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| "setdefaults" | |
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| "%plot --format svg" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "### Project Ideas so far\n", | |
| "\n", | |
| "- Nothing yet...probably something heat transfer related\n", | |
| "\n", | |
| "- Modeling Propulsion or Propagation of Sound Waves\n", | |
| "\n", | |
| "- Low Thrust Orbital Transfer\n", | |
| "\n", | |
| "- Tracking motion of a satellite entering orbit until impact\n", | |
| "\n", | |
| "- What ever you think is best.\n", | |
| "\n", | |
| "- You had heat transfer project as an option; that sounded cool\n", | |
| "\n", | |
| "- Heat transfer through a pipe\n", | |
| "\n", | |
| "- I would prefer to do something with beam/plate mechanics or vibrations than a heat transfer or thermo problem\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Questions from you:\n", | |
| "\n", | |
| "- Is attempting to divide by zero an acceptable project idea?\n", | |
| "\n", | |
| "- Would it be alright if we worked in a group of 4?\n", | |
| "\n", | |
| "- What are acceptable project topics?\n", | |
| "\n", | |
| "- How do the exams look? \n", | |
| "\n", | |
| "- Is there no pdf for the lecture today?\n", | |
| "\n", | |
| "- Thank you for making the formatted lectures available!\n", | |
| "\n", | |
| "- did you do anything cool over spring break?\n", | |
| "\n", | |
| "- Could we have a group of 4? We don't want to have to choose which one of us is on their own.\n", | |
| "\n", | |
| "- In HW 5 should there be 4 vectors as an input?\n", | |
| "\n", | |
| "- Would it be possible for me to join a group of 3? I seem to be the odd man out in two 3 member groups that my friends are in." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Statistics and Curve-Fitting\n", | |
| "## Linear Regression\n", | |
| "\n", | |
| "Often, we have a model with empirical parameters. (e.g. Young's modulus, Poisson's ratio, drag coefficient, coefficient of restitution, spring constant)\n", | |
| "\n", | |
| "Experimental measurements are prone to a number of stochastic (random) factors:\n", | |
| "\n", | |
| "- Environmental noise\n", | |
| " \n", | |
| "- Measurement Uncertainty\n", | |
| " \n", | |
| "- Factors not accounted in model (e.g. 2D effects of 1D approximation)\n", | |
| "\n", | |
| "These can lead to **noise** (lack of precision) and **bias** (lack of accuracy)\n", | |
| "\n", | |
| "Consider a piece of glass being stretched. \n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "It is clear that a straight line is a \"good\" fit, but how good and what line?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Statistics\n", | |
| "\n", | |
| "How do we describe *precision* and *accuracy*?\n", | |
| "\n", | |
| "- mean\n", | |
| "\n", | |
| "- standard deviation\n", | |
| "\n", | |
| "Take our class dart problem\n" | |
| ] | |
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| "\t<use color=\"rgb(153, 102, 0)\" transform=\"translate(342.2,196.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 0)\" transform=\"translate(398.9,125.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_4a\"><title>gnuplot_plot_4a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(323.1,96.1) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(280.7,168.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(294.4,157.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(316.9,249.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(366.5,167.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 153, 0)\" transform=\"translate(323.1,96.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_5a\"><title>gnuplot_plot_5a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(88.8,81.4) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(156.8,294.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(466.3,67.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(440.6,193.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(326.8,113.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(459.5,131.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(374.1,108.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(428.3,114.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(293.2,170.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(343.5,208.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 0)\" transform=\"translate(88.8,81.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_6a\"><title>gnuplot_plot_6a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(347.2,145.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(368.1,193.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(434.3,110.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(310.0,156.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(291.4,99.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(363.0,206.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 51)\" transform=\"translate(347.2,145.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_7a\"><title>gnuplot_plot_7a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(369.4,201.6) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(339.4,187.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(231.9,98.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(288.5,164.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(279.2,239.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 0, 51)\" transform=\"translate(369.4,201.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_8a\"><title>gnuplot_plot_8a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(399.3,156.3) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(366.1,169.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(461.3,110.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(334.9,204.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(513.4,61.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 0, 51)\" transform=\"translate(399.3,156.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_9a\"><title>gnuplot_plot_9a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(337.4,128.0) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(320.4,121.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(324.4,153.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(323.3,161.