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kbarbary/for_owen.ipynb

Created May 18, 2015 19:32
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Some calculus for Owen
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for_owen.ipynb
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"input": [
"using Gadfly\n",
"using Calculus\n",
"using Roots"
],
"language": "python",
"metadata": {},
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"input": [
"f(x) = ((x/2)^(x/30 + 2))/5"
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"f (generic function with 1 method)"
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"cell_type": "code",
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"input": [
"# find where f(x) = 10\n",
"xmax = fzeros(x->f(x)-10., 0., 15.)[1]"
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"language": "python",
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"outputs": [
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"10.554496766925327"
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"input": [
"plot(f, 0., xmax)"
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" init_pan_zoom(root);\n",
"\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" xgridlines.data(\"unfocused_strokedash\",\n",
" xgridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
" ygridlines.data(\"unfocused_strokedash\",\n",
" ygridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
"\n",
" // emphasize grid lines\n",
" var destcolor = root.data(\"focused_xgrid_color\");\n",
" xgridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"focused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // reveal zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 1.0}, 250);\n",
"};\n",
"\n",
"\n",
"// Unemphasize grid lines on mouse out.\n",
"Gadfly.plot_mouseout = function(event) {\n",
" var root = this.plotroot();\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" var destcolor = root.data(\"unfocused_xgrid_color\");\n",
"\n",
" xgridlines.attr(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"unfocused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // hide zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 0.0}, 250);\n",
"};\n",
"\n",
"\n",
"var set_geometry_transform = function(root, tx, ty, scale) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
"\n",
" var old_scale = root.data(\"scale\");\n",
"\n",
" var xscale = xscalable ? scale : 1.0,\n",
" yscale = yscalable ? scale : 1.0;\n",
"\n",
" tx = xscalable ? tx : 0.0;\n",
" ty = yscalable ? ty : 0.0;\n",
"\n",
" var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
"\n",
" root.selectAll(\".geometry, image\")\n",
" .forEach(function (element, i) {\n",
" element.transform(t);\n",
" });\n",
"\n",
" bounds = root.plotbounds();\n",
"\n",
" if (yscalable) {\n",
" var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
" root.selectAll(\".xfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(xfixed_t);\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .transform(xfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
" element.transform(unscale_t);\n",
"\n",
" var y = cy * scale + ty;\n",
" element.attr(\"visibility\",\n",
" bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" if (xscalable) {\n",
" var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
" var xtrans = new Snap.Matrix().translate(tx, 0);\n",
" root.selectAll(\".yfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(yfixed_t);\n",
" });\n",
"\n",
" root.select(\".xlabels\")\n",
" .transform(yfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
"\n",
" element.transform(unscale_t);\n",
"\n",
" var x = cx * scale + tx;\n",
" element.attr(\"visibility\",\n",
" bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
" var size_attribs = [\"font-size\"];\n",
" var unscaled_selection = \".geometry, .geometry *\";\n",
" if (xscalable) {\n",
" size_attribs.push(\"rx\");\n",
" unscaled_selection += \", .xgridlines\";\n",
" }\n",
" if (yscalable) {\n",
" size_attribs.push(\"ry\");\n",
" unscaled_selection += \", .ygridlines\";\n",
" }\n",
"\n",
" root.selectAll(unscaled_selection)\n",
" .forEach(function (element, i) {\n",
" // circle need special help\n",
" if (element.node.nodeName == \"circle\") {\n",
" var cx = element.attribute(\"cx\"),\n",
" cy = element.attribute(\"cy\");\n",
" unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
" cx, cy);\n",
" element.transform(unscale_t);\n",
" return;\n",
" }\n",
"\n",
" for (i in size_attribs) {\n",
" var key = size_attribs[i];\n",
" var val = parseFloat(element.attribute(key));\n",
" if (val !== undefined && val != 0 && !isNaN(val)) {\n",
" element.attribute(key, val * old_scale / scale);\n",
" }\n",
" }\n",
" });\n",
"};\n",
"\n",
"\n",
"// Find the most appropriate tick scale and update label visibility.\n",
"var update_tickscale = function(root, scale, axis) {\n",
" if (!root.hasClass(axis + \"scalable\")) return;\n",
"\n",
" var tickscales = root.data(axis + \"tickscales\");\n",
" var best_tickscale = 1.0;\n",
" var best_tickscale_dist = Infinity;\n",
" for (tickscale in tickscales) {\n",
" var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
" if (dist < best_tickscale_dist) {\n",
