examples/Spq_creation_examples.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Spq-creation-examples.ipynb",
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qNz8jTJn2R_3"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ytBXYRMXKWTt"
      },
      "source": [
        "### Download SPQ from GitHub"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yd9A09tPJ3O4"
      },
      "source": [
        "!git clone -q https://github.com/ketakopter/spq.git\n",
        "%cd -q spq"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pip install ."
      ],
      "metadata": {
        "id": "v20PRsnOm55y",
        "outputId": "e3a33821-e73f-41e0-888b-9e8c47c1d3e3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Processing /content/spq\n",
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from spq==0.1.0) (1.26.4)\n",
            "Building wheels for collected packages: spq\n",
            "  Building wheel for spq (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for spq: filename=spq-0.1.0-py3-none-any.whl size=13407 sha256=52d0761f5046c542d99a62f7f9d258a98db4696bcfdb6e639ec3ddadd32b4d38\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-819d6cds/wheels/c0/98/d6/3bb39041b87d23f58d81c67f16f5258185ee7666ad87a08c1f\n",
            "Successfully built spq\n",
            "Installing collected packages: spq\n",
            "Successfully installed spq-0.1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KlSqLEs-2Tmv"
      },
      "source": [
        "### Other modules"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1_OJz7gU2WDG"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DeG1Vx8KKfXz"
      },
      "source": [
        "## Load SPQ with a custom file"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SpuD8eACN8K8"
      },
      "source": [
        "The modules provided in the `spq.spq` package load the definitions from a json file. We can use the `spq.spq.environ` module to load them from the file specified in the `SPQFILE` environment variable.\n",
        "\n",
        "In the examples directory we have a json file ready to be used:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AsO09wHjKydM"
      },
      "source": [
        "import json\n",
        "with open(\"examples/pq-roman.json\") as fp:\n",
        "  roman_units = json.load(fp)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vRTVkeYbK0cO",
        "outputId": "4ab99c5f-101f-45ba-c2c1-4f4a07536079"
      },
      "source": [
        "roman_units['physical_quantities']"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[{'name': 'Dist',\n",
              "  'main_unit': 'pes',\n",
              "  'conversions': [{'from': 'pes', 'to': 'digitus', 'factor': 16.0},\n",
              "   {'from': 'pes', 'to': 'palmus', 'factor': 4.0},\n",
              "   {'from': 'passus', 'to': 'pes', 'factor': 5.0},\n",
              "   {'from': 'stadium', 'to': 'pes', 'factor': 625.0}]},\n",
              " {'name': 'Vol',\n",
              "  'main_unit': 'congius',\n",
              "  'conversions': [{'from': 'congius', 'to': 'quartarius', 'factor': 24.0},\n",
              "   {'from': 'amphora', 'to': 'congius', 'factor': 8.0}]}]"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lAuw0oHLONhr"
      },
      "source": [
        "The syntax of the json file is pretty self-explanatory, but you can see in the sections below what to expect from unit conversions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YCf65lS0cBKg"
      },
      "source": [
        "We can set the `SPQFILE` environment variable to load the physical quantities from there."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6m7JlaskSt4Q"
      },
      "source": [
        "import os\n",
        "os.environ[\"SPQFILE\"] = \"examples/pq-roman.json\""
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vyTN8TQ2dPnI"
      },
      "source": [
        "And now the `spq.spq.environ` module loads the physical quantities into its namespace."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dLnx6_KXTOVB"
      },
      "source": [
        "from spq.spq.environ import Dist, Vol"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c0u0As52TP9g",
        "outputId": "bf5c9590-8b71-4592-f56b-f32b94f606e7"
      },
      "source": [
