echelle de teinte.ipynb

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    "<div id=\"Titre\"></div>\n",
    "\n",
    "# TP1 - Echelle de teinte\n",
    "\n",
    "Vous pouvez modifier chaque cellule en cliquant dessus (même les cellules texte). Cliquez sur \"Exécuter\" pour revenir à l'affichage classique ou avoir un retour des programmes pythons."
   ]
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  {
   "cell_type": "markdown",
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    "<h3>Matériel :</h3>\n",
    "<ul><li>Arduino nano</li>\n",
    "    <li>Breadboard</li>\n",
    "    <li>Fils</li>\n",
    "    <li>Photoresistance</li>\n",
    "    <li>Resistance $1 k\\Omega$</li>\n",
    "    <li>laser rouge</li>\n",
    "    <li>4 cuves de spectroscopie notées \"4\", \"3\", \"2\" et \"1\" contenant des solutions aqueuses de sulfate de cuivre de concentration 0,05 mol/L, 0,10 mol/L, 0,20 mol/L et 0,40 mol/L respectivement</li>\n",
    "    <li>1 cuve de spectroscopie notée \"Blanc\" contenant uniquement le solvant (eau)</li>\n",
    "    <li>1 cuve de spectroscopie notée \"X\" contenant une solution de sulfate de cuivre de concentration 0,175 mol/L</li>\n",
    "    <li>Ordinateur</li></ul>\n",
    "    <br>\n",
    "<h3>Logiciels :</h3>\n",
    "<ul><li>Winpython ou autre IDE python</li>\n",
    "<li>Navigateur web type Mozilla firefox</li>\n",
    "    <li>IDE Arduino</li></ul>\n",
    "    <br>"
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   "cell_type": "code",
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   "source": [
    "# imports à exécuter une fois au début\n",
    "from math import log\n",
    "from scipy.optimize import curve_fit\n",
    "import matplotlib.pyplot as plt"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "%matplotlib notebook"
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   "cell_type": "markdown",
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   "source": [
    "# Sujet\n",
    "On dispose de 4 solutions aqueuses de sulfate de cuivre $Cu_{(aq)}^{2+} + SO_{4 (aq)}^{2-}$\n",
    "<br>\n",
    "Leur concentration massique est donnée dans le tableau suivant :\n",
    "\n",
    "\n",
    "| Identifiant | Concentration (g/L) |\n",
    "|-------------|---------------------|\n",
    "| Blanc       |                0    |\n",
    "| 1           |                64   |\n",
    "| 2           |                32   |\n",
    "| 3           |                16   |\n",
    "| 4           |                8    | \n",
    "\n",
    "On dispose aussi d'une <b>cuve \"X\"</b> contenant une solution aqueuse de sulfate de cuivre de concentration massique inconnue.\n"
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   "cell_type": "markdown",
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   "source": [
    "Si on veut déterminer la valeur de la concentration de x, il faut réaliser une mesure quantitative de cette couleur. Nous allons donc utiliser un composant dont la résistance varie en fonction de la lumière qu’il reçoit : <b>la photorésistance.</b>\n",
    "Pour déterminer la valeur de la résistance <b>$\\boldsymbol{R_{1}}$</b> de la photorésistance, on utilise une carte Arduino et une résistance de valeur connue <b>$\\boldsymbol{R_{2} = 1000\\ \\Omega}$</b>. On réalise le montage de la <b>figure 1</b> sans brancher la carte à l’ordinateur dans un premier temps.\n",
    "<p><center><b>Figure 1. Montage à Réaliser</b>\n",
    "<img src=\"TP1_figure1.png\"></center>\n",
    "Il est équivalent au montage ci-dessous :\n",
    "<center><b>Figure 2. Schéma électrique équivalent</b>\n",
    "<img src=\"TP1_figure2.png\"></center></p>"
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    "On a $\\boldsymbol{U_0\\ =\\ U_1\\ +\\ U_2}$ d'après la loi des mailles.\n",
    "<p>De plus, $\\boldsymbol{I_1\\ =\\ \\frac{U_1}{R_1}\\ =\\ I_2\\ =\\ \\frac{U_2}{R_2}\\ =\\ I}$. "
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "Le montage réalisé sur la carte Arduino nous permet de mesurer U2. On connaît U0 et R2. Ce qui nous intéresse ici est la valeur de R1.\n",
    "<p>On a $\\boldsymbol{R_1\\ =\\ \\frac{U_1\\ \\times\\ R_2}{U_2}}$ et comme $\\boldsymbol{U_1\\ =\\ U_0\\ -\\ U_2}$ cela donne:</p>\n",
    "<p>$\\boldsymbol{R_1\\ =\\ \\frac{(U_0\\ -\\ U_2)\\times\\ R_2}{U_2}\\ =\\ \\frac{R_2\\ \\times\\ U_0}{U_2}\\ -\\ R_2}$</p>"
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   "source": [
    "U<sub>2</sub> est mesuré par le convertisseur analogique numérique de la carte Arduino qui numérise une tension entre 0 et 5V sur 10 bits. Ainsi, elle nous renvoie une valeur entière entre 0 et 2<sup>10</sup> - 1; 0 pour une tension de 0V et 1023 pour une tension de 5V.\n",