" best_tickscale_dist = dist;\n",
" best_tickscale = tickscale;\n",
" }\n",
" }\n",
"\n",
" if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
" root.data(axis + \"tickscale\", best_tickscale);\n",
" var mark_inscale_gridlines = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" var mark_inscale_labels = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
" root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
" }\n",
"};\n",
"\n",
"\n",
"var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
" var old_scale = root.data(\"scale\");\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" // compute the viewport derived from tx, ty, and scale\n",
" var x_min = -width * scale - (scale * width - width),\n",
" x_max = width * scale,\n",
" y_min = -height * scale - (scale * height - height),\n",
" y_max = height * scale;\n",
"\n",
" var x0 = bounds.x0 - scale * bounds.x0,\n",
" y0 = bounds.y0 - scale * bounds.y0;\n",
"\n",
" var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
" ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
"\n",
" tx += x0;\n",
" ty += y0;\n",
"\n",
" // when the scale change, we may need to alter which set of\n",
" // ticks is being displayed\n",
" if (scale != old_scale) {\n",
" update_tickscale(root, scale, \"x\");\n",
" update_tickscale(root, scale, \"y\");\n",
" }\n",
"\n",
" set_geometry_transform(root, tx, ty, scale);\n",
"\n",
" root.data(\"scale\", scale);\n",
" root.data(\"tx\", tx);\n",
" root.data(\"ty\", ty);\n",
"};\n",
"\n",
"\n",
"var scale_centered_translation = function(root, scale) {\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var scale0 = root.data(\"scale\");\n",
"\n",
" // how off from center the current view is\n",
" var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
" yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
"\n",
" // rescale offsets\n",
" xoff = xoff * scale / scale0;\n",
" yoff = yoff * scale / scale0;\n",
"\n",
" // adjust for the panel position being scaled\n",
" var x_edge_adjust = bounds.x0 * (1 - scale),\n",
" y_edge_adjust = bounds.y0 * (1 - scale);\n",
"\n",
" return {\n",
" x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
" y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
" };\n",
"};\n",
"\n",
"\n",
"// Initialize data for panning zooming if it isn't already.\n",
"var init_pan_zoom = function(root) {\n",
" if (root.data(\"zoompan-ready\")) {\n",
" return;\n",
" }\n",
"\n",
" // The non-scaling-stroke trick. Rather than try to correct for the\n",
" // stroke-width when zooming, we force it to a fixed value.\n",
" var px_per_mm = root.node.getCTM().a;\n",
"\n",
" // Drag events report deltas in pixels, which we'd like to convert to\n",
" // millimeters.\n",
" root.data(\"px_per_mm\", px_per_mm);\n",
"\n",
" root.selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
" if (sw > 0) {\n",
" element.attribute(\"stroke-width\", sw);\n",
" element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
" }\n",
" });\n",
"\n",
" // Store ticks labels original tranformation\n",
" root.selectAll(\".xlabels > text, .ylabels > text\")\n",
" .forEach(function (element, i) {\n",
" var lm = element.transform().localMatrix;\n",
" element.data(\"static_transform\",\n",
" new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
" });\n",
"\n",
" var xgridlines = root.select(\".xgridlines\");\n",
" var ygridlines = root.select(\".ygridlines\");\n",
" var xlabels = root.select(\".xlabels\");\n",
" var ylabels = root.select(\".ylabels\");\n",
"\n",
" if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
" if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
" if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
" if (root.data(\"xtickscales\") === undefined) {\n",
"\n",
" // index all the tick scales that are listed\n",
" var xtickscales = {};\n",
" var ytickscales = {};\n",
" var add_x_tick_scales = function (element, i) {\n",
" xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
" var add_y_tick_scales = function (element, i) {\n",
" ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
"\n",
" if (xgridlines) xgridlines.selectAll(\"path\").forEach(add_x_tick_scales);\n",
" if (ygridlines) ygridlines.selectAll(\"path\").forEach(add_y_tick_scales);\n",
" if (xlabels) xlabels.selectAll(\"text\").forEach(add_x_tick_scales);\n",
" if (ylabels) ylabels.selectAll(\"text\").forEach(add_y_tick_scales);\n",
"\n",
" root.data(\"xtickscales\", xtickscales);\n",
" root.data(\"ytickscales\", ytickscales);\n",
" root.data(\"xtickscale\", 1.0);\n",
" }\n",
"\n",
" var min_scale = 1.0, max_scale = 1.0;\n",
" for (scale in xtickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" for (scale in ytickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" root.data(\"min_scale\", min_scale);\n",
" root.data(\"max_scale\", max_scale);\n",
"\n",
" // store the original positions of labels\n",
" if (xlabels) {\n",
" xlabels.selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"x\", element.asPX(\"x\"));\n",
" });\n",
" }\n",
"\n",
" if (ylabels) {\n",
" ylabels.selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"y\", element.asPX(\"y\"));\n",
" });\n",
" }\n",
"\n",
" // mark grid lines and ticks as in or out of scale.\n",
" var mark_inscale = function (element, i) {\n",
