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src/wafo/doc/tutorial_scripts/WAFO Chapter 2.ipynb

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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CHAPTER2 Modelling random loads and stochastic waves\n",
    "====================================================\n",
    "\n",
    "Chapter2 contains the commands used in Chapter 2 of the tutorial and present some tools for analysis of random functions with respect to their correlation, spectral and distributional properties. The presentation is divided into three examples: \n",
    "\n",
    "Example1 is devoted to estimation of different parameters in the model.\n",
    "Example2 deals with spectral densities and\n",
    "Example3 presents the use of WAFO to simulate samples of a Gaussian process.\n",
    "\n",
    "Some of the commands are edited for fast computation. \n",
    "\n",
    "Section 2.1 Introduction and preliminary analysis\n",
    "=================================================\n",
    "\n",
    "Example 1: Sea data\n",
    "-------------------\n",
    "Observed crossings compared to the expected for Gaussian signals\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import wafo\n",
    "import wafo.objects as wo\n",
    "xx = wafo.data.sea()\n",
    "me = xx[:, 1].mean()\n",
    "sa = xx[:, 1].std()\n",
    "xx[:, 1] -= me\n",
    "ts = wo.mat2timeseries(xx)\n",
    "tp = ts.turning_points()\n",
    "\n",
    "cc = tp.cycle_pairs()\n",
    "lc = cc.level_crossings()\n",
    "_=lc.plot()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average number of upcrossings per time unit\n",
    "----------------------------------------------\n",
    "Next we compute the mean frequency as the average number of upcrossings per time unit of the mean level (= 0); this may require interpolation in the crossing intensity curve, as follows.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f0 = 0.224071\n"
     ]
    }
   ],
   "source": [
    "T = xx[:, 0].max() - xx[:, 0].min()\n",
    "f0 = np.interp(0, lc.args, lc.data, 0) / T  #! zero up-crossing frequency \n",
    "print('f0 = %g' % f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turningpoints and irregularity factor\n",
    "----------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fm = 0.456159, alpha = 0.491212, \n"
     ]
    }
   ],
   "source": [
    "fm = len(tp.data) / (2 * T)   # frequency of maxima\n",
    "alfa = f0 / fm                # approx Tm24/Tm02\n",
    "\n",
    "print('fm = %g, alpha = %g, ' % (fm, alfa))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually examine data\n",
    "------------------------\n",
    "We finish this section with some remarks about the quality of the measured data. Especially sea surface measurements can be of poor quality. We shall now check the  quality of the dataset {\\tt xx}. It is always good practice to visually examine the data before the analysis to get an impression of the quality, \n",
    "non-linearities and narrow-bandedness of the data.First we shall plot the data and zoom in on a specific region. A part of sea data is visualized with the following commands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, -2, 2]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot_wave('k-', tp, '*', nfig=1, nsub=1)\n",
