02SimpleWall.ipynb

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    "# [Weather data and solar radiation](01WeatherData.ipynb)\n",
    "\n",
    "# Thermal circuit and state-space representation for a thermal circuit with capacities in every node: simple wall\n",
    "\n",
    "## Introduction\n",
    "### Objectives\n",
    "\n",
    "- Model heat transfer with a thermal network.\n",
    "- Obtain the mathematical model as a system of differential algebraic equations (DAE).\n",
    "- Find the steady-state solution.\n",
    "- Transform the system of DAE into state-space representation.\n",
    "- Find the eigenvalues and study the numerical stability.\n",
    "- Simulate by using Euler methods for numerical integration.\n",
    "\n",
    "### Summary\n",
    "\n",
    "This notebook calculates the temperature distribution in a two-layer wall in steady-state and in a dynamic simulation. The code:\n",
    "- Imports Python standard modules (NumPy, Pandas, Matplotlib), and functions from a local module (dm4bem).\n",
    "- Defines the physical characteristics of the materials used to construct the wall and of the air inside the room. The characteristics include thermal conductivity, density, specific heat, and width.\n",
    "- Creates a data frame to store information about the wall, including the materials used to construct it, and calculates the surface area of the wall and the volume of the air inside the room.\n",
    "- Calculates the thermal resistances and thermal capacities of the wall and the air.\n",
    "- Sets up the differential-algebraic system of equations (DAE) model by creating the conductance matrix, capacity matrix, arc-node incidence matrix, and input vectors.\n",
    "- Solves the DAE model to determine the steady-state temperature distribution in the wall when the outdoor temperature is 1 °C and when the heat input is 1 W. It then calculates the indoor temperature based on the results of the DAE model.\n",
    "- Converts the DAE model to a state-space representation and calculates the eigenvalues of the state matrix.\n",
    "- Calculates the maximum time step that can be used to solve the state-space model and the settling time.\n",
    "- Integrates in time the state-space model using Euler explicit and implicit methods. The results are plotted for step-response and for response to the outdoor temperature."
   ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import dm4bem"
   ]
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   "source": [
    "## Physical characteristics and mathematical model\n",
    "\n",
    "Let’s consider the heat transfer through a plane wall which separates the outside air, at [temperature](https://en.m.wikipedia.org/wiki/Temperature) $T_o$, from the inside air. [Heat flow rate](https://en.m.wikipedia.org/wiki/Rate_of_heat_flow) $\\dot{Q}_h$ is added to the inside air by a [fan-coil](https://en.m.wikipedia.org/wiki/Fan_coil_unit) (see Figure 1).\n",
    "\n",
    "![wall](./figures/02_wall.svg)\n",
    "> Figure 1. Plane wall and its thermal network model. The concrete wall is divided in four [meshes](https://en.m.wikipedia.org/wiki/Types_of_mesh) and the insulation in two."
   ]
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   "source": [
    "The wall is composed of two materials: concrete and insulation. The thermal properties of the materials of the wall are:"
   ]
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Conductivity</th>\n",
       "      <th>Density</th>\n",
       "      <th>Specific heat</th>\n",
       "      <th>Width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Layer_1</th>\n",
       "      <td>1.40</td>\n",
       "      <td>2300.0</td>\n",
       "      <td>880</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Layer_2</th>\n",
       "      <td>0.04</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1210</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "         Conductivity  Density  Specific heat  Width\n",
       "Layer_1          1.40   2300.0            880   0.20\n",
       "Layer_2          0.04     16.0           1210   0.08"
      ]
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   "source": [
    "concrete = {'Conductivity': 1.400,\n",
    "            'Density': 2300.0,\n",
    "            'Specific heat': 880,\n",
    "            'Width': 0.2}\n",
    "\n",
    "insulation = {'Conductivity': 0.040,\n",
    "              'Density': 16.0,\n",
    "              'Specific heat': 1210,\n",
    "              'Width': 0.08}\n",
    "\n",
    "wall = pd.DataFrame.from_dict({'Layer_1': concrete,\n",
    "                               'Layer_2': insulation},\n",
    "                              orient='index')\n",
    "wall"
   ]
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Density</th>\n",
       "      <th>Specific heat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Air</th>\n",
       "      <td>1.2</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "     Density  Specific heat\n",
       "Air      1.2           1000"
      ]
     },
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    }
   ],
   "source": [
    "air = {'Density': 1.2,\n",
    "       'Specific heat': 1000}\n",
    "\n",
    "pd.DataFrame(air, index=['Air'])"
   ]
  },
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   "source": [
    "We'll consider the convection coefficients, in W/(m²·K), for indoor and outdoor:"
   ]
  },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>in</th>\n",
       "      <th>out</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>h</th>\n",
       "      <td>4.0</td>\n",
       "      <td>10.0</td>\n",
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      "text/plain": [
       "    in   out\n",
       "h  4.0  10.0"
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   "source": [
    "# convection coefficients, W/(m²·K)\n",
    "h = pd.DataFrame([{'in': 4., 'out': 10.}], index=['h'])\n",
    "h"
   ]
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   "source": [
    "Let's consider the surface area of the wall 3 x 3 m² and the volume of the indoor air is 3 x 3 x 3 m³."
   ]
  },
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   "source": [
    "S_wall = 3 * 3      # m², wall surface area\n",
    "V_air = 3 * 3 * 3   # m³, indoor air volume"
   ]
  },
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   "source": [
    "## Thermal network model\n",
    "\n",
    "The wall consists of two layers: concrete and insulation. The first layer is discretized in 4 [meshes](https://en.m.wikipedia.org/wiki/Types_of_mesh) and the second layer in 2 meshes. By adding together the resistances which are in series, a simpler thermal network is obtained (Figue 2).\n",
    "\n",
    "![RC](./figures/02_RC_model.svg)\n",
    "> Figure 2. Thermal network model of a simple wall obtained from Figure 1 by using the equivalent of the resistances in series. This model contains capacities in every node.\n",
    "\n",
    "The circuit (or the network) is an [oriented](https://en.m.wikipedia.org/wiki/Orientation_(graph_theory)) weighted graph composed of:\n",
    "- oriented branches: temperature sources and resistances (or conductances) through which crosses a flow rate;\n",
    "- nodes: flow rate sources and capacities characterized by a temperature;\n",
    "- incidence relation: how the nodes are connected by the oriented branches.\n",
    "\n",
    "The circuit (or the network) is described by:\n",
    "- elements: resistances (or conductances) and capacities;\n",
    "- sources: temperatures and heat flow rates;\n",
    "- connections: an oriented graph which shows how the nodes of temperature are connected by oriented branches of flow rates.\n",
    "\n",
    "[Network (or circuit) analysis](https://en.m.wikipedia.org/wiki/Network_analysis_(electrical_circuits)) means finding the temperatures and the flow rates when the circuit (i.e. the elements, sources and their connections) is given.\n",
    " \n",
    "The circuit elements of the thermal network are the resistances and the capacities. Their values are found by using the thermo-physical properties of the materials: [thermal conductivity](https://en.m.wikipedia.org/wiki/Thermal_conductivity), [specific heat capacity](https://en.m.wikipedia.org/wiki/Specific_heat_capacity) and [density](https://en.m.wikipedia.org/wiki/Density), and the geometrical values: [width](https://en.m.wikipedia.org/wiki/Length), [surface area](https://en.m.wikipedia.org/wiki/Surface_area) and [volume](https://en.m.wikipedia.org/wiki/Volume).\n",
    "\n",
    "The parameters are grouped in matrices of parameters, or [coefficent matrices](https://en.m.wikipedia.org/wiki/Coefficient_matrix), and the variables are in [vectors](https://en.m.wikipedia.org/wiki/Vector_(mathematics_and_physics)). The variables are physical inputs, modelled by temperature and flow rate sources, and physical outputs, modelled by temperatures of the nodes and flow rates through the branches. \n",
    "\n",
    "The circuits model physical systems which are [causal](https://en.m.wikipedia.org/wiki/Causal_system): the values of the outputs depend on past and current values of the inputs (but not on future values of the inputs)."
   ]
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   "source": [
    "### Resistances\n",
    "\n",
    "The [thermal resistances](https://en.m.wikipedia.org/wiki/Thermal_resistance) for [thermal conduction](https://en.m.wikipedia.org/wiki/Thermal_conduction) are of the form:\n",
    "\n",
    "$$R_{cd} = \\frac{w}{\\lambda S}$$\n",
    "\n",
    "where:\n",
    "\n",
    "- $w$ is the [width](https://en.m.wikipedia.org/wiki/Length) of the material, m;\n",
    "- $\\lambda$ - [thermal conductvity](https://en.m.wikipedia.org/wiki/Thermal_conductivity) of the material, W/(m·K);\n",
    "- $S$ - [surface area](https://en.m.wikipedia.org/wiki/Surface_area) of the wall, m²."
   ]
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   "source": [
    "# conduction\n",
    "R_cd = wall['Width'] / (wall['Conductivity'] * S_wall)  # K/W"
   ]
  },
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   "source": [
    "The thermal resistances for [convection](https://en.m.wikipedia.org/wiki/Convection_(heat_transfer) are of the form:\n",
    "\n",
    "$$R_{cv} = \\frac{1}{h S}$$\n",
    "\n",
    "where:\n",
    "- $h$ is the [convection coefficient](https://en.m.wikipedia.org/wiki/Newton%27s_law_of_cooling#Mathematical_formulation_of_Newton's_law), W/m² K;\n",
    "- $S$ - surface area of the wall, m²."
   ]
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   "source": [
    "# convection\n",
    "R_cv = 1 / (h * S_wall)     # K/W"
   ]
  },
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    "### Capacities\n",
    "The [thermal capacities](https://en.m.wikipedia.org/wiki/Heat_capacity) of the wall are of the form:\n",
    "\n",
    "$$C_w= m_w c_w= \\rho_w c_w w_w S_w$$\n",
    "\n",
    "where:\n",
    "- $m_w = \\rho_w w_w S_w$ is the [mass](https://en.m.wikipedia.org/wiki/Mass) of the material of the wall, kg;\n",
    "- $c_w$ - [specific heat capacity](https://en.m.wikipedia.org/wiki/Specific_heat_capacity) of the material, J/(kg⋅K);\n",
    "- $\\rho_w$ - [density](https://en.m.wikipedia.org/wiki/Density) of the material, kg/m³;\n",
    "- $w_w$ - width of the wall, m;\n",
    "- $S_w$ - surface area of the wall, m²"
   ]
  },
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   "source": [
    "C_wall = wall['Density'] * wall['Specific heat'] * wall['Width'] * S_wall"
   ]
  },
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   "source": [
    "The thermal capacity of the air is:\n",
    "\n",
    "$$C_a = m_a c_a = \\rho_a c_a V_a$$\n",
    "\n",
    "where:\n",
    "- $m_a = \\rho_a V_a$ is the mass of the air, kg;\n",
    "- $\\rho_w$ - [density](https://en.m.wikipedia.org/wiki/Density) of air, kg/m³;\n",
    "- $c_a$ - specific heat capacity of the air, J/(kg⋅K);\n",
    "- $V_a$ - volume of the air in the thermal zone, m³."
