Lecture1_Into2Pytorch.ipynb

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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/eldadHaber/CompGeo2023/blob/main/Lecture1_Into2Pytorch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "cZPKeGIOoRpw"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Arrays/Tensors and indexing\n",
        "a0 = torch.tensor([])\n",
        "a1 = torch.zeros(5)\n",
        "a2 = torch.zeros(5, 6)\n",
        "a3 = torch.zeros(4, 5, 6)\n",
        "\n",
        "print(a0.shape, a1.shape, a2.shape, a3.shape)\n"
      ],
      "metadata": {
        "colab": {
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        },
        "id": "0bflhuarosJ_",
        "outputId": "038b66d0-dc90-4c4b-ce7a-7b56c6904110"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([0]) torch.Size([5]) torch.Size([5, 6]) torch.Size([4, 5, 6])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Special tensors\n",
        "ZeroTen = torch.zeros(2,3,4,5)\n",
        "OneTen  = torch.ones(2,1,4,5)\n",
        "RandTen = torch.randn(2,1,4,5)  # or rand\n",
        "\n",
        "# Initializing tensor with some numbers\n",
        "A = torch.tensor([[1.0,2,3],[4,5,6]])\n",
        "print(A)\n",
        "print(A.shape)"
      ],
      "metadata": {
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        },
        "id": "U4IwBQnVpI1-",
        "outputId": "ba75ad82-508b-477d-9c57-9b72cf8a982d"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[1., 2., 3.],\n",
            "        [4., 5., 6.]])\n",
            "torch.Size([2, 3])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# changing/adding dimension\n",
        "A = A.unsqueeze(0)\n",
        "print(A.shape)\n",
        "A = A.squeeze(0)\n",
        "print(A.shape)\n",
        "A = A.unsqueeze(-1)\n",
        "print(A.shape)\n",
        "\n",
        "# Stacking tensors and repeating them\n",
        "A = torch.repeat_interleave(A, 5, dim=-1)\n",
        "print('shape of A after stacking', A.shape)\n"
      ],
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        "id": "8JsqjqH6p2F4",
        "outputId": "a21d7f95-baa6-4e30-d9f5-3b9faadeaac8"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([1, 2, 3])\n",
            "torch.Size([2, 3])\n",
            "torch.Size([2, 3, 1])\n",
            "shape of A after stacking torch.Size([2, 3, 5])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Access the tensor\n",
        "print(A[1,2,4])\n",
        "\n",
        "print(A[0,0,:])  # the full last dim\n",
        "print(A[0,:,0])  # the full first dim\n",
        "print(A[:,0,0])  # the full zero's dim\n",
        "\n"
      ],
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        "id": "TjD11D6UrZuo",
        "outputId": "26e89f88-03ad-4a3c-c4f0-1070aa676056"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(6.)\n",
