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Fractals_Test
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Fractals.ipynb
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"source": "%pylab notebook\n%load_ext cython\nimport sympy as smp\nfrom scipy.special import lambertw\nfrom tqdm import tqdm_notebook\nfrom time import perf_counter",
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"text": "Populating the interactive namespace from numpy and matplotlib\n",
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"source": "%%cython -a\n\nimport cython\nimport numpy as np\ncimport numpy as np\nDTYPE = np.float64\nctypedef np.float64_t DTYPE_t\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\n@cython.profile(False)\n@cython.optimize.unpack_method_calls(False)\ncdef np.ndarray[np.complex128_t, ndim=2] f(np.ndarray[np.complex128_t, ndim=2] _x, np.ndarray[np.complex128_t, ndim=2] z):\n # Iteration function used to compute successive iterations of the fractal set\n return z**_x\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\n@cython.profile(False)\n@cython.optimize.unpack_method_calls(False)\n@cython.initializedcheck(False)\ndef fractalVals(np.ndarray[DTYPE_t, ndim=2] zRe, np.ndarray[DTYPE_t, ndim=2] zIm, np.int32_t iterations, np.complex128_t z_0=1):\n \n # Iterations controls the total number of iterations used to compute the set\n # z_0 is a control parameter that allows one to vary the initial state by some complex number\n # Which then can create effects like swirling the original fractal pattern\n \n assert zRe.dtype == DTYPE and zIm.dtype == DTYPE\n cdef np.ndarray[np.complex128_t, ndim=2] z = z_0*np.array(zRe, dtype=np.complex128) + 1j*np.array(zIm, dtype=np.complex128)\n cdef np.ndarray[np.complex128_t, ndim=2] X_n = z_0*(zRe + 1j*zIm)\n cdef np.ndarray[np.complex128_t, ndim=2] temp_n = zRe + 1j*zIm\n cdef np.ndarray[DTYPE_t, ndim=2] resArray = np.zeros((zRe.shape[0], zIm.shape[1]), dtype=DTYPE)\n cdef np.int32_t n = 0\n \n for i in range(iterations):\n X_n = f(X_n, z)\n temp_n = f(f(temp_n, z), z)\n n += 2\n resArray[np.abs(temp_n - X_n) < 5e-15] = (n - i)\n # Checks for divergence by checking if values are no longer finite (don't fit into 64-bit floats or are nans)\n resArray[np.logical_and(np.logical_not(np.isfinite(X_n)), resArray == 0)] = -(i + 1)\n resArray[resArray >= iterations - 1] = -iterations + 1\n return resArray",
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class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n<pre class='cython code score-8 '> __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 3, __pyx_L1_error)\n <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_np, __pyx_t_1) &lt; 0) __PYX_ERR(0, 3, __pyx_L1_error)\n <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>: <span class=\"k\">cimport</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n<pre class=\"cython line score-11\" onclick='toggleDiv(this)'>+<span class=\"\">05</span>: <span class=\"n\">DTYPE</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float64</span></pre>\n<pre class='cython code score-11 '> __pyx_t_1 = <span 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class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n<pre class=\"cython line score-19\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>: <span class=\"k\">cdef</span> <span class=\"kt\">np</span>.<span class=\"kt\">ndarray</span>[<span class=\"kt\">np</span>.<span class=\"nf\">complex128_t</span><span class=\"p\">,</span> <span class=\"nf\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">f</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">complex128_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">_x</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">complex128_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">z</span><span class=\"p\">):</span></pre>\n<pre class='cython code score-19 '>static PyArrayObject *__pyx_f_46_cython_magic_0b7d2e9dada1313c8a1bfd8400920a02_f(PyArrayObject *__pyx_v__x, PyArrayObject *__pyx_v_z) {\n __Pyx_LocalBuf_ND __pyx_pybuffernd__x;\n __Pyx_Buffer __pyx_pybuffer__x;\n __Pyx_LocalBuf_ND __pyx_pybuffernd_z;\n __Pyx_Buffer __pyx_pybuffer_z;\n PyArrayObject *__pyx_r = NULL;\n <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f\", 0);\n __pyx_pybuffer__x.pybuffer.buf = NULL;\n __pyx_pybuffer__x.refcount = 0;\n __pyx_pybuffernd__x.data = NULL;\n __pyx_pybuffernd__x.rcbuffer = &amp;__pyx_pybuffer__x;\n 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class=\"bp\">False</span><span class=\"p\">)</span></pre>\n<pre class=\"cython line score-0\">&#xA0;<span class=\"\">20</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">initializedcheck</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n<pre class=\"cython line score-119\" onclick='toggleDiv(this)'>+<span class=\"\">21</span>: <span class=\"k\">def</span> <span