   ]
  },
  {
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   "execution_count": 9,
   "id": "4a63c133-c8b3-409c-a5f3-d3df4d447157",
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   "source": [
    "C_air = air['Density'] * air['Specific heat'] * V_air"
   ]
  },
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   "source": [
    "## Differential algebraic equations (DAE)\n",
    "\n",
    "The number of temperature nodes and of flow branches of the thermal network depend on the number of [meshes](https://en.m.wikipedia.org/wiki/Types_of_mesh) obtained by the discretization of the wall."
   ]
  },
  {
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   "source": [
    "# number of temperature nodes and flow branches\n",
    "no_θ = no_q = 7"
   ]
  },
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    "### Conductance matrix $G$\n",
    "The resistances are grouped in the conductance matrix, which is diagonal:\n",
    "$$G = \\begin{bmatrix}\n",
    "R_0^{-1} &  &  & \\\\ \n",
    " & R_1^{-1} &  & \\\\ \n",
    " &  & ... & \\\\ \n",
    " &  &  & R_{n_q-1}^{-1}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "where:\n",
    "- $n_q$ is the number of flow rate branches, $n_q = 7$;\n",
    "- $R_0 = R_{cv,out} + R_{cd,c} / 8$ ; this resistance is composed of outdoor convection, $R_{cv,out}$, and conduction in 1/8th of the concrete width, $R_{cd,c} / 8$; since the concrete is discretized in 4 meshes, there are 8 resistances, each one of value $R_{cd,c} / 8$;\n",
    "- $R_1 = R_2 = R_3 = R_{cd,c} / 8 + R_{cd,c} / 8 = R_{cd,c} / 4$; two resistances $R_{cd,c} / 8$ are added, resulting in $R_{cd,c} / 4$;\n",
    "- $R_4 = R_{cd,c} / 8 + R_{cd,i} / 4$; this resistance is formed by a slice of concrete, $R_{cd,c} / 8$, and a slice of insulation, $R_{cd,i} / 4$;\n",
    "- $R_5 = R_{cd,i} / 4 + R_{cd,i} / 4 = R_{cd,i} / 2$; two meshes of insulation, each one with resistance $R_{cd,i} / 4$, are in series; \n",
    "- $R_6 = R_{cd,i} / 4 + R_{cv,in}$; this resistance is composed of conduction in the insulation,$R_{cd,i} / 4$, and convection at the inside surface of the wall, $R_{cv,in}$.\n",
    "\n",
    "*Note*: A branche is formed by a temperature source and a thermal resistance (or conductance). Each branch of the network needs to have a resistance (or a conductance) but not necessarily a source of temperature."
   ]
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   "source": [
    "# Conductance matrix\n",
    "R = np.zeros([no_q])\n",
    "R[0] = R_cv['out'] + R_cd['Layer_1'] / 8\n",
    "R[1] = R[2] = R[3] = R_cd['Layer_1'] / 4\n",
    "R[4] = R_cd['Layer_1'] / 8 + R_cd['Layer_2'] / 4\n",
    "R[5] = R_cd['Layer_2'] / 2\n",
    "R[6] = R_cd['Layer_2'] / 4 + R_cv['in']\n",
    "G = np.diag(np.reciprocal(R))"
   ]
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   "source": [
    "### Capacity matrix $C$\n",
    "The capacities are grouped in the capacity matrix, which is diagonal:\n",
    "\n",
    "$$C = \\begin{bmatrix}\n",
    "C_0 &  &  & \\\\ \n",
    " & C_1 &  & \\\\ \n",
    " &  & ... & \\\\ \n",
    " &  &  & C_{n_θ-1}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "where:\n",
    "- $n_θ$ is the number of temperature nodes, $n_θ = 7$;\n",
    "- $C_0 = C_1 = C_2 = C_3 = C_{w, concrete} / 4$; since the concrete layer is divided in 4 meshes, the capacity of a slice is 1/4 of the capacity of the concrete layer;\n",
    "- $C_4 = C_5 = C_{w, insulation} / 2$; since the insulation layer is divided in 2 meshes, the capacity of a slice is 1/2 of the capacity of the insulation layer;\n",
    "- $C_6 = C_{a}$, the capacity of the indoor air.\n",
    "\n",
    "*Note*: Not every temperature node needs to have a capacity. The capacity of a surface is zero, since its mass is zero (because its volume is zero)."
   ]
  },
  {
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   "source": [
    "# Capacity matrix\n",
    "C = np.zeros(no_θ)\n",
    "C[0] = C[1] = C[2] = C[3] = C_wall['Layer_1'] / 4\n",
    "C[4] = C[5] = C_wall['Layer_2'] / 2\n",
    "C[6] = C_air\n",
    "C = np.diag(C)"
   ]
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   "source": [
    "### Arc-node incidence matrix $A$\n",
    "The [incidence matrix](https://en.m.wikipedia.org/wiki/Incidence_matrix)  shows the relation between oriented branches (i.e. flow rates) and nodes (i.e. temperatures). The rows in the incidence matrix $A$ correspond to the branches containing the heat flow rates $q_k$ across the resistances $R_k$ and the columns correspond to the temperature nodes $\\theta_l$. In the row corresponding to the branch $q_k$ in the position of the node $\\theta_l$ there is -1 if the flow $q_k$ leaves the node, +1 if the flow $q_k$ enters into the node $\\theta_k$ and 0 if the resistance $R_k$ is not connected to the temperature node $\\theta_k$ [[Ghiaus, 2013](https://doi.org/10.1016/j.energy.2012.10.024)]:\n",
    "\n",
    "$$A_{kl} = \\begin{cases}\\phantom{-}\n",
    "0 & \\text{if branch } q_k \\text{ is not connected to node }  \\theta_l \\\\ \n",
    "+1 & \\text{if branch } q_k \\text{ enters into node }  \\theta_l\\\\ \n",
    "-1 & \\text{if branch } q_k \\text{ gets out of node }  \\theta_l \n",
    "\\end{cases}$$\n",
    "\n",
    "The matrix $-A$ is a difference operator for the vector $\\theta$ of temperatures, $-A \\equiv \\Delta$. That is, $e = -A \\theta$ or $e = \\Delta \\theta$ is the vector of differences between temperatures connected by resistances [[Ghiaus, 2013](https://doi.org/10.1016/j.energy.2012.10.024)]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "db33412d-392f-42ab-8ab2-d575a92387a8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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       "      <th>3</th>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.0</td>\n",
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       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
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       "      <th>4</th>\n",
       "      <td>-0.0</td>\n",
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       "      <td>-0.0</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.0</td>\n",
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       "      <th>6</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
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      "text/plain": [
       "     0    1    2    3    4    5    6\n",
       "0  1.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0\n",
       "1 -1.0  1.0 -0.0 -0.0 -0.0 -0.0 -0.0\n",
       "2 -0.0 -1.0  1.0 -0.0 -0.0 -0.0 -0.0\n",
       "3 -0.0 -0.0 -1.0  1.0 -0.0 -0.0 -0.0\n",
       "4 -0.0 -0.0 -0.0 -1.0  1.0 -0.0 -0.0\n",
       "5 -0.0 -0.0 -0.0 -0.0 -1.0  1.0 -0.0\n",
       "6 -0.0 -0.0 -0.0 -0.0 -0.0 -1.0  1.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Arc-node incidence matrix\n",
    "A = np.eye(no_q, no_θ + 1)\n",
    "A = -np.diff(A, n=1, axis=1)\n",
    "pd.DataFrame(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56eb38e9-0c0c-472b-92d3-dad771c5f07d",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Vectors of temperature sources $b$ and flow rate sources $f$\n",
    "First, we will set all the temperature sources $b$ and flow sources $f$ to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4469f034-4713-49f6-b643-edda218cff58",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input vectors\n",
    "b = np.zeros(no_q)  # temperatures\n",
    "f = np.zeros(no_θ)  # flow rates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af6da2dd-405a-42b9-b933-bcd4d2a500ef",
   "metadata": {
    "tags": []
   },
   "source": [
    "Their values will be changed depending on the conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aa13fa8-af4b-4ff8-a3ad-a39060d89de0",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Differential algebraic equations\n",
    "The system of [Differential-Algebraic Equations](https://en.m.wikipedia.org/wiki/Differential-algebraic_system_of_equations) (DAE) is [[Ghiaus, 2013](https://doi.org/10.1016/j.energy.2012.10.024)]:\n",
    "\n",
    "$$C\\dot{\\theta} = -A^T G A \\theta + A^T G b + f$$\n",
    "or\n",
    "$$C\\dot{\\theta} = -\\Delta^T G \\Delta \\theta - \\Delta^T G b + f$$\n",