    "\n",
    "plt.axis([0, 2, -2, 2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finding possible spurious points\n",
    "------------------------------------\n",
    "However, if the amount of data is too large for visual examinations one could use the following criteria to find possible spurious points. One must be careful using the criteria for extremevalue analysis, because\n",
    "it might remove extreme waves that are OK and not spurious."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found 0 missing points\n",
      "Found 0 spurious positive jumps of Dx\n",
      "Found 0 spurious negative jumps of Dx\n",
      "Found 37 spurious positive jumps of D^2x\n",
      "Found 200 spurious negative jumps of D^2x\n",
      "Found 244 consecutive equal values\n",
      "Found the total of 1149 spurious points\n"
     ]
    }
   ],
   "source": [
    "import wafo.misc as wm\n",
    "dt = ts.sampling_period()\n",
    "# dt = np.diff(xx[:2,0])\n",
    "dcrit = 5 * dt\n",
    "ddcrit = 9.81 / 2 * dt * dt\n",
    "zcrit = 0\n",
    "inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 2.2 Frequency Modeling of Load Histories\n",
    "---------------------------------------------------\n",
    "Periodogram: Raw spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lmax = 9500\n",
    "S = ts.tospecdata(L=Lmax)\n",
    "S.plot()\n",
    "_=plt.axis([0, 5, 0, 0.7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate moments  \n",
    "-------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigma = 0.472955, m0 = 0.472955\n"
     ]
    }
   ],
   "source": [
    "mom, text = S.moment(nr=4)\n",
    "print('sigma = %g, m0 = %g' % (sa, np.sqrt(mom[0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 2.2.1 Random functions in Spectral Domain - Gaussian processes\n",
    "--------------------------------------------------------------------------\n",
    "Smoothing of spectral estimate \n",
    "----------------------------------\n",
    "By decreasing Lmax the spectrum estimate becomes smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lmax0 = 200; Lmax1 = 50\n",
    "S1 = ts.tospecdata(L=Lmax0)\n",
    "S2 = ts.tospecdata(L=Lmax1)\n",
    "S1.plot('-.')\n",
    "_=S2.plot()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Estimated autocovariance\n",
    "----------------------------\n",
    "Obviously knowing the spectrum one can compute the covariance\n",
    "function. The following code will compute the covariance for the \n",
    "unimodal spectral density S1 and compare it with estimated \n",
    "covariance of the signal xx."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lmax = 85\n",
    "R1 = S1.tocovdata(nr=1)   \n",
    "Rest = ts.tocovdata(lag=Lmax)\n",
    "R1.plot('.')\n",
    "Rest.plot()\n",
    "_=plt.axis([0, 25, -0.1, 0.25])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in Figure below that the covariance function corresponding to the spectral density S2 significantly differs from the one estimated directly from data. It can be seen in Figure above that the covariance corresponding to S1 agrees much better with the estimated covariance function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(([<matplotlib.lines.Line2D at 0x2585dab92c8>],\n",