            "tensor([1., 1., 1., 1., 1.])\n",
            "tensor([1., 2., 3.])\n",
            "tensor([1., 4.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Class activity\n",
        "\n",
        "Generate a 4D tensor of size 5,10,15,20\n",
        "where for every i, j, k we have that\n",
        "A[i, :, j, k] = [0, 1,2,3,4,5,6,7,8,9]"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "code",
      "source": [
        "# More tensor operations\n",
        "n = A.numel() # Number of elements\n",
        "a = A.mean()  # same as A.sum()/A.numel()\n",
        "a0 = A.mean(dim=0)\n",
        "a1 = A.mean(dim=1)\n",
        "\n",
        "avec = A.flatten() # or A.view(-1)\n",
        "print(A)\n",
        "print(avec)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cGQOkJJcqbY5",
        "outputId": "a477905b-da0a-4746-d165-932ef4aebe54"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[[1., 1., 1., 1., 1.],\n",
            "         [2., 2., 2., 2., 2.],\n",
            "         [3., 3., 3., 3., 3.]],\n",
            "\n",
            "        [[4., 4., 4., 4., 4.],\n",
            "         [5., 5., 5., 5., 5.],\n",
            "         [6., 6., 6., 6., 6.]]])\n",
            "tensor([1., 1., 1., 1., 1., 2., 2., 2., 2., 2., 3., 3., 3., 3., 3., 4., 4., 4.,\n",
            "        4., 4., 5., 5., 5., 5., 5., 6., 6., 6., 6., 6.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Accesing parts of the array\n",
        "print('A = ', A)\n",
        "A1 = A[1:, :, :] # or  A[1:, None, None]\n",
        "print('A1 = ', A1)\n",
        "A2 = A[:-1, :, :] # \n",
        "print('A2 = ', A2)\n",
        "\n",
        "A3 = A[:, :, [1,3]]\n",
        "print('A3 = ', A3)"
      ],
      "metadata": {
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        "id": "2LcDUC0Uso2i",
        "outputId": "e233cee8-f369-4627-a60b-c4fde6515fc1"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A =  tensor([[[1., 1., 1., 1., 1.],\n",
            "         [2., 2., 2., 2., 2.],\n",
            "         [3., 3., 3., 3., 3.]],\n",
            "\n",
            "        [[4., 4., 4., 4., 4.],\n",
            "         [5., 5., 5., 5., 5.],\n",
            "         [6., 6., 6., 6., 6.]]])\n",
            "A1 =  tensor([[[4., 4., 4., 4., 4.],\n",
            "         [5., 5., 5., 5., 5.],\n",
            "         [6., 6., 6., 6., 6.]]])\n",
            "A2 =  tensor([[[1., 1., 1., 1., 1.],\n",
            "         [2., 2., 2., 2., 2.],\n",
            "         [3., 3., 3., 3., 3.]]])\n",
            "A3 =  tensor([[[1., 1.],\n",
            "         [2., 2.],\n",
            "         [3., 3.]],\n",
            "\n",
            "        [[4., 4.],\n",
            "         [5., 5.],\n",
            "         [6., 6.]]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Logical operations\n",
        "A = torch.randn(4,5)\n",