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(289.3,175.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 0, 51)\" transform=\"translate(337.4,128.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_10a\"><title>gnuplot_plot_10a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(369.0,151.4) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(333.4,155.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(358.3,158.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(302.5,154.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(344.5,208.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(338.2,150.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(362.1,106.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(305.8,145.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(315.9,199.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(369.7,118.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(325.8,104.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 51)\" transform=\"translate(369.0,151.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_11a\"><title>gnuplot_plot_11a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(330.4,110.6) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(318.9,312.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(496.3,135.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(285.8,105.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(296.9,135.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 102)\" transform=\"translate(330.4,110.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_12a\"><title>gnuplot_plot_12a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(437.9,120.4) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(333.0,115.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(412.6,175.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(426.3,204.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(366.6,122.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(293.7,140.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(295.5,108.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(333.3,158.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(433.4,149.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(315.9,164.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 102)\" transform=\"translate(437.9,120.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_13a\"><title>gnuplot_plot_13a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(354.2,203.3) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(322.6,162.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(366.6,164.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(392.1,124.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(398.5,209.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(346.4,164.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(358.1,142.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(385.8,226.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(242.0,314.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(314.0,184.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 102)\" transform=\"translate(354.2,203.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_14a\"><title>gnuplot_plot_14a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(331.1,157.1) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(355.7,133.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(324.8,198.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(275.0,155.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(256.2,162.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(294.2,143.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(351.8,154.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(345.3,147.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(353.4,148.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(353.5,125.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 102, 102)\" transform=\"translate(331.1,157.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_15a\"><title>gnuplot_plot_15a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(279.1,166.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(319.4,108.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(412.0,106.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(451.9,114.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(340.5,204.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 102, 102)\" transform=\"translate(279.1,166.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_16a\"><title>gnuplot_plot_16a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(307.3,132.3) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(356.1,91.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(314.8,173.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(328.6,201.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(320.5,211.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(311.9,195.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(304.8,167.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(389.6,146.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(342.0,166.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(313.3,173.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 102, 102)\" transform=\"translate(307.3,132.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_17a\"><title>gnuplot_plot_17a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(473.0,98.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(290.9,31.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(369.4,200.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(394.5,213.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(463.2,224.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 153, 153)\" transform=\"translate(473.0,98.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_18a\"><title>gnuplot_plot_18a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(312.8,190.5) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(379.6,184.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(333.0,145.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(366.3,189.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(346.0,162.