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@randombrein
Created October 23, 2016 21:40
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sinusoidal_monotonic_curve notebook
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{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# -*- coding: utf-8 -*-\n",
"\n",
"\"\"\"\n",
"Monotonic increasing sinusoidal curve with same entrance/exit angle\n",
"\"\"\"\n",
"import numpy as np\n",
"import pylab"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def discrt_tan(x0, y0, x1, y1):\n",
" \"\"\" discrete tangent function for tuple of points \"\"\"\n",
" return np.divide(np.subtract(y1,y0), np.subtract(x1,x0))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def curve(xs, size, mid_angle=0.0):\n",
" \"\"\" monotonic raising curve function with sinusoidal accent.\n",
" \n",
" Function for a monotonic raising curve with same entrance/exit angle.\n",
" Sinusoidal setup for *monotonic increasing* constraints angles in following fashion;\n",
" - mid_angle must be between [0..pi/4) - approaching pi/4 yields straight line.\n",
" - generated entrance/exit angles are between [45..~63.43] degrees\n",
" \n",
" The curve is expresses as;\n",
" y = x + [sin(2PI * x / size)] / accent \n",
"\n",
" Args:\n",
" xs (array like): input value(s)\n",
" size: size range of the input/output values\n",
" mid_angle: middle angle of the sinusoidal in radians\n",
" \n",
" Returns:\n",
" array-like curve value.\n",
"\n",
" Raises:\n",
" `ValueError` for params. that out of range;\n",
" mid_angle - must be between [0..pi/4)\n",
" xs - must be in range between [0..size]\n",
"\n",
" Todo: \n",
" - `accent` does not well-define middle angle parameter.\n",
" - if curve will not be limited in size range, derivation will be step-wise continuous.\n",
" More calculation can be made for continuous derivation. (tangents at 0 and size)\n",
" \n",
" \"\"\"\n",
" if mid_angle<0 or mid_angle>=np.pi/4:\n",
" raise ValueError(\"mid-angle must be between [0..pi/4)\")\n",
"\n",
" if np.any(xs < 0) or np.any(xs > size):\n",
" raise ValueError(\"xs must be between [0..size]\")\n",
"\n",
" accent = 2*np.pi/size * np.tan(np.pi/4+mid_angle) # TODO: not well-defined mid-angle param.\n",
" return xs + np.sin(2*np.pi*xs/size) / accent"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"### testing values...\n",
"x= 1.000000000000000, y=1.000000000000000\n",
"x= 0.999999999990000, y=0.999999999980000\n",
"x= 0.500000000000000, y=0.500000000000000\n"
]
}
],
"source": [
"\"\"\" \n",
"Test and plot `curve` function for various values and mid_angle degrees\n",
"\"\"\"\n",
"eps = 1e-11\n",
"#eps = np.finfo(float).eps\n",
"size = 1\n",
"\n",
"print \"### testing values...\"\n",
"print \"x= {:.15f}, y={:.15f}\".format(size, curve(size, size))\n",
"print \"x= {:.15f}, y={:.15f}\".format(np.subtract(size,eps), curve(np.subtract(size,eps), size))\n",
"print \"x= {:.15f}, y={:.15f}\".format(size/2.0, curve(size/2.0, size))\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# angles at 0, mid, size\n",
"mids = [0, np.pi/128, np.pi/64, np.pi/32, np.pi/16, np.pi/8, np.pi/6, np.pi/4-eps]\n",
"max_err = 0.0\n",
"\n",
"params = {'legend.fontsize': 'small',\n",
" 'axes.labelsize': 'small',\n",
" 'axes.titlesize':'small',\n",
" 'xtick.labelsize':'small',\n",
" 'ytick.labelsize':'small'}\n",
"pylab.rcParams.update(params)\n",
"colc = 2\n",
"rowc = (len(mids)+1)/colc\n",
"f, axarr = pylab.subplots(rowc, colc)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"### testing angles...\n",
"mid (input) = 0.000000000000000\n",
"angle at mid = 0.000000000000000\n",
"angle at 0 = 63.434948822922017\n",
"angle at size = 63.434948822922017\n",
