Numerical_Optimaztion_V2.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "machine_shape": "hm",
      "gpuType": "A100"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "# -*- coding: utf-8 -*-\n",
        "\"\"\"numerical optimization.ipynb\n",
        "\n",
        "Automatically generated by Colaboratory.\n",
        "\n",
        "Original file is located at\n",
        "    https://colab.research.google.com/drive/198F_LlewbdSe-XGcbU1U5cWRdL-kZUy6\n",
        "\"\"\"\n",
        "import sys\n",
        "import torch\n",
        "import torch.optim as optim\n",
        "import torch.nn as nn\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "lwfJel-P0YRs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class NumericalOptimizor(nn.Module):\n",
        "\n",
        "    def __init__(self, num_points, y0):\n",
        "        super().__init__()\n",
        "        self.y =  nn.Parameter(y0[None,:] + ((torch.rand(1, 2048, 3)-0.5*torch.ones(1, 2048, 3))) * 2 * 0.1)\n",
        "\n",
        "    def pair_wise_loss(self, p1, p2):\n",
        "        l1 = self.array2samples_distance(p1, p2)\n",
        "        l2 = self.array2samples_distance(p2, p1)\n",
        "        return (l1 + l2) / 2\n",
        "\n",
        "\n",
        "    def array2samples_distance(self, array1, array2):\n",
        "        \"\"\"\n",
        "        arguments:\n",
        "            array1: the array, size: (num_point, num_feature)\n",
        "            array2: the samples, size: (num_point, num_feature)\n",
        "        returns:\n",
        "            distances: each entry is the distance from a sample to array1\n",
        "        \"\"\"\n",
        "        num_point1, num_features1 = array1.shape\n",
        "        num_point2, num_features2 = array2.shape\n",
        "        expanded_array1 = array1.repeat(num_point2, 1).cuda()\n",
        "        expanded_array2 = torch.reshape(\n",
        "                torch.unsqueeze(array2, 1).repeat(1, num_point1, 1),\n",
        "                (-1, num_features2)).cuda()\n",
        "        distances = (expanded_array1-expanded_array2)* (expanded_array1-expanded_array2)\n",
        "\n",
        "        distances = torch.sum(distances,dim=1)\n",
        "        distances = torch.reshape(distances, (num_point2, num_point1))\n",
        "        distances = torch.min(distances,dim=1)[0]\n",
        "        distances = torch.mean(distances)\n",
        "        return distances\n",
        "\n",
        "\n",
        "    def forward(self, ys):\n",
        "        ys.cuda()\n",
        "        self.y.cuda()\n",
        "        num = ys.shape[0]\n",
        "        total_loss = 0\n",
        "        for idx in range(num):\n",
        "            yi = ys[idx]\n",
        "            loss = self.pair_wise_loss(self.y.squeeze(), yi)\n",
        "            total_loss += loss\n",
        "        return total_loss"
      ],
      "metadata": {
        "id": "ArTpKgAT0i3M"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pc = np.load('/content/real_point_0.npy')\n",
        "pc = torch.from_numpy(pc)\n",
        "pc.max() - pc.min()\n",
        "\n",
        "torch.manual_seed(0)\n",
        "error_stretch = 0.1\n",
        "samples = []\n",
        "for i in range(30):\n",
        "\n",
        "    sample = pc[None,:] + ((torch.rand(1, 2048, 3)-0.5*torch.ones(1, 2048, 3))) * 2 * error_stretch\n",
        "\n",
        "    samples.append(sample)\n",
        "\n",
        "\n",
        "gens = torch.cat(samples, dim=0)\n",
        "\n",
        "\n",
        "num_opt = NumericalOptimizor(2048,pc)\n",
        "\n",
        "gens.cuda()\n",
        "num_opt.cuda()\n",
        "\n",
        "optimizer = torch.optim.Adam(num_opt.parameters())\n",
        "\n",
        "try:\n",
        "    for t in range(1000):\n",
        "        loss = num_opt(gens)\n",
        "        print('[%d/%d] CD_LOSS: %.4f '\n",
        "              % (t, 5000, loss))\n",
        "\n",
        "        f=open('/content/loss_pred_with_one_input_with_gaussian_30_samples_0.txt','a')\n",
        "\n",
        "        f.write('\\n'+'[%d/%d] CD_LOSS: %.4f '\n",
        "              % (t, 5000, loss))\n",
        "        f.close()\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "except KeyboardInterrupt:\n",
        "    pred = num_opt.y.detach().cpu().numpy()\n",
        "    np.save('/content/numerical_optimization_pred_with_one_input_with_gaussian_30_samples'+str(0)+'.npy', pred)\n",
        "\n",