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 153, 153)\" transform=\"translate(312.8,190.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_19a\"><title>gnuplot_plot_19a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(324.3,119.9) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(375.4,185.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(287.3,167.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(369.0,135.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(337.2,139.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 153, 153)\" transform=\"translate(324.3,119.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_20a\"><title>gnuplot_plot_20a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(334.3,137.7) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(332.0,151.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(352.7,161.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(340.0,194.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(339.1,162.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 204, 153)\" transform=\"translate(334.3,137.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_21a\"><title>gnuplot_plot_21a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(322.6,155.8) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(314.4,143.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(337.7,172.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(329.7,151.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(338.5,176.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 204, 153)\" transform=\"translate(322.6,155.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_22a\"><title>gnuplot_plot_22a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(333.0,135.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(356.3,155.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(333.0,66.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(372.0,157.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(333.0,95.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 204, 153)\" transform=\"translate(333.0,135.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_23a\"><title>gnuplot_plot_23a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(289.2,159.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(322.6,78.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(368.5,89.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(402.4,108.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(399.6,246.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 255, 204)\" transform=\"translate(289.2,159.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_24a\"><title>gnuplot_plot_24a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(346.8,137.0) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(348.9,162.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(360.3,159.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(318.9,223.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(341.1,161.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 255, 204)\" transform=\"translate(346.8,137.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_25a\"><title>gnuplot_plot_25a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(498.8,143.4) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(454.3,102.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(405.2,209.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(370.8,233.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(300.2,140.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 255, 204)\" transform=\"translate(498.8,143.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_26a\"><title>gnuplot_plot_26a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(346.4,164.2) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(359.8,163.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(373.2,162.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(386.8,162.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(400.2,162.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 255, 204)\" transform=\"translate(346.4,164.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_27a\"><title>gnuplot_plot_27a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(387.0,144.7) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(335.5,154.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(301.2,154.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(308.9,171.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(363.9,180.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 0, 204)\" transform=\"translate(387.0,144.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_28a\"><title>gnuplot_plot_28a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(388.9,153.9) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(255.7,125.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(341.2,130.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(228.0,209.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(263.2,160.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 51, 255)\" transform=\"translate(388.9,153.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_29a\"><title>gnuplot_plot_29a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(340.9,156.9) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(303.9,137.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(286.5,136.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(348.8,148.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(343.3,273.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 51, 51, 255)\" transform=\"translate(340.9,156.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_30a\"><title>gnuplot_plot_30a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(327.0,133.8) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(351.5,157.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(341.9,195.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(383.8,198.4) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(437.6,238.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(102, 51, 255)\" transform=\"translate(327.0,133.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_31a\"><title>gnuplot_plot_31a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(475.6,128.8) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(212.7,277.