    "\n",
    "which contains the matrices and vectors characterizing the circuit:\n",
    "- elements: conductances $G$ and capacities $C$;\n",
    "- sources: temperatures $b$ and heat flow rates $f$;\n",
    "- incidence relation: incidence matrix $A$ which shows how the nodes of temperature are connected by oriented branches of flow rates or difference matrix $\\Delta \\equiv -A$ which operates differences between the temperatures in the nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ec653e1-cbe7-40dc-90ba-5d1095f716d0",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Steady-state solution\n",
    "\n",
    "In [steady-state](https://en.m.wikipedia.org/wiki/Steady_state), i.e., $\\dot{\\theta} = 0$, the solution of the system of  Differential-Algebraic Equations (DAE) is:\n",
    "\n",
    "$$\\theta = (A^T G A)^{-1}(A^T G b + f)$$\n",
    "$$q = G (-A \\theta + b)$$\n",
    "\n",
    "Let's consider two steady-states:\n",
    "\n",
    "1) The outdoor temperature is $T_o = 1\\, \\mathrm{^\\circ C}$, i.e. $b_0 = 1$.\n",
    "2) The indoor flow introduced by the fan-coil is $\\dot{Q}_h = 1\\, \\mathrm{W}$, i.e. $f_6 \\equiv f_{end} = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "289cbc74-3fe1-4104-83ed-11f7cbd0cc7b",
   "metadata": {},
   "source": [
    "### Reponse to outdoor temperature variation\n",
    "\n",
    "The outdoor temperature is $T_o = 1\\, \\mathrm{^\\circ C}$, i.e. $b_0 = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "43fc79c0-69f3-46aa-ae2e-c5e6856a1ca4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When To = 1°C, the temperatures in steady-state are: [1. 1. 1. 1. 1. 1. 1.] °C\n",
      "The indoor temperature is: 1.000 °C\n"
     ]
    }
   ],
   "source": [
    "b[0] = 1\n",
    "θ_steady_To = np.linalg.inv(A.T @ G @ A) @ (A.T @ G @ b + f)\n",
    "np.set_printoptions(precision=3)\n",
    "print('When To = 1°C, the temperatures in steady-state are:', θ_steady_To, '°C')\n",
    "print(f'The indoor temperature is: {θ_steady_To[-1]:.3f} °C')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd375fb-5d64-4215-a068-ce0f8da929fb",
   "metadata": {},
   "source": [
    "### Reponse to indoor flow rate variation\n",
    "\n",
    "The indoor flow introduced by the fan-coil is $\\dot{Q}_h = 1\\, \\mathrm{W}$, i.e. $f_6 \\equiv f_{end} = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "66202ab6-f2be-491f-9bfe-e7793e38390f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When Qh = 1W, the temperatures in steady-state are: [0.013 0.017 0.021 0.025 0.083 0.194 0.277] °C\n",
      "The indoor temperature is: 0.277 °C\n"
     ]
    }
   ],
   "source": [
    "b[0] = 0\n",
    "f[-1] = 1\n",
    "θ_steady_Qh = np.linalg.inv(A.T @ G @ A) @ (A.T @ G @ b + f)\n",
    "print('When Qh = 1W, the temperatures in steady-state are:', θ_steady_Qh, '°C')\n",
    "print(f'The indoor temperature is: {θ_steady_Qh[-1]:.3f} °C')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6803f7d1-6ed3-4010-ad18-496ded1af9fa",
   "metadata": {
    "tags": []
   },
   "source": [
    "## State-space representation\n",
    "If matrix $C$ is [invertible (or non-singular)](https://en.m.wikipedia.org/wiki/Invertible_matrix), then the system of Differential-Algebraic Equations (DAE)\n",
    "\n",
    "$$C\\dot{\\theta} = -A^T G A \\theta + A^T G b + f$$\n",
    "\n",
    "can be put in the [state-space](https://en.m.wikipedia.org/wiki/State-space_representation) representation\n",
    "\n",
    "$$\\left\\{\\begin{array}{rr}\n",
    "\\dot{\\theta}=A_s \\theta + B_s u\\\\ \n",
    "y = C_s \\theta + D_s u\n",
    "\\end{array}\\right.$$\n",
    "\n",
    "where:\n",
    "- $\\theta$ is the state vector of temperatures;\n",
    "- $u = \\begin{bmatrix} b \\\\ f\\end{bmatrix}$ - vector of inputs (temperature sources $b$ and flow sources $f$);\n",
    "- $A_s = -C^{-1} A^T G A$ - state matrix, $\\dim A = n_\\theta \\times n_\\theta$;\n",
    "- $B_s = C^{-1}\\begin{bmatrix}\n",
    "A^T G & I\n",
    "\\end{bmatrix}$ - input matrix, $\\dim B = n_\\theta \\times n_u$;\n",
    "- $C_s = \\begin{bmatrix} 0 & 0 & ... &1 \\end{bmatrix}$ - output matrix, $\\dim C = 1 \\times n_\\theta$;\n",
    "- $D_s = \\begin{bmatrix} 0 & 0 & ... &0 \\end{bmatrix}$ - feedthrough (or feedforward matrix, $\\dim D = 1 \\times n_u$.\n",
    "\n",
    "The first equation, $ \\dot{\\theta}=A_s \\theta + B_s u $, is called *state* or *system* equation and the second equation, $ y = C_s \\theta + D_s u $, is called *observation* equation,"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "015f0b5b-0ff8-45f0-b9fb-ed76c31d1ff4",
   "metadata": {
    "tags": []
   },
   "source": [
    "The state matrix is $A_s = -C^{-1} A^T G A$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a6356bc1-0658-401e-a4db-5795c93ee248",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <td>-3.6e-04</td>\n",
       "      <td>2.8e-04</td>\n",
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       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
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       "      <th>1</th>\n",
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       "      <th>2</th>\n",
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       "      <td>-5.5e-04</td>\n",
       "      <td>2.8e-04</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
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       "      <th>3</th>\n",
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       "      <td>0.0e+00</td>\n",
       "      <td>2.8e-04</td>\n",
       "      <td>-3.0e-04</td>\n",
       "      <td>1.9e-05</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
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       "      <th>4</th>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>2.5e-03</td>\n",
       "      <td>-3.8e-03</td>\n",
       "      <td>1.3e-03</td>\n",
       "      <td>0.0e+00</td>\n",
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       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>1.3e-03</td>\n",
       "      <td>-3.0e-03</td>\n",
       "      <td>1.7e-03</td>\n",
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       "      <th>6</th>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>0.0e+00</td>\n",
       "      <td>3.7e-04</td>\n",
       "      <td>-3.7e-04</td>\n",
       "    </tr>\n",
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       "         0        1        2        3        4        5        6\n",
       "0 -3.6e-04  2.8e-04  0.0e+00  0.0e+00  0.0e+00  0.0e+00  0.0e+00\n",
       "1  2.8e-04 -5.5e-04  2.8e-04  0.0e+00  0.0e+00  0.0e+00  0.0e+00\n",
       "2  0.0e+00  2.8e-04 -5.5e-04  2.8e-04  0.0e+00  0.0e+00  0.0e+00\n",
       "3  0.0e+00  0.0e+00  2.8e-04 -3.0e-04  1.9e-05  0.0e+00  0.0e+00\n",
       "4  0.0e+00  0.0e+00  0.0e+00  2.5e-03 -3.8e-03  1.3e-03  0.0e+00\n",
       "5  0.0e+00  0.0e+00  0.0e+00  0.0e+00  1.3e-03 -3.0e-03  1.7e-03\n",
       "6  0.0e+00  0.0e+00  0.0e+00  0.0e+00  0.0e+00  3.7e-04 -3.7e-04"
      ]
     },
     "execution_count": 17,
     "metadata": {},
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    }
   ],
   "source": [
    "# State matrix\n",
    "As = -np.linalg.inv(C) @ A.T @ G @ A\n",
    "pd.set_option('precision', 1)\n",
    "pd.DataFrame(As)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a5dc77c-73b3-40d5-9ce7-ab435daf6e70",
   "metadata": {
    "tags": []
   },
   "source": [
    "The input matrix is\n",
    "$B_s = C^{-1}\\begin{bmatrix}\n",
    "A^T G & I\n",
    "\\end{bmatrix}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3209c96b-2b15-40ee-b88d-9ef2f999b3ed",
   "metadata": {},
   "outputs": [
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       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>2.77e-04</td>\n",
       "      <td>-2.77e-04</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.10e-06</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>2.77e-04</td>\n",
       "      <td>-2.77e-04</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.10e-06</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>2.77e-04</td>\n",
       "      <td>-1.91e-05</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.10e-06</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>2.49e-03</td>\n",