        "T = A>0\n",
        "print(T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pQIloftqtK6q",
        "outputId": "191e23f9-8c0a-4e10-e4fc-01001637b018"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ True,  True,  True,  True,  True],\n",
            "        [False,  True, False, False,  True],\n",
            "        [ True, False,  True,  True,  True],\n",
            "        [ True,  True,  True, False, False]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Indexing with logical operations\n",
        "a = torch.arange(7,7+12)\n",
        "print(a)\n",
        "A = torch.reshape(a, [3, 4])\n",
        "print(A)\n",
        "\n",
        "T = A>12\n",
        "print(T)\n",
        "\n",
        "B = A[T]\n",
        "D = T*A\n",
        "print(B)\n",
        "print(D)"
      ],
      "metadata": {
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        },
        "id": "_lwKL5QztqGu",
        "outputId": "efb68e31-6c78-43ac-a60f-0c212bf12d4f"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([ 7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18])\n",
            "tensor([[ 7,  8,  9, 10],\n",
            "        [11, 12, 13, 14],\n",
            "        [15, 16, 17, 18]])\n",
            "tensor([[False, False, False, False],\n",
            "        [False, False,  True,  True],\n",
            "        [ True,  True,  True,  True]])\n",
            "tensor([13, 14, 15, 16, 17, 18])\n",
            "tensor([[ 0,  0,  0,  0],\n",
            "        [ 0,  0, 13, 14],\n",
            "        [15, 16, 17, 18]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Class activity\n",
        "\n",
        "Generate a random tensor $A$ os size $10 \\times 11 \\times 12$.\n",
        "Find the location of all the entries that are bigger than $0$.\n",
        "Return a tensor with $0$ on these locations\n",
        "and the origianl number otherwise"
      ],
      "metadata": {
        "id": "vrHbV2lK7D-w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# More special arrays\n",
        "x = torch.arange(4)\n",
        "print('x = ', x)\n",
        "y = torch.arange(5)\n",
        "print('y = ', y)\n",
        "\n",
        "[X, Y] = torch.meshgrid(x,y)\n",
        "print('X = ',X)\n",
        "print('Y = ',Y)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s04NRxlHuc4t",
        "outputId": "62826b5f-49c4-46ce-e90a-f5e76bd07e9b"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x =  tensor([0, 1, 2, 3])\n",
            "y =  tensor([0, 1, 2, 3, 4])\n",
            "X =  tensor([[0, 0, 0, 0, 0],\n",
            "        [1, 1, 1, 1, 1],\n",
            "        [2, 2, 2, 2, 2],\n",
            "        [3, 3, 3, 3, 3]])\n",
            "Y =  tensor([[0, 1, 2, 3, 4],\n",
            "        [0, 1, 2, 3, 4],\n",
            "        [0, 1, 2, 3, 4],\n",