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(335.9,286.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(219.2,20.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(211.9,160.2) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(153, 51, 255)\" transform=\"translate(475.6,128.8) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_32a\"><title>gnuplot_plot_32a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(343.4,237.5) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(453.3,236.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(349.3,156.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(426.6,137.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(388.3,73.7) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(204, 51, 255)\" transform=\"translate(343.4,237.5) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_33a\"><title>gnuplot_plot_33a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(356.2,161.9) scale(3.00)\" xlink:href=\"#gpPt5\"/></g>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(314.6,144.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(344.8,147.1) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(333.4,182.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(366.1,196.0) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb(255, 51, 255)\" transform=\"translate(356.2,161.9) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_34a\"><title>gnuplot_plot_34a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n", | |
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| "source": [ | |
| "darts=dlmread('compiled_data.csv',',');\n", | |
| "x_darts=darts(:,1).*cosd(darts(:,2));\n", | |
| "y_darts=darts(:,1).*sind(darts(:,2));\n", | |
| "\n", | |
| "colormap(colorcube(length(darts(:,3))))\n", | |
| "\n", | |
| "scatter(x_darts, y_darts, [], darts(:,3))\n", | |
| "xlabel('x position (cm)')\n", | |
| "ylabel('y position (cm)')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 25, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "mu_x = 0.90447\r\n" | |
| ] | |
| } | |
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| "source": [ | |
| "mu_x=mean(x_darts)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 26, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "s_x = 4.2747\r\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "s_x=std(x_darts)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 27, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "mu_y = 0.88450\r\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "mu_y=mean(y_darts)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 28, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "s_y = 4.6834\r\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "s_y=std(y_darts)" | |
| ] | |
| }, | |
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| "cell_type": "code", | |
| "execution_count": 83, | |
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| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "\t<g id=\"gnuplot_plot_1a\"><title>gnuplot_plot_1a</title>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "\t<g id=\"gnuplot_plot_9a\"><title>gnuplot_plot_9a</title>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "\t<g id=\"gnuplot_plot_12a\"><title>gnuplot_plot_12a</title>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "\t<g id=\"gnuplot_plot_13a\"><title>gnuplot_plot_13a</title>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 128)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
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| "source": [ | |
| "x_vals=linspace(-15,20,30);\n", | |
| "hist(x_darts,x_vals,1);\n", | |
| "[histFreq, histXout] = hist(x_darts, 30);\n", | |
| "binWidth = histXout(2)-histXout(1);\n", | |
| "bar(histXout, histFreq/binWidth/sum(histFreq));\n", | |
| "pdfnorm = @(x) 1/sqrt(2*s_x^2*pi).*exp(-(x-mu_x).^2/2/s_x^2);\n", | |
| "%cdfnorm = @(x) 1/2*(1+erf((x-mu_x)./sqrt(2*s_x^2)));\n", | |
| "%hist(x_darts,x_vals,trapz(x,f))%,cdfnorm(max(x_darts))/2)\n", | |
| "hold on;\n", | |
| "plot(x_vals,pdfnorm(x_vals))\n", | |
| "n=2; % n=1, 68% confidence, n=2, 95% confidence, n=3, 99% conf\n", | |
| " plot([mu_x+n*s_x,mu_x+n*s_x],[0,0.1],'r-')\n", | |
| " plot([mu_x-n*s_x,mu_x-n*s_x],[0,0.1],'r-')\n", | |
| "\n", | |
| "xlabel('x position (cm)')\n", | |
| "ylabel('relative counts')" | |
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| { | |
| "cell_type": "code", | |
| "execution_count": 84, | |
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| "y_vals=linspace(-15,20,30);\n", | |
| "hist(y_darts,y_vals,1);\n", | |
| "[histFreq, histXout] = hist(y_darts, 30);\n", | |
| "binWidth = histXout(2)-histXout(1);\n", | |
| "bar(histXout, histFreq/binWidth/sum(histFreq));\n", | |
| "pdfnorm = @(x) 1/sqrt(2*s_y^2*pi).*exp(-(x-mu_y).^2/2/s_y^2);\n", | |
| "%cdfnorm = @(x) 1/2*(1+erf((x-mu_x)./sqrt(2*s_x^2)));\n", | |
| "%hist(x_darts,x_vals,trapz(x,f))%,cdfnorm(max(x_darts))/2)\n", | |
| "hold on;\n", | |
| "plot(y_vals,pdfnorm(y_vals))\n", | |
| "n=2; % n=1, 68% confidence, n=2, 95% confidence, n=3, 99% conf\n", | |
| " plot([mu_y+n*s_y,mu_y+n*s_y],[0,0.1],'r-')\n", | |
| " plot([mu_y-n*s_y,mu_y-n*s_y],[0,0.1],'r-')\n", | |
| "\n", | |
| "xlabel('x position (cm)')\n", | |
| "ylabel('relative counts')" | |
| ] | |
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| "x_exp=empirical_cdf(x_vals,x_darts);\n", | |
| "plot(x_vals,x_exp)\n", | |
| "hold on;\n", | |
| "plot(x_vals,normcdf(x_vals,mu_x,s_x),'k-')\n", | |
| "legend('experimental CDF','Normal CDF','Location','SouthEast')" | |
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| "\t<path d=\"M0,-1.33 L-1.33,0.67 L1.33,0.67 z\" id=\"gpPt7\" stroke=\"currentColor\" stroke-width=\"0.222\"/>\n", | |
| "\t<use fill=\"currentColor\" id=\"gpPt8\" stroke=\"none\" xlink:href=\"#gpPt7\"/>\n", | |
| "\t<use id=\"gpPt9\" stroke=\"currentColor\" transform=\"rotate(180)\" xlink:href=\"#gpPt7\"/>\n", | |
| "\t<use fill=\"currentColor\" id=\"gpPt10\" stroke=\"none\" xlink:href=\"#gpPt9\"/>\n", | |
| "\t<use id=\"gpPt11\" stroke=\"currentColor\" transform=\"rotate(45)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use fill=\"currentColor\" id=\"gpPt12\" stroke=\"none\" xlink:href=\"#gpPt11\"/>\n", | |