" element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
" };\n",
"\n",
" if (xgridlines) xgridlines.selectAll(\"path\").forEach(mark_inscale);\n",
" if (ygridlines) ygridlines.selectAll(\"path\").forEach(mark_inscale);\n",
" if (xlabels) xlabels.selectAll(\"text\").forEach(mark_inscale);\n",
" if (ylabels) ylabels.selectAll(\"text\").forEach(mark_inscale);\n",
"\n",
" // figure out the upper ond lower bounds on panning using the maximum\n",
" // and minum grid lines\n",
" var bounds = root.plotbounds();\n",
" var pan_bounds = {\n",
" x0: 0.0,\n",
" y0: 0.0,\n",
" x1: 0.0,\n",
" y1: 0.0\n",
" };\n",
"\n",
" if (xgridlines) {\n",
" xgridlines\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
" pan_bounds.x0 = bounds.x1 - bbox.x;\n",
" }\n",
" if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
" pan_bounds.x1 = bounds.x0 - bbox.x;\n",
" }\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" if (ygridlines) {\n",
" ygridlines\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
" pan_bounds.y0 = bounds.y1 - bbox.y;\n",
" }\n",
" if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
" pan_bounds.y1 = bounds.y0 - bbox.y;\n",
" }\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" // nudge these values a little\n",
" pan_bounds.x0 -= 5;\n",
" pan_bounds.x1 += 5;\n",
" pan_bounds.y0 -= 5;\n",
" pan_bounds.y1 += 5;\n",
" root.data(\"pan_bounds\", pan_bounds);\n",
"\n",
" root.data(\"zoompan-ready\", true)\n",
"};\n",
"\n",
"\n",
"// Panning\n",
"Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var dx0 = root.data(\"dx\"),\n",
" dy0 = root.data(\"dy\");\n",
"\n",
" root.data(\"dx\", dx);\n",
" root.data(\"dy\", dy);\n",
"\n",
" dx = dx - dx0;\n",
" dy = dy - dy0;\n",
"\n",
" var tx = tx0 + dx,\n",
" ty = ty0 + dy;\n",
"\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
" var root = this.plotroot();\n",
" root.data(\"dx\", 0);\n",
" root.data(\"dy\", 0);\n",
" init_pan_zoom(root);\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onend = function(event) {\n",
" var root = this.plotroot();\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_scroll = function(event) {\n",
" if (event.shiftKey) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var new_scale = root.data(\"scale\") * Math.pow(2, 0.002 * event.wheelDelta);\n",
" new_scale = Math.max(\n",
" root.data(\"min_scale\"),\n",
" Math.min(root.data(\"max_scale\"), new_scale))\n",
" update_plot_scale(root, new_scale);\n",
" event.stopPropagation();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseover = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseout = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomout_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var min_scale = root.data(\"min_scale\"),\n",
" scale = root.data(\"scale\");\n",
" Snap.animate(\n",
" scale,\n",
" Math.max(min_scale, scale / 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomin_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var max_scale = root.data(\"max_scale\"),\n",
" scale = root.data(\"scale\");\n",
"\n",
" Snap.animate(\n",
" scale,\n",
" Math.min(max_scale, scale * 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_track_click = function(event) {\n",
" // TODO\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mousedown = function(event) {\n",
" this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mouseup = function(event) {\n",
" this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"// compute the position in [0, 1] of the zoom slider thumb from the current scale\n",
"var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
" if (scale >= 1.0) {\n",
" return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));\n",
" }\n",
" else {\n",
" return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));\n",
" }\n",
"}\n",
"\n",
"\n",
"var update_plot_scale = function(root, new_scale) {\n",
" var trans = scale_centered_translation(root, new_scale);\n",
" set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
"\n",
" root.selectAll(\".zoomslider_thumb\")\n",
" .forEach(function (element, i) {\n",
" var min_pos = element.data(\"min_pos\"),\n",
" max_pos = element.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
" element.transform(new Snap.Matrix().translate(\n",
" Math.max(min_pos, Math.min(\n",
" max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
" });\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {\n",
" var root = this.plotroot();\n",
" var min_pos = this.data(\"min_pos\"),\n",
" max_pos = this.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"old_scale\");\n",
"\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
" dx / (max_pos - min_pos);\n",
"\n",
" // compute the new scale\n",
" var new_scale;\n",
" if (xpos >= 0.5) {\n",
" new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));\n",
" }\n",
" else {\n",
" new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +\n",
" Math.log(min_scale));\n",
" }\n",
" new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
"\n",
" update_plot_scale(root, new_scale);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragstart = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" // keep track of what the scale was when we started dragging\n",
