gp-spectral.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Stochaskell, version 0.1.0\n",
       "Copyright (C) 2015-2020 David A Roberts\n",
       "This program comes with ABSOLUTELY NO WARRANTY.\n",
       "This is free software, and you are welcome to redistribute it\n",
       "under certain conditions; see the LICENSE for details.\n",
       "\n",
       "Using installation directory at \n",
       "  /home/jovyan/stochaskell"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "{-# LANGUAGE FlexibleContexts, MonadComprehensions, NoImplicitPrelude, RebindableSyntax, TypeFamilies #-}\n",
    "import Language.Stochaskell\n",
    "stochaskell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    ":opt svg\n",
    "import Language.Stochaskell.Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "let t = 10\n",
    "let xTest = [i/10 | i <- [1..100]] :: [Double]\n",
    "let xData = [1..10] :: [Double]\n",
    "yData <- map real <$> sequence [simulate (normal (sin (real x)) 0.1 :: P R) | x <- xData]\n",
    "toRenderable $ do\n",
    "  plot $ line \"\" [xTest `zip` (sin <$> xTest)]\n",
    "  plot $ points \"\" $ xData `zip` list yData"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cov ils x y = exp (- ((x - y) * ils)^2 / 2)\n",
    "\n",
    "let covTest = linspace (-t,t) 200\n",
    "toRenderable . plot $ line \"\" [zip covTest $ cov 1 0 <$> covTest]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "-- equivalent to `cov` fn for m -> infinity\n",
    "covApprox :: R -> Z -> P R -> R -> R -> R\n",
    "covApprox t m sd x y = amp 0 + 2 * sum' v where\n",
    "  amp j = pdf sd (j / (2*t)) / (2*t)\n",
    "  v = vector [ let w = 2*pi * (x - y) * cast j / (2*t)\n",
    "               in amp (cast j) * cos w\n",
    "             | j <- 1...m ]\n",
    "\n",
    "toRenderable $ do\n",
    "  plot $ line \"exact\" [zip covTest $ cov 1 0 <$> covTest]\n",
    "  let sd = normal 0 (1 / (2*pi))\n",
    "  sequence [plot $ line (\"M=\"++ show m) [zip covTest $ real . covApprox t m sd 0 <$> covTest] | m <- [4,6,8]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "-- gp using covApprox can be written as a trig polynomial\n",
    "gpTrigPoly :: R -> Z -> P R -> R -> RVec -> RVec -> R -> R\n",
    "gpTrigPoly t m sd z a b x = z * amp 0 + sqrt 2 * sum' v where\n",
    "  amp j = sqrt $ pdf sd (j / (2*t)) / (2*t)\n",
    "  v = vector [ let w = 2*pi * x * cast j / (2*t)\n",
    "               in amp (cast j) * ((a!j) * cos w + (b!j) * sin w)\n",
    "             | j <- 1...m ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model :: R -> Z -> Z -> P (R,RVec,RVec,R,R,RVec,RVec)\n",
    "model t m nData = do\n",
    "  z <- normal 0 1 :: P R\n",
    "  a <- normals (vector [ 0 | j <- 1...m ]) (vector [ 1 | j <- 1...m ]) :: P RVec\n",
    "  b <- normals (vector [ 0 | j <- 1...m ]) (vector [ 1 | j <- 1...m ]) :: P RVec\n",
    "  eta <- gamma 1 1\n",
    "  ils <- gamma 1 1\n",
    "  xData <- joint vector [ uniform 0 10 | i <- 1...nData ]\n",
    "  let sd = normal 0 (ils / (2*pi))\n",
    "      y i = eta * gpTrigPoly t m sd z a b (xData!i)\n",
    "  yData <- joint vector [ normal (y i) 0.1 | i <- 1...nData ]\n",
    "  return (z,a,b,eta,ils,xData,yData)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--- Generating Stan code ---\n",
       "functions {\n",
       "  // https://github.com/stan-dev/stan/issues/452\n",
       "  real to_real(real x) { return x; }\n",
       "}\n",
       "data {\n",
       "  \n",
       "  \n",
       "  \n",
       "  \n",
       "  \n",
       "  vector[10] x_stan_0_5;\n",
       "  vector[10] x_stan_0_6;\n",
       "}\n",
       "parameters {\n",
       "  real x_stan_0_0;\n",
       "  vector[20] x_stan_0_1;\n",
       "  vector[20] x_stan_0_2;\n",
       "  real x_stan_0_3;\n",
       "  real x_stan_0_4;\n",
       "  \n",
       "  \n",
       "}\n",
       "model {\n",
       "  \n",
       "  \n",
       "  \n",
       "  real v_0_3;\n",
       "  real v_0_4;\n",
       "  real v_0_5;\n",
       "  real v_0_6;\n",
       "  real v_0_7;\n",
       "  real v_0_8;\n",
       "  \n",
       "  \n",
       "  \n",
       "  vector[20] v_0_12;\n",
       "  vector[20] v_0_13;\n",
       "  \n",
       "  \n",
       "  \n",
       "  v_0_3 = to_real(x_stan_0_4) ./ to_real(6.283185307179586);\n",
       "  v_0_4 = normal_lpdf(0 | 0, v_0_3);\n",
       "  v_0_5 = exp(v_0_4);\n",
       "  v_0_6 = to_real(v_0_5) ./ to_real(20);\n",
       "  v_0_7 = sqrt(v_0_6);\n",
       "  v_0_8 = x_stan_0_0 .* v_0_7;\n",
       "  \n",
       "  \n",
       "  \n",
       "  for (i_1_1 in 1:20) {\n",
       "  \n",
       "    v_0_12[i_1_1] = 0;\n",
       "  }\n",
       "  for (i_1_1 in 1:20) {\n",
       "  \n",
       "    v_0_13[i_1_1] = 1;\n",
       "  }\n",
       "\n",
       "  x_stan_0_0 ~ normal(0, 1);\n",
       "  x_stan_0_1 ~ normal(v_0_12, v_0_13);\n",
       "  x_stan_0_2 ~ normal(v_0_12, v_0_13);\n",
       "  x_stan_0_3 ~ gamma(1, 1);\n",
       "  x_stan_0_4 ~ gamma(1, 1);\n",
       "  \n",
       "  for (i_1_1 in 1:10) {\n",
       "    real v_1_0;\n",
       "    vector[20] v_1_1;\n",
       "    real v_1_2;\n",
       "    real v_1_3;\n",
       "    real v_1_4;\n",
       "    real v_1_5;\n",
       "    v_1_0 = 6.283185307179586 .* x_stan_0_5[i_1_1];\n",
       "    for (i_2_1 in 1:20) {\n",
       "      real v_2_0;\n",
       "      real v_2_1;\n",
       "      real v_2_2;\n",
       "      real v_2_3;\n",
       "      real v_2_4;\n",
       "      real v_2_5;\n",
       "      real v_2_6;\n",
       "      real v_2_7;\n",
       "      real v_2_8;\n",
       "      real v_2_9;\n",
       "      real v_2_10;\n",
       "      real v_2_11;\n",
       "      real v_2_12;\n",
       "      v_2_0 = to_real(i_2_1) ./ to_real(20);\n",
       "      v_2_1 = normal_lpdf(v_2_0 | 0, v_0_3);\n",
       "      v_2_2 = exp(v_2_1);\n",
       "      v_2_3 = to_real(v_2_2) ./ to_real(20);\n",
       "      v_2_4 = sqrt(v_2_3);\n",
       "      v_2_5 = v_1_0 .* i_2_1;\n",
       "      v_2_6 = to_real(v_2_5) ./ to_real(20);\n",
       "      v_2_7 = cos(v_2_6);\n",
       "      v_2_8 = x_stan_0_1[i_2_1] .* v_2_7;\n",
       "      v_2_9 = sin(v_2_6);\n",
       "      v_2_10 = x_stan_0_2[i_2_1] .* v_2_9;\n",
       "      v_2_11 = v_2_8 + v_2_10;\n",
       "      v_2_12 = v_2_4 .* v_2_11;\n",
       "      v_1_1[i_2_1] = v_2_12;\n",
       "    }\n",
       "    v_1_2 = 0;\n",
       "    for (i_2_0 in 1:20) {\n",
       "      real i_2_11;\n",
       "      real i_2_12;\n",
       "      i_2_11 = v_1_1[i_2_0];\n",
       "      i_2_12 = v_1_2;\n",
       "      {\n",
       "      real v_2_0;\n",
       "      v_2_0 = i_2_11 + i_2_12;\n",
       "      v_1_2 = v_2_0;\n",
       "      }\n",
       "    }\n",
       "    v_1_3 = 1.4142135623730951 .* v_1_2;\n",
       "    v_1_4 = v_0_8 + v_1_3;\n",
       "    v_1_5 = x_stan_0_3 .* v_1_4;  x_stan_0_6[i_1_1] ~ normal(v_1_5, 0.1);\n",
       "  }\n",
       "}\n",
       "\n",
       "make -C /home/jovyan/stochaskell/cmdstan /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761\n",
       "make[1]: Entering directory '/home/jovyan/stochaskell/cmdstan'\n",
       "\n",
       "--- Translating Stan model to C++ code ---\n",
       "bin/stanc  --o=/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.hpp /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan\n",
       "Model name=model_e6bf13ca62b8b7b248101d3b53de582f6eebd761_model\n",
       "Input file=/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan\n",
       "Output file=/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.hpp\n",
       "\n",
       "--- Compiling, linking C++ code ---\n",
       "g++ -std=c++1y -pthread -Wno-sign-compare     -O3 -I src -I stan/src -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.69.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include    -DBOOST_RESULT_OF_USE_TR1 -DBOOST_NO_DECLTYPE -DBOOST_DISABLE_ASSERTS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION     -c  -x c++ -o /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.o /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.hpp\n",
       "g++ -std=c++1y -pthread -Wno-sign-compare     -O3 -I src -I stan/src -I stan/lib/stan_math/ -I stan/lib/stan_math/lib/eigen_3.3.3 -I stan/lib/stan_math/lib/boost_1.69.0 -I stan/lib/stan_math/lib/sundials_4.1.0/include    -DBOOST_RESULT_OF_USE_TR1 -DBOOST_NO_DECLTYPE -DBOOST_DISABLE_ASSERTS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION                   src/cmdstan/main.o stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_4.1.0/lib/libsundials_idas.a  /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.o -o /home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761\n",
       "make[1]: Leaving directory '/home/jovyan/stochaskell/cmdstan'\n",
       "--- Sampling Stan model ---\n",
       "/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761 method=sample num_samples=1000 num_warmup=1000 save_warmup=0 thin=1 adapt engaged=1 algorithm=hmc engine=nuts max_depth=10 metric=diag_e stepsize=1.0 stepsize_jitter=0.0 data file=/tmp/stan-59ed7c2ded52e227/stan.data init=/tmp/stan-59ed7c2ded52e227/stan.init output file=/tmp/stan-59ed7c2ded52e227/stan.csv\n",
       "method = sample (Default)\n",
       "  sample\n",
       "    num_samples = 1000 (Default)\n",
       "    num_warmup = 1000 (Default)\n",
       "    save_warmup = 0 (Default)\n",
       "    thin = 1 (Default)\n",
       "    adapt\n",
       "      engaged = 1 (Default)\n",
       "      gamma = 0.050000000000000003 (Default)\n",
       "      delta = 0.80000000000000004 (Default)\n",
       "      kappa = 0.75 (Default)\n",
       "      t0 = 10 (Default)\n",
       "      init_buffer = 75 (Default)\n",
       "      term_buffer = 50 (Default)\n",
       "      window = 25 (Default)\n",
       "    algorithm = hmc (Default)\n",
       "      hmc\n",
       "        engine = nuts (Default)\n",
       "          nuts\n",
       "            max_depth = 10 (Default)\n",
       "        metric = diag_e (Default)\n",
       "        metric_file =  (Default)\n",
       "        stepsize = 1 (Default)\n",
       "        stepsize_jitter = 0 (Default)\n",
       "id = 0 (Default)\n",
       "data\n",
       "  file = /tmp/stan-59ed7c2ded52e227/stan.data\n",
       "init = /tmp/stan-59ed7c2ded52e227/stan.init\n",
       "random\n",
       "  seed = -1 (Default)\n",
       "output\n",
       "  file = /tmp/stan-59ed7c2ded52e227/stan.csv\n",
       "  diagnostic_file =  (Default)\n",
       "  refresh = 100 (Default)\n",
       "\n",
       "\n",
       "Gradient evaluation took 0.00022 seconds\n",
       "1000 transitions using 10 leapfrog steps per transition would take 2.2 seconds.\n",
       "Adjust your expectations accordingly!\n",
       "\n",
       "\n",
       "Iteration:    1 / 2000 [  0%]  (Warmup)\n",
       "Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
       "Exception: normal_lpdf: Scale parameter is -0.00763495, but must be > 0!  (in '/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan' at line 42)\n",
       "\n",
       "If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
       "but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
       "\n",
       "Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
       "Exception: normal_lpdf: Scale parameter is -0.106511, but must be > 0!  (in '/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan' at line 42)\n",
       "\n",
       "If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
       "but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
       "\n",
       "Iteration:  100 / 2000 [  5%]  (Warmup)\n",
       "Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
       "Exception: normal_lpdf: Scale parameter is -0.00585475, but must be > 0!  (in '/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan' at line 42)\n",
       "\n",
       "If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
       "but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
       "\n",
       "Iteration:  200 / 2000 [ 10%]  (Warmup)\n",
       "Iteration:  300 / 2000 [ 15%]  (Warmup)\n",
       "Iteration:  400 / 2000 [ 20%]  (Warmup)\n",
       "Iteration:  500 / 2000 [ 25%]  (Warmup)\n",
       "Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
       "Exception: normal_lpdf: Scale parameter is -0.0366805, but must be > 0!  (in '/home/jovyan/stochaskell/cache/stan/model_e6bf13ca62b8b7b248101d3b53de582f6eebd761.stan' at line 42)\n",
       "\n",
       "If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
       "but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
       "\n",
       "Iteration:  600 / 2000 [ 30%]  (Warmup)\n",
       "Iteration:  700 / 2000 [ 35%]  (Warmup)\n",
       "Iteration:  800 / 2000 [ 40%]  (Warmup)\n",
       "Iteration:  900 / 2000 [ 45%]  (Warmup)\n",
       "Iteration: 1000 / 2000 [ 50%]  (Warmup)\n",
       "Iteration: 1001 / 2000 [ 50%]  (Sampling)\n",
       "Iteration: 1100 / 2000 [ 55%]  (Sampling)\n",
       "Iteration: 1200 / 2000 [ 60%]  (Sampling)\n",
       "Iteration: 1300 / 2000 [ 65%]  (Sampling)\n",
       "Iteration: 1400 / 2000 [ 70%]  (Sampling)\n",
       "Iteration: 1500 / 2000 [ 75%]  (Sampling)\n",
       "Iteration: 1600 / 2000 [ 80%]  (Sampling)\n",
       "Iteration: 1700 / 2000 [ 85%]  (Sampling)\n",
       "Iteration: 1800 / 2000 [ 90%]  (Sampling)\n",
       "Iteration: 1900 / 2000 [ 95%]  (Sampling)\n",
       "Iteration: 2000 / 2000 [100%]  (Sampling)\n",
       "\n",
       " Elapsed Time: 15.7447 seconds (Warm-up)\n",
       "               8.34643 seconds (Sampling)\n",
       "               24.0911 seconds (Total)\n",
       "\n",
       "Stan took 24.656232831s\n",
       "# stan_version_major = 2\n",
       "# stan_version_minor = 20\n",
       "# stan_version_patch = 0\n",
       "# model = model_e6bf13ca62b8b7b248101d3b53de582f6eebd761_model\n",
       "# method = sample (Default)\n",
       "#   sample\n",
       "#     num_samples = 1000 (Default)\n",
       "#     num_warmup = 1000 (Default)\n",