| "\t<path d=\"M0,1.330 L1.265,0.411 L0.782,-1.067 L-0.782,-1.076 L-1.265,0.411 z\" id=\"gpPt13\" stroke=\"currentColor\" stroke-width=\"0.222\"/>\n", | |
| "\t<use fill=\"currentColor\" id=\"gpPt14\" stroke=\"none\" xlink:href=\"#gpPt13\"/>\n", | |
| "\t<filter filterUnits=\"objectBoundingBox\" height=\"1\" id=\"textbox\" width=\"1\" x=\"0\" y=\"0\">\n", | |
| "\t <feFlood flood-color=\"white\" flood-opacity=\"1\" result=\"bgnd\"/>\n", | |
| "\t <feComposite in=\"SourceGraphic\" in2=\"bgnd\" operator=\"atop\"/>\n", | |
| "\t</filter>\n", | |
| "\t<filter filterUnits=\"objectBoundingBox\" height=\"1\" id=\"greybox\" width=\"1\" x=\"0\" y=\"0\">\n", | |
| "\t <feFlood flood-color=\"lightgrey\" flood-opacity=\"1\" result=\"grey\"/>\n", | |
| "\t <feComposite in=\"SourceGraphic\" in2=\"grey\" operator=\"atop\"/>\n", | |
| "\t</filter>\n", | |
| "</defs>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"rgb(255, 255, 255)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,282.1 L280.0,201.0 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,282.1 L280.0,201.0 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,282.1 L74.5,119.9 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M280.0,201.0 L280.0,38.8 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,282.1 L485.5,119.9 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,119.9 L280.0,38.8 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,119.9 L280.0,38.8 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M485.5,282.1 L280.0,201.0 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,282.1 L498.5,287.2 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M280.0,201.0 L267.0,195.9 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(507.1,300.6)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-20</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M459.8,292.2 L254.4,211.1 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M459.8,292.2 L472.8,297.4 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M254.4,211.1 L241.3,205.9 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(481.4,310.7)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-15</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M434.1,302.3 L228.7,221.2 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M434.1,302.3 L447.2,307.5 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M228.7,221.2 L215.6,216.1 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(455.7,320.8)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-10</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M408.4,312.5 L203.0,231.4 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M408.4,312.5 L421.5,317.6 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M203.0,231.4 L189.9,226.2 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(430.0,331.0)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-5</tspan></text>\n", | |
| "\t</g>\n", | |
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| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M382.7,322.6 L177.3,241.5 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M382.7,322.6 L395.8,327.8 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M177.3,241.5 L164.2,236.4 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(404.3,341.1)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M357.0,332.8 L151.6,251.6 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M357.0,332.8 L370.1,337.9 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M151.6,251.6 L138.5,246.5 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(378.7,351.3)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">5</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M331.3,342.9 L125.9,261.8 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M331.3,342.9 L344.4,348.1 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M125.9,261.8 L112.8,256.6 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(353.0,361.4)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">10</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M305.6,353.0 L100.2,271.9 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M305.6,353.0 L318.7,358.2 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M100.2,271.9 L87.2,266.8 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(327.3,371.5)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">15</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,363.2 L74.5,282.1 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M280.0,363.2 L293.0,368.3 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,282.1 L61.5,276.9 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"start\" transform=\"translate(301.6,381.7)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">20</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M74.5,282.1 L280.0,201.0 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,282.1 L65.6,285.6 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M280.0,201.0 L288.9,197.5 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(59.7,296.6)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-20</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M100.2,292.2 L305.6,211.1 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M100.2,292.2 L91.3,295.7 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M305.6,211.1 L314.6,207.6 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(85.4,306.7)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-15</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M125.9,302.3 L331.3,221.2 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M125.9,302.3 L117.0,305.9 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M331.3,221.2 L340.2,217.7 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(111.1,316.9)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-10</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M151.6,312.5 L357.0,231.4 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M151.6,312.5 L142.7,316.0 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M357.0,231.4 L365.9,227.9 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(136.8,327.0)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">-5</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M177.3,322.6 L382.7,241.5 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M177.3,322.6 L168.4,326.1 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M382.7,241.5 L391.6,238.0 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(162.5,337.2)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M203.0,332.8 L408.4,251.6 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M203.0,332.8 L194.1,336.3 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M408.4,251.6 L417.3,248.1 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(188.2,347.3)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">5</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M228.7,342.9 L434.1,261.8 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M228.7,342.9 L219.8,346.4 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M434.1,261.8 L443.0,258.3 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(213.9,357.4)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">10</tspan></text>\n", | |
