least_sq_fit_exercise.ipynb

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    "<center><b>Least Squares Fitting using SciPy curve_fit</b></center>\n",
    "\n",
    "Taking <a href=\"https://web.archive.org/web/20060309210852/http://www.einstein-online.info/en/spotlights/binding_energy/binding_energy/index.txt\">data</a> of binding energies of nucleii, a model fit of the Semi-Empirical Mass formula can be made.\n",
    "\n",
    "Semi-Empirical Mass Formula:\n",
    "<center>$B = a_vA-a_sA^{2/3}-a_c\\frac{Z^2}{A^{1/3}}-a_a\\frac{(N-Z)^2}{A}+\\delta(A)$</center>\n",
    "\n",
    "Reading data from the file using numpy loadtxt, only the 1st, 2nd and 5th columns are of interest."
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    "#NAME: Least Squares Fitting\n",
    "#DESCRIPTION: Fitting a model to a set of data.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from IPython.display import display\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, fixed\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "with open('data_SEMF.dat') as f:\n",
    "    lines = (line for line in f if not line.startswith('#'))\n",
    "    read_data = np.loadtxt(lines, delimiter = ' ', usecols=(0, 1, 5), unpack = True)"
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    "The curve_fit function has the following usage. If we have a model function, $f$, we assume the data, $y$, is simply $y = f(x) +$ errors then a curve fit can be performed in the following way:\n",
    "\n",
    "1. Define the model function which takes $x$ and some free parameters and returns the model solution\n",
    "\n",
    "2. Call the curve_fit function, passing it the model function, the x data, the y data and optionally a list of initial values for the fitting parameters\n",
    "\n",
    "3. curve_fit will return 2 tuples: the first contains the least squared fit model parameters and the second contains the covariance matrix\n",
    "\n",
    "4. Finally the model function can be called individually, passing it the fitted parameters, in order to obtain the fitted model"
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    "from scipy.optimize import curve_fit\n",
    "\n",
    "def model_fit(data,term_mask,exclude):\n",
    "    A = data[0][exclude:]\n",
    "    Z = data[1][exclude:]\n",
    "    B = data[2][exclude:]\n",
    "\n",
    "    def _semi_empirical_mass(X, a_v, a_s, a_c, a_a, a_p):\n",
    "        model = np.zeros_like(X)\n",
    "        if term_mask[0]:\n",
    "            vol = a_v\n",
    "            model += vol\n",
    "        if term_mask[1]:\n",
    "            sa = -a_s*X**(-1./3.)\n",
    "            model += sa\n",
    "        if term_mask[2]:\n",
    "            es = -a_c*Z**2*X**(-4./3.)\n",
    "            model += es\n",
    "        if term_mask[3]:\n",
    "            asy = -a_a*((X-2*Z)**2)*X**(-2)\n",
    "            model += asy\n",
    "        if term_mask[4]:\n",
    "            N = X-Z\n",
    "            parity = np.zeros_like(X)\n",
    "            for i in range(len(parity)):\n",
    "                if N[i] % 2 == 0 and Z[i] % 2 == 0:\n",
    "                    parity[i] = a_p*X[i]**(-3./4.)\n",
    "                elif N[i] % 2 == 1 and Z[i] % 2 == 1:\n",
    "                    parity[i] = -a_p*X[i]**(-3./4.)\n",
    "                else:\n",
    "                    parity[i] = 0.0\n",
    "            model += parity/X\n",
    "        \n",
    "        return model\n",
    "\n",
    "    p0 = [15.8,18.0,0.72,23.5,33.5]\n",
    "    popt, pcov = curve_fit(_semi_empirical_mass, A, B, p0 = p0)\n",
    "    \n",
    "    model = _semi_empirical_mass(A, popt[0], popt[1], popt[2], popt[3], popt[4])\n",
    "    ax.set_title((str(popt)))\n",
    "    line.set_data(A,model)\n",
    "    display(fig)\n",
    "\n",
    "def widget_update(b_v = True,b_s = True,b_c = True,b_a = True,b_p = True, exclude=0):\n",
    "    term_mask = [b_v,b_s,b_c,b_a,b_p]\n",
    "    model_fit(read_data,term_mask,exclude)"
   ]
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    "Below is an interactive plot for the binding energy data and the fitted SEMF model. The fitted parameters are shown in the figure title and individual terms in the SEMF can be turned off to see their effect."
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       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></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 = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.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<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 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": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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   "source": [
    "fig = plt.figure(figsize = (12,6))\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "ax.set_xlabel('Atomic Number / A')\n",
    "ax.set_ylabel('Binding Energy per Nucleon (MeV) / (B/A)')\n",
    "\n",
    "ax.plot(read_data[0],read_data[2],'bx')\n",
    "ax.set_xlim([0,max(read_data[0])])\n",
    "\n",
    "line, = ax.plot([],[],'r-')\n",
    "\n",
    "interact(widget_update, b_v = widgets.Checkbox(description='Volume Term',value=True),\n",
    "                        b_s = widgets.Checkbox(description='Surface Area Term',value=False),\n",
    "                        b_c = widgets.Checkbox(description='Coulomb Term',value=False),\n",
    "                        b_a = widgets.Checkbox(description='Asymmetry Term',value=False),\n",
    "                        b_p = widgets.Checkbox(description='Parity Term',value=False),\n",
    "                        exclude = widgets.IntSlider(description='Exclude first n points',\n",
    "                        min=0,max=50))"
   ]
  },
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   "source": [
    "<center><b>Exercise: Model fitting </b></center>\n",
    "\n",
    "There is a data file called <i>data_exercise.dat</i> which contains a broad spectral line feature. It is proposed that the spectral line should either have a Lorentzian profile, due to lifetime broadening, or a Gaussian profile, due to thermal broadening. These have the following functional forms:\n",
    "\n",
    "Lorentzian:\n",
    "<center>$P(\\omega) \\propto \\frac{1}{(\\omega-\\omega_0)^2+\\omega_s^2}$</center>\n",
    "Gaussian:\n",
    "<center>$P(\\omega) \\propto \\frac{1}{\\sqrt{2\\pi \\sigma}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$</center>\n",
    "\n",
    "Write a program using curve_fit to fit a Gaussian and Lorentzian to the spectral feature and identify which model is a better fit. The frequency is given in THz and the emitting substance can assumed to be hydrogen.\n",
    "\n",
    "For the chosen model, find the physical parameters e.g. decay time $\\tau_s$ for lifetime broadening or temperature $T$ for thermal broadening"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": []
  }
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