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      "source": [
        "# For tips on running notebooks in Google Colab, see\n# https://pytorch.org/tutorials/beginner/colab\n%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "Warm-up: numpy\n==============\n\nA third order polynomial, trained to predict $y=\\sin(x)$ from $-\\pi$ to\n$pi$ by minimizing squared Euclidean distance.\n\nThis implementation uses numpy to manually compute the forward pass,\nloss, and backward pass.\n\nA numpy array is a generic n-dimensional array; it does not know\nanything about deep learning or gradients or computational graphs, and\nis just a way to perform generic numeric computations.\n"
      ]
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\nimport math\n\n# Create random input and output data\nx = np.linspace(-math.pi, math.pi, 2000)\ny = np.sin(x)\n\n# Randomly initialize weights\na = np.random.randn()\nb = np.random.randn()\nc = np.random.randn()\nd = np.random.randn()\n\nlearning_rate = 1e-6\nfor t in range(2000):\n    # Forward pass: compute predicted y\n    # y = a + b x + c x^2 + d x^3\n    y_pred = a + b * x + c * x ** 2 + d * x ** 3\n\n    # Compute and print loss\n    loss = np.square(y_pred - y).sum()\n    if t % 100 == 99:\n        print(t, loss)\n\n    # Backprop to compute gradients of a, b, c, d with respect to loss\n    grad_y_pred = 2.0 * (y_pred - y)\n    grad_a = grad_y_pred.sum()\n    grad_b = (grad_y_pred * x).sum()\n    grad_c = (grad_y_pred * x ** 2).sum()\n    grad_d = (grad_y_pred * x ** 3).sum()\n\n    # Update weights\n    a -= learning_rate * grad_a\n    b -= learning_rate * grad_b\n    c -= learning_rate * grad_c\n    d -= learning_rate * grad_d\n\nprint(f'Result: y = {a} + {b} x + {c} x^2 + {d} x^3')"
      ]
    }
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