| "\t</g>\n", | |
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| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "\t\t<text><tspan font-family=\"{}\">15</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
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| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,363.2 L485.5,282.1 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M280.0,363.2 L271.1,366.7 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "\t\t<text><tspan font-family=\"{}\">20</tspan></text>\n", | |
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| "</g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,201.0 L485.5,282.1 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,282.1 L62.0,282.1 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,288.1)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0</tspan></text>\n", | |
| "\t</g>\n", | |
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| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,282.1 L498.0,282.1 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,168.6 L485.5,249.6 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,249.6 L62.0,249.6 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,255.6)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0.2</tspan></text>\n", | |
| "\t</g>\n", | |
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| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,136.2 L485.5,217.2 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,217.2 L62.0,217.2 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,223.2)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0.4</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
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| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,103.7 L485.5,184.8 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,184.8 L62.0,184.8 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,190.8)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0.6</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
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| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
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| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,71.3 L485.5,152.4 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,152.4 L62.0,152.4 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,158.4)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">0.8</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
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| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,152.4 L498.0,152.4 \" stroke=\"black\"/></g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M74.5,119.9 L280.0,38.8 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"gray\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path class=\"gridline\" d=\"M280.0,38.8 L485.5,119.9 \" stroke=\"gray\" stroke-dasharray=\"2,4\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M74.5,119.9 L62.0,119.9 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(43.9,125.9)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">1</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M485.5,119.9 L498.0,119.9 \" stroke=\"black\"/></g>\n", | |
| "\t<g id=\"gnuplot_plot_1a\"><title>gnuplot_plot_1a</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(296.5,141.3) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
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| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(244.8,114.6) scale(3.00)\" xlink:href=\"#gpPt5\"/>\n", | |
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| "% plot the distribution in x- and y-directions\n", | |
| "gauss2d = @(x,y) exp(-((x-mu_x).^2/2/s_x^2+(y-mu_y).^2/2/s_y^2));\n", | |
| "\n", | |
| "x=linspace(-20,20,31);\n", | |
| "y=linspace(-20,20,31);\n", | |
| "scatter3(x_darts, y_darts,ones(length(x_darts),1))\n", | |
| "xlabel('x position (cm)')\n", | |
| "ylabel('y position (cm)')\n", | |
| "hold on\n", | |
| "[X,Y]=meshgrid(x,y);\n", | |
| "view([1,1,1])\n", | |
| "\n", | |
| "surf(X,Y,gauss2d(X,Y))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Monte Carlo Simulations\n", | |
| "\n", | |
| "Monte Carlo models use random numbers to either understand statistics or generate a solution. \n", | |
| "\n", | |
| "### Example 1:\n", | |
| "#### Calculate $\\pi$ with random numbers. \n", | |
| "\n", | |
| "Assuming we can actually generate random numbers (a topic of philosophical and heated debates) we can populate a unit square with random points and determine the ratio of points inside and outside of a circle.\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The ratio of the area of the circle to the square is:\n", | |
| "\n", | |
| "$\\frac{\\pi r^{2}}{4r^{2}}=\\frac{\\pi}{4}$\n", | |
| "\n", | |
| "So if we know the fraction of random points that are within the unit circle, then we can calculate $\\pi$\n", | |
| "\n", | |
| "(number of points in circle)/(total number of points)=$\\pi/4$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 96, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "function our_pi=montecarlopi(N)\n", | |
| " % Create random x-y-coordinates\n", | |
| "\n", | |
| " x=rand(N,1);\n", | |
| " y=rand(N,1);\n", | |
| " R=sqrt(x.^2+y.^2); % compute radius\n", | |