    "Ainsi, lorsque <b>la carte Arduino renvoie 534</b> il s'agit de la mesure d'une tension $U\\ =\\ \\frac{534.\\ \\times\\ 5.}{1023.}\\ =\\ 2.61\\ V$</p>"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "<p>Si on note <b>n</b> la valeur entière renvoyée par la carte Arduino, on peut exprimer la valeur de la tension $\\boldsymbol{U_2\\ =\\ n\\ \\times\\ 0.00489}$. </p>\n",
    "<b>C'est valable pour toute mesure analogique (ports A0 à A7)</b>"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "<p>D'où $\\boldsymbol{R_1\\ =\\ \\frac{R_2\\ \\times\\ 5.}{n\\ \\times\\ 0.00489}\\ -\\ R_2}$</p>"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "Le programme Arduino <a href=\"./photoresistance_cor.ino\" target=\"_blank\">photoresistance_cor.ino</a> fourni permet à la carte de renvoyer la valeur de la résistance <b>R<sub>1</sub></b> environ <b>deux fois par seconde.</b>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "<p>Un fois le montage de la <b>figure 1.</b> réalisé, téléversez ce programme vers la carte Arduino. Attention de bien régler le <b style=\"color:red;\">type de carte, le port et le processeur</b>.</p>\n",
    "<p>Nous allons maintenant réaliser des mesures de l'intensité de la lumière qui traverse un échantillon de solution. Pour cela, placer le laser rouge en face de la photorésistance comme sur la <b>figure 3.</b> Ouvrir alors le <b>moniteur série</b> du logiciel Arduino. Réglez le débit binaire à la même valeur que dans votre programme (115200 ici). Vous pouvez alors lire la valeur de la résistance R<sub>1</sub> de la photorésistance.\n",
    "<p><center><b>Figure 3. Montage expérimental</b>\n",
    "<img src=\"TP1_figure3.jpg\"></center></p>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Positionnez les différentes cuves (blanc, 1, 2, 3, 4 et X) entre le laser et la photorésistance. Notez les valeurs obtenues <b style=\"color:red;\">dans des listes python ci-dessous</b> puis cliquez sur exécuter une fois terminé."
   ]
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  {
   "cell_type": "code",
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   "source": [
    "#Rentrez vos valeurs ici sous forme d'une liste python puis exécutez la cellule.\n",
    "\n",
    "R1 = [] #rentrer ici les valeurs de resistance dans l'ordre blanc, 4, 3, 2, 1 (celui de C)\n",
    "C = [0.,8.,16.,32.,64.] #et ici les concentrations correspondantes.\n",
    "Rx = 0 #rentrer ici la valeur de la résistance de la solution inconnue"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<b style=\"color:red;\">Le programme python</b> ci-dessous permet de tracer le graphique représentant $\\boldsymbol{R_1}$ <b>en fonction de la concentration</b> pour les solutions \"blanc\", 1, 2, 3, 4 sous la forme de croix. Il affiche également un titre, et des informations sur les deux axes.\n",
    "<p>Vous pourrez utiliser <a href=\"./methode_courbe.ipynb\" target=\"_blank\">la fiche méthode_courbe fournie</a> pour le compléter ou modifier ce code pour voir l'intérêt de chaque ligne.</p>"
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       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } 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 * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\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 overridden (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",
       "    var width = fig.canvas.width/mpl.ratio\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 + '\" width=\"' + width + '\">');\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 width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (5,) and (0,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-8825e4dd2f8e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m#Graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Figure 4.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mR1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"+\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Valeur de la photorésistance R1 en fonction de la concentration C\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   3356\u001b[0m                       mplDeprecation)\n\u001b[1;32m   3357\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3358\u001b[0;31m         \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3359\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3360\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1853\u001b[0m                         \u001b[0;34m\"the Matplotlib list!)