            "        [0, 1, 2, 3, 4]])\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/torch/functional.py:504: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at ../aten/src/ATen/native/TensorShape.cpp:3190.)\n",
            "  return _VF.meshgrid(tensors, **kwargs)  # type: ignore[attr-defined]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Array operation\n",
        "Z = X*Y         # Pointwise multiplication\n",
        "Z = (X**2)*Y\n",
        "Z = torch.sin(X)*torch.cos(Y)\n",
        "Z = torch.abs(X)"
      ],
      "metadata": {
        "id": "R_mkp_gkvZXA"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Example - generating the matlab function\n",
        "x = torch.arange(57)\n",
        "y = torch.arange(58)\n",
        "# Make them from -3,3\n",
        "x = 6*((x/x.max())-0.5)\n",
        "y = 6*((y/y.max())-0.5)\n",
        "\n",
        "[X, Y] = torch.meshgrid(x,y)\n",
        "\n",
        "Z =  3*(1-X)**2 * torch.exp(-(X**2) - (Y+1)**2) \\\n",
        "  - 10*(X/5 - X**3 - Y**5)*torch.exp(-X**2-Y**2) \\\n",
        "   - 1/3*torch.exp(-(X+1)**2 - Y**2)\n",
        "\n",
        "plt.imshow(Z)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "Bw0MGdfTvvjs",
        "outputId": "4c14865c-42de-414a-b0d2-f1a20ef25830"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
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              "<Figure size 432x288 with 1 Axes>"
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            "image/png": 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GodZF1+ocNH0JvfmFqBR1fiEqRZ1fiEpZLz9/ZluutBeQhuAmcwK9sRA1Dt+9Fms1vxprPb8Wt0G63nphmeeY7galb+Jw3iOUEozaHpTR6lF67b2kRHde8yfLdPvB8aTxc5oeOGiJdbC9UK6LHx6n+k7snCGmgGmR2G7b5Pdfl7a16Itxm5dU59Kocbn1poRzAoedHtCbX4hKUecXolLU+YWolLVK3Z2lFPpcSvsVBMLbgDZyu0dzANdif67T/hbk7m5RrHjrSOxH7uzEubs3dije/hVK+9UNyjzTuZM0393C3/LkHgW++SaaHvm1FvwsUp91vhw1t4fB0uQ+1ffuU07xntO8CL3fet6n9viLtsiuHtXV7iXnovkcsm2Qcdb7jI78GacMAOjNL0S1qPMLUSnFzm9mW2b2BTP7ipk9aWa/Ofr8rWb2qJk9Y2afMbON0rmEEOvDNJp/F8Cd7v6KmXUB/IuZ/S2AXwbwCXe/z8z+EMDdAD65QFsXBy+M51TdPCcwjNseho/TfAHHELSvUS6B3fgRdF6d7PcP9f/+hamMNqXATv6059KmNdD0B21P9o82Upvs4vkFLlcdzm2EJbCAtIz2VcqnwO0rw3j+po1xm2MArpDm53Nd8y5tj99/4XwE282xC0n+hDnGNkyi+Ob3fa5nMeiO/jmAOwH85ejz8wDuWoiFQoiFMJXmN7O2mT0O4BKAhwD8O4DL7q9NnT4H4OSEY+8xswtmdmFwdWceNgsh5sBUnd/dB+7+DgCnANwB4AenvYC7n3P30+5+un10+5BmCiHmTSM/v7tfNrNHAPwogGNm1hm9/U8BeH4RBr5GwS2apDrmktKtcFE4l0PmdnywtVmvcdrlMK6dxRzFsfcpPpxLiVPuwTAtHJf39kTT000o/WlvkCo9N19w4LWjnQsluxk6lwd+/h6lI+cSWVxW+/IwTqd98zBepzFMipMH5xrG5+ZzXR7E7VcGNN/QHz8wLt/NuRXSHImFOYBl+PnN7M1mdmz08xEA7wXwFIBHAHxwtNsZAPfPbo4QYllM8+Y/AeC8mbWx/8fis+7+oJl9HcB9ZvZbAL4M4FMLtFMIMWeKnd/dvwrgnQd8/k3s6//DkxvKl0ZBNGbhFNnRMB/AMNjuXRrGU2ot24zH1y1y9fkeXTyUEXSuRGIUSqgayQYLhoNJ1SJeCsuVXrNXysP3m61OJEfuaoVnWZR0wQF7lH78aj++31w151L/e6J2l1JxXfNMld5hXKX3hf4tUfvF3s3x/r1Ycrwa2MZ2F1OlJzIrcxMP+aAV4SdEpajzC1Ep6vxCVMr6LukthISy5qSVnRh2SPMHZbK