       "      <td>-1.29e-03</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.43e-04</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.29e-03</td>\n",
       "      <td>-1.72e-03</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>1.43e-04</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>3.70e-04</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>3.09e-05</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0         1         2         3         4         5         6   \\\n",
       "0  8.38e-05 -2.77e-04  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00   \n",
       "1  0.00e+00  2.77e-04 -2.77e-04  0.00e+00  0.00e+00  0.00e+00  0.00e+00   \n",
       "2  0.00e+00  0.00e+00  2.77e-04 -2.77e-04  0.00e+00  0.00e+00  0.00e+00   \n",
       "3  0.00e+00  0.00e+00  0.00e+00  2.77e-04 -1.91e-05  0.00e+00  0.00e+00   \n",
       "4  0.00e+00  0.00e+00  0.00e+00  0.00e+00  2.49e-03 -1.29e-03  0.00e+00   \n",
       "5  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  1.29e-03 -1.72e-03   \n",
       "6  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  3.70e-04   \n",
       "\n",
       "         7         8         9         10        11        12        13  \n",
       "0  1.10e-06  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  \n",
       "1  0.00e+00  1.10e-06  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  \n",
       "2  0.00e+00  0.00e+00  1.10e-06  0.00e+00  0.00e+00  0.00e+00  0.00e+00  \n",
       "3  0.00e+00  0.00e+00  0.00e+00  1.10e-06  0.00e+00  0.00e+00  0.00e+00  \n",
       "4  0.00e+00  0.00e+00  0.00e+00  0.00e+00  1.43e-04  0.00e+00  0.00e+00  \n",
       "5  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  1.43e-04  0.00e+00  \n",
       "6  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  3.09e-05  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Input matrix\n",
    "Bs = np.linalg.inv(C) @ np.block([A.T @ G, np.eye(no_θ)])\n",
    "pd.set_option('precision', 2)\n",
    "pd.DataFrame(Bs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21300bdb-5397-4da3-b897-2d14e010e1d6",
   "metadata": {
    "tags": []
   },
   "source": [
    "The input vector is formed by stacking the vector of temperature sources $b$ and the vector of flow sources $f$:\n",
    "$$u = \\begin{bmatrix} b \\\\ f\\end{bmatrix}$$\n",
    "\n",
    "However, many sources in the model are zero. For our example, there are only two sources: $T_o$ and $\\dot{Q}_h$. Therefore,\n",
    "$$b = \\begin{bmatrix}\n",
    "T_o\\\\ \n",
    "0\\\\ \n",
    "...\\\\ \n",
    "0\n",
    "\\end{bmatrix}$$\n",
    "and\n",
    "$$f = \\begin{bmatrix}\n",
    "0\\\\ \n",
    "0\\\\ \n",
    "...\\\\ \n",
    "\\dot{Q}_h\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "Since the sources that are always zero have no influence on the outputs, they can be eliminated from the input vector, which becomes:\n",
    "\n",
    "$$u = \\begin{bmatrix} T_o \\\\ \\dot{Q}_h\\end{bmatrix}$$\n",
    "\n",
    "that is, only the columns that correspond to existing sources, i.e., the 1st and the last columns, are kept in matrix $B_s$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f6dd7129-672e-4239-82ed-7a557c0916a1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>To</th>\n",
       "      <th>Qh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.38e-05</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>0.00e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.00e+00</td>\n",
       "      <td>3.09e-05</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "         To        Qh\n",
       "0  8.38e-05  0.00e+00\n",
       "1  0.00e+00  0.00e+00\n",
       "2  0.00e+00  0.00e+00\n",
       "3  0.00e+00  0.00e+00\n",
       "4  0.00e+00  0.00e+00\n",
       "5  0.00e+00  0.00e+00\n",
       "6  0.00e+00  3.09e-05"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select columns for which the input vector is not zero\n",
    "# 1st for To and last for Qh\n",
    "Bs = Bs[:, [0, -1]]\n",
    "pd.DataFrame(Bs, columns=['To', 'Qh'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5673cfbb-4f87-4649-a38c-151e6fec0efc",
   "metadata": {
    "tags": []
   },
   "source": [
    "The output matrix $C_s$ extracts the values of interest from the state vector (the vector of temperatures). In our case, the temperature of interest is the indoor temperature,\n",
    "$$T_o \\equiv  \\theta_6 = \\begin{bmatrix}\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\theta_0\\\\ \n",
    "\\theta_1\\\\ \n",
    "\\theta_2\\\\ \n",
    "\\theta_3\\\\ \n",
    "\\theta_4\\\\ \n",
    "\\theta_5\\\\ \n",
    "\\theta_6\n",
    "\\end{bmatrix} = C_s \\theta$$\n",
    "\n",
    "which gives\n",
    "\n",
    "$$C_s = \\begin{bmatrix}\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1\n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "50b2af3c-cc3d-4bd5-973e-f3d28b6c6829",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Output matrix\n",
    "Cs = np.zeros((1, no_θ))\n",
    "# output: last temperature node\n",
    "Cs[:, -1] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c89f7bd-c9cb-467d-9b6b-eff6a50f49c2",
   "metadata": {
    "tags": []
   },
   "source": [
    "The feedthrough matrix $D_s$ has one row (the number of outputs) and two columns, the number of inputs in vector $u$, which is the same as the number of columns of matrix $B_s$. In this case, $D_s$ is composed entirely of zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "bed9883f-94da-435e-93ec-fc5230603cae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Feedthrough (or feedforward) matrix\n",
    "Ds = np.zeros(Bs.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac4cf6ec-7887-4636-848a-f246a3e81f35",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Eigenvalue analysis\n",
    "\n",
    "### Time constants\n",
    "\n",
    "The [stability condition for explicit Euler method](https://en.m.wikipedia.org/wiki/Euler_method#Numerical_stability) requires that all eigenvalues $\\lambda _i \\in \\mathbb{Z}$ of the state matrix $A_s$ satisfy the condition\n",
    "\n",
    "$$ \\left | 1 + \\lambda _i \\Delta t \\right | \\leq 1, \\forall i $$\n",
    "\n",
    "If all eigenvalues of state matrix $A_s$ are real, as is the case for thermal networks, then the above condition becomes:\n",
    "\n",
    "$$ -2 \\leq \\lambda _i\\Delta t\\leq 0, \\forall i $$.\n",
    "\n",
    "Since the eigenvalues $\\lambda_i$ are related to the time constants $T_i$,\n",
    "\n",
    "$$ \\lambda _i = - \\frac{1}{T_i} $$\n",
    "\n",
    "it results that the condition for stability is \n",
    "\n",
    "$$ 0 \\leq \\Delta t \\leq \\min (-2 / \\lambda_i) = 2 \\min (T_i)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5946e145-25e6-44f6-8779-0197f8a79ac8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time constants: \n",
      " [  208.1   441.   1051.   1731.8 62794.2  4925.9  9141.6] s \n",
      "\n",
      "2 x Time constants: \n",
      " [   416.1    881.9   2101.9   3463.6 125588.4   9851.9  18283.1] s \n",
      "\n",
      "Max time step Δt = 416.11 s\n"
     ]
    }
   ],
   "source": [
    "λ = np.linalg.eig(As)[0]    # minimum eigenvalue of matrix A\n",
    "max_Δt = min(-2 / λ)\n",
    "\n",
    "np.set_printoptions(precision=1)\n",
    "print('Time constants: \\n', -1 / λ, 's \\n')\n",
    "print('2 x Time constants: \\n', -2 / λ, 's \\n')\n",
    "print(f'Max time step Δt = {max_Δt:.2f} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce6aacd0-a76e-4f81-b4f3-6ffc2a36226b",
   "metadata": {},
   "source": [
    "### Time step\n",
    "\n",
    "We choose a time step a multiple of 60 s which is smaller than the maximum admited for stability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "778057b4-8cee-4951-8857-5c6c943d8cf4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Δt = 360.0 s\n"
     ]
    }
   ],
   "source": [
    "# time step\n",
    "Δt = np.floor(max_Δt / 60) * 60   # s\n",
    "print(f'Δt = {Δt} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04944474-81b5-4bf9-b3b8-bb106be8ee57",
   "metadata": {},
   "source": [
    "### Settling time\n",
