{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "trymosek.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ueow-AI7gR0L"
      },
      "source": [
        "# MOSEK in Python online demo\n",
        "\n",
        "You can run this notebook in Google Colab (or any other environment that provides ``!pip install``) as is. There is no need to install a license or anything else.\n",
        "\n",
        "The optimization will be performed on https://solve.mosek.com/."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_ZpMkdiQ_kBw"
      },
      "source": [
        "# Install MOSEK if not already installed\n",
        "!pip install mosek"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d3cCd6K_ARrJ"
      },
      "source": [
        "# In this example we use the Fusion API\n",
        "#    https://docs.mosek.com/latest/pythonfusion/index.html\n",
        "# One could also use the lower level Optimizer API for Python\n",
        "#    https://docs.mosek.com/latest/pythonapi/index.html\n",
        "from mosek.fusion import *\n",
        "import sys\n",
        "import numpy as np\n",
        "\n",
        "# Set up a very simple linear regression problem for demonstration\n",
        "def mosek_least_squares(m, n, A, b, log):\n",
        "  M = Model()\n",
        "  x = M.variable(n)\n",
        "  t = M.variable()\n",
        "\n",
        "  # t >= ||Ax-b||_2\n",
        "  M.constraint(Expr.vstack(t, Expr.sub(Expr.mul(A, x), b)),\n",
        "               Domain.inQCone())\n",
        "  \n",
        "  M.objective(ObjectiveSense.Minimize, t)\n",
        "\n",
        "  # Use the online demo optimization server\n",
        "  M.optserverHost(\"http://solve.mosek.com:30080\") \n",
        "  M.setLogHandler(sys.stdout if log else None)\n",
        "  M.solve()\n",
        "\n",
        "  print(\"Problem status: {prosta}\".format(prosta=M.getProblemStatus()))\n",
        "  print(\"residual: {t}\".format(t=t.level()[0]))\n",
        "\n",
        "  if M.getProblemStatus() == ProblemStatus.PrimalAndDualFeasible:\n",
        "    return x.level()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SoN82ezKk0rT",
        "outputId": "c1014dfa-1a9d-45f7-ab95-ed7d0ac91e06"
      },
      "source": [
        "# Random example\n",
        "m, n = 20, 15\n",
        "A = np.random.randn(m, n)\n",
        "b = np.random.randn(m)\n",
        "\n",
        "x = mosek_least_squares(m, n, A, b, False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Problem status: ProblemStatus.PrimalAndDualFeasible\n",
            "residual: 1.5633248125910382\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "Fs_f-nu-lHZF",
        "outputId": "5e21aabf-6a0d-456a-cfa7-e639b39958b3"
      },
      "source": [
        "# 2-dimensional example with intercept\n",
        "m = 30\n",
        "X = np.random.rand(m)\n",
        "Y = 3 * X + 1 + 0.5*(np.random.rand(m)-0.5)\n",
        "\n",
        "a = mosek_least_squares(m, 2, np.vstack((X,np.ones(m))).transpose(), Y, False)\n",
        "\n",
        "print(\"Regression line: {0:.3f} x + {1:.3f}\".format(a[0], a[1]))\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "d = np.linspace(0, 1, 2)\n",
        "plt.scatter(X, Y)\n",
        "plt.plot(d, a[0] * d + a[1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Problem status: ProblemStatus.PrimalAndDualFeasible\n",
            "residual: 0.689564246467142\n",
            "Regression line: 2.902 x + 1.034\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f87327f9ac8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JAe5oo5Bo4I4"
      },
      "source": [
        "# What now?\n",
        "\n",
        "The demo service at https://solve.mosek.com has size limitations. If you want to use MOSEK on your own grab and install a [trial](https://www.mosek.com/try/) or [academic](https://www.mosek.com/products/academic-licenses/) license and remove the call to ``M.optserverHost`` to optimize locally.\n",
        "\n",
        "Alternatively, install your own [OptServer](https://github.com/MOSEK/Dockerfiles/tree/master/optserver-demo), install a license there, and redirect to it in the ``M.optserverHost`` call."
      ]
    }
  ]
}