4JJYdiTW+9WOtZ6zTWdcH6Z5si8p1bcXnHm7QfENhriK8D8m8R0k78z3LaOukkG7JO9fE9ZS4YfMVf3PrVYfkMgvdaQDwcj/W3Zd6seZnrrSOTNz2Mml+1vj/tRe3X9qL99/pjW3b69PyX3b1JeHVhTmAsLQdCFXpFULkUOcXolLU+YWolOVrfpvwM7Ub+/VJNw7Y3b45PkFrizT/gONmydfeof2pZHeo0zlmYLgdzwEM6NpJuS4yJYwwTUKWO7GdtLo12Z745nPCsanvOHhgpRRTzqWpyE7wHEAAp8a6xn7+vdjPv9nitF3xTXypNXm9CS/R/fZeXJL7xb342O+S5r+6F/j5uRxaP6/5kaShI+OUxksIcVjU+YWoFHV+ISplpX7+rJ+6oV/f6JtwyqtwtWWL4qwTyNfeopJboFJgoa3DpDxX3O7dRKm6WfNvTp4DGG6Qxqd5Dd7uXV4MAGpnNH9RuE/2QyfltUppqlnjZ/z+7OffpfRYL+/Ffv4OiWVO+9XN5B/j5cLfpdh91vgvX4u3Xws0/6DPmj+fvrzk54/a04dJROjNL0SlqPMLUSnq/EJUynI1vyHWlklA+YSfcZCfP24nGj+zLp5Plpy7Q6WZeS0Ap/YO5ggSO7gk91Fu8/6xLeFcBccADLZioeik+bFB6cY6nH7MD/wZKJd9TiRocH+TtencLmBtsjM8FZ1rt0epu1v58hG8FqDTGjvUhxxDQJr/ai8+dmcvbl/djfff2xvbNiQ/P8jPz+XSSnMAUUvr+YUQTVDnF6JS1PmFqJTVrudvENuf+P05zp0rbpFGGgQ7OK3Pd8qzx2WvWqzHMnMVgyS+YHL5LQDok+an5egYbAU+7i2aayCNb1txQHhrI263SUuHbd5mBWcxl5gO7zevVed8dayt04SB9L2CNl+Xy2Dt7MW6m1N9X21R6vTg3Jxem9s8v8DtUOMDwGA3sK1Hmj0piZ5vJ2XMwxCNBjEAIXrzC1Ep6vxCVMrSh/3hqC1ZRRpuK1SYTVx9PLyh0Nfwam6TXXVA6q4zCudNUlyF4b2UPozdc8mwn117NLQPQ3aH5LpjVx4P87tdbsfLW7vt8fY2ufpahWE/D90HwbC/T0PxPg37E1lQqlYTHcvbuJpSXhYkajL4nrxcmO3sU4guh+wOOKV70LbCEt5S1ePDpurKoTe/EJWizi9EpajzC1Ep65W6O1eBqPRnipf0ZnZljc8pwIacQqmwJDXcnKYMj/elIrLJ9uwyXUp31ermXXms8Tc78f6dQPN3My6wg2DNH7rUOPt4GXYN0vOJSlPRnAk9aJ4T2C8xOZnIRZy4L8kucs8lqbjYfRdup22UXSx17RVSo9uU7rwcevMLUSnq/EJUytSd38zaZvZlM3tw1H6rmT1qZs+Y2WfMLL+cSgixVjTR/B8F8BSA6/WPfhvAJ9z9PjP7QwB3A/hkk4uXykDnNiZpqFn38BxAJoaA04A3TZMc2pLEHzTR9ACcQoujtNY0N8Hfo1VYlsshu+2g3W6o+XkeJJwDGFg+ZqBQpTzx1YftNEUYtQcljZ/R1nzdJJ12fqlysiw32J81frLMmf36TcqhMfNM42VmpwD8NIA/GrUNwJ0A/nK0y3kAdzUwTwixYqYd9v8ugF/F+O/TGwFcdvfrf8+eA3DyoAPN7B4zu2BmFwY7OzMZK4SYH8XOb2Y/A+CSuz92mAu4+zl3P+3up9vbk6ujCCGWyzSa/10AftbM3g9gC/ua//cAHDOzzujtfwrA87Mak437pz9TrMtZa7OGyq0bKGn8JJY/s9yYU4qn6cYopqCwf7a8WYFENrKmDX4eDHkCgVKEZTQ+EMfFl/blWH5uJ8eHWpv3LaW4Znh7lN6N9y0ss01KavH+mWMbavzDLtvNUXzzu/vH3f2Uu98O4MMA/tHdfw7AIwA+ONrtDID7D2eCEGIVzOLn/xiAXzazZ7A/B/Cp+ZgkhFgGjcJ73f2fAPzT6OdvArhj/iYJIZbBCkp0h3WdGojYpn5+JtxeOldTQtnIGp/jDfiOc8xB7pbw3EMhrr1F6cn6iXAcG8N+fuM5ADYlWTc/3r/5ev5CbH/YLvjai2nCM9o5KZFVKqFVWoMf7j9PjT8nFN4rRKWo8wtRKSvO3jvZh1ZI6Fp0eyWuwVwV2eTgwvacbEiqC/N4jrYXvmdkK7u5ePicX2GaDNX7w/FYlENwmy7pjcJ7k/RXPKyPZUGyVHaQ+SIF115paJ5z5xVdvsn26cPC5z7MVxovIcRhUecXolLU+YWolDVL4zXZDVjyCpachtHxs+qlZK1scGrW+PzntWgo7R5Wv6VwUq48NKSLJVWM2OUWpP3i5b7lZbd07sBOdt3x0ljW9J5ZCrt/wlCXFzQ9h9g2Cd0uhfeWzoXM9jXQ+Ize/EJUijq/EJWizi9EpayX5g8prqPNb26SEmxWQp3fJGIZOED78VLkQP+yDvdE41MKMI4LoNTeURgt37+Gmj+6VhKP0CwdVhIKm1nSWypzVdTxWc1P50Z+e1HX545tuj1DIUTjNfTmF6JS1PmFqBR1fiEqZX01P1MSMg3jAhZmS0M/fjatFOLy4I6MXsUBaxbYv85lysKYhFnvVy4dVtOlspny1eX4+4Zlr5ChoS++ke9+jn77aTU+oze/EJWizi9EpajzC1EpN47mL9FwTmCe557rqZPa4plFCXxhPjZZV5DR/LnLHkQuHVbJrqbx95Hmn1HTN9DhRS29gBJa03JYnR+iN78QlaLOL0SlqPMLUSmvH81fYh4iaR6UfMX8wTCzdci5AwoLHJJ2GNs/4/0Jc+GVdPgsvvoZ4+2ZmeLvZ92/AYv49dWbX4hKUecXolLqGfbPkSZVdZik+nDhWtH+A96Yd5