    "The settling time is about four times the largest time constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7bcf63a1-4831-4ea0-8074-ec2dcfe43243",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Settling time: 251176.86 s = 69.77 h\n"
     ]
    }
   ],
   "source": [
    "# settling time\n",
    "t_settle = 4 * max(-1 / λ)\n",
    "print(f'Settling time: {t_settle:.2f} s = {t_settle / 3600:.2f} h')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9607c44f-3d74-433e-94af-4cfd94009793",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Time integration using explicit and implicit Euler methods\n",
    "We will study the dynamic response of the model to: \n",
    "- a step variation of a source (outdoor temperature $T_o$ or indoor flow $\\dot{Q}_h$);\n",
    "- variation of outdoor temperature given by weather data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "004b7645-e93f-4d7a-b3be-eda0726b08fe",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step input: outdoor temperature\n",
    "\n",
    "The [step response](https://en.m.wikipedia.org/wiki/Step_response) is the time evolution of the output(s) when the input is a [step function](https://en.m.wikipedia.org/wiki/Heaviside_step_function). Usually, the zero initial conditions (i.e. the system is at rest and there is no accumulations of energy in the capacities) are considered.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a5aaf06-f1af-4ed2-88b7-a9beaf6326a5",
   "metadata": {
    "tags": []
   },
   "source": [
    "The number of time steps depends on the settling time and the time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a8a81faa-b36f-442e-bb1d-c27c58ccfef8",
   "metadata": {
    "tags": []
   },
   "outputs": [
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       "      <th>697</th>\n",
       "      <td>250920.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>698 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         time\n",
       "0         0.0\n",
       "1       360.0\n",
       "2       720.0\n",
       "3      1080.0\n",
       "4      1440.0\n",
       "..        ...\n",
       "693  249480.0\n",
       "694  249840.0\n",
       "695  250200.0\n",
       "696  250560.0\n",
       "697  250920.0\n",
       "\n",
       "[698 rows x 1 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of time steps\n",
    "n = int(np.ceil(t_settle / Δt))\n",
    "# time vector\n",
    "t = np.arange(0, n * Δt, Δt)\n",
    "pd.DataFrame(t, columns=['time'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21f5c5f7-9c6c-4922-9002-59c9220add47",
   "metadata": {},
   "source": [
    "Let's assume that the outdoor temperature $T_o$ has a step variation of 1°C (the indoor heat flow is zero, $\\dot{Q}_h = 0$).\n",
    "\n",
    "The input vector is formed by the vector of outdoor temperature and vector of indoor heat-flow rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8beaea55-da77-4700-813e-90e7f6e2b8c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>688</th>\n",
       "      <th>689</th>\n",
       "      <th>690</th>\n",
       "      <th>691</th>\n",
       "      <th>692</th>\n",
       "      <th>693</th>\n",
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      ],
      "text/plain": [
       "   0    1    2    3    4    5    6    7    8    9    ...  688  689  690  691  \\\n",
       "0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  ...  1.0  1.0  1.0  1.0   \n",
       "1  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  ...  0.0  0.0  0.0  0.0   \n",
       "\n",
       "   692  693  694  695  696  697  \n",
       "0  1.0  1.0  1.0  1.0  1.0  1.0  \n",
       "1  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "\n",
       "[2 rows x 698 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = np.block([[np.ones([1, n])],    # To = [1, 1, ... , 1]\n",
    "              [np.zeros([1, n])]])  # Qh = [0, 0, ... , 0]\n",
    "pd.DataFrame(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22aa2c9c-6d2a-4275-a7da-328a73678d47",
   "metadata": {},
   "source": [
    "Let's assume zero initial conditions for the temperature vector (i.e., all temperatures and their derivatives are zero) for explicit and implicit Euler integration methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "45d89d6a-7246-4cae-b2ee-47cac89128f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial values for temperatures obtained by explicit and implicit Euler\n",
    "θ_exp = np.zeros([no_θ, t.shape[0]])\n",
    "θ_imp = np.zeros([no_θ, t.shape[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b1dddb-7ab4-4a06-a3dc-c7af53e6f00f",
   "metadata": {
    "tags": []
   },
   "source": [
    "The formula for [Euler](https://en.m.wikipedia.org/wiki/Euler_method) forward (or explicit) integration is:\n",
    "\n",
    "$$ \\theta_{k+1} = (I + \\Delta t A_s) \\theta _k + \\Delta t B_s u_k $$\n",
    "\n",
    "For Euler backward (or implicit) integration it is:\n",
    "\n",
    "$$\\theta_{k+1} = (I - \\Delta t A_s)^{-1} ( \\theta _k + \\Delta t B_s u_k )$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "02a1d979-9d72-4f1a-922f-d69e7710874b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# time integration: Euler explicit & implicit\n",
    "for k in range(t.shape[0] - 1):\n",
    "    θ_exp[:, k + 1] = (np.eye(no_θ) + Δt * As) @\\\n",
    "        θ_exp[:, k] + Δt * Bs @ u[:, k]\n",
    "    θ_imp[:, k + 1] = np.linalg.inv(np.eye(no_θ) - Δt * As) @\\\n",
    "        (θ_imp[:, k] + Δt * Bs @ u[:, k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fafd87a2-0fbf-448a-890e-fb764d98cef0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(t / 3600, θ_exp[-1, :], t / 3600, θ_imp[-1, :])\n",
    "ax.set(xlabel='Time, $t$ / h',\n",
    "       ylabel='Air temperature, $θ$ / °C',\n",
    "       title='Step input: $T_o$')\n",
    "ax.legend(['Euler explicit', 'Euler implicit'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba736672-9e92-4fed-9b4d-b0bb439b6062",
   "metadata": {
    "tags": []
   },
   "source": [
    "> Figure 3. Step response to outdoor temperature $T_o$ obtained by explicit and implicit Euler integration of the state-space model. For small time steps, the two solutions are practically identical."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab0db10a-5856-499d-a091-fc7a5e241be1",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step input: indoor heat flow rate\n",
    "\n",
    "Let's consider that the indoor heat flow rate $\\dot{Q}_h$ has a step variation of 1 W (the outdoor temperature is zero, $T_o = 0$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ccdb13ba-33af-48d2-8d23-c41811bf4262",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "   692  693  694  695  696  697  \n",
       "0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "1  1.0  1.0  1.0  1.0  1.0  1.0  \n",
       "\n",
       "[2 rows x 698 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = np.block([[np.zeros([1, n])],   # To = [0, 0, ... , 0]\n",
    "              [np.ones([1, n])]])   # Qh = [1, 1, ... , 1]\n",
    "pd.DataFrame(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "231e50c0-a0dc-473d-8524-b07af73e55a9",
   "metadata": {},
   "source": [
    "We initialize again to zero the temperature vector for explicit and implicit Euler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a634b12f-c35b-4dfe-bedd-5abbe8f77bb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "θ_exp = np.zeros([no_θ, t.shape[0]])\n",
    "θ_imp = np.zeros([no_θ, t.shape[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb201c0d-5f4e-47b9-b486-65ff911d327e",
   "metadata": {
    "tags": []
   },
   "source": [
    "The formula for Euler forward (or explicit) integration is\n",
    "\n",
    "$$ \\theta_{k+1} = (I + \\Delta t A_s) \\theta _k + \\Delta t B_s u_k $$\n",
    "\n",
    "and for Euler backward (or implicit) integration it is\n",
    "\n",
    "$$\\theta_{k+1} = (I - \\Delta t A_s)^{-1} ( \\theta _k + \\Delta t B_s u_k )$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "de5bd0bd-1623-402f-9d99-d458f804ec10",
   "metadata": {},
   "outputs": [],
   "source": [
    "for k in range(t.shape[0] - 1):\n",
    "    θ_exp[:, k + 1] = (np.eye(no_θ) + Δt * As) @\\\n",
    "        θ_exp[:, k] + Δt * Bs @ u[:, k]\n",
    "    θ_imp[:, k + 1] = np.linalg.inv(np.eye(no_θ) - Δt * As) @\\\n",