        "print(Dist._units, Vol._units)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['pes', 'digitus', 'palmus', 'passus', 'stadium'] ['congius', 'quartarius', 'amphora']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dyBqYd_RTaYK",
        "outputId": "27f02a79-72de-45a9-8dc1-1459fbfd5aac"
      },
      "source": [
        "a = Dist.frompes(1)\n",
        "print(a.digitus)\n",
        "print(a.palmus)\n",
        "print(a.pes)\n",
        "print(a.passus)\n",
        "print(a.stadium)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "16.0\n",
            "4.0\n",
            "1.0\n",
            "0.2\n",
            "0.0016\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-c1aj0K7Tdoj",
        "outputId": "8380b295-013b-4ca2-8f0e-f3c377836c7c"
      },
      "source": [
        "print(Dist.fromstadium([1, 15]))"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[625.0 9375.0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JAeUEn18Vbui",
        "outputId": "a15f8ce0-78d3-4345-be17-6fc6e8d12e87"
      },
      "source": [
        "print(Vol.fromamphora([1, 10]).congius)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 8. 80.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Dc2LhsbNVe6m",
        "outputId": "067116a6-bd77-4643-eed3-6ceb17d2fd8a"
      },
      "source": [
        "print(Vol.fromamphora(1).quartarius)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "192.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iw6QMDITm4Sf"
      },
      "source": [
        "## Create physical quantities at runtime"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The `spq.base` package provides the functionalities to create physical quantities in a variety of ways. Most of the utilities are available in the `spq.base.pq` (for physical quantities) module, whereas `spq.base.gr` provides functionalities related to graphs."
      ],
      "metadata": {
        "id": "OIdIBQND-8WY"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7GEuv5aXoG8R"
      },
      "source": [
        "### Load from external file"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z7b5ylx2nNsn"
      },
      "source": [
        "We can load into variables physical quantities from a json file. The quantities are loaded into a list. Thus, one \"needs\" to know what quantities are defined if they want to directly assing them to objects; the order is the same as in the json file."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7vZ42VYlVt1S"
      },
      "source": [
        "from spq.base.pq import createPqsFromJsonFile\n",
        "\n",
        "Dist, Vol = createPqsFromJsonFile(\"examples/pq-roman.json\")"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gJHZIewxoKne"
      },
      "source": [
        "OK, now the quantities are the same as above..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A4L-of9WnuBd",
        "outputId": "0acbf16a-036d-4e8e-8093-0eff270f950d"
      },
      "source": [
        "print(Dist._units)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['pes', 'digitus', 'palmus', 'passus', 'stadium']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6e2MJyblsmCe"
      },
      "source": [
        "### Create a physical quantity from a dict"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vHCuIJuMssit"
      },
      "source": [
        "We can create a physical quantity if we specify the conversions between units, the main unit, and the name of the physical quantity in a dictionary. Basically, mimicking the structure of the json example.\n",
        "\n",
        "Note that we don't need to specify *all* conversions. If everything is connected, it will work."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_IMyigwSnwHh"
      },
      "source": [
        "astro_dict = {\n",
        "    'name': 'AstroDist',\n",
        "    'main_unit': 'm',\n",
        "    'conversions': [{'from': 'km',\n",
        "                     'to': 'm',\n",
        "                     'factor': 1.0e3},\n",
        "                    {'from': 'au',\n",
        "                     'to': 'km',\n",
        "                     'factor': 149.5e6},\n",
        "                    {'from': 'ly',\n",
        "                     'to': 'au',\n",
        "                     'factor': 63241.0},\n",
        "                    {'from': 'pc',\n",