\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1854\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1855\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1856\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1857\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1525\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1526\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1527\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1528\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1529\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_grab_next_args\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    404\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    405\u001b[0m                 \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 406\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    407\u001b[0m                 \u001b[0;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    408\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs)\u001b[0m\n\u001b[1;32m    381\u001b[0m             \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    382\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 383\u001b[0;31m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    384\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    385\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'plot'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.7/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m    240\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    241\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[0;32m--> 242\u001b[0;31m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[1;32m    243\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    244\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (5,) and (0,)"
     ]
    }
   ],
   "source": [
    "#Exécutez cette cellule pour recalculer la courbe et l'affichage. \n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "#Graphique\n",
    "plt.figure(\"Figure 4.\")\n",
    "plt.plot(C,R1,\"+\")\n",
    "\n",
    "plt.title(\"Valeur de la photorésistance R1 en fonction de la concentration C\")\n",
    "plt.xlabel(\"Concentration C (g/L)\")\n",
    "plt.ylabel(\"Résistance R1 (ohm)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Voici ci-dessous <b style=\"color:red;\">un programme python</b> permettant de construire la liste des $\\boldsymbol{log(R_1)}$ pour les différentes valeurs de $R_1$. On peut utiliser directement la fonction log car elle a déjà été importée au début de la feuille."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécutez cette cellule pour recalculer la liste logR1.\n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "logR1 = []\n",
    "for val in R1:\n",
    "    logR1.append(log(val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour tracer le graphique représentant $\\boldsymbol{log(R_1)}$ <b>en fonction de la concentration</b> pour les solutions \"blanc\", 1, 2, 3, 4 sous la forme de croix, voici le programme nécessaire:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécutez cette cellule pour recalculer la courbe et l'affichage. \n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "plt.figure(\"Figure 5.\")  \n",
    "plt.plot(C,logR1,\"+\")\n",
    "\n",
    "plt.title(\"log(R1) en fonction de la concentration C\")\n",
    "plt.xlabel(\"Concentration C (g/L)\")\n",
    "plt.ylabel(\"log(R1)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut s'affranchir de la quantité de lumière absorbée par l'eau et la cuve en plastique en traçant $\\boldsymbol{log(R_1)\\ -\\ log(R_1blanc)}$<b> en fonction de la concentration massique.</b>\n",
    "Il faut donc écrire <b style=\"color:red;\">un programme python</b> permettant de construire la liste <b>logR1moinslogR0</b> regroupant ces valeurs.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécutez cette cellule pour recalculer la liste logR1moinslogR0 (logR1 dont on retire la valeur du blanc).\n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "\n",
    "\n",
    "#Construction de la liste calculée à partir des valeurs expérimentales\n",
    "R0 = R1[0] #valeur du blanc\n",
    "\n",
    "logR1moinslogR0 = []\n",
    "for i in range(len(R1)):\n",
    "    logR1moinslogR0.append(log(R1[i]) - log(R0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Voici maintenant <b style=\"color:red;\">un programme python</b> permettant de <b>modéliser</b> cette série de données par une <b>fonction linéaire</b>. Le programme suivant sert à afficher sur un même <b>graphique</b> les points expérimentaux, le modèle et l'équation du modèle.</p>\n",