| " num_in_circle=sum(R<1);\n", | |
| " total_num_pts =length(R);\n", | |
| " our_pi = 4*num_in_circle/total_num_pts;\n", | |
| "end\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 98, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
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| "text": [ | |
| "mean value for pi = 3.132400\n", | |
| "standard deviation is 0.054925\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "test_pi=zeros(10,1);\n", | |
| "for i=1:10\n", | |
| " test_pi(i)=montecarlopi(1000);\n", | |
| "end\n", | |
| "fprintf('mean value for pi = %f\\n',mean(test_pi))\n", | |
| "fprintf('standard deviation is %f',std(test_pi))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
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| "source": [ | |
| "### Example 2\n", | |
| "#### Determine uncertainty in failure stress based on geometry\n", | |
| "\n", | |
| "In this example, we know that a steel bar will break under 940 MPa tensile stress. The bar is 1 mm by 2 mm with a tolerance of 1 %. What is the range of tensile loads that can be safely applied to the beam?\n", | |
| "\n", | |
| "$\\sigma_{UTS}=\\frac{F_{fail}}{wh}$\n", | |
| "\n", | |
| "$F_{fail}=\\sigma_{UTS}wh$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 112, | |
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| "N=1000;\n", | |
| "r=rand(N,1);\n", | |
| "wmean=1; % in mm\n", | |
| "wmin=wmean-wmean*0.01;\n", | |
| "wmax=wmean+wmean*0.01;\n", | |
| "hmean=2; % in mm\n", | |
| "hmin=hmean-hmean*0.01;\n", | |
| "hmax=hmean+hmean*0.01;\n", | |
| "\n", | |
| "wrand=wmin+(wmax-wmin)*r;\n", | |
| "hrand=hmin+(hmax-hmin)*r;\n", | |
| "\n", | |
| "uts=940; % in N/mm^2=MPa\n", | |
| "\n", | |
| "Ffail=uts.*wrand.*hrand*1e-3; % force in kN\n", | |
| "hist(Ffail,20,1)\n", | |
| "xlabel('failure load (kN)')\n", | |
| "ylabel('relative counts')" | |
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| "Normally, the tolerance is not a maximum/minimum specification, but instead a normal distribution that describes the standard deviation, or the 68 % confidence interval.\n", | |
| "\n", | |
| "So instead, we should generate normally distributed dimensions." | |
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| "N=1000;\n", | |
| "wmean=1; % in mm\n", | |
| "wstd=wmean*0.01; % standard deviation in mm\n", | |
| "hmean=2; % in mm\n", | |
| "hstd=hmean*0.01; % standard deviation in mm\n", | |
| "\n", | |
| "\n", | |
| "wrand=normrnd(wmean,wstd,[N,1]);\n", | |
| "hrand=normrnd(hmean,hstd,[N,1]);\n", | |
| "uts=940; % in N/mm^2=MPa\n", | |
| "\n", | |
| "Ffail=uts.*wrand.*hrand*1e-3; % force in kN\n", | |
| "hist(Ffail,20,1)\n", | |
| "xlabel('failure load (kN)')\n", | |
| "ylabel('relative counts')" | |
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| "## Linear Least Squares Regression\n", | |
| "\n", | |
| "When approximating a set of data as a polynomial, there will always be error introduced (except in 2 cases). \n", | |
| "\n", | |
| "For a straight line, the actual data points, $y_{i}$ as a function of the independent variable, $x_{i}$, is:\n", | |
| "\n", | |
| "$y_{i}=a_{0}+a_{1}x_{i}+e_{i}$\n", | |
| "\n", | |
| "where $a_{0}$ and $a_{1}$ are the intercept and slope of the line and $e_{i}$ is the error between the approximate function and the recorded data point. \n", | |
| "\n", | |
| "We make the following assumptions in this analysis:\n", | |
| "\n", | |
| "1. Each x has a fixed value; it is not random and is known without error.\n", | |
| "\n", | |
| "2. The y values are independent random variables and all have the same variance.\n", | |
| "\n", | |
| "3. The y values for a given x must be normally distributed.\n", | |
| "\n", | |
| "The total error is \n", | |
| "\n", | |
| "$\\sum_{i=1}^{n}e_{i}=\\sum_{i=1}^{n}(y_{i}-a_{0}-a_{1}x_{i})$\n", | |
| "\n", | |
| "we don't care about the sign though. One approach has been demonstrated to provide a unique solution is minimizing the sum of squares error or\n", | |
| "\n", | |
| "$S_{r}=\\sum_{i=1}^{n}e_{i}^{2}=\\sum_{i=1}^{n}(y_{i}-a_{0}-a_{1}x_{i})^{2}$\n", | |
| "\n", | |
| "Where, $S_{r}$ is the sum of squares error (SSE). \n", | |
| "\n", | |
| "$\\frac{\\partial S_{r}}{\\partial a_{0}}=-2\\sum(y_{i}-a_{0}-a_{1}x_{i})$\n", | |
| "\n", | |
| "$\\frac{\\partial S_{r}}{\\partial a_{1}}=-2\\sum(y_{i}-a_{0}-a_{1}x_{i})x_{i}$\n", | |
| "\n", | |
| "The minimum $S_{r}$ occurrs when the partial derivatives are 0. \n", | |
| "\n", | |
| "$\\sum y_{i}= \\sum a_{0}+\\sum a_{1}x_{i}$\n", | |
| "\n", | |
| "$\\sum x_{i}y_{i}= \\sum a_{0}x_{i}+\\sum a_{1}x_{i}^{2}$\n", | |
| "\n", | |
| "$\\left[\\begin{array}{c}\n", | |
| "\\sum y_{i}\\\\\n", | |
| "\\sum x_{i}y_{i}\\end{array}\\right]=\n", | |
| "\\left[\\begin{array}{cc}\n", | |
| "n & \\sum x_{i}\\\\\n", | |
| "\\sum x_{i} & \\sum x_{i}^{2}\\end{array}\\right]\n", | |
| "\\left[\\begin{array}{c}\n", | |
| "a_{0}\\\\\n", | |
| "a_{1}\\end{array}\\right]$\n", | |
| "\n", | |
| "\n", | |
| "$b=Ax$\n", | |
| "\n" | |
| ] | |
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| "### Example \n", | |
| "\n", | |
| "Find drag coefficient with best-fit line to experimental data\n", | |
| "\n", | |
| "|i | v (m/s) | F (N) |\n", | |
| "|---|---|---|\n", | |
| "|1 | 10 | 25 |\n", | |
| "|2 | 20 | 70 |\n", | |
| "|3 | 30 | 380|\n", | |
| "|4 | 40 | 550|\n", | |
| "|5 | 50 | 610|\n", | |
| "|6 | 60 | 1220|\n", | |
| "|7 | 70 | 830 |\n", | |
| "|8 |80 | 1450|" | |
| ] | |
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| "a =\n", | |
| "\n", | |
| " -234.286\n", | |
| " 19.470\n", | |
| "\n" | |
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| "How do we know its a \"good\" fit? \n", | |
| "\n", | |
| "Can compare the sum of squares error to the total sum of squares of the dependent variable (here F). \n", | |
| "\n", | |
| "$S_{r}=\\sum(y_{i}-a_{0}-a_{1}x_{i})^{2}$\n", | |
| "\n", | |
| "$S_{t}=\\sum(y_{i}-\\bar{y})^{2}$\n", | |
| "\n", | |
| "Then, we can calculate the *coefficient of determination*, $r^{2}$ or *correlation coefficient*, r. \n", | |
| "\n", | |
| "$r^{2}=\\frac{S_{t}-S_{r}}{S_{t}}$\n", | |
| "\n", | |
| "This represents the relative improvement of assuming that y is a function of x (if the x-values are not random and the y-values are random)\n", | |
| "\n", | |
