sampling finished. Exiting MultiNest
\n", " analysing data from ./pmn$_$transmission/template_.txt
\n", " analysing data from ./pmn$_$transmission/template_.txt
\n", " analysing data from ./pmn$_$transmission/template_.txt
\n", " analysing data from ./pmn$_$transmission/template_.txt
\n", "\n", "\n", "\n", "\n", "### STEP 4\n", "When this is done, it is time to plot. Open the routine, \"plot_PMN_transmission.py\". This will make the usual obnoxious corner plots, a reconstructed \"TP\" profile (which is kind of meaningless), and will generate sample spectra from random parameter vectors drawn from the posterior. This last part takes some time. When this is complete a nice 1-,2-sigma spectral spread plot will pop up. Feel free to manipulate this to make plots to your liking. Note, the spectral draws will be saved as a python pickle so that you can twiddle with plot adjustments without haveing to regenerate that each time. \n", "\n", "That's it! You are done! So after having worked throught his notebook you should feel comfortable playing around with the forward model to gain an understanding of how each parameter influences the spectrum, comfortable running both the dynesty and pymultinest samplers, and plotting up standard output/results. Good luck. Note, there is no warrenty, if you get an unpysical answer, that's on you =)\n", "\n", "Feel free to move onto the emission tutorial!\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }