SineWavePrediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dfe3cf75-9e09-4349-8017-4b8f8f42b712",
   "metadata": {},
   "source": [
    "# Importing the necessary Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c5d730b2-8941-469b-b339-ff09e3e92390",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "from torch.utils.data import TensorDataset, DataLoader\n",
    "import pandas as panda\n",
    "import math\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "63d9f306-13d3-4428-8be6-8bce3ff7a018",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize hyper parameters\n",
    "input_size = 1 # X-Value\n",
    "output_size = 1 # Y-Value\n",
    "hidden_size = 4\n",
    "\n",
    "# Tells you how many data to look back on. For example, 1 tells the computer to only look at the current/most recent one. While a 2 will look back in the previous one and the current one.\n",
    "sequence_length = 1\n",
    "\n",
    "num_layers = 3\n",
    "learning_rate = 0.1 # high learning rate with the Adagrad optimizer \n",
    "batch_size = 32\n",
    "num_epochs = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba8d1014-361f-46ce-a7e0-cff31ff3067b",
   "metadata": {},
   "source": [
    "# Generating the Sine Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c0571158-9bde-4027-a645-e7e42764ccc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# using linspace I was able to generate about 998 numbers in between 0 and 2pi.\n",
    "xValues = np.linspace(0, 2*math.pi, 1000)\n",
    "# taking the generated x-values I then ran them through the sine function to get a y-value\n",
    "yValues = np.sin(xValues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "359f72d4-c3a3-461f-bee1-56ffb59b3579",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Sine Wave')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualizes the real sine wave\n",
    "plt.plot(xValues,yValues)\n",
    "plt.title('Sine Wave')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11516858-9481-4a59-a95c-c63a0c34cd7e",
   "metadata": {},
   "source": [
    "Combine the Xs and Ys into one dataframe. Mainly because the dataframe is easy to understand. \n",
    "Convert said dataframe into a numpy array\n",
    "Use such numpy array to make into tensor array\n",
    "Then use the tensor to a dataloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ffbdd7bf-2660-4cd4-bba9-c50ad539b6e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<torch.utils.data.dataset.TensorDataset object at 0x30bac0090>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n# split the datasets\\n# xTr, xTe = xValues[:640], xValues[640:]\\n# yTr, yTe = yValues[:640], yValues[640:]\\n# convert the numpy arrays into tensor for better performance\\n# xTrainData = torch.from_numpy(xTr)\\n# xTestData = torch.from_numpy(xTe)\\n# yTrainData = torch.from_numpy(yTr)\\n# yTestData = torch.from_numpy(yTe)\\n'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Combine the X and Y values into a dataframe mainly for combination of x and y simplicity\n",
    "SineDF = panda.DataFrame(data = {'X-Values': xValues, 'Y-Values': yValues})\n",
    "# Use the Dataframe to change to tensor array\n",
    "SineNPArray = np.expand_dims(SineDF.to_numpy(), axis=1)\n",
    "\n",
    "xTensor = torch.from_numpy(SineNPArray[:, 0, :1]).float()\n",
    "yTensor = torch.from_numpy(SineNPArray[:, 0, 1:]).float()\n",
    "\n",
    "# Now to Dataset/Dataloader\n",
    "dataset = TensorDataset(xTensor, yTensor)\n",
    "dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)\n",
    "print(dataset)\n",
    "\n",
    "\"\"\"\n",
    "# split the datasets\n",
    "# xTr, xTe = xValues[:640], xValues[640:]\n",
    "# yTr, yTe = yValues[:640], yValues[640:]\n",
    "# convert the numpy arrays into tensor for better performance\n",
    "# xTrainData = torch.from_numpy(xTr)\n",
    "# xTestData = torch.from_numpy(xTe)\n",
    "# yTrainData = torch.from_numpy(yTr)\n",
    "# yTestData = torch.from_numpy(yTe)\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "499d49e5-0f51-4ed8-bc11-76dc89c908d8",
   "metadata": {},
   "source": [
    "# Creating the RNN Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b46c8d54-1540-4315-bb25-484286d88913",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SineRNN(nn.Module):\n",
    "    def __init__(self, input_size, hidden_size, output_size, num_layers):\n",
    "        super(SineRNN, self).__init__() \n",
    "        \n",
    "        self.hidden_size = hidden_size # initialize the hidden size\n",
    "       \n",
    "        self.num_layers = num_layers # initialize the number of layers\n",
    "       \n",
    "        self.rnn = nn.RNN(input_size = input_size, hidden_size=hidden_size, num_layers = num_layers, batch_first = True) \n",