class=\"nf\">fractalVals</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">DTYPE_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">zRe</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">DTYPE_t</span><span 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PyObject *__pyx_pw_46_cython_magic_0b7d2e9dada1313c8a1bfd8400920a02_1fractalVals(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n PyArrayObject *__pyx_v_zRe = 0;\n PyArrayObject *__pyx_v_zIm = 0;\n __pyx_t_5numpy_int32_t __pyx_v_iterations;\n __pyx_t_double_complex __pyx_v_z_0;\n PyObject *__pyx_r = 0;\n <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"fractalVals (wrapper)\", 0);\n {\n static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_zRe,&amp;__pyx_n_s_zIm,&amp;__pyx_n_s_iterations,&amp;__pyx_n_s_z_0,0};\n PyObject* values[4] = {0,0,0,0};\n if (unlikely(__pyx_kwds)) {\n Py_ssize_t kw_args;\n const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n switch (pos_args) {\n case 4: values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n case 3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n case 2: 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"source": "def fractalSet(axes, event=None, iterations=32, cbar=None, resolution=384):\n if (event is not None and event.button == 1):\n Rez = np.linspace(*axes.get_xlim(), resolution)\n Imz = np.linspace(*axes.get_ylim()[::-1], resolution)\n else:\n Rez = np.linspace(-10, 10, resolution)\n Imz = np.linspace(-10, 10, resolution)\n plt.cla()\n t0 = perf_counter()\n a = fractalVals(Rez[:, None], Imz[None, :], iterations=iterations)\n axes.set_title(\"Time to Compute: {:.2e}s\\n Iterations: {:.2e}\".format(perf_counter() - t0, iterations))\n img = axes.imshow(a.T, vmin=-iterations, vmax=iterations, \n extent=[Rez.min(), Rez.max(), Imz.min(), Imz.max()], \n interpolation='none', cmap='magma')\n if (cbar is None):\n cbar = axes.get_figure().colorbar(img)\n return img, cbar\n\ndef dimensionEstimate(iterations=64):\n # Estimates dimension by iteratively computing the total number\n # of non-diverged pixels and comparing it to the total number of pixels along an axis\n # Basically box counting...\n i = 4\n while i <= 2048:\n Rez = np.linspace(-1.05, 0.65, i)\n Imz = np.linspace(-0.8, 0.8, i)\n a = fractalVals(Rez[:, None], Imz[None, :], iterations=iterations)\n print(np.log((a>0).sum())/np.log(i))\n i *= 2",
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"source": "fig = figure(0, figsize=(10,10))\nax = gca()\nim, cbar = fractalSet(ax)\ncid = fig.canvas.mpl_connect('button_release_event', lambda event: fractalSet(ax, event=event, cbar=cbar))\nax.set_xlabel(\"Re(z)\")\nax.set_ylabel(\"Im(z)\")",
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' +\n 'Firefox 4 and 5 are also supported but you ' +\n 'have to enable WebSockets in about:config.');\n };\n}\n\nmpl.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 = $('<div/>');\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 this.ws.close();\n }\n\n this.ws.onmessage = this._make_on_message_function(this);\n\n this.ondownload = ondownload;\n}\n\nmpl.figure.prototype._init_header = function() {\n var titlebar = $(\n '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n 'ui-helper-clearfix\"/>');\n var titletext = $(\n '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n 'text-align: center; padding: 3px;\"/>');\n titlebar.append(titletext)\n this.root.append(titlebar);\n this.header = titletext[0];\n}\n\n\n\nmpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n\n}\n\n\nmpl.figure.prototype._root_extra_style = function(canvas_div) {\n\n}\n\nmpl.figure.prototype._init_canvas = function() {\n var fig = this;\n\n var canvas_div = $('<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 = $('<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 = $('<canvas/>');\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\nmpl.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) {\n // put a spacer in here.\n continue;\n }\n var button = $('<button/>');\n button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n 'ui-button-icon-only');\n button.attr('role', 'button');\n button.attr('aria-disabled', 'false');\n button.click(method_name, toolbar_event);\n button.mouseover(tooltip, toolbar_mouse_event);\n\n var icon_img = $('<span/>');\n icon_img.addClass('ui-button-icon-primary ui-icon');\n icon_img.addClass(image);\n icon_img.addClass('ui-corner-all');\n\n var tooltip_span = $('<span/>');\n tooltip_span.addClass('ui-button-text');\n tooltip_span.html(tooltip);\n\n button.append(icon_img);\n button.append(tooltip_span);\n\n nav_element.append(button);\n }\n\n var fmt_picker_span = $('<span/>');\n\n var fmt_picker = $('<select/>');\n fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n fmt_picker_span.append(fmt_picker);\n nav_element.append(fmt_picker_span);\n this.format_dropdown = fmt_picker[0];\n\n for (var ind in mpl.extensions) {\n var fmt = mpl.extensions[ind];\n var option = $(\n '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n fmt_picker.append(option)\n }\n\n // Add hover states to the ui-buttons\n $( \".ui-button\" ).hover(\n function() { $(this).addClass(\"ui-state-hover\");},\n function() { $(this).removeClass(\"ui-state-hover\");}\n );\n\n var status_bar = $('<span class=\"mpl-message\"/>');\n nav_element.append(status_bar);\n this.message = status_bar[0];\n}\n\nmpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n // which will in turn request a refresh of the image.