    "        (θ_imp[:, k] + Δt * Bs @ u[:, k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b39e3552-b359-4ed4-b55a-7071d6adeb5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jLgg7kojIW+gMI2Rrt3fwwG8e48H4PfjcRdg7vxJ2JBGRIekMI0SpdIav3buU78ZuJVLdgF30A/UwKyJlS2cYIbrr6Q2cte2nHBXbCB/4BdRMCTuSiMiwVDBCsr2jlwd++98sjv0K5v0VHPWesCOJiOyVLkmF5J8eXsPX/cdE4xVwwQ1hxxER2ScVjBCs3NJG8/Jfc1ZkOZFz/wbqDgo7kojIPqlghODmx17musQvSDfMgpOvDDuOiEhe1IZRYss37aLilcUcndgI5/4rxBJhRxIRyYvOMErslsdX89XE/aQbj4G3/WXYcURE8qaCUUKvbusgvvYRZvEG0Xd9DSLRsCOJiORNBaOEfvLUeq6J/xfp+llwzEVhxxERKYgKRom0dPWz4c+/4+32KtF3fE5nFyIy6qhglMjPn32dj9uvSVdOhPkfDTuOiEjBVDBKwN357bMrOD/6AtETPwaJ6rAjiYgUTAWjBJ5d38Jp7Y8SIw0nXh52HBGR/aKCUQL3L32dj8SWkJ75DphyZNhxRET2yz4LhpkdaWbvGGL5O83siOLEGjs6+1I0v/RbDrVtRBd8Iuw4IiL7LZ8zjJuBjiGW92TXyV48tnIrizJ/IBWvg2PeF3YcEZH9lk/BmOXuKwYvdPelwKwRTzTGPLbidRbGlhI99kKIV4YdR0Rkv+VTMPb2LVc1UkHGos6+FLz2BHV0Y2/7YNhxREQOSD4F4zkzu2rwQjP7FPD8yEcaO363ZjuLeJpkxUQ4/Oyw44iIHJB8eqv9IvCgmX2UNwvEAiAB/K8i5RoTnlixnn+MvkD0uEsgGg87jojIAdlnwXD3bcAZZnYO8Lbs4v9y998VNdko15tMk3xlCdXRXjjuA2HHERE5YHmNh2Fm1cCz7r6kyHnGjD+tb+FMX0oqVkPssLfclSwiMurk8xzG54EfA3eY2RcP5MPMbKGZvWxma83suiHWf9TMVmRfT5vZCfnuW26eXLOd86LLsCPP0yBJIjIm5HOGcTlBm4UBS9nPZy/MLArcCpwPNBE0pi9291U5m60Hznb3VjNbBNwBnJrnvmVl85o/Mc1a4ehFYUcRERkR+RSMfwb+Mzt98wF81inAWndfB2Bm9wDvB3Z/6bv70znbPwPMyHffcrKppZuj2v6Ixw078vyw44iIjIh8Gr3vBe4dgc+aDmzKmW8CTt3L9p8CflPovmZ2NXA1wMyZM/c36wH5w6s7OC/6Z/qmzaeytjGUDCIiI62UnQ/aEMt8yA2DO7I+BXyt0H3d/Q53X+DuCxobw/myfm7VOo6PrKPi6PeE8vkiIsWQ111SI6QJODRnfgawZfBGZnY8cCewyN2bC9m3HGQyjm98igiuh/VEZEwp5RnGc8AcM5ttZgngEmBx7gZmNpOgveRj7v5KIfuWi5e3dTA/9SKpSCVMXxB2HBGREbPPMwwzOx14xt2HvASUL3dPmdnngEeBKPATd19pZtdk198OfBOYDPzQzABS2ctLQ+57IHmK5bkNLZwWWUVq+inEdDutiIwh+d5We6uZvQI8Ajzi7lv358Pc/WHg4UHLbs+ZvhK4Mt99y9HKV9fx8cgmfI7GvhCRsSWfu6SuATCzo4FFwF1mVg8sISggf3T3dFFTjhLuTmTjUwCY2i9EZIzJuw3D3de4+03uvhA4F3gK+CvgT8UKN9psbO7muL5l9Edr4OD5YccRERlR+3WXlLv3EFweKvtLRKX07IYWToq8SvKQBSSipbwBTUSk+Ep5l9SY9+Jrmzkqsomqw08PO4qIyIjTn8EjKLlpKVEcDj057CgiIiMun9tqZwHXAkcALcAy4FfuvrGoyUaZnv40jbuWB7/R6SeFHUdEZMTlc0nql8Aa3uwt9gTgD2Z2q5lVFDPcaLLqjTZOsFfprDscqiaGHUdEZMTlUzCi7v5jd38CaHH3qwjONjYQdD8uwPLXd/H2yFqiM08JO4qISFHkUzB+m33KGrId/rl7yt3/BVDrbtaW9SuZbB1UzT4t7CgiIkWRT6P3l4Gvm9lS4JBs9+HdBMWiea97jiORzc8HEzPU4C0iY9M+zzDcPePu3wbOIhhn4iDgJOAlgie/x7323iTTutaQilRA49FhxxERKYq8b6t1926CHmLLspfYML20uY1jbSPdE+cyQQ/sicgYpQf3RsDqLe0cG9lAfPr8sKOIiBSN/hweAdtef4V664ZD54cdRUSkaHSGMRK2rgjeDz4h3BwiIkW03wXDzA7Wg3uQzjj1bWvIEIGpx4YdR0SkaA7kDOM/gDVm9p2RCjMavd7SzVG+no7aWZCoDjuOiEjR7Hcbhru/24JxVMf1n9Uvb21nXmQjmWlnhh1FRKSo8j7DsMBlZvbN7PxM4ORyHVu7VDZs2sR0a6b2sBPDjiIiUlSFXJL6IcHT3Zdm5zsIOiQc17o3vQhA/JC3hZxERKS4Crkkdaq7n2hmfwZw91YzSxQp16hhza8EE43HhBtERKTICjnDSJpZlGwHhGbWCGSKkmqU6E2mmdS9jr5oDUw4JOw4IiJFVUjB+B7wIDDVzL4NPAX8Q1FSjRLrd3ZxJJvpnnAEmIUdR0SkqPK6JJW9G+oPwPPAeYABH3D31UXMVvbW7+xiQWQzNJ4fdhQRkaLLq2C4u5vZQ+5+EsHoewJs3rKF99ou+mccF3YUEZGiK+SS1DNmpsEecvRsCU6wEgeN60dRRGScKKRgnENQNF4zsxVm9qKZrSjkw8xsoZm9bGZrzey6IdYfbWb/Y2Z9ZvbVQes2ZD9zWXYwp9BFml8OJhrnhhtERKQECrmt9oAGS8reYXUrcD7QBDxnZovdfVXOZi3A54EPDHOYc9x954HkGCnuzoTO1+i3ChL1M8OOIyJSdIUUjMuHWf73ee5/CrDW3dcBmNk9wPuB3QXD3bcD283sLwrIFYrmrn4OS2+ivWE2UyLq9FdExr5Cvum6cl5pgjOOWQXsPx3YlDPflF2WLwceM7Pns+OKh2r9zi6OiGwhNWlO2FFEREqikCFa/2/ufLaX2kKGax3qQQUvYP93uPsWM5sKPG5ma9z9D2/5kKCYXA0wc2bxLhVt3LqTk20nuw5S+4WIjA8Hci2lGji8gO2bgENz5mcAW/Ld2d23ZN+3EzxAeMow293h7gvcfUFjY2MB8QrTsnktABMOUcEQkfEh7zMMM3uRN88IokAj8H8K+KzngDlmNhvYDFwCfCTPz64BIu7ekZ2+gPzbToqif3tQMCKTjwgzhohIyRTS6H1hznQK2ObuqXx3dveUmX0OeJSg4PzE3Vea2TXZ9beb2UHAUmACkDGzLxKMtzEFeDB44JwYcLe7P1JA9hEX27U+mJg0O8wYIiIlU0jB+Ky7fy13gZn90+Ble+PuDwMPD1p2e870VoJLVYO1A2UzYLa7U9+ziZ54HVXVk8KOIyJSEoW0YQzVYdIBPZsxWu3s7Ge6b6WzRs9fiMj4sc8zDDP7DPBZ4PBBT3bXAU8XK1g529TazSzbSrrh1LCjiIiUTD6XpO4GfgP8I5DbnUeHu7cUJVWZa9q5ixNsJ62NavAWkfFjnwXD3duANuBSM5sIzAEqAcyMoZ6FGOva31hP1Jy6g48KO4qISMkUclvtlcAXCBqllwGnAf8DnFuUZGWsf0dwS23FVD3lLSLjRyGN3l8ATgY2uvs5wNuBHUVJVeaiu2+pLeS5RRGR0a2QgtHr7r0AZlbh7muAcfmYc03n6/REqqFmSthRRERKppDnMJrMrAF4iKAvp1YK6NpjrEhnnEn9W2ivnU6VxvEWkXGkkDG9P+/uu4C/M7MlQD0Q6tPWYXijrYeD2UGyVndIicj4ktclKXd3gjOLgfkn3X2xu/cXK1i52tTSw3TbSWSiHtoTkfFFY3oXaNv2rUywHiqnzAo7iohISRXShnEOcI2ZbSAYRMkITj6OL0awctW+LbhDqu4g3SElIuNLycb0HivSzRsBiE/SJSkRGV8KuST1OvBO4HJ330gwNsa0oqQqY9GOpmCiXgVDRMaXQgrGD4HTgUuz8x3ArSOeqMxVdm2h3xJ6BkNExp1CCsap7n4t0Avg7q1AoiipypS7U9//Bu2Jg0DPYIjIOFNIwUiaWZTsMK1m1ghkipKqTHX0pZjmO+mtPiTsKCIiJVdIwfge8CAw1cy+DTwF/ENRUpWprW29TLedpCcMNSigiMjYlvddUu7+MzN7HjiP4JbaD7j76qIlK0NbW9o4ytrYrDukRGQcKuS2WrIdDq4pUpay1/HGOgCqGg8LOYmISOkVMh5GJcFQrWcStGM8Bdw20IPteNCbfQZjwkHqR0pExp9CzjB+SnAr7fez85cC/wH81UiHKlfeugmAmPqREpFxqJCCMdfdT8iZX2Jmy0c6UDmLdL0RTNQdHG4QEZEQFHKX1J/N7LSBGTM7FfjjyEcqXxU922iPNEBsXD1+IiICFHaGcSrwcTN7PTs/E1htZi8yTjohrO3fQVdVIxPCDiIiEoJCCsbCoqUYBTr7UkzOtNBfpWcwRGR8KuQ5jI3FDFLutrb1MM1a6Kob90OCiMg4lXcbhpktMLMHzewFM1thZi+a2YpCPszMFprZy2a21syuG2L90Wb2P2bWZ2ZfLWTfYtva2kGjtROrV4O3iIxPhVyS+hnw/wEvsh99SGX7oboVOB9oAp4zs8Xuvipnsxbg88AH9mPfourYEXRrXjn50FJ9pIhIWSmkYOxw98UH8FmnAGvdfR2Amd0DvB/Y/aXv7tuB7Wb2F4XuW2y9LZsBqJ2iNgwRGZ8KKRjfMrM7gSeAvoGF7v6fee4/HdiUM99EcOfViO5rZlcDVwPMnDlyD9il27YAUDlJBUNExqdCCsYngKOBOG9eknIg34Ix1AASPtL7uvsdwB0ACxYsyPf4+9axNXjXQ3siMk4VUjBOcPd5B/BZTUBuA8AMYEsJ9h0R8e5tJIkRr55cyo8VESkbhTzp/YyZHXsAn/UcMMfMZptZArgEyLdN5ED2HRHVfdtpj02CSCG/MhGRsaOQM4wzgcvNbD1BG4ZRwBPe7p4ys88BjwJR4CfuvtLMrsmuv93MDgKWAhOAjJl9ETjW3duH2reA7AesLrmTrpqp6PxCRMarkj7p7e4PAw8PWnZ7zvRWgstNee1bKn2pNFMyzfRVHRPGx4uIlIVCrq+8DrwTuDz71LcD04qSqsw0d/Yz1VrJ1B4UdhQRkdAUUjB+CJxOMA4GBGNj3DriicpQc0sLE6yHyIRDwo4iIhKagnqrdfcTzezPAO7emm2AHvM6dgSPgFRMVMEQkfGrkDOMZLaLDgcws0b2o4uQ0ai7NRg4qWayCoaIjF+FFIzvAQ8CU83s2wRjev9jUVKVmf5dwUN7E1QwRGQcK6R785+Z2fPAeQS31H7A3VcXLVkZSXdsByBer0ZvERm/8i4YZvZP7v41YM0Qy8Y0695JBiNSNSnsKCIioSnkktT5QyxbNFJBylm8dycdkQkQLeQeARGRsWWf34Bm9hngs8DhgwZMqgP+WKxg5aSqv5mu+CTqww4iIhKifP5kvhv4DUEDd+5Idx3u3lKUVGXE3alLtdJXo05BRGR822fBcPc2oI03H9gbV7r700z0NpKVh4cdRUQkVOp6dR9auvqZYm14TWPYUUREQpVXwbDAuBzMurWtjVrrJVI3NewoIiKhyqtguLsDDxU3Snnqag7GaYpPGBf9LIqIDKvQAZROLlqSMtWzaxsAVQ16aE9ExrdCHiw4B/i0mW0EuihwAKXRKtkWdAtSM1ljeYvI+FZIwRgXD+kN5p1BtyDVE3WGISLjWyF9SW0sZpByZV07gvcaNXqLyPi2zzYMM3sq+95hZu3Z94FXW/EjhivW20wnNRCvDDuKiEio8nlw78zse13ucjM7E/hIkXKVjcq+ZtpjE6kNO4iISMgK6k3PzOYTPPH9YWA98EARMpWVmmQL3RUTw44hIhK6fDofPAq4hKBQNAP3Aubu5xQ5W1mYkGmlp2JO2DFEREKXzxnGGuC/gfe5+1oAM/tSUVOViVQ6Q4O30VGpjgdFRPJ5cO8vga3AEjP7VzMbGHFvzNvV1UsDXVCtgiEiss+C4e4PuvuHgaOB3wNfAqaZ2W1mdkGR84VqV+tOIubEalUwRETy7hrE3bvc/WfufiEwA1jGnuNjjDmdrUG3IPHaKSEnEREJ3351b+7uLe7+I3c/d6QDlZPuXcFT3lUN6tpcRKSk42GY2UIze9nM1prZW85Ost2ofy+7foWZnZizboOZvWhmy8xsaSny9rXvBKCmQU95i4gU9BzGgTCzKHArcD7QBDxnZovdfVXOZouAOdnXqcBt2fcB57j7zhJFJtXZDEDdJHVtLiJSyjOMU4C17r7O3fuBe4D3D9rm/cBPPfAM0GBmoXUT611BwVAbhohIaQvGdGBTznxTdlm+2zjwmJk9b2ZXD/chZna1mS01s6U7duw4oMDW00KKKFTU7XtjEZExrpQFY6hnN7yAbd7h7icSXLa61szOGupD3P0Od1/g7gsaGw+ssTrW10pHZALYuHjsRERkr0pZMJqA3HHBZwBb8t3G3QfetwMPElziKqqK5C66ovXF/hgRkVGhlAXjOWCOmc02swRB/1SLB22zGPh49m6p04A2d3/DzGrMrA7AzGqAC4CXih24KtVGX1wFQ0QESniXlLunzOxzwKNAFPiJu680s2uy628HHgbeC6wFuoFPZHefBjxowaWhGHC3uz9S7My16Q76EkcU+2NEREaFkhUMAHd/mKAo5C67PWfagWuH2G8dcELRA+ZIpTM00M5WdW0uIgKU+MG90aS9J0kDnVCtgiEiAioYw2prayFuaUw91YqIACW+JDWadLcG/UhF1VOtyKiVTCZpamqit7c37Chlp7KykhkzZhCPx/PeRwVjGD3twUN/iTo95S0yWjU1NVFXV8esWbMwPU+1m7vT3NxMU1MTs2fPzns/XZIaRn+248HKevVUKzJa9fb2MnnyZBWLQcyMyZMnF3zmpYIxjFTnQE+16nhQZDRTsRja/vxeVDCG4V0tANRqLAwREUAFY3i9LaTdiNXotloR2X/RaJT58+fvft144437dZwrrriC+++/H4Arr7ySVatWDbvt4sWLd3/OQw89tNdtC6FG72HEelrosFoaItGwo4jIKFZVVcWyZctG9Jh33nnnXtdfdNFFXHTRRUBQMC688EKOPfbYA/5cFYxhxPrb6IxMoCHsICIyIq7/1UpWbWkf0WMee8gEvvW+4wrer62tjVNOOYXFixczd+5cLr30Us4991yuuuoqamtr+fSnP82SJUuYOHEi99xzD4N73n7Xu97Fd77zHRYsWMAjjzzCN77xDdLpNFOmTOGJJ57grrvuYunSpXzkIx9h8eLFPPnkk9xwww088MADHHHE/nd3pEtSw6hItdMb0zgYInJgenp69rgkde+991JfX88PfvADrrjiCu655x5aW1u56qqrAOjq6uLEE0/khRde4Oyzz+b6668f9tg7duzgqquu4oEHHmD58uXcd999e6w/44wzuOiii/iXf/kXli1bdkDFAnSGMayKVAf9lQ1hxxCREbI/ZwIjYbhLUueffz733Xcf1157LcuXL9+9PBKJ8OEPfxiAyy67jIsvvnjYYz/zzDOcddZZu5+lmDRp0siGH0RnGMOoznSSSkwIO4aIjFGZTIbVq1dTVVVFS0vLsNvt7fZXdy/pbcMqGENwd2q9i3RCY2GISHHcdNNNHHPMMfz85z/nk5/8JMlkEggKycDdUHfffTdnnnnmsMc4/fTTefLJJ1m/fj3AkIWnrq6Ojo6OEcmsS1JD6O5LUUcXVKpgiMiBGWjDGLBw4UI++clPcuedd/Lss89SV1fHWWedxQ033MD1119PTU0NK1eu5KSTTqK+vp5777132GM3NjZyxx13cPHFF5PJZJg6dSqPP/74HttccsklXHXVVXzve9/j/vvvP6B2DAuGoBibFixY4EuXLi14vzd27OTgW49g2dwvMf/Svxv5YCJSEqtXr+aYY44JO0ZBamtr6ezsLMlnDfX7MbPn3X3BUNvrktQQutuC07pIdUO4QUREyogKxhB6OoKCEVPBEJESK9XZxf5QwRhCf2dQMBK1xb1FTURkNFHBGEJ/VysAFSoYIiK7qWAMId29