       "  [Text(0.5, 1.0, 'Auto Covariance Function '),\n",
       "   Text(0.5, 0, 'Lag [s]'),\n",
       "   Text(0, 0.5, 'ACF')]),\n",
       " [(([<matplotlib.lines.Line2D at 0x2585dc61588>], []), None),\n",
       "  (([<matplotlib.lines.Line2D at 0x2585dc76b48>], []), None)])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2 = S2.tocovdata(nr=1)\n",
    "R2.plot('.')\n",
    "Rest.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 2.2.2 Transformed Gaussian models\n",
    "-------------------------------------------\n",
    "We begin with computing skewness and kurtosis for the data set xx and compare it with the second order wave approximation proposed by Winterstein:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import wafo.stats as ws\n",
    "rho3 = ws.skew(xx[:, 1])\n",
    "rho4 = ws.kurtosis(xx[:, 1])\n",
    "\n",
    "sk, ku = S1.stats_nl(moments='sk')"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Comparisons of 3 transformations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import wafo.transform.models as wtm\n",
    "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata()\n",
    "g = wtm.TrLinear(mean=me, sigma=sa).trdata() # Linear transformation \n",
    "glc, gemp = lc.trdata(mean=me, sigma=sa)\n",
    "\n",
    "glc.plot('b-') #! Transf. estimated from level-crossings\n",
    "gh.plot('b-.') #! Hermite Transf. estimated from moments\n",
    "g.plot('r')\n",
    "plt.grid('on')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test Gaussianity of a stochastic process\n",
    "------------------------------------------\n",
    "TESTGAUSSIAN simulates  e(g(u)-u) = int (g(u)-u)^2 du  for Gaussian processes given the spectral density, S. The result is plotted if test0 is given. This is useful for testing if the process X(t) is Gaussian.\n",
    "If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.\n",
    "\n",
    "As we see from the figure below: none of the simulated values of test1 is above 1.00. Thus the data significantly departs from a Gaussian distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test0 = glc.dist2gauss()\n",
    "# the following test takes time\n",
    "N = len(xx)\n",
    "test1 = S1.testgaussian(ns=N, cases=50, test0=test0)\n",
    "is_gaussian = sum(test1 > test0) > 5 \n",
    "print(is_gaussian)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalplot of data xx\n",
    "------------------------\n",
    "indicates that the underlying distribution has a \"heavy\" upper tail and a \"light\" lower tail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_=ws.probplot(ts.data.ravel(), dist='norm', plot=plt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 2.2.3 Spectral densities of sea data\n",
    "-----------------------------------------------\n",