        "                     'to': 'ly',\n",
        "                     'factor': 3.26156}\n",
        "    ]\n",
        "}"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r4tViiGzt1iM"
      },
      "source": [
        "from spq.base.pq import createPqFromDict\n",
        "\n",
        "AstroDist = createPqFromDict(astro_dict)"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Uzyslewkt9JX",
        "outputId": "15bf5d5e-a053-4cfe-bc6b-88be0018c79b"
      },
      "source": [
        "AstroDist.fromly(1).m"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9454529500000000.0"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9JZ5IZjiuFLh",
        "outputId": "af9d7693-9a57-4b3c-e245-b243dc18dffb"
      },
      "source": [
        "AstroDist.fromkm(np.linspace(1.5e8, 1.5e9, 2)).au"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.00334448, 10.03344482])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QTMaNZf74s3L"
      },
      "source": [
        "The conversions specified in a dict are simple linear scalings, although an offset can be specified too. Each conversion is a dictionary with keys `from`, `to`, `factor` and optionally `origin`.\n",
        "\n",
        "In the examples above it is clear how a simple linear conversion is specified. For example, to convert from _km_ to _m_, one has to multiply by a factor of 1000, thus the conversion is:\n",
        "\n",
        "```\n",
        "{'from'  : 'km',\n",
        " 'to'    : 'm',\n",
        " 'factor': 1000.0 }\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ADVVvf395tCC"
      },
      "source": [
        "A typical example where an offset is needed is the temperature.\n",
        "\n",
        "The conversion from Celsius to Fahrenheit degrees is given by `degC = 5/9*(degF − 32)` or conversely `degF = 9/5*degC + 32`. The Kelvin is `K = degC + 273.15`, and the Rankine `degR = degF + 459.67`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ugBIQA_g2NBU"
      },
      "source": [
        "temp_dict = {\n",
        "    'name': 'Temp',\n",
        "    'main_unit': 'K',\n",
        "    'conversions': [\n",
        "                    {\n",
        "                    \"from\": \"degC\",\n",
        "                    \"to\": \"degF\",\n",
        "                    \"factor\": 1.8,\n",
        "                    \"origin\": 32.0\n",
        "                },\n",
        "                {\n",
        "                    \"from\": \"degC\",\n",
        "                    \"to\": \"K\",\n",
        "                    \"factor\": 1.0,\n",
        "                    \"origin\": 273.15\n",
        "                },\n",
        "                {\n",
        "                    \"from\": \"degF\",\n",
        "                    \"to\": \"degR\",\n",
        "                    \"factor\": 1.0,\n",
        "                    \"origin\": 459.67\n",
        "                }\n",
        "    ]\n",
        "}"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NZIFgMQd8J99"
      },
      "source": [
        "Temp = createPqFromDict(temp_dict)"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L6K8Bo_T8NMt",
        "outputId": "7c5f82cd-4b6e-4368-a6f9-66dcf8e8a416"
      },
      "source": [
        "print(Temp.fromdegC(0).K)\n",
        "print(Temp.fromdegC(0).degF)\n",
        "print(Temp.fromdegC(0).degR)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "273.15\n",
            "32.0\n",
            "491.67\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5aVmXJmV8Ri9",
        "outputId": "0c838b68-9a33-49d5-e176-4fbdbff95367"
      },
      "source": [
        "print(Temp.fromdegR(0).K)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-5.684341886080802e-14\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zs9KwOkG-L9P"
      },
      "source": [
        "### Create a physical quantity with a list of conversions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eA8NSqI3Datj"
      },
      "source": [
        "We can create a physical quantity from a list of conversions, with each item in the list being a tuple of the form `(from, to, factor, origin)` (the last one is optional and defaults to 0)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-cF2jiA-DzDc"
      },
      "source": [