    "        # The layer above uses Pytorch's RNN and passes in the proper parameters\n",
    "        \n",
    "        self.fc = nn.Linear(hidden_size, output_size)\n",
    "        # This is the fully connected layer with a linear transformation \n",
    "   \n",
    "    def forward(self, x): # In this method the input is fed into the model which is then used to create an output\n",
    "        # I need clarification in this part of the model, got no idea how these lines below accomplish the purpose of the forward method\n",
    "        h0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size)\n",
    "        out, _ = self.rnn(x, h0)\n",
    "        out = self.fc(out[:, -1, :])\n",
    "        return out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1d33468-b678-4ee4-81aa-bbd6d6410b86",
   "metadata": {},
   "source": [
    "# Train the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "085c1d50-9339-44d6-a2cb-0d6eac01fe02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "Epoch [10/1000], Loss: 0.07696\n",
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      "Epoch [20/1000], Loss: 0.03972\n",
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      "Epoch [40/1000], Loss: 0.07973\n",
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      "Epoch [50/1000], Loss: 0.05763\n",
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      "Epoch [60/1000], Loss: 0.08589\n",
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      "Epoch [70/1000], Loss: 0.02987\n",
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      "Epoch [80/1000], Loss: 0.07986\n",
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      "Epoch [90/1000], Loss: 0.01525\n",
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      "Epoch [110/1000], Loss: 0.00168\n",
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      "Epoch [130/1000], Loss: 0.00024\n",
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      "Epoch [140/1000], Loss: 0.00019\n",
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      "Epoch [160/1000], Loss: 0.00021\n",
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      "Epoch [170/1000], Loss: 0.00043\n",
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      "Epoch [200/1000], Loss: 0.00014\n",
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      "Epoch [210/1000], Loss: 0.00147\n",
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      "Epoch [230/1000], Loss: 0.00007\n",
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      "Epoch [240/1000], Loss: 0.00019\n",
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      "Epoch [260/1000], Loss: 0.00014\n",
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      "Epoch [270/1000], Loss: 0.00020\n",
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      "Epoch [290/1000], Loss: 0.00011\n",
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      "Epoch [300/1000], Loss: 0.00011\n",
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      "Epoch [320/1000], Loss: 0.00016\n",
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      "Epoch [330/1000], Loss: 0.00011\n",
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      "Epoch [360/1000], Loss: 0.00043\n",
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      "Epoch [390/1000], Loss: 0.00007\n",
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      "Epoch [400/1000], Loss: 0.00013\n",
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      "Epoch [420/1000], Loss: 0.00008\n",
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      "Epoch [430/1000], Loss: 0.00011\n",
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      "Epoch [450/1000], Loss: 0.00013\n",
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      "Epoch [460/1000], Loss: 0.00008\n",
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      "Epoch [480/1000], Loss: 0.00002\n",
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      "Epoch [490/1000], Loss: 0.00011\n",
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      "Epoch [510/1000], Loss: 0.00008\n",
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      "Epoch [520/1000], Loss: 0.00010\n",
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      "Epoch [530/1000], Loss: 0.00007\n",
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      "Epoch [550/1000], Loss: 0.00007\n",
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      "Epoch [580/1000], Loss: 0.00006\n",
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      "Epoch [590/1000], Loss: 0.00013\n",
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      "Epoch [610/1000], Loss: 0.00009\n",
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      "Epoch [620/1000], Loss: 0.00008\n",