\n this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n}\n\nmpl.figure.prototype.send_message = function(type, properties) {\n properties['type'] = type;\n properties['figure_id'] = this.id;\n this.ws.send(JSON.stringify(properties));\n}\n\nmpl.figure.prototype.send_draw_message = function() {\n if (!this.waiting) {\n this.waiting = true;\n this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n }\n}\n\n\nmpl.figure.prototype.handle_save = function(fig, msg) {\n var format_dropdown = fig.format_dropdown;\n var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n fig.ondownload(fig, format);\n}\n\n\nmpl.figure.prototype.handle_resize = function(fig, msg) {\n var size = msg['size'];\n if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n fig._resize_canvas(size[0], size[1]);\n fig.send_message(\"refresh\", {});\n };\n}\n\nmpl.figure.prototype.handle_rubberband = function(fig, msg) {\n 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\nmpl.figure.prototype.handle_figure_label = function(fig, msg) {\n // Updates the figure title.\n fig.header.textContent = msg['label'];\n}\n\nmpl.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\nmpl.figure.prototype.handle_message = function(fig, msg) {\n fig.message.textContent = msg['message'];\n}\n\nmpl.figure.prototype.handle_draw = function(fig, msg) {\n // Request the server to send over a new figure.\n fig.send_draw_message();\n}\n\nmpl.figure.prototype.handle_image_mode = function(fig, msg) {\n fig.image_mode = msg['mode'];\n}\n\nmpl.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.\nmpl.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\nmpl.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 */\nfunction 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\nmpl.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\nmpl.figure.prototype._key_event_extra = function(event, name) {\n // Handle any extra behaviour associated with a key event\n}\n\nmpl.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\nmpl.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\nmpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n this.message.textContent = tooltip;\n};\nmpl.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\nmpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n\nmpl.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\nmpl.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\nmpl.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\nmpl.figure.prototype.close_ws = function(fig, msg){\n fig.send_message('closing', msg);\n // fig.ws.close()\n}\n\nmpl.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\nmpl.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\nmpl.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\nmpl.figure.prototype._root_extra_style = function(el){\n var fig = this\n el.on(\"remove\", function(){\n\tfig.close_ws(fig, {});\n });\n}\n\nmpl.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\nmpl.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 // select the cell after this one\n var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n IPython.notebook.select(index + 1);\n }\n}\n\nmpl.figure.prototype.handle_save = function(fig, msg) {\n fig.ondownload(fig, null);\n}\n\n\nmpl.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.\nif (IPython.notebook.kernel != null) {\n IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n}\n"
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"cell_type": "code",
"source": "ax.set_xlabel(\"Im(z)\")\nax.set_xlabel(\"Re(z)\")",
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"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.text.Text at 0x7f19e39dba20>"
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"source": "test = np.ones((4,4), dtype=np.complex128)",
"execution_count": 6,
"outputs": []
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{
"metadata": {
"ExecuteTime": {
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"cell_type": "code",
"source": "f(test, 1+1j).shape",
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"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "(4, 4)"
},
"metadata": {},
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"outputs": []
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"gist": {
"id": "cde966e3dab255a56d502b220c346c69",
"data": {
"description": "Fractals_Test",
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