        "Let's create lists based on the SI prefix conversion factors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s2YoLBrJ8VaY"
      },
      "source": [
        "si_prefixes = {\n",
        "  'Y': 1e24,\n",
        "  'Z': 1e21,\n",
        "  'E': 1e18,\n",
        "  'P': 1e15,\n",
        "  'T': 1e12,\n",
        "  'G': 1e9,\n",
        "  'M': 1e6,\n",
        "  'k': 1e3,\n",
        "  'h': 1e2,\n",
        "  'da': 1e1,\n",
        "  'd': 1e-1,\n",
        "  'c': 1e-2,\n",
        "  'm': 1e-3,\n",
        "  'μ': 1e-6,\n",
        "  'n': 1e-9,\n",
        "  'p': 1e-12,\n",
        "  'f': 1e-15,\n",
        "  'a': 1e-18,\n",
        "  'z': 1e-21,\n",
        "  'y': 1e-24\n",
        "}"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jRj0c_p6_0Bm",
        "outputId": "c702432b-5a3c-4f37-d3f3-f5f55935bdf5"
      },
      "source": [
        "length_units = [(k+'m', 'm', v) for k,v in si_prefixes.items()]\n",
        "length_units"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('Ym', 'm', 1e+24),\n",
              " ('Zm', 'm', 1e+21),\n",
              " ('Em', 'm', 1e+18),\n",
              " ('Pm', 'm', 1000000000000000.0),\n",
              " ('Tm', 'm', 1000000000000.0),\n",
              " ('Gm', 'm', 1000000000.0),\n",
              " ('Mm', 'm', 1000000.0),\n",
              " ('km', 'm', 1000.0),\n",
              " ('hm', 'm', 100.0),\n",
              " ('dam', 'm', 10.0),\n",
              " ('dm', 'm', 0.1),\n",
              " ('cm', 'm', 0.01),\n",
              " ('mm', 'm', 0.001),\n",
              " ('μm', 'm', 1e-06),\n",
              " ('nm', 'm', 1e-09),\n",
              " ('pm', 'm', 1e-12),\n",
              " ('fm', 'm', 1e-15),\n",
              " ('am', 'm', 1e-18),\n",
              " ('zm', 'm', 1e-21),\n",
              " ('ym', 'm', 1e-24)]"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MjuwicEXD9nC",
        "outputId": "49b057c9-0aac-4947-91c6-a34a1a0a69d4"
      },
      "source": [
        "mass_units = [(k+'g', 'g', v, 0.0) for k,v in si_prefixes.items()] # The fourth item in the tuple is for example's sake.\n",
        "mass_units"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('Yg', 'g', 1e+24, 0.0),\n",
              " ('Zg', 'g', 1e+21, 0.0),\n",
              " ('Eg', 'g', 1e+18, 0.0),\n",
              " ('Pg', 'g', 1000000000000000.0, 0.0),\n",
              " ('Tg', 'g', 1000000000000.0, 0.0),\n",
              " ('Gg', 'g', 1000000000.0, 0.0),\n",
              " ('Mg', 'g', 1000000.0, 0.0),\n",
              " ('kg', 'g', 1000.0, 0.0),\n",
              " ('hg', 'g', 100.0, 0.0),\n",
              " ('dag', 'g', 10.0, 0.0),\n",
              " ('dg', 'g', 0.1, 0.0),\n",
              " ('cg', 'g', 0.01, 0.0),\n",
              " ('mg', 'g', 0.001, 0.0),\n",
              " ('μg', 'g', 1e-06, 0.0),\n",
              " ('ng', 'g', 1e-09, 0.0),\n",
              " ('pg', 'g', 1e-12, 0.0),\n",
              " ('fg', 'g', 1e-15, 0.0),\n",
              " ('ag', 'g', 1e-18, 0.0),\n",
              " ('zg', 'g', 1e-21, 0.0),\n",
              " ('yg', 'g', 1e-24, 0.0)]"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VPwco7AwEP7Y"
      },
      "source": [
        "Once we have a list of conversions, we need to create a graph out of it, which connects all units and contains all the conversion factors. The `spq.base.gr` module provides a function for that. The input list has only the one-direction conversion factors; the created graph contains the two-way linear conversions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mxCGXb-jANpW"
      },
      "source": [
        "from spq.base.gr import graphOfLinearScaling\n",
        "\n",
        "length_graph = graphOfLinearScaling(length_units)\n",
        "mass_graph   = graphOfLinearScaling(mass_units)"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ic7FZAmQEfth"
      },
      "source": [
        "A physical quantity is created with a graph (as explained above, containing all the units and their conversions linked), and the main unit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VUvFVLurAwGb"
      },
      "source": [
        "from spq.base.pq import createPq\n",
        "\n",
        "Length = createPq(length_graph, 'm')\n",
        "Mass   = createPq(mass_graph, 'kg')"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DEBeq5C6FanH"