        "    print('Interrupted')\n",
        "    sys.exit(0)\n",
        "\n",
        "pred = num_opt.y.detach().cpu().numpy()\n",
        "\n",
        "np.save('/content/numerical_optimization_pred_with_one_input_with_gaussian_30_samples'+str(0)+'.npy', pred)\n"
      ],
      "metadata": {
        "id": "MAJO0TYh0onj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!nvidia-smi\n",
        "!python -c \"import torch; print(torch.__version__)\""
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WEiPDFHM3_v3",
        "outputId": "02064c6e-3739-4df5-9efb-2362072dbd8f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tue Sep 12 16:09:11 2023       \n",
            "+-----------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 525.105.17   Driver Version: 525.105.17   CUDA Version: 12.0     |\n",
            "|-------------------------------+----------------------+----------------------+\n",
            "| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                               |                      |               MIG M. |\n",
            "|===============================+======================+======================|\n",
            "|   0  NVIDIA A100-SXM...  Off  | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   35C    P0    51W / 400W |  14677MiB / 40960MiB |      0%      Default |\n",
            "|                               |                      |             Disabled |\n",
            "+-------------------------------+----------------------+----------------------+\n",
            "                                                                               \n",
            "+-----------------------------------------------------------------------------+\n",
            "| Processes:                                                                  |\n",
            "|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |\n",
            "|        ID   ID                                                   Usage      |\n",
            "|=============================================================================|\n",
            "+-----------------------------------------------------------------------------+\n",
            "2.0.1+cu118\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import plotly.express as px\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import plotly.graph_objects as go\n",
        "import torch"
      ],
      "metadata": {
        "id": "CY1QDnAv7tEs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gt = np.load('/content/real_point_0.npy',allow_pickle='TRUE')\n",
        "pre = np.load('/content/pred_with_one_input_with_gaussian_30_samples_0.npy',allow_pickle='TRUE')\n",
        "gt_ = torch.from_numpy(gt)\n",
        "pre_ = torch.from_numpy(pre)"
      ],
      "metadata": {
        "id": "Sf4hFvli7vr4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def array2samples_distance(array1, array2):\n",
        "    \"\"\"\n",
        "    arguments:\n",
        "        array1: the array, size: (num_point, num_feature)\n",
        "        array2: the samples, size: (num_point, num_feature)\n",
        "    returns:\n",
        "        distances: each entry is the distance from a sample to array1\n",
        "    \"\"\"\n",
        "    num_point1, num_features1 = array1.shape\n",
        "    num_point2, num_features2 = array2.shape\n",
        "    expanded_array1 = array1.repeat(num_point2, 1)\n",
        "    expanded_array2 = torch.reshape(\n",
        "            torch.unsqueeze(array2, 1).repeat(1, num_point1, 1),\n",
        "            (-1, num_features2))\n",
        "    distances = (expanded_array1-expanded_array2)* (expanded_array1-expanded_array2)\n",
        "\n",
        "    distances = torch.sum(distances,dim=1)\n",
        "    distances = torch.reshape(distances, (num_point2, num_point1))\n",
        "    distances = torch.min(distances,dim=1)[0]\n",
        "    distances = torch.mean(distances)\n",
        "    return distances\n"
      ],
      "metadata": {
        "id": "_hB8QcGc77vS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "input = gt_[None,:] + ((torch.rand(1, 2048, 3)-0.5*torch.ones(1, 2048, 3))) * 2 * 0.1\n",
        "# input = torch.from_numpy(input)"
      ],
      "metadata": {
        "id": "rh27L-bP7-mR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dist1= array2samples_distance(gt_.squeeze(),input.squeeze())\n",
        "dist1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "snfZzwys8IJz",