    "Example 2: Different forms of spectra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4zAxXGZnZWJwQKkjXOHcZedQ0MxuLE0IFGe8uo4baaupqqtyGYGYjckKoEAODQ/QODNE4RkIAaHH3FWY2ipwalSXNzWG1oYjYvp/x2AR19ac9nY5RZQRpj6duQzCzEeR6l9HTwFPAyJ3kJKqB5fsdkU1IZrS08UoI7uDOzEaTa0K4LyKePdYKku4oQDw2QXsGxxmnhOAusM1sFLm2IXxM0pJx1jl5f4Oxict0WDda19cZzQ01rjIysxHlWkJ4LfBpSQuBB4C1wJ3p+/0RMRgRPZMUo+Wgs3fs4TMzMl1gm5kNl1MJISLeERGrgP8LPAQ8BrwEuAV4YvLCs1xlSghj9WUErjIys9Hl23XF30XEcZkPkr4OfKiwIdlEdPblVkJorq+hp3+IvoEh6mp817GZ7ZHvFWGnpOdmPkTEbcChhQ3JJmLPXUbjlxAAdrmUYGbD5FtCeBvwfUn3AbcBxwC+spSA3SWEHG47haSDu3lNo3eEZ2bTT14lhIh4GHg+8AtgIXA/cOYkxGV52t2GkMODaeAusM1sX3mVECTNA14P9AA/Be6OiO7JCMzys6tngLrqKuprxr/tNLO+mVm2fNsQfgy0Ap8D/hPYIemBgkdleevo7R/3oTTIGlfZzyKY2TD5tiE0R8SnJb02Ik6V9FfAyskIzPLT0TNAU8P4p3N3QnCVkZkNk28JIfPwWa+kGRFxFW5DKAkdvYM01deOu56rjMxsNPmWEL6Y9nx6BfBtSX8GDih8WJavjt5+msd5BgGgqa4GyVVGZravnEsIkqqAwyKiPSK+RHKn0TLg7MkKznLX0ZtblVFVlWiqr/GoaWa2j5wTQkQMAadlff5eRHw4Iu4tVDCS/lHSvZLukXSZpIZCbbvSdfQMjPuUckZLg7uvMLN95duGsFbSJ9LSQkFJOgD4B2BVRBxNMr7CuYXeT6VK2hBySwgeE8HMRpJvG8IykqeT3y1pNXAXcFdE/LCA8cyQ1A80AhsLtN2K19Hbv7vBeDyzZtSyo8slBDPbW75PKr8+Io4AngV8CngEOLEQgUTEU8AXgSdJRmjbERG/Gb6epPMkrZG0pq2trRC7Lnv9g0P09A/lXEKYO7OObV19kxyVmZWbnBKCpJMl7R4+MyJ6I+L2iPhuRBSkt1NJc0gaqA8ElgAzJb1p+HoRcWFErIqIVa2trYXYddnLjIWQa0KY44RgZiPItYTwFuA2SZdLequkRZMQy+nAYxHRFhH9wNUk/SbZODLtATknhMZatnX1ExGTGZaZlZmcriAR8S4ASYcDrwQuljQL+D3wK+DGiBjcz1ieBJ4nqRHoJrmjac1+bnNayPR0msttpwBzGusYHAp29gwwa8b4D7OZ2fSQbxvCAxHx5Yg4A3gp8CfgdcDq/Q0kIlYDPwJuB+5OY7twf7c7HXTkWUKYO7MOgG2drjYysz3y7e30euCsiNhJUo3UAPxTRBTkyhIRnwA+UYhtTSe7evMsIaQJob2rjxXMnLS4zKy85Ps8weyIyIya9k5gDvDNwodl+ci7hNDoEoKZ7Svf5xD6JdUAfwv8e0RcKcn1/EXWkeddRpkqo3YnBDPLkm9COB+4k6Sq6CPpvKaCRmR568yzymh2Y9KQvN0Pp5lZlrwSQkRcIulqYDAiuiWtBG6anNAsV5nbTscbTzmjqb6G2mrR7mcRzCxLviUEIqIja/oR4O8KGpHlraN3gJl11VRXafyVAUnMaaxzG4KZ7WXcRmVJL5P0TUnHp5/Pm/ywLB/59HSaMXdmndsQzGwvuVxF3kNSCviXdHCc4yc3JMtXrmMhZJvTWOc2BDPbSy63nbZFxPaI+CDwcuCESY7J8rSjuz/vJ47nzKx1G4KZ7SWXhPDzzEREfAS4ZPLCsYnY3t3H7HwTQqOrjMxsb+MmhIj4ybBZF0xSLDZBEykhtDbX097ZR//g0CRFZWblJq8nlSVdBGyWtF7S6rSx+X2TFJvlaHtXP7PTp49ztaA5GZ10a0fvZIRkZmUo39tOXwgsjIj+dMjL44BjCx+W5WpwKNjVM0BLniWEBc31AGzZ2cviWTMmIzQzKzP5JoSbSfov2pKOcPYU8IuCR2U529md3CmUbxvCgpY0IexyCcHMEvl2bnchcL2kD0p6YTomghXRjjQh5NuGkKky2rKrp+AxmVl5yjchfB+4kqRk8R7gz5IeLXhUlrPtmRJCY34JYV5THVJSZWRmBvlXGW1IxyzYTVJ9AeOxPE20hFBbXcXcxjpXGZnZbvmWENZKen/2jIjwFaWItqcPl+VbQoDk1tM2VxmZWSrfEsJC4HRJ/0wy1OWdwNqI+GHBI7OcZBqV873LCGBBS4NLCGa2W77dX78edlcTHQUcA5wIOCEUSaY/onyrjCC59fShTbsKHZKZlam8u7+G3dVEt6evgpE0G7gIOBoI4G0R4fEWxrCju58ZtdXU11Tn/d0FzfVs7ehlaCioyrHrbDOrXDm1IUga98Kfyzo5+Arwq4g4nOSht/sLsM2Ktr27f0LtB5AkhIGh4Bn3aWRm5F5COELSXWMsF7BfzyRIagFeBLwVICL6AF+pxjGRfowylsxOnlDeuL2b1mbfLGY23eWaEA7PYZ3B/QkEOAhoA74j6TjgNuD9EdG5n9utaPuTEJbOaQRgw7Zujls2u5BhmVkZyikhRMQTkx0ISSzPAd4XEaslfQX4CPDx7JXSEdvOA1i+fPkUhFXadnT186x5jRP67tK5SQlhw7auQoZkZmUq3+cQJtMGkgffVqeff0SSIPYSERdGxKqIWNXa2jqlAZaiZzr7mNeUX0+nGS0NtcyaUct6JwQzo4QSQkRsAtZLOiyddRpwXxFDKnlDQ0F7Zy/zZk68/n/pnBls2NZdwKjMrFxN6LZTSTOBnojY33aD4d4HXCqpDlhHMpazjWJbVx9DAfMnWEIAWDankYe3+FkEM8sxIUiqAs4F3kgypnIvUC+pjaT76wsj4uH9DSYi1gKr9nc700XmdtF5TftXQvj9g1uICCQ/i2A2neVaZfR74GDgo8CiiFgWEQtIBsy5GfiCpDdNUow2iq1ptxPz9yMhLJvbSO/AEFs7fIev2XSXa5XR6RHRP3xmRLQDVwFXSZrYvY82YVvTEsL+VBktnZPcabR+W5efRTCb5nIqIWSSgaSvSPqNpF9L+g9Jxw9fx6ZOIUoImVtWH9/qxz3Mprt8G5XvB34G1AJHAt+XdEFEfK3gkdm4nunspbpKE34wDeBZ82ZSUyUe2dJRwMjMrBzl29vpBVkffyHpa8CtgBNCETzT0ce8mXX71TFdbXUVB86fyUObnRDMpruJ3nb6LmAl0AzsLGhElrOtHb37dYdRxiELm7hvo0+j2XQ30QfTfkFSfbQU+HzhwrF8bO3o268G5YyVC5p5sr2Lnv