      },
      "source": [
        "Note that even if in the list of the mass units all related to `g`, the quantity can be initialized with a different main unit (in this case `kg`) and it will work properly."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_0Ru-nR8BFHg",
        "outputId": "41ec7d04-1a8f-4229-cd6f-8380d502ce52"
      },
      "source": [
        "print(Length.frommm(1).μm)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1000.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LcyE-D_XBIW0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "017fb5e5-9059-4f0c-bb57-c1f96ac91157"
      },
      "source": [
        "print(Mass.fromg(1))\n",
        "print(Mass.fromg(1).kg)\n",
        "print(Mass(1).kg)\n",
        "print(Mass.frommg(1).μg)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.001\n",
            "0.001\n",
            "1.0\n",
            "1000.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GeebPoI__BUK"
      },
      "source": [
        "### Create a physical quantity from a graph"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JGjA4NFm_GH7"
      },
      "source": [
        "The ultimate way of defining a physical quantity is with a graph containing the relationships between the units.\n",
        "\n",
        "Such a graph needs to contain units at the nodes (e.g. `m` or `ft`), and the edges represent the functions used to convert from one unit to another. SPQ assumes that the functions are of the form `to = from2to(from)`.\n",
        "\n",
        "For example, the edge joining `m` and `ft` would have a function performing `ft = m / 0.3048`. The edge joining `ft` and `m` would have the inverse conversion, `m = ft * 0.3048`.\n",
        "\n",
        "The `gr` module within the package has a small implementation of graphs."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ot6e__Su9xhD"
      },
      "source": [
        "from spq.base.gr import Gr\n",
        "\n",
        "def m2ft(m):\n",
        "  return m / 0.3048\n",
        "def ft2m(ft):\n",
        "  return ft * 0.3048\n",
        "\n",
        "dist_graph = Gr()\n",
        "dist_graph.addEdge('m', 'ft', m2ft)\n",
        "dist_graph.addEdge('ft', 'm', ft2m)\n",
        "\n",
        "Dist = createPq(dist_graph, 'm')"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n41uKnYiSJz8",
        "outputId": "1ea57c9a-6deb-435f-8e5a-09c79b917c30"
      },
      "source": [
        "print(Dist(4.1))\n",
        "print(Dist(4.1).ft)\n",
        "print(Dist.fromft(3.53))\n",
        "print(Dist.fromft(3.53).m)\n",
        "print(Dist.fromft(3.53).ft)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.1\n",
            "13.451443569553804\n",
            "1.075944\n",
            "1.075944\n",
            "3.53\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e6tBhvI6TUGr"
      },
      "source": [
        "By using directly the graph, we are not limited to linear scaling."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "75bEnGutSKoB"
      },
      "source": [
        "dist_graph.addEdge('m', 'expm', lambda m: np.exp(m))\n",
        "dist_graph.addEdge('expm', 'm', lambda expm: np.log(expm))\n",
        "\n",
        "Dist = createPq(dist_graph, 'm')"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "_eSdfCPIVdFn",
        "outputId": "b2115635-a65f-4f92-a1ac-862bd7a5cfd0"
      },
      "source": [
        "x = Dist(np.linspace(0, 2, 10))\n",
        "\n",
        "plt.plot(x.m, x.expm, '-o')\n",
        "plt.plot(x.m, x.ft, '-o')\n",
        "plt.grid()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "J6zCsZ55W78x",
        "outputId": "e39c3c35-0081-488e-ce04-4a89f5f7541a"
      },
      "source": [
        "y = Dist.fromexpm(np.geomspace(1, np.exp(2), 10))\n",
        "\n",
        "plt.plot(y.m, y.expm, '-o')\n",
        "plt.plot(y.m, y.ft, '-o')\n",
        "plt.grid()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5kE2GqupaGFX"
      },
      "source": [
        "The physical quantity creation methods follow the path described above: the contents of the json file are converted into a list of dicts; a dict is converted into a list of tuples; the list of tuples is converted into a graph of linear scalings; the physical quantity is created from the graph."
      ]
    }
  ]
}