    "<p>Vous pourrez utiliser <a href=\"./methode_modele.ipynb\" target=\"_blank\">la fiche méthode_modele fournie</a> pour modifier ce code et faire des essais.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécutez cette cellule pour recalculer le modèle. \n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "\n",
    "\n",
    "#Ecrire la fonction du modèle (x est la variable et a un parametre à optimiser -il peut y en avoir plusieurs-)\n",
    "def lineaire(x,a):\n",
    "    return a*x    \n",
    "\n",
    "#Optimiser les valeurs des paramètres\n",
    "params,covariance = curve_fit(lineaire,C,logR1moinslogR0)\n",
    "\n",
    "#Construire la liste de valeurs pour le modèle (on peut changer xmax et xmin pour changer les limites du modèle)\n",
    "xmax = 70.\n",
    "xmin = 0.\n",
    "modelex=[]\n",
    "modeley=[]\n",
    "for i in range(100):\n",
    "    modelex.append(xmin + i * (xmax - xmin) / 99.)\n",
    "    modeley.append(lineaire(modelex[i], *params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécutez cette cellule pour recalculer la courbe et l'affichage. \n",
    "#Il faudra le faire à chaque fois que vous changez les valeurs de la liste R1.\n",
    "\n",
    "\n",
    "plt.figure(\"Figure 6.\")\n",
    "\n",
    "#Tracé des points expérimentaux avec quelques paramètres facultatifs\n",
    "plt.plot(C,logR1moinslogR0,\"+\",markersize=10.,markeredgewidth=3.,label=\"points expérimentaux\")\n",
    "   \n",
    "#Tracé du modèle (avec affichage de l'équation)\n",
    "plt.plot(modelex,modeley,label=\"modele: Y = {:.2E} C\".format(*params))\n",
    "\n",
    "plt.xlim([xmin,xmax])\n",
    "plt.ylim([0.,1.75])\n",
    "plt.xlabel(\"Concentration C (g/L)\")\n",
    "plt.ylabel(\"log(R1) - log(R1_blanc)\")\n",
    "plt.title(\"Utilisation d'une photorésistance pour mesurer une concentration\")\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faut ensuite calculer la valeur de $\\boldsymbol{log(R_X)\\ -\\ log(R_0)}$ pour la solution inconnue X et de la stocker dans une variable Ax puis utiliser l'équation du modèle pour revenir à Cx: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ax = log(Rx) - log(R1[0])\n",
    "print(Ax)\n",
    "\n",
    "Cm = Ax / params[0]\n",
    "print(\"La concentration massique est de {:.2f} g/L\".format(Cm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi faire de la lecture graphique sur la figure interactive (figure 6. avec le modèle) en promenant la souris sur le graphique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vous pouvez recommencer la manipulation en utilisant une LED rouge, pilotée par la carte arduino comme source lumineuse. Le programme arduino <a href=\"./photoresistance2.ino\" target=\"_blank\">photoresistance2.ino</a> permet de renvoyer directement la valeur de log(R) en s'affranchissant de la lumière ambiante. \n",
    "<p> Refaites vos mesures avec ce dispositif puis reportez les dans le programme python ci-dessous avant de l'exécuter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "logR = []\n",
    "C = [0.,8.,16.,32.,64.] \n",
    "logRx = 0.\n",
    "\n",
    "logRmoinslogR0 = []\n",
    "for val in logR:\n",
    "    logRmoinslogR0 = val - logR[0]\n",
    "    \n",
    "logRxmoinslogR0.append(logRx - logR[0])\n",
    "\n",
    "def lineaire(x,a):\n",
    "    return a*x    \n",
    "\n",
    "#Optimiser les valeurs des paramètres\n",
    "params2,covariance2 = curve_fit(lineaire,C,logRmoinslogR0)\n",
    "\n",
    "#Construire la liste de valeurs pour le modèle (on peut changer xmax et xmin pour changer les limites du modèle)\n",
    "xmax = 70.\n",
    "xmin = 0.\n",
    "modelex2=[]\n",
    "modeley2=[]\n",
    "for i in range(100):\n",
    "    modelex2.append(xmin + i * (xmax - xmin) / 99.)\n",
    "    modeley2.append(lineaire(modelex[i], *params2))\n",
    "    \n",
    "Cm2 = logRxmoinslogR0 / params2[0]\n",
    "    \n",
    "    \n",
    "    \n",
    "plt.figure(\"Figure 7.\")\n",
    "\n",
    "#Tracé des points expérimentaux avec quelques paramètres facultatifs\n",
    "plt.plot(C,logRmoinslogR0,\"+\",markersize=10.,markeredgewidth=3.,label=\"points expérimentaux\")\n",
    "plt.plot([0,Cm2,Cm2],[logRxmoinslogR0,logRxmoinslogR0,0],\"red\",label = \"Cm = {:.2f}\".format(Cm2))   \n",
    "#Tracé du modèle (avec affichage de l'équation)\n",
    "plt.plot(modelex2,modeley2,label=\"modele: Y = {:.2E} C\".format(*params2))\n",
    "\n",
    "plt.xlim([xmin,xmax])\n",
    "plt.xlabel(\"Concentration C (g/L)\")\n",
    "plt.ylabel(\"log(R1) - log(R1_blanc)\")\n",
    "plt.title(\"Utilisation d'une photorésistance pour mesurer une concentration\")\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2><a href=\"#Titre\">Retour au début du TP</a></h2>"
   ]
  }
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