kldmZTdeXDoxsNO5ssoz1wf7p2g32ZdXbXhaxClerNL0SlqPMLUSlTDfvN7FkAV7A/8Oy7+2kzuxXAZwDcDuBZAB9y95cWY6YQYt400fw/7u4vBu2zAB5293vN7Oyo/bG5Wvd6pKGrKpTLTVNrJbvnTtAkDdqBF59+W/HcDXT9jaLpmXXwPM8y7P8AgPOjn88DuGt2c4QQy2Lazu8APm9mj5nZPaPPjrv7xdHPLwA4ftCBZnaPmV0wswuDnZ0ZzRVCzItph/3vdvfnzewtAB4ys38NN7q7G5d8GW87B+AcAGydvG0NBjtCCGDKzu/uz4/+v2RmnwNwB4BvmdkJd79oZicAXFqgnWtFo6zipdLiDeICkl1ZSzddhjvPEma56zTcPlNMwbz3n4F10PU5isN+M9s2s5uv/wzgJwE8AeABAGdGu50BcP+ijBRCzJ9p3vzHAXzO9l8rHQB/5u5/Z2ZfBPBZM7sbwH8A+NDizBRCzJti53f3bwL4oQM+/zaA9yzCKCHE4lFs/7JpFMwf759oyIbzB8ncxJI0aWPtu6a+eWbdNX0JhfcKUSnq/EJUijq/EJUizT8HQu03c5mwnI6cUbMX5wzmxby18Iq09Y2u6UvozS9EpajzC1Ep6vxCVIo0/5xpFPfflKYatGms/6JYI+38etfxTdCbX4hKUecXolI07F8wiyweXKTCIa6G9dOjN78QlaLOL0SlqPMLUSnS/CumiUZd6PzAGiMdvxj05heiUtT5hagUdX4hKsWcazwt8mJm/4X9ZJ9vAvBiYfdVILuaIbuasQq7vt/d33zQhqV2/tcuanbB3U8v/cIFZFczZFcz1s0uDfuFqBR1fiEqZVWd/9yKrltCdjVDdjVjrexaieYXQqweDfuFqBR1fiEqZamd38zeZ2bfMLNnzOzsMq99gC2fNrNLZvZE8NmtZvaQmT09+v8NS7bpNjN7xMy+bmZPmtlH18GukQ1bZvYFM/vKyLbfHH3+VjN7dPRMP2NmG8u2bWRH28y+bGYProtdZvasmX3NzB43swujz1b+LK+ztM5vZm0AfwDgpwC8HcBHzOzty7r+AfwxgPfRZ2cBPOzubwPw8Ki9TPoAfsXd3w7gRwD84ugerdouANgFcKe7/xCAdwB4n5n9CIDfBvAJd/8BAC8BuHsFtgHARwE8FbTXxa4fd/d3BP79dXiW+7j7Uv4B+FEAfx+0Pw7g48u6/gSbbgfwRND+BoATo59PAPjGiu27H8B719CuowC+BOCHsR+x1jnoGS/RnlPY70h3AngQ+6lL18GuZwG8iT5bm2e5zGH/SQD/GbSfG322Thx394ujn18AcHxVhpjZ7QDeCeBRrIldo6H14wAuAXgIwL8DuOzu/dEuq3qmvwvgVwEMR+03roldDuDzZvaYmd0z+mwtniWg9fwTcXc3W81KcjO7CcBfAfgld3/ZbLyQf5V2ufsAwDvM7BiAzwH4wVXYEWJmPwPgkrs/ZmY/tmp7iHe7+/Nm9hYAD5nZv4YbV/ksgeVO+D0P4LagfWr02TrxLTM7AQCj/y8t2wAz62K/4/+pu//1utgV4u6XATyC/eH0MTO7/hJZxTN9F4CfNbNnAdyH/aH/762BXXD350f/X8L+H8s7sEbPcpmd/4sA3jaahd0A8GEADyzx+tPwAIAzo5/PYF9zLw3bf8V/CsBT7v4762LXyLY3j974MLMj2J+LeAr7fwQ+uCrb3P3j7n7K3W/H/u/UP7r7z63aLjPbNrObr/8M4CcBPIE1eJavseQJkPcD+Dfsa8VfX9VEx8iWPwdwEUAP+5rwbuxrxYcBPA3gHwDcumSb3o19nfhVAI+P/r1/1XaNbPtfAL48su0JAL8x+vx/APgCgGcA/AWAzRU+0x8D8OA62DW6/ldG/568/ntZ7MAAAAA0SURBVPu+Ds/y+j+F9wpRKYrwE6JS1PmFqBR1fiEqRZ1fiEpR5xeiUtT5hagUdX4hKuW/AVNnppYFg6Y3AAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# More plotting\n",
        "x = torch.linspace(0,2*np.pi, 257)\n",
        "u = x*torch.sin(5*x)\n",
        "v = x*torch.cos(5*x)\n",
        "\n",
        "plt.plot(u,v)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "rH0iTXBhw1Cb",
        "outputId": "565ef5cb-4a24-4e66-d14a-fc3a2267072c"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1b95f02d30>]"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# loops\n",
        "A = torch.rand(6,2,3)\n",
        "for i in range(5):\n",
        "  A[i+1, :, :] = A[i, :, :]*A[i+1, :, :]\n",
        "\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hPtkSfPuz8TA",
        "outputId": "797eb40e-55f1-4d82-d348-950993b43824"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[[2.8667e-01, 6.0383e-02, 7.1158e-01],\n",
            "         [8.0774e-01, 3.1776e-01, 5.8678e-01]],\n",