5CP1ZiZuUkr4Qg6UpJR0TEkxHxLeAs4N8mJzQbz9aO3v1qUM44ZEETQwHr2tywbDad5Vtl9H3gCiVPMN0GNAFDBY/KcvJMgUoIhy5sBuDhLbs4cknLfm/PzMpTvo3K1wDXSDoWOJ6khPGLyQjMxtbRO0B3/2BB2hBWzG+kpko8sGkXZxcgNjMrT7l2XaGIiMzniLgLuGusdWxybdrRA8DiWQ37va36mmoOX9zMneu37/e2zKx85dx1haT3SdprAAJJdZJeKum7wFsKH56NJpMQFrXsf0IAOH7ZbO7asIOhIed0s+kq14RwBsmIaJdJ2ijpPkmPAQ8DbwC+HBEXT1KMNoKndyRdVi+eNaMg2ztu6Ww6egdYt9XPI5hNV7mOmNYDfB34etpn0XygOyJcx1AkmRLCgpbC9D90fDqE5tr1O1i5oLkg2zSz8pJTCUHSCZIWwe4+i14GfFfS+ZLmTmaANrKnd/Ywd2YdDbXVBdneQa1NNNXXsHb9toJsz8zKT65VRt8A+gAkvQj4AnAJsAO4cHJCs7Fs3tFTsPYDgOoq8ezls1m9rr1g2zSz8pJrQqhOu7oGOIdkQJyrIuLjJF1Y2BR7ekdPQe4wyvaClfN5eEsHm3f2FHS7ZlYeck4IkjLtDacB12Utm1B/SLZ/Nu3sYVGBE8IpK+cDcOMjWwu6XTMrD7kmhMuA6yX9BOgG/gggaSVJtZFNoZ7+Qdo7+wpeQjhycQtzGmv5kxOC2bSU611G/ybpd8Bi4DdZD6BVAe+brOBsZJkqnYUFbEMAqKoSp6yczw0PbWVoKParW20zKz85d24XETdHxI8jojNr3kMRcXshA5JULekOST8r5HYrycbtmaeUC/MMQraXHbmQrR293OG7jcymnYl2fz2Z3k/StbaNYv22LgCWz20s+LZfcvgCaqvFr+/dXPBtm1lpK6mEIGkp8BfARcWOpZStb++iukosnl3YKiOAloZaTlk5n1/dswl3TWU2vZRUQgD+H/BhxuhSW9J5ktZIWtPW1jZ1kZWQJ9u7WDyrgdrqyTl9Zx69mCfbu7jDnd2ZTSslkxAkvQrYEhG3jbVeRFwYEasiYlVra+sURVdanmzvmpTqoowzj11MY101V966ftL2YWalp2QSAnAK8GpJjwOXAy+V9P3ihlSa1rd3T2pCaKqv4S+OWcxP79xIZ+/ApO3HzEpLySSEiPhoRCyNiBXAucB1EfGmIodVcrr6Btja0cuySUwIAOecsIzOvkF+fvfTk7ofMysdJZMQLDfr25Nuryc7ITz3WXM4qHWmq43MppGSTAgR8YeIeFWx4yhF69sn75bTbJI4Z9Uy1jyxjUe27JrUfZlZaSjJhGCje3KKEgLAa5+zlNpq8f2bn5z0fZlZ8TkhlJkn27uYWVfNnMbaSd9Xa3M9rz7uAK64dT3bu/omfX9mVlxOCGVmw7Yuls1tRJqafobe+aID6e4f5NLVLiWYVTonhDIz2c8gDHf4ohZedGgr37nxcXoHBqdsv2Y29ZwQykhEsL69e9LvMBruvBcexNaOXv7njqemdL9mNrWcEMrI1o4+uvsHp7SEAHDKynkcubiFb9ywjsEh929kVqmcEMrIVN5hlE0S733pSta1dfLTOzdO6b7NbOo4IZSRzDMIy+YWfhyE8Zxx1CIOX9TMV373MAODo/Y9aGZlzAmhjGQSwtI5U1tCgGQ0tQ+cfiiPbe3kJ2tdSjCrRE4IZeSJ9i4WttTTUFtdlP2/4qiFHLWkhfOvcynBrBI5IZSRdW0dHDh/ZtH2L4l/PP1Qnnimi8vdx5FZxXFCKCOPbe3koNamosZw2hELOHHFXP7fbx9iV09/UWMxs8JyQigT2zr72NbVz0FFLCFAUkr42F8cwdaOPi64/tGixmJmheWEUCbWbe0A4KDW4iYEgOOWzebs45dw0R8fY+P27mKHY2YF4oRQJta1dQJw4PziVhllfOgVhxHA53/5QLFDMbMCcUIoE+u2dlJTJZbNmfpnEEaydE4j7z71YH5650b++HBbscMxswJwQigTj7V1snxeIzXVpXPK3v3ig1kxr5F//cm99PS74zuzclc6Vxcb07qtHRxUItVFGQ211XzmNUfz2NZONzCbVQAnhDIwOBQ8/kwXB5dAg/JwLzyklbOOW8LXf/8oD27yUJtm5cwJoQxs3N5N38BQUR9KG8snzzqSlhk1/O8r19I34CeYzcpVySQEScsk/V7S/ZLulfT+YsdUKh5ty9xyWlpVRhnzmur53F8ew70bd/K16x4udjhmNkElkxCAAeCfIuII4HnA/5J0ZJFjKgmPbc3cclqaJQSAlx+1iL96zlL+6w+PctsT24odjplNQMkkhIh4OiJuT6d3AfcDBxQ3qtKwrq2T5oYa5jfVFTuUMX3i1UeyZHYD7/vB7Wzr7Ct2OGaWp5JJCNkkrQCeDaweYdl5ktZIWtPWNj3uf8/0YSSp2KGMqaWhlq//zXPZ2tHHB65Yy5BHVzMrKyWXECQ1AVcBH4iIncOXR8SFEbEqIla1trZOfYBFsK6to+h9GOXqmKWz+NezjuT6h9r46nWPFDscM8tDSSUESbUkyeDSiLi62PGUgs7eATbu6CnJW05H88aTlvPa5xzAl3/7kIfcNCsjJZMQlNSHfAu4PyK+VOx4SsXDW5I7jA5d2FzkSHInic+/9hhOWDGHf/rhnW5kNisTJZMQgFOANwMvlbQ2fZ1Z7KCK7YskEJoAABAHSURBVKH0Ya/DFpVPQgCor6nmG29exeJZDZx3yZrdt86aWekqmYQQEX+KCEXEsRFxfPr6RbHjKrYHN++iobaKZUUYR3l/zZ1Zx3feegISvPGbq3ePCW1mpalkEoKN7KHNuzhkQTNVVaV9h9FoDmpt4ntvP4nu/kHe8M2bPX6CWQlzQihxD27aVVbtByM5YnEL33v7iezo6ud1F9zEOlcfmZUkJ4QStq2zjy27ejlsUWl2WZGPY5fO5rLznkdP/yCvu+Am7nlqR7FDMrNhnBBK2P1PJ49hHLaopciRFMbRB8ziynedTH1NFed84yauvW9zsUMysyxOCCXs7vRX9DEHzCpyJIVzcGsTV7/nFA5e0MR531vD1//wCBF+otmsFDghlLC7n9rBAbNnMHdmafdhlK9Fsxq48u9P5lXHLuE/fvUg77zkNvd9ZFYCnBBK2L0bd3L0AZVRXTRcQ2015597PP/6qiO5/qEtnHn+H/nzI1uLHZbZtOaEUKJ29vTz2NbOiqouGk4Sb3vBgVz97lNoqK3mby5azYd/dCfbu1xaMCsGJ4QSde9TSYPy0RWcEDKOWTqLX/zDC3nXqQdz1e1PcfqXrucna59y24LZFHNCKFG3P5n0/3Ps0tlFjmRqzKir5iOvPJxr3nsKS2bP4P2Xr+W1//1nbl73TLFDM5s2nBBK1OrH2jl0YVPFNSiP56gls/jxe07hC689hqe393DuhTfzlm/fwl0bthc7NLOK54RQggYGh7jt8XZOOnBesUMpiuoqce6Jy/nDh17MR195OGvXb+fVX7uRc75xE7+9b7MH3jGbJDXFDsD2dc/GnXT2DXLigXOLHUpRNdRW8/enHswbTlrOFbes5zs3PsY7LlnDQa0z+ZsTl/OaZx/A/Kb6YodpVjFcQihBq9N685MOmt4JIaOloZZ3vuggrv/wS/jKucfT0lDLZ39+P8/73O945yVr+NU9T9PdN1jsMM3KnksIJei392/m8EXNLGhuKHYoJaW2uoqzjz+As48/gIc37+JHt23g6jue4tr7NtNQW8Wph7ZyxtGLOPXQBdOu7cWsEJwQSsyWnT2seWIbHzjt0GKHUtIOWdjMR888gg+94jBuebydX92ziV/fu4lf35v0j3TUkhZesHI+p6yczwkr5jKjrrrIEZuVPieEEvPrezcRAWces6jYoZSFmuoqnn/wfJ5/8Hw+edZR3PXUDv70cBt/emQr37nxcb5xwzpqq8URi1s4ftlsjl82m+OWzebAeTPLdowJs8nihFBCIoKrbn+Kg1tnckiZj4FQDFVV2n3Rf+9LD6Grb4BbH9/GzeueYe2T27nqtg1cctMTADTV13DIwiYOW9jMIQubOWxhM4cubKK1uZ5keG+z6ccJoYTcvK6dteu385mzjyp2KBWhsa6GUw9t5dRDWwEYHAoebetg7ZPbuWfjDh7avIvf3LeZy29dv/s7zQ01LJ/byPK5jSxLX8vnNnLA7BksbKmnqb7GCcMqlhNCiYgIzv/dw7Q21/O6VcuKHU5Fqq4Shy5s5tCFzbyePX/jrR29PLRpFw9t3sWjbZ2s39bFQ5t38bsHttA3MLTXNhrrqlnY0sCC5vrd763N9cxprGN2Yy1zZtYxp7GW2Y11zJ5RS021b+Sz8lFSCUHSGcBXgGrgooj4QpFDmjL/ff2j3LTuGT7zmqNpqHUD6FSa31TP/JX1PH/l/L3mDw0FW3b18mR7F0/v6Gbzzh427+xly65eNu/s4a4N29m0s4ee/qFRtgwtDTXMbqyjuaGGmfU1NNcn700NNTTVJ6+Z9TU01VfTVF9LY301DTXVNNRW0VBbnb6qqM/Mq6l224dNmpJJCJKqgf8CXgZsAG6VdE1E3FfcyCbX+vYuvvWnx7j4z49z1nFLeNNJy4sdkqWqqsSiWQ0smjX67b8RQWffINs6+9je1c+2rr7k1dnHtq5+tncl7529A+zqHWDTzh46egeSzz0D9A6MnkxGU1ddRf3uhJEki9rqKmqrRU2V0ukqaqq1e35tdRU1VVnT1aIufa+pqqKuporqKlEtUVUlqpWUqCTtPb8KqobNSz7vO7969zJRpT3LJRDJe5LbMvOSdbKXJy8hSNdPpknXqRq2XNqzLSldnm6LvbaftdxVgLuVTEIATgQeiYh1AJIuB84GCp4QzvzKH+kbHNqrN83YZ2Kvyd3r7j0vs17sM2/49PDtAOxKLwoAbzn5WXz0zCP8j7PMSNr9S3/ZBJ4j7B8corN3IE0Sg3T0DtA7MEhv/xA9/YP0DAzSk5lO33sHMu/JvN6BQfoHg/7BIQbS966+AQaGgr6BIQaGgoHBod3r7F5vKJk36K5AAHYnimQ6mVLWsuTz7omxl+81b+Rt7rsN5fQ9CVqbG/jl+1+Y+8HlqJQSwgHA+qzPG4CThq8k6TzgPIDlyyf2a3rlgqY9/wmyrr/DT8CwxfucqOx197qM77XNvU9y9uLGumpWzJ/JSw5bwIr5M/M8CqsEtdVVSXtDY/EepBsaiiRpDA0xOBQMDcFgJIkiInZPZ88fynofcf5QZG0jadAfjGR+kPxYCpJlQ5kfW+m8oSHSdWLPe7D7e0PpfNL3vbeZvX5m+3um2Wf9YCj2bCsTB+z5obfn88jLh72l6+T23eE/Gof/8Bxt/eaG2pFO5X4rpYQw0k/jfX66RMSFwIUAq1atmtBPm/Pf8OyJfM2sIlVViboqUeeebKa9UvoXsAHIvr1mKbCxSLGYmU07pZQQbgUOkXSgpDrgXOCaIsdkZjZtlEyVUUQMSHov8GuS206/HRH3FjksM7Npo2QSAkBE/AL4RbHjMDObjkqpysjMzIrICcHMzAAnBDMzSzkhmJkZAIrhj8qVEUltwBMT/Pp8YGsBwymmSjmWSjkO8LGUoko5Dti/Y3lWRLSOtKCsE8L+kLQmIlYVO45CqJRjqZTjAB9LKaqU44DJOxZXGZmZGeCEYGZmqemcEC4sdgAFVCnHUinHAT6WUlQpxwGTdCzTtg3BzMz2Np1LCGZmlsUJwczMgGmQECSdIelBSY9I+sgIy+slXZEuXy1pxdRHOb4cjuOtktokrU1f7yhGnOOR9G1JWyTdM8pySTo/Pc67JD1nqmPMVQ7H8mJJO7LOyb9OdYy5krRM0u8l3S/pXknvH2Gdkj83OR5HWZwXSQ2SbpF0Z3osnxphncJev5Lh5irzRdKN9qPAQUAdcCdw5LB13gNckE6fC1xR7LgneBxvBb5W7FhzOJYXAc8B7hll+ZnAL0lG0HsesLrYMe/HsbwY+Fmx48zxWBYDz0mnm4GHRvg3VvLnJsfjKIvzkv6dm9LpWmA18Lxh6xT0+lXpJYQTgUciYl1E9AGXA2cPW+ds4Lvp9I+A01R6I93nchxlISJuANrHWOVs4JJI3AzMlrR4aqLLTw7HUjYi4umIuD2d3gXcTzLOebaSPzc5HkdZSP/OHenH2vQ1/C6ggl6/Kj0hHACsz/q8gX3/cexeJyIGgB3AvCmJLne5HAfAX6VF+R9JWjbC8nKQ67GWi5PTIv8vJR1V7GBykVY7PJvkF2m2sjo3YxwHlMl5kVQtaS2wBbg2IkY9J4W4flV6QhgpUw7PsLmsU2y5xPhTYEVEHAv8lj2/GspNOZyPXN1O0m/MccBXgf8pcjzjktQEXAV8ICJ2Dl88wldK8tyMcxxlc14iYjAijicZY/