       "#     save_warmup = 0 (Default)\n",
       "#     thin = 1 (Default)\n",
       "#     adapt\n",
       "#       engaged = 1 (Default)\n",
       "#       gamma = 0.050000000000000003 (Default)\n",
       "#       delta = 0.80000000000000004 (Default)\n",
       "#       kappa = 0.75 (Default)\n",
       "#       t0 = 10 (Default)\n",
       "#       init_buffer = 75 (Default)\n",
       "#       term_buffer = 50 (Default)\n",
       "#       window = 25 (Default)\n",
       "#     algorithm = hmc (Default)\n",
       "#       hmc\n",
       "#         engine = nuts (Default)\n",
       "#           nuts\n",
       "#             max_depth = 10 (Default)\n",
       "#         metric = diag_e (Default)\n",
       "#         metric_file =  (Default)\n",
       "#         stepsize = 1 (Default)\n",
       "#         stepsize_jitter = 0 (Default)\n",
       "# id = 0 (Default)\n",
       "# data\n",
       "#   file = /tmp/stan-59ed7c2ded52e227/stan.data\n",
       "# init = /tmp/stan-59ed7c2ded52e227/stan.init\n",
       "# random\n",
       "#   seed = -1 (Default)\n",
       "# output\n",
       "#   file = /tmp/stan-59ed7c2ded52e227/stan.csv\n",
       "#   diagnostic_file =  (Default)\n",
       "#   refresh = 100 (Default)\n",
       "# Adaptation terminated\n",
       "# Step size = 0.0606685\n",
       "# Diagonal elements of inverse mass matrix:\n",
       "# 0.373408, 0.311495, 0.412781, 0.480178, 0.492721, 0.492969, 0.624931, 0.759556, 0.98318, 0.944732, 0.813175, 1.0754, 0.992736, 1.10151, 0.863845, 1.1199, 1.03045, 0.898382, 0.990462, 0.931562, 1.08195, 0.456203, 0.514514, 0.756294, 0.462145, 0.426067, 0.485763, 0.628156, 0.799072, 0.765683, 1.06579, 1.00344, 0.9537, 0.985086, 0.920023, 0.834636, 1.04615, 0.96495, 0.836129, 0.908569, 0.912248, 0.0825406, 0.0403844\n",
       "# \n",
       "#  Elapsed Time: 15.7447 seconds (Warm-up)\n",
       "#                8.34643 seconds (Sampling)\n",
       "#                24.0911 seconds (Total)\n",
       "# \n",
       "\n",
       "Extracting: x_stan_0_0, x_stan_0_1, x_stan_0_2, x_stan_0_3, x_stan_0_4\n",
       "--- Removing temporary files ---"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "let t = 10\n",
    "    m = 20\n",
    "    nData = 10\n",
    "z0 <- real <$> (normal 0 1 :: IO Double) :: IO R\n",
    "a0 <- fromList <$> sequence [ normal 0 1 | _ <- [1..integer m] ] :: IO RVec\n",
    "b0 <- fromList <$> sequence [ normal 0 1 | _ <- [1..integer m] ] :: IO RVec\n",
    "let eta0 = 1\n",
    "    ils0 = 10 / t\n",
    "samples <- hmcStanInit 1000\n",
    "    [ (z',a',b',eta',ils')\n",
    "    | (z',a',b',eta',ils',xData',yData') <- model t m nData\n",
    "    , xData' == list xData, yData' == list yData\n",
    "    ] (z0,a0,b0,eta0,ils0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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   ],
   "source": [
    "toRenderable $ do\n",
    "  plot $ points \"data\" $ sort $ list xData `zip` list (real <$> yData)\n",
    "  setColors [black `withOpacity` 0.1]\n",
    "  plot $ line \"posterior\" [xTest `zip` fTest | (i,(z,a,b,eta,ils)) <- [0..] `zip` samples\n",
    "                          , i `mod` 100 == 0\n",
    "                          , let sd = normal 0 (ils / (2*pi))\n",
    "                                f = real . (eta *) . gpTrigPoly t m sd z a b . real\n",
    "                                fTest = f <$> xTest :: [Double]\n",
    "                          ]"
   ]
  }
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