            "\n",
            "        [[2.5516e-01, 5.4448e-02, 1.5260e-01],\n",
            "         [5.9220e-01, 3.2916e-02, 1.7659e-03]],\n",
            "\n",
            "        [[2.2774e-01, 3.6538e-02, 3.9769e-02],\n",
            "         [1.5841e-01, 3.2358e-02, 1.7536e-03]],\n",
            "\n",
            "        [[4.0127e-02, 2.0139e-02, 9.4770e-03],\n",
            "         [1.5391e-01, 2.2338e-03, 1.7293e-03]],\n",
            "\n",
            "        [[2.6628e-02, 1.1533e-02, 6.6209e-03],\n",
            "         [8.6008e-02, 2.1392e-03, 9.7965e-04]],\n",
            "\n",
            "        [[2.1596e-02, 1.0270e-02, 1.0460e-03],\n",
            "         [3.2519e-02, 3.4537e-04, 2.5921e-04]]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# loops\n",
        "A = torch.rand(8,2,3)\n",
        "n = A.shape[0]\n",
        "# Allocate memory for p\n",
        "p = torch.zeros(n)\n",
        "for i in range(n):\n",
        "  p[i] = (A[i, :, :]**i).mean()\n",
        "\n",
        "print(p)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aSRTr3PK0kA2",
        "outputId": "db4c7c66-875f-4663-9940-fb0cb9a14151"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([1.0000, 0.5294, 0.2071, 0.5079, 0.0814, 0.0561, 0.1372, 0.0730])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Homework\n",
        "\n",
        "1. Generate a random (pos and neg) tensor, $A$, of size $100 \\times 100$. Find all its entries that are bigger than $m = 0.5$. What is their mean?\n",
        "\n",
        "2. Use a loop and compute the same entries as above for m = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\n",
        "\n",
        "3. The command torch.dot(u,v) computes the dot product between 2 1D tensors. In a single line write the dot product of A = torch.randn(3,4,5) and B = torch.randn(3,4,5)\n",
        "\n",
        "4. Given A = torch.randn(3,4,5), compute the dot product of the A[2, :, :] and A[0,:,:]\n",
        "\n",
        "5. (HARD) Given A = torch.randn(3,4,5), compute EVERY dot product (for i, j, k, s) of the form A[:, i, j] and A[:,k,s]  (hint, you will more than a single loop) and store it in an appropriate size tensor\n",
        "\n",
        "6. The solution of the wave equation \n",
        "$$ u_{tt} = u_{xx} $$\n",
        "is given by \n",
        "$$ u(x,t) = {\\frac 12}(f(x+t) + f(x-t)) $$\n",
        "where $f(x) = u(x,0)$.\n",
        "If $u(x,0) = \\exp(-10x^2) \\sin(x)$\n",
        "plot the solution for $t = 0$, $t=1$ and $t=10$\n",
        "\n",
        "7. Plot the function \n",
        "$$ z = \\exp(-10(x^2+y^2))\\sin(2\\pi x)\\sin(2\\pi y) $$\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "CZ5oAwrlyEbE"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "pdKlSPf2xtCF"
      },
      "execution_count": 15,
      "outputs": []
    }
  ]
}