C4DqCSoYIiIDVDCGkBkoGPUabU9EZIAKxlB6dwFQWdsQagwRGf1qa2tH5Di///3vufDCC4E9uy8fzhlnnAHAhg0buPvuu0ckgwrGEKyvjW4qsFgi7CgiIm9x0UUXcd111+11m6effhoY2YKhJ72HEOtvp9NqqQ47iIiMnN9cB1tfHNljHjQPFuU3INLvf/97vvWtbzFt2jSWLVvGxRdfzLx587jlllvo6enhoYce4ogjjuCKK66gsrKSlStXsm3bNr773e/uPrMYMNB9+Q9+8AO2bdvGNddcw7p16wC47bbbOOOMM3Y/AHjdddexevVq5s+fz+WXX86XvvSl/f5xVTCGEE920B0ZmdNIEZEBy5cvZ/Xq1UyaNInDDz+cK6+8kmeffZZbbrmF73//+9x8881AcFbw5JNP8tprr3HOOeewdu3aYY/5+c9/nrPPPpsHH3yQdDr9luc4brzxRr7zne/w61//+oDzq2AMoSLVQW9UBUNkTMnzTKCYTj75ZA4++GAAjjjiCC644AIA5s2bx5IlS3Zv96EPfYhIJMKcOXM4/PDDWbNmzbDH/N3vfsdPf/pTIBgOtr6+eH3glbQNw8wWmtnLZrbWzN5yAc4C38uuX2FmJ+a770iqTHfQF1PX5iIysioqKnZPRyKR3fORSIRUKrV73eAuy0vZhfnelKxgmFkUuBVYBBwLXGpmgweZXQTMyb6uBm4rYN8RU53pJBlXwRCRcNx3331kMhlee+011q1bx9y5c4fd9rzzzuO2224DIJ1O096+5zC0I9m9eSnPME4B1rr7OnfvB+4B3j9om/cDP/XAM0CDmR2c574jpta7NHiSiIRm7ty5nH322SxatIjbb7+dysrKYbe95ZZbWLJkCfPmzeOkk05i5cqVe6w//vjjicVinHDCCdx0000HlKtk3Zub2QeBhe5+ZXb+Y8Cp7v65nG1+Ddzo7k9l558AvgbM2te+Oce4muDshJkzZ560cePGwoK6s/SmD8KR72bBRZ8p+OcUkfIxGrs3v+KKK7jwwgv54Ac/WPTPKrR781I2eg91EW5wtRpum3z2DRa63wHcAcF4GIUEDBIYC778QMG7iYiMdaUsGE3AoTnzM4AteW6TyGNfEZFR76677go7wrBK2YbxHDDHzGabWQK4BFg8aJvFwMezd0udBrS5+xt57isi8hZjeVTRA7E/v5eSnWG4e8rMPgc8CkSBn7j7SjO7Jrv+duBh4L3AWqAb+MTe9i1VdhEZnSorK2lubmby5Mllc2tqOXB3mpub99qYPhSN6S0iY1YymaSpqYne3t6wo5SdyspKZsyYQTwe32N5uTR6i4iUVDweZ/bs2WHHGDPUW62IiORFBUNERPKigiEiInkZ043eZrYDKPBR792mADtHME4xjaasoLzFNJqygvIW0/5mPczdG4daMaYLxoEws6XD3SlQbkZTVlDeYhpNWUF5i6kYWXVJSkRE8qKCISIieVHBGN4dYQcowGjKCspbTKMpKyhvMY14VrVhiIhIXnSGISIieVHBEBGRvKhgDGJmC83sZTNba2bXhZ1nMDP7iZltN7OXcpZNMrPHzezV7PvEMDPmMrNDzWyJma02s5Vm9oXs8rLLbGaVZvasmS3PZr2+XLPmMrOomf05O2JlWec1sw1m9qKZLTOzpdllZZnXzBrM7H4zW5P993t6GWedm/2dDrzazeyLI51XBSOHmUWBW4FFwLHApWZ2bLip3uIuYOGgZdcBT7j7HOCJ7Hy5SAFfcfdjgNOAa7O/03LM3Aec6+4nAPOBhdlxWcoxa64vAKtz5ss97znuPj/nGYFyzXsL8Ii7Hw2cQPA7Lsus7v5y9nc6HziJYHiIBxnpvO6uV/YFnA48mjP/deDrYecaIucs4KWc+ZeBg7PTBwMvh51xL9l/CZxf7pmBauAF4NRyzkow+uQTwLnAr8v93wOwAZgyaFnZ5QUmAOvJ3hhUzlmHyH4B8Mdi5NUZxp6mA5ty5puyy8rdNA9GJiT7PjXkPEMys1nA24E/UaaZs5d3lgHbgcfdvWyzZt0M/DWQyVlWznkdeMzMnjezq7PLyjHv4cAO4N+yl/vuNLMayjPrYJcAP89Oj2heFYw9DTUkl+47HgFmVgs8AHzR3dvDzjMcd097cFo/AzjFzN4WcqRhmdmFwHZ3fz7sLAV4h7ufSHDZ91ozOyvsQMOIAScCt7n724EuyuTy095kh7C+CLivGMdXwdhTE3BozvwMYEtIWQqxzcwOBsi+bw85zx7MLE5QLH7m7v+ZXVzWmd19F/B7gvaics36DuAiM9sA3AOca2b/j/LNi7tvyb5vJ7jGfgrlmbcJaMqeYQLcT1BAyjFrrkXAC+6+LTs/onlVMPb0HDDHzGZnK/UlwOKQM+VjMXB5dvpygnaCsmDBQMo/Bla7+3dzVpVdZjNrNLOG7HQV8G5gDWWYFcDdv+7uM9x9FsG/1d+5+2WUaV4zqzGzuoFpgmvtL1GGed19K7DJzOZmF50HrKIMsw5yKW9ejoKRzht2A025vYD3Aq8ArwF/E3aeIfL9HHgDSBL8FfQpYDJBw+er2fdJYefMyXsmwWW9FcCy7Ou95ZgZOB74czbrS8A3s8vLLusQ2d/Fm43eZZmXoF1gefa1cuD/rzLOOx9Ymv338BAwsVyzZvNWA81Afc6yEc2rrkFERCQvuiQlIiJ5UcEQEZG8qGCIiEheVDBERCQvKhgiIpIXFQwREcmLCoaIiORFBUMkh5lNzhlTYKuZbc6ZT5jZ0yXIMMPMPryX9T8ys3fkzM/KHR9FpFhUMERyuHuzvzmuwO3ATQPz7t7v7meUIMZ5BP0WDedU4JkS5BDZgwqGSAHMrDP7F/2abJfXL5nZz8zs3Wb2x+zIZqfkbH9ZdhS/Zdkzg+g+jn8m8F3gg9l9Zg9afwzwirunB+0aNbN/zY4U+Fi2LyyREaWCIbJ/jiQYke144GjgIwT9Zn0V+Abs/nL/MEGX3vOBNPDRvR3U3Z8i6ATz/dmzmvWDNlkEPDLErnOAW939OGAX8Jf79VOJ7EUs7AAio9R6d38RwMxWEgyD6Wb2IsGIiBBcWjoJeC7otJcq8uteei7BSGlDeQ/wiWHyLMtOP5+TQWTEqGCI7J++nOlMznyGN/+/MuDf3f3r+R7UzCYDbe6eHGJdNdDg2TEl9pInTVCcREaULkmJFM8TBG0RUwHMbJKZHZadfsLMhhr+dzbDD9p1DrCkKElF8qCCIVIk7r4K+FuCMaxXAI8DB5tZhKANpGWI3dYAU7KN6YPvyBqu/UKkJDQehkiJZccJ/6S7f7nA/V4ATh3qcpVIKahgiIhIXnRJSkRE8qKCISIieVHBEBGRvKhgiIhIXlQwREQkLyoYIiKSFxUMERHJy/8PqIrMj+9zRqsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(t / 3600, θ_exp[-1, :], t / 3600, θ_imp[-1, :])\n",
    "ax.set(xlabel='Time, $t$ / h', ylabel='Air temperature, $θ$ / °C', title='Step input: $Q_h$')\n",
    "ax.legend(['Explicit', 'Implicit'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1e749af-0093-41f2-be11-5f79eaf0207e",
   "metadata": {
    "tags": []
   },
   "source": [
    "> Figure 4. Step response to indoor heat flow rate $\\dot{Q}_h$ obtained by explicit and implicit Euler integration of the state-space model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43472649-b64d-4165-8269-aeb752898315",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Simulation with outdoor temperature from weather data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2d6c4c1-6454-4bdf-94a7-c96335596e57",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Outdoor temperature from weather data\n",
    "We want the weather data for Lyon from `start_date`to `end_date`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "e93f760c-381f-4729-99e9-b209cee7ea98",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "start_date = '2000-04-10'\n",
    "end_date = '2000-05-15'\n",
    "filename = './weather_data/FRA_Lyon.074810_IWEC.epw'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42e3bb53-5406-4c21-a06f-e021fe7429cd",
   "metadata": {},
   "source": [
    "From the weather data, only the air temperature, the direct solar radiation on a normal surface and the diffuse solar radiation on a horizontal surface are kept. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "460b93f7-256c-4339-befd-43944e5bd496",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "[data, meta] = dm4bem.read_epw(filename, coerce_year=None)\n",
    "# weather = data[[\"temp_air\", \"dir_n_rad\", \"dif_h_rad\"]]\n",
    "weather = data[[\"temp_air\"]]\n",
    "del data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a71d288a-a902-417f-9dbd-e6486fd53f11",
   "metadata": {},
   "source": [
    "In the weather data file, each month is taken from another year. We will replace the years with only one value, e.g. 2000, then keep only the values between `start_date` and `end_date`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "eac78fba-d23d-4b02-a0d0-85f452cc0e58",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>temp_air</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-04-10 00:00:00+01:00</th>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-10 01:00:00+01:00</th>\n",
       "      <td>4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-10 02:00:00+01:00</th>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-10 03:00:00+01:00</th>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-10 04:00:00+01:00</th>\n",
       "      <td>3.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-15 19:00:00+01:00</th>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-15 20:00:00+01:00</th>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-15 21:00:00+01:00</th>\n",
       "      <td>12.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-15 22:00:00+01:00</th>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-15 23:00:00+01:00</th>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>864 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                           temp_air\n",
       "2000-04-10 00:00:00+01:00       5.1\n",
       "2000-04-10 01:00:00+01:00       4.5\n",
       "2000-04-10 02:00:00+01:00       3.8\n",
       "2000-04-10 03:00:00+01:00       3.2\n",
       "2000-04-10 04:00:00+01:00       3.1\n",
       "...                             ...\n",
       "2000-05-15 19:00:00+01:00      14.0\n",
       "2000-05-15 20:00:00+01:00      14.0\n",
       "2000-05-15 21:00:00+01:00      12.6\n",
       "2000-05-15 22:00:00+01:00      12.0\n",
       "2000-05-15 23:00:00+01:00      12.0\n",
       "\n",
       "[864 rows x 1 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weather.index = weather.index.map(lambda t: t.replace(year=2000))\n",
    "weather = weather.loc[start_date:end_date]\n",
    "pd.DataFrame(weather)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a9bf28f6-ba5e-409d-a11d-13febf5905a5",
   "metadata": {},
   "outputs": [
    {
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       "      <th>2</th>\n",
       "      <td>7200</td>\n",
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       "    <tr>\n",
       "      <th>862</th>\n",
       "      <td>3103200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>863</th>\n",
       "      <td>3106800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>864 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0\n",
       "0          0\n",
       "1       3600\n",
       "2       7200\n",
       "3      10800\n",
       "4      14400\n",
       "..       ...\n",
       "859  3092400\n",
       "860  3096000\n",