"error = 0.000000000000000\n",
"\n",
"mid (input) = 1.406250000000000\n",
"angle at mid = 2.743356220947988\n",
"angle at 0 = 62.875102443868506\n",
"angle at size = 62.875145696260006\n",
"error = 0.000043252391499\n",
"\n",
"mid (input) = 2.812500000000000\n",
"angle at mid = 5.350622806191602\n",
"angle at 0 = 62.320139856975096\n",
"angle at size = 62.320070920928096\n",
"error = 0.000068936047001\n",
"\n",
"mid (input) = 5.625000000000000\n",
"angle at mid = 10.166408930807496\n",
"angle at 0 = 61.222397716083037\n",
"angle at size = 61.222371172931183\n",
"error = 0.000026543151854\n",
"\n",
"mid (input) = 11.250000000000000\n",
"angle at mid = 18.357053614464810\n",
"angle at 0 = 59.059159537795054\n",
"angle at size = 59.059128214218411\n",
"error = 0.000031323576643\n",
"\n",
"mid (input) = 22.500000000000000\n",
"angle at mid = 30.361214238417741\n",
"angle at 0 = 54.735610317245346\n",
"angle at size = 54.735600989722563\n",
"error = 0.000009327522783\n",
"\n",
"mid (input) = 29.999999999999996\n",
"angle at mid = 36.205907006902549\n",
"angle at 0 = 51.738033800290154\n",
"angle at size = 51.738102185061891\n",
"error = 0.000068384771737\n",
"\n",
"mid (input) = 44.999999999427040\n",
"angle at mid = 45.000000000000000\n",
"angle at 0 = 45.000000000286477\n",
"angle at size = 45.000000000000000\n",
"error = 0.000000000286477\n",
"\n"
]
}
],
"source": [
"print \"\\n### testing angles...\"\n",
"\n",
"for i,mid in enumerate(mids):\n",
" print \"mid (input) = {:.15f}\".format(np.rad2deg(mid))\n",
" t = discrt_tan(size/2.0, curve(size/2.0, size, mid),\n",
" np.add(size/2.0,eps), curve(np.add(size/2.0,eps), size, mid))\n",
" print \"angle at mid = {:.15f}\".format(np.rad2deg(np.arctan(t)))\n",
"\n",
" t = discrt_tan(0, curve(0, size, mid),\n",
" eps, curve(eps, size, mid))\n",
" print \"angle at 0 = {:.15f}\".format(np.rad2deg(np.arctan(t)))\n",
"\n",
" t1 = discrt_tan(size, curve(size, size, mid),\n",
" np.subtract(size,eps), curve(np.subtract(size,eps), size, mid))\n",
" print \"angle at size = {:.15f}\".format(np.rad2deg(np.arctan(t1)))\n",
"\n",
" # error\n",
" err = np.abs(np.subtract(np.rad2deg(np.arctan(t1)), np.rad2deg(np.arctan(t))))\n",
" max_err = np.maximum(max_err, err)\n",
" print \"error = {:.15f}\\n\".format(err)\n",
"\n",
" # plot\n",
" xs = np.linspace(0, size, 100)\n",
" ys = curve(xs, size, mid)\n",
" row = i/colc\n",
" col = i - row*colc\n",
"\n",
" axarr[row, col].plot(xs, ys)\n",
" axarr[row, col].set_title('mid_angle={:.4f} rad.'.format(mid))\n",
" axarr[row, col].text(0.95, 0.15, 'alpha={:.6f} deg.'.format(np.rad2deg(np.arctan(t))),\n",
" verticalalignment='bottom', horizontalalignment='right',\n",
" transform=axarr[row, col].transAxes,\n",
" color='green', fontsize=10)\n",
" axarr[row, col].text(0.95, 0.03, 'err={:.6f} deg.'.format(err),\n",
" verticalalignment='bottom', horizontalalignment='right',\n",
" transform=axarr[row, col].transAxes,\n",
" color='red', fontsize=10)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Max. Error = 0.000068936047001\n"
]
},
{
"data": {
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2LFPpJ0m+D1XVD+d/qNd+ca3O2DhDI/pHaMyJmIRzl392ufaa1itJ+Wd/fVav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\nJLj11uwPRhYOcqk943DkDGJjbQ3y4MEWk+DWW22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XBuI52FMq/1BZVh5bKaa/kXmH5t3z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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ee0ff90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"print\"Max. Error = {:.15f}\".format(max_err)\n",
"pylab.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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