5ESUcPW6Wg56TSE8IGIPuX8lJg42jrSKoBZlF61QDjHkdEPBMRvenHbwLPnaLYCi2Xc1YWImJnpsgfyWiAtZLmFzmsUUmqJbmIXhoRV4+wSlmcm/GOo9zOC0BEbAf+AJwxbFFBr1+VnhBuBQ6RdKCkOpJGl2uGrXMN8JZ0+q+B6yJtoSkh4x7HsLrcV5PUnZaja4C/Te9oeR6wIyKeLnZQEyFpUaY+V9KJJP/fniluVCNL4/wWcH9EfGmU1Ur+3ORyHOVyXiS1SpqdTs8ATgceGLZaQa9fJTWmcqFFxICk9wK/JrlT59sRca+kTwNrIuIakn8835P0CElmPbd4EY8sx+P4B0mvBgZIjuOtRQt4DJIuI7nLY76kDcAnSBrLiIgLSMbUPhN4BOgC/q44kY4vh2P5a+DdkgaAbuDcEvyxkXEK8Gbg7rTOGuD/AMuhrM5NLsdRLudlMfBdSdUkSevKiPjZZF6/3HWFmZkBlV9lZGZmOXJCMDMzwAnBzMxSTghmZgY4IZiZWcoJwcqGpMGsHirX7nfPjiVEe3qrvWg/t/NJSR/M+nyypG+Osu6M9O/YV+oPZtnUqOjnEKzidKeP8Y9IUk3an0u5uiIi3jt85n4e1xnAr0ZaEBHdwPGSHp/gtq3CuIRgZS39Zf1DST8FfpPO+5CkW9OO/j6Vte7HlIwp8VtJl2V+SUv6g6RV6fT8zAUy7VjsP7O29ffp/Ben3/mRpAckXZr15OsJkv6cdpx2i6RmSX+UdHxWHDdKOjaf45LUJOl3km6XdLeks7PW3X1cwGHDNnUa8FtJR6XxrE2P5ZCJ/s2tcrmEYOVkRtbTp49FxF+m0ycDx0ZEu6SXA4eQdBku4BpJLwI6SZ7ifDbJv/vbgdvG2d/bSbpnOEFSPXCjpN+ky54NHEXSl8+NwCmSbgGuAM6JiFsltZA8CXsRyZPjH5B0KFAfEXflcLzZx1UD/GVE7Eyrd26WdA3JeAwjHle6Xn9E7JD0WeArEXGpku5PqnPYv00zTghWTkarMro2IjIder08fd2Rfm4iSRDNwI8jogsgvZiO5+XAsZL+Ov08K91WH3BLRGxIt7UWWEHS9fDTEXErJJ2opct/CHxc0oeAtwEX53i82ccl4HNpchsi6fZ4IfDCMY7r5aSlJuAm4GOSlgJXR8TDOcZg04irjKwSdGZNC/h8RByfvlZGxLfSZaP10zLAnv8LDcO29b6sbR0YEZkLbG/WeoMkP6400j7Si/W1JIOZvB74wQSO641AK/DcNCluzop1tON6JWn7QUT8gKTTw27g15JemmMMNo04IVil+TXwNiX94SPpAEkLgBuAv0zvrGkGzsr6zuPs6S78r4dt691KulNG0qGSZo6x7weAJZJOSNdvTqt6IKk2Oh+4NetXfz5mAVsiol/SS4BnpfNHPK60TeNYYG36+SBgXUScT9JD5phtGDY9ucrIKkpE/EbSEcBNaTtvB/CmiLhd0hUkF8gngD9mfe2LwJWS3gxclzX/IpKqoNvTC2wb8Jox9t0n6Rzgq0q6K+4m6bK4IyJuk7QT+M4ED+1S4KeS1qTH8EC6z9GO67nAHVm9eJ4DvElSP7AJ+PQE47AK5t5ObVqS9EmSC/UXp2h/S0gGODk8IoZGWP5WYNVIt51OcH//QjIO9+U5rPt4uu+thdi3lS9XGZlNMkl/SzKu78dGSgapbuCV+/tgWkZEfHa8ZJB5MI1kDIfR4rJpxCUEMzMDXEIwM7OUE4KZmQFOCGZmlnJCMDMzwAnBzMxS/x9e5mZxuDff0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import wafo.spectrum.models as wsm\n",
    "Hm0 = 7; Tp = 11;\n",
    "spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata()\n",
    "_=spec.plot()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Directional spectrum and Encountered directional spectrum\n",
    "=========================================================\n",
    "Directional spectrum\n",
    "---------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "D = wsm.Spreading('cos2s')\n",
    "Sd = D.tospecdata2d(spec)\n",
    "_=Sd.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encountered directional spectrum\n",
    "--------------------------------- "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "#clf()\n",
    "#Se = spec2spec(Sd,'encdir',0,10);\n",
    "#plotspec(Se), hold on\n",
    "#plotspec(Sd,1,'--'), hold off\n",
    "##!wafostamp('','(ER)')\n",
    "#disp('Block = 17'),pause(pstate)\n",
    "#\n",
    "##!#! Frequency spectra\n",
    "#clf\n",
    "#Sd1 =spec2spec(Sd,'freq');\n",
    "#Sd2 = spec2spec(Se,'enc');\n",
    "#plotspec(spec), hold on\n",
    "#plotspec(Sd1,1,'.'),\n",
    "#plotspec(Sd2),\n",
    "##!wafostamp('','(ER)')\n",
    "#hold off\n",
    "#disp('Block = 18'),pause(pstate)\n",
    "#\n",
    "##!#! Wave number spectrum\n",
    "#clf\n",
    "#Sk = spec2spec(spec,'k1d')\n",
    "#Skd = spec2spec(Sd,'k1d')\n",
    "#plotspec(Sk), hold on\n",