" root.data(\"old_scale\", root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragend = function(event) {\n",
"};\n",
"\n",
"\n",
"var toggle_color_class = function(root, color_class, ison) {\n",
" var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
" var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
" if (ison) {\n",
" guides.animate({opacity: 0.5}, 250);\n",
" geoms.animate({opacity: 0.0}, 250);\n",
" } else {\n",
" guides.animate({opacity: 1.0}, 250);\n",
" geoms.animate({opacity: 1.0}, 250);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.colorkey_swatch_click = function(event) {\n",
" var root = this.plotroot();\n",
" var color_class = this.data(\"color_class\");\n",
"\n",
" if (event.shiftKey) {\n",
" root.selectAll(\".colorkey text\")\n",
" .forEach(function (element) {\n",
" var other_color_class = element.data(\"color_class\");\n",
" if (other_color_class != color_class) {\n",
" toggle_color_class(root, other_color_class,\n",
" element.attr(\"opacity\") == 1.0);\n",
" }\n",
" });\n",
" } else {\n",
" toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
" }\n",
"};\n",
"\n",
"\n",
"return Gadfly;\n",
"\n",
"}));\n",
"\n",
"\n",
"//@ sourceURL=gadfly.js\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
" require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
" factory(Snap, Gadfly);\n",
" });\n",
" } else {\n",
" factory(glob.Snap, glob.Gadfly);\n",
" }\n",
"})(window, function (Snap, Gadfly) {\n",
" var fig = Snap(\"#fig-9084f11d17c14f11bb74a8481762c281\");\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-4\")\n",
" .mouseenter(Gadfly.plot_mouseover)\n",
".mouseleave(Gadfly.plot_mouseout)\n",
".mousewheel(Gadfly.guide_background_scroll)\n",
".drag(Gadfly.guide_background_drag_onmove,\n",
" Gadfly.guide_background_drag_onstart,\n",
" Gadfly.guide_background_drag_onend)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-7\")\n",
" .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-7\")\n",
" .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-8\")\n",
" .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-8\")\n",
" .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-12\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-12\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-12\")\n",
" .click(Gadfly.zoomslider_zoomin_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-14\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-14\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-14\")\n",
" .click(Gadfly.zoomslider_track_click);\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-15\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-15\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-15\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-15\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-15\")\n",
" .drag(Gadfly.zoomslider_thumb_dragmove,\n",
" Gadfly.zoomslider_thumb_dragstart,\n",
" Gadfly.zoomslider_thumb_dragend)\n",
".mousedown(Gadfly.zoomslider_thumb_mousedown)\n",
".mouseup(Gadfly.zoomslider_thumb_mouseup)\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-16\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-16\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-9084f11d17c14f11bb74a8481762c281-element-16\")\n",
" .click(Gadfly.zoomslider_zoomout_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
" });\n",
"]]> </script>\n",
"</svg>\n"
],
"metadata": {},
"output_type": "pyout",
"png": 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"text": [
"Plot(...)"
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"cell_type": "code",
"collapsed": false,
"input": [
"# compute derivative every 0.5\n",
"xr = collect(0.5:0.5:xmax)\n",
"fprime = [derivative(f, x) for x=xr]\n",
"for i in 1:length(xr)\n",
" println(\"f'($(xr[i])) = $(fprime[i])\")\n",
"end"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"f'(0.5) = 0.048700718677844444\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"f'(1.0) = 0.0982157373291931\n",
"f'(1.5) = 0.1504908725443042\n",
"f'(2.0) = 0.20666666666640088\n",
"f'(2.5) = 0.26767253562073196\n",
"f'(3.0) = 0.3343682666188282\n",
"f'(3.5) = 0.4076038825764437\n",
"f'(4.0) = 0.48825228845588803\n",
"f'(4.5) = 0.5772305574930221\n",
"f'(5.0) = 0.6755159164598241\n",
"f'(5.5) = 0.7841591669420475\n",
"f'(6.0) = 0.9042969392764026\n",
"f'(6.5) = 1.037163567544162\n",
"f'(7.0) = 1.1841030744404357\n",
"f'(7.5) = 1.3465815973126793\n",
"f'(8.0) = 1.526200501494607\n",
"f'(8.5) = 1.7247103808948685\n",
"f'(9.0) = 1.9440261207322602\n",
"f'(9.5) = 2.1862431851424957\n",
"f'(10.0) = 2.4536552907904383\n",
"f'(10.5) = 2.748773628144314\n"
]
}
],
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},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# the derivative of curve length is sqrt((dy/dx)^2 + dx^2)\n",
"# integrate that expression:\n",
"curvelen, err = quadgk(x -> sqrt(derivative(f, x)^2 + 1.), 0., xmax)\n",
"println(\"curvelen is $curvelen\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"curvelen is 15.642992722304774\n"
]
}
],
"prompt_number": 17
},
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"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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