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      "Epoch [630/1000], Loss: 0.00002\n",
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      "Epoch [640/1000], Loss: 0.00005\n",
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      "Epoch [650/1000], Loss: 0.00007\n",
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      "Epoch [670/1000], Loss: 0.00004\n",
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      "Epoch [680/1000], Loss: 0.00010\n",
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      "Epoch [690/1000], Loss: 0.00017\n",
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      "Epoch [700/1000], Loss: 0.00025\n",
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      "Epoch [710/1000], Loss: 0.00040\n",
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      "Epoch [740/1000], Loss: 0.00008\n",
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      "Epoch [770/1000], Loss: 0.00003\n",
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      "Epoch [800/1000], Loss: 0.00005\n",
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      "Epoch [810/1000], Loss: 0.00004\n",
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      "Epoch [830/1000], Loss: 0.00008\n",
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      "Epoch [840/1000], Loss: 0.00008\n",
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      "Epoch [850/1000], Loss: 0.00017\n",
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      "Epoch [860/1000], Loss: 0.00004\n",
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      "Epoch [870/1000], Loss: 0.00009\n",
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      "Epoch [900/1000], Loss: 0.00005\n",
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      "Epoch [910/1000], Loss: 0.00004\n",
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      "Epoch [920/1000], Loss: 0.00005\n",
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      "Epoch [930/1000], Loss: 0.00008\n",
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      "Epoch [940/1000], Loss: 0.00004\n",
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      "Epoch [950/1000], Loss: 0.00005\n",
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      "Epoch [960/1000], Loss: 0.00005\n",
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      "Epoch [970/1000], Loss: 0.00003\n",
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      "Epoch [980/1000], Loss: 0.00006\n",
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      "Epoch [990/1000], Loss: 0.00007\n",
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      "Epoch [1000/1000], Loss: 0.00004\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = SineRNN(input_size, hidden_size, output_size, num_layers) # defines the model and inserts the proper parameters \n",
    "criterion = nn.MSELoss() # helps calculate the loss\n",
    "optimizer = torch.optim.Adagrad(model.parameters(), lr=learning_rate) # I chose Adagrad as I am most familiar\n",
    "losses = [] # The loss array for the graph\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    epoch_loss = 0.0 # start loss value for each batch\n",
    "    model.train(True)\n",
    "\n",
    "    for inputs, targets in dataloader:\n",
    "        print(index)\n",
    "        optimizer.zero_grad() # clears the gradient\n",
    "        outputs = model(inputs.unsqueeze(1))\n",
    "        loss = criterion(outputs, targets)\n",
    "        \n",
    "        loss.backward() # applies backpropogation\n",
    "        optimizer.step() # updates model parameters\n",
    "        \n",
    "        epoch_loss += loss.item() # calculates total loss\n",
    "        \n",
    "    losses.append(epoch_loss)\n",
    "\n",
    "    if (epoch + 1) % 10 == 0: ## Only prints the tench epoch\n",
    "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.5f}')\n",
    "    \n",
    "plt.figure()\n",
    "plt.plot(range(num_epochs), losses)\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Training Loss over Epochs')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "642390c1-76a6-437a-9c31-e5d650d5930a",
   "metadata": {},
   "source": [
    "# Model Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "43767eff-7b37-4da0-9321-cdf7415b6d65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    model.eval()\n",
    "    predictions = model(xTensor.unsqueeze(1))\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(xValues, yValues, linewidth = '5', label='Actual Sine Wave')\n",
    "plt.plot(xValues, predictions.numpy(), linewidth = '5', linestyle = ':', label='Model Predictions')\n",
    "plt.xlabel('x - axis')\n",
    "plt.ylabel('y - axis')\n",
    "plt.title('Sine Wave and The Model Predictions')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}