    "#plotspec(Skd,1,'--'), hold off\n",
    "##!wafostamp('','(ER)')\n",
    "#disp('Block = 19'),pause(pstate)\n",
    "#\n",
    "##!#! Effect of waterdepth on spectrum\n",
    "#clf\n",
    "#plotspec(spec,1,'--'), hold on\n",
    "#S20 = spec;\n",
    "#S20.S = S20.S.*phi1(S20.w,20);\n",
    "#S20.h = 20;\n",
    "#plotspec(S20),  hold off\n",
    "##!wafostamp('','(ER)')\n",
    "#disp('Block = 20'),pause(pstate)\n",
    "#\n",
    "##!#! Section 2.3 Simulation of transformed Gaussian process\n",
    "##!#! Example 3: Simulation of random sea    \n",
    "##! The reconstruct function replaces the spurious points of seasurface by\n",
    "##! simulated data on the basis of the remaining data and a transformed Gaussian\n",
    "##! process. As noted previously one must be careful using the criteria \n",
    "##! for finding spurious points when reconstructing a dataset, because\n",
    "##! these criteria might remove the highest and steepest waves as we can see\n",
    "##! in this plot where the spurious points is indicated with a '+' sign:\n",
    "##!\n",
    "#clf\n",
    "#[y, grec] = reconstruct(xx,inds);\n",
    "#waveplot(y,'-',xx(inds,:),'+',1,1)\n",
    "#axis([0 inf -inf inf])\n",
    "##!wafostamp('','(ER)')\n",
    "#disp('Block = 21'),pause(pstate)\n",
    "#\n",
    "##! Compare transformation (grec) from reconstructed (y) \n",
    "##! with original (glc) from (xx)\n",
    "#clf\n",
    "#trplot(g), hold on\n",
    "#plot(gemp(:,1),gemp(:,2))\n",
    "#plot(glc(:,1),glc(:,2),'-.')\n",
    "#plot(grec(:,1),grec(:,2)), hold off \n",
    "#disp('Block = 22'),pause(pstate)\n",
    "#\n",
    "##!#!\n",
    "#clf\n",
    "#L = 200;\n",
    "#x = dat2gaus(y,grec);\n",
    "#Sx = dat2spec(x,L);\n",
    "#disp('Block = 23'),pause(pstate)\n",
    "#      \n",
    "##!#!\n",
    "#clf\n",
    "#dt = spec2dt(Sx)\n",
    "#Ny = fix(2*60/dt) #! = 2 minutes\n",
    "#Sx.tr = grec;\n",
    "#ysim = spec2sdat(Sx,Ny);\n",
    "#waveplot(ysim,'-')\n",
    "##!wafostamp('','(CR)')\n",
    "#disp('Block = 24'),pause(pstate)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimated spectrum compared to Torsethaugen spectrum\n",
    "-------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fp = 1.1;dw = 0.01\n",
    "H0 = S1.characteristic('Hm0')[0]\n",
    "St = wsm.Torsethaugen(Hm0=H0,Tp=2*np.pi/fp).tospecdata(np.arange(0,5+dw/2,dw))  \n",
    "S1.plot()\n",
    "St.plot('-.')\n",
    "_=plt.axis([0, 6, 0, 0.4])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transformed Gaussian model compared to Gaussian model\n",
    "-------------------------------------------------------\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = St.sampling_period()\n",
    "va, sk, ku = St.stats_nl(moments='vsk' )\n",
    "#sa = sqrt(va)\n",
    "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)\n",
    " \n",
    "ysim_t = St.sim(ns=240, dt=0.5)\n",
    "xsim_t = ysim_t.copy()\n",
    "xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])\n",
    "\n",
    "ts_y = wo.mat2timeseries(ysim_t)\n",
    "ts_x = wo.mat2timeseries(xsim_t)\n",
    "_=ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
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