        "outputId": "9f682e43-cc6e-42ec-ce3e-1868d75d58c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.0032)"
            ]
          },
          "metadata": {},
          "execution_count": 215
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dist2= array2samples_distance(gt_.squeeze(),pre_.squeeze())\n",
        "dist2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QGPIdGR_8NB8",
        "outputId": "997a64b4-c218-4c31-bcb6-ccda96d3e7f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.0026)"
            ]
          },
          "metadata": {},
          "execution_count": 216
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import plotly.express as px\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import plotly.graph_objects as go\n",
        "import torch"
      ],
      "metadata": {
        "id": "niNUf4M68Sdm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gt = np.load('/content/real_point_0.npy',allow_pickle='TRUE')\n",
        "pre = np.load('/content/pred_with_one_input_with_gaussian_30_samples_0.npy',allow_pickle='TRUE')\n",
        "pre = np.squeeze(pre)"
      ],
      "metadata": {
        "id": "d6pkKFar8Xr6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gt_df = pd.DataFrame(gt, columns=['x', 'y', 'z'])\n",
        "pred_df = pd.DataFrame(pre, columns=['x', 'y', 'z'])\n",
        "pred_df.x += 1.9\n",
        "gt_df['label'] = 'gt'\n",
        "pred_df['label'] = 'pred'\n",
        "all_points_df = pd.concat([gt_df, pred_df])"
      ],
      "metadata": {
        "id": "UuqKUUMX8hzz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig = px.scatter_3d(all_points_df, x='x', y='y', z='z', color='label')\n",
        "fig.update_traces(marker_size = 1)\n",
        "fig.update_scenes(aspectmode='data')\n",
        "fig.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "dsQjtuRi8j9A",
        "outputId": "cc326e3e-2b85-4323-e4a3-6c563b38df9b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
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          "metadata": {}
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "gt = np.load('/content/real_point_0.npy',allow_pickle='TRUE')\n",
        "# pre = np.load('/content/pred_with_real_gaussian_input_0.npy',allow_pickle='TRUE')\n",
        "# pre = np.load('/content/pred_with_one_input_with_gaussian_0.npy',allow_pickle='TRUE')\n",
        "# pre = np.squeeze(pre)\n",
        "gt_ = torch.from_numpy(gt)\n",
        "pre = gt_[None,:] + ((torch.rand(1, 2048, 3)-0.5*torch.ones(1, 2048, 3))) * 2 * 0.1\n",
        "# pre = (torch.rand(2048, 3)-0.5*torch.ones(2048, 3))\n",
        "pre= pre.squeeze().numpy()"
      ],
      "metadata": {
        "id": "m5bAJMrO8qDB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gt_df = pd.DataFrame(gt, columns=['x', 'y', 'z'])\n",
        "pred_df = pd.DataFrame(pre, columns=['x', 'y', 'z'])\n",
        "pred_df.x += 0.8\n",
        "gt_df['label'] = 'gt'\n",
        "pred_df['label'] = 'pred'\n",
        "all_points_df = pd.concat([gt_df, pred_df])"
      ],
      "metadata": {
        "id": "drwgG48g8sN0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig = px.scatter_3d(all_points_df, x='x', y='y', z='z', color='label')\n",
        "fig.update_traces(marker_size = 1)\n",
        "fig.update_scenes(aspectmode='data')\n",
        "fig.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "l76UmLjf8ucj",
        "outputId": "2e38d0b9-e00d-4fca-a418-98459a4557d3"
      },
      "execution_count": null,
      "outputs": [
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              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import plotly.express as px"
      ],
      "metadata": {
        "id": "iqW7Iwzt97MW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "with open('/content/loss_pred_with_one_input_with_gaussian_30_samples_0.txt') as f:\n",
        "    lines = f.readlines()\n",
        "\n",
        "loss_line = [np.array(l.split())[2].astype(float)[np.newaxis,...] for l in lines if l.strip() != '']\n",
        "loss_line = np.concatenate(loss_line, axis=0)"
      ],
      "metadata": {
        "id": "db10NxhGAQif"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(loss_line, label='loss_line',alpha=0.6)\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 450
        },
        "id": "txehrVDqJSj3",
        "outputId": "ae36137d-5aec-428a-c1e7-6365396c6649"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x79036980fa30>"
            ]
          },
          "metadata": {},
          "execution_count": 226
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}