| "For further information regarding statistical work on regression, look at \n", | |
| "[NIST Statistics Handbook](http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd44.htm)" | |
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| "St = 1.8083e+06\n", | |
| "St = 1.8083e+06\n" | |
| ] | |
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| "Sr=sum((y-a(1)-a(2)*x).^2);\n", | |
| "St=std(y)^2*(length(y)-1)\n", | |
| "St=sum((y-mean(y)).^2)" | |
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| "r2 = 0.88049\n", | |
| "r = 0.93834\n" | |
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| "r2=(St-Sr)/St\n", | |
| "r=sqrt(r2)" | |
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| "### Limiting cases \n", | |
| "\n", | |
| "#### $r^{2}=0$ $S_{r}=S{t}$\n", | |
| "\n", | |
| "#### $r^{2}=1$ $S_{r}=0$" | |
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| "\t<path d=\"M535.0,384.0 L535.0,371.5 M535.0,16.7 L535.0,29.2 \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(535.0,408.0)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">1</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "\t<path d=\"M45.6,16.7 L45.6,384.0 L535.0,384.0 L535.0,16.7 L45.6,16.7 Z \" stroke=\"black\"/></g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n", | |
| "\t<path d=\"M53.9,121.7 L53.9,25.7 L197.3,25.7 L197.3,121.7 L53.9,121.7 Z \" stroke=\"black\"/></g>\n", | |
| "\t<g id=\"gnuplot_plot_1a\"><title>Case 1</title>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n", | |
| "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(197.3,55.7)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">Case 1</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(45.6,370.7) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(70.1,368.4) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(94.6,375.3) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(119.1,377.5) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(143.6,365.5) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(168.1,367.3) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(192.6,383.9) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(217.1,357.1) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(241.6,354.6) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(266.1,358.4) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(290.5,351.9) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(315.0,355.1) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(339.5,378.4) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(364.0,372.1) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(388.5,381.4) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(413.0,378.2) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(437.5,358.9) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(462.0,372.1) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(486.5,378.7) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(511.0,369.9) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(92.0,49.7) scale(12.00)\" xlink:href=\"#gpPt3\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "\t<g id=\"gnuplot_plot_2a\"><title>Case 2</title>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n", | |
| "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(197.3,103.7)\">\n", | |
| "\t\t<text><tspan font-family=\"{}\">Case 2</tspan></text>\n", | |
| "\t</g>\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(45.6,384.0) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(100.0,343.2) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(154.4,302.4) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(208.7,261.6) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(263.1,220.8) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(317.5,179.9) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(371.9,139.1) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(426.2,98.3) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(480.6,57.5) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(535.0,16.7) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "\t<use color=\"rgb( 0, 128, 0)\" transform=\"translate(92.0,97.7) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n", | |
| "</g>\n", | |
| "\t</g>\n", | |
| "<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 128, 0)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n", | |
| "</g>\n", | |
| "</g>\n", | |
| "</svg>" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.SVG object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "gen_examples\n", | |
| "plot(x1(1:50:end),y1(1:50:end),'s',x2,y2,'o')\n", | |
| "legend('Case 1','Case 2','Location','NorthWest')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 157, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "a1 =\n", | |
| "\n", | |
| " 0.0497269\n", | |
| " 0.0016818\n", | |
| "\n", | |
| "a2 =\n", | |
| "\n", | |
| " 0\n", | |
| " 1\n", | |
| "\n", | |
| "Sr1 = 0.82607\n", | |
| "St1 = 0.82631\n", | |
| "coefficient of determination in Case 1 is 0.000286\n", | |
| "Sr2 = 0\n", | |
| "St2 = 1.0185\n", | |
| "coefficient of determination in Case 2 is 1.000000\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "b1=[sum(y1);sum(x1.*y1)];\n", | |
| "A1=[length(x1),sum(x1);\n", | |
| " sum(x1), sum(x1.^2)];\n", | |
| " \n", | |
| "a1=A1\\b1\n", | |
| "\n", | |
| "b2=[sum(y2);sum(x2.*y2)];\n", | |
| "A2=[length(x2),sum(x2);\n", | |
| " sum(x2), sum(x2.^2)];\n", | |
| " \n", | |
| "a2=A2\\b2\n", | |
| "\n", | |
| "Sr1=sum((y1-a1(1)-a1(2)*x1).^2)\n", | |
| "St1=sum((y1-mean(y1)).^2)\n", | |
| "fprintf('coefficient of determination in Case 1 is %f\\n',1-Sr1/St1)\n", | |
| "\n", | |
| "Sr2=sum((y2-a2(1)-a2(2)*x2).^2)\n", | |
| "St2=sum((y2-mean(y2)).^2)\n", | |
| "\n", | |
| "fprintf('coefficient of determination in Case 2 is %f\\n',1-Sr2/St2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Octave", | |
| "language": "octave", | |
| "name": "octave" | |
| }, | |
| "language_info": { | |
| "file_extension": ".m", | |
| "help_links": [ | |
| { | |
| "text": "MetaKernel Magics", | |
| "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" | |
| } | |
| ], | |
| "mimetype": "text/x-octave", | |
| "name": "octave", | |
| "version": "0.19.14" | |
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| } |