       "861  3099600\n",
       "862  3103200\n",
       "863  3106800\n",
       "\n",
       "[864 rows x 1 columns]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# time vector for weather data at 1 h time step\n",
    "tw = np.arange(0, 3600 * weather.shape[0], 3600)\n",
    "pd.DataFrame(tw)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec3e289-46c2-472a-9850-67be3c25a4fd",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Resample the weather data\n",
    "The time vector for simulation is at time step $\\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "cbb1d6d8-7425-474d-99c2-797519ed8579",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# time vector for simulation\n",
    "t = np.arange(0, 3600 * weather.shape[0], Δt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bdfc80d-267c-4180-9a57-b05f1f99fbc3",
   "metadata": {
    "tags": []
   },
   "source": [
    "The outdoor temperature $T_o$ (which is at a time step of $1 \\, \\mathrm{hour} = 3600 \\, \\mathrm{s}$) needs to be re-sampled at a time step equal to $\\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "79ebcaff-6a67-44ef-919d-84179cdd7f03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>θ °C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.00e+00</th>\n",
       "      <td>5.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.60e+02</th>\n",
       "      <td>5.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7.20e+02</th>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.08e+03</th>\n",
       "      <td>4.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.44e+03</th>\n",
       "      <td>4.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.11e+06</th>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.11e+06</th>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.11e+06</th>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.11e+06</th>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.11e+06</th>\n",
       "      <td>12.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8640 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           θ °C\n",
       "0.00e+00   5.10\n",
       "3.60e+02   5.04\n",
       "7.20e+02   4.98\n",
       "1.08e+03   4.92\n",
       "1.44e+03   4.86\n",
       "...         ...\n",
       "3.11e+06  12.00\n",
       "3.11e+06  12.00\n",
       "3.11e+06  12.00\n",
       "3.11e+06  12.00\n",
       "3.11e+06  12.00\n",
       "\n",
       "[8640 rows x 1 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# resample outdoor temperature at timestep Δt\n",
    "θ_out = np.interp(t, tw, weather['temp_air'])\n",
    "pd.DataFrame(θ_out, index=t, columns=['θ °C'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55dad0f4-91b2-47cd-99fc-c514403ab019",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Input vector\n",
    "The input vector $u$ is formed as a block vector from outdoor temperature and indoor heat flow $\\dot{Q}_h$, which is zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "e58752a7-c128-468f-9095-d8005c691131",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>8630</th>\n",
       "      <th>8631</th>\n",
       "      <th>8632</th>\n",
       "      <th>8633</th>\n",
       "      <th>8634</th>\n",
       "      <th>8635</th>\n",
       "      <th>8636</th>\n",
       "      <th>8637</th>\n",
       "      <th>8638</th>\n",
       "      <th>8639</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>To</th>\n",
       "      <td>5.1</td>\n",
       "      <td>5.04</td>\n",
       "      <td>4.98</td>\n",
       "      <td>4.92</td>\n",
       "      <td>4.86</td>\n",
       "      <td>4.8</td>\n",
       "      <td>4.74</td>\n",
       "      <td>4.68</td>\n",
       "      <td>4.62</td>\n",
       "      <td>4.56</td>\n",
       "      <td>...</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Qh</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 8640 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0     1     2     3     4     5     6     7     8     9     ...  8630  \\\n",
       "To   5.1  5.04  4.98  4.92  4.86   4.8  4.74  4.68  4.62  4.56  ...  12.0   \n",
       "Qh   0.0  0.00  0.00  0.00  0.00   0.0  0.00  0.00  0.00  0.00  ...   0.0   \n",
       "\n",
       "    8631  8632  8633  8634  8635  8636  8637  8638  8639  \n",
       "To  12.0  12.0  12.0  12.0  12.0  12.0  12.0  12.0  12.0  \n",
       "Qh   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  \n",
       "\n",
       "[2 rows x 8640 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# input vector [To, Qh]\n",
    "u = np.block([[θ_out],\n",
    "             [np.zeros(θ_out.shape[0])]])\n",
    "pd.DataFrame(u, index=['To', 'Qh'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6709c8f4-b0f3-4d05-bf05-402588fc4e91",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Time integration\n",
    "The responses are obtained by initializing the temperature vectors for explicit and implicit Euler and by integrating in time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "537a9217-949e-411c-b6c6-79a6f0029680",
   "metadata": {},
   "outputs": [],
   "source": [
    "θ_exp = 15 * np.ones([no_θ, t.shape[0]])\n",
    "θ_imp = 15 * np.ones([no_θ, t.shape[0]])\n",
    "for k in range(u.shape[1] - 1):\n",
    "    θ_exp[:, k + 1] = (np.eye(no_θ) + Δt * As) @\\\n",
    "        θ_exp[:, k] + Δt * Bs @ u[:, k]\n",
    "    θ_imp[:, k + 1] = np.linalg.inv(np.eye(no_θ) - Δt * As) @\\\n",
    "        (θ_imp[:, k] + Δt * Bs @ u[:, k])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c10c044b-c1b6-47f7-a3ca-c868d81960ba",
   "metadata": {},
   "source": [
    "#### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "325d6b49-685e-46c9-a663-3f53d0abd23d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(t / 3600 / 24, θ_out, label='Outdoor temperature')\n",
    "ax.plot(t / 3600 / 24, θ_exp[-1, :], label='Indoor temperature')\n",
    "ax.set(xlabel='Time, $t$ / day',\n",
    "       ylabel='Air temperature, $θ$ / °C',\n",
    "       title='Explicit Euler')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f71a32-c758-405b-8062-a4358c957ba4",
   "metadata": {},
   "source": [
    "> Figure 5. Simulation of wall response to the variation of the outdoor temperature obtained with Euler **explicit** method for integration in time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4b737753-1900-4c53-b307-07da0361d5ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(t / 3600 / 24, θ_out, label='Outdoor temperature')\n",
    "ax.plot(t / 3600 / 24, θ_imp[-1, :], label='Indoor temperature')\n",
    "ax.set(xlabel='Time $t$ / day]',\n",
    "       ylabel='Air temperature, $θ$ / °C',\n",
    "       title='Implicit Euler')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d785a7a-a339-457e-bd4a-d44e6b2bf8e9",
   "metadata": {},
   "source": [
    "> Figure 6. Simulation of wall response to the variation of the outdoor temperature obtained with Euler **implicit** method for integration in time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4075e33-f12a-4de7-a24f-f89df2af70f3",
   "metadata": {},
   "source": [
    "### Simulation with outdoor temperature from weather data by using Pandas\n",
    "\n",
    "The same code as in the prevoius section with the differenec that Pandas are used for plotting the results of the simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "e86e74c2-1e48-481b-b917-b519a167f663",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation with outdoor temperature from weather data with Pandas\n",
    "# -----------------------------------------------------------------\n",
    "start_date = '2000-04-10'\n",
    "end_date = '2000-05-15'\n",
    "\n",
    "# read data and keep air temperature\n",
    "filename = './weather_data/FRA_Lyon.074810_IWEC.epw'\n",
    "[data, meta] = dm4bem.read_epw(filename, coerce_year=None)\n",
    "weather = data[[\"temp_air\"]].copy()\n",
    "del data\n",
    "\n",
    "# replace years with year 2000 and select time interval\n",
    "weather.index = weather.index.map(lambda t: t.replace(year=2000))\n",
    "weather = weather.loc[start_date:end_date]\n",
    "\n",
    "# resample weather data\n",
    "data = weather['temp_air']\n",
    "data = data.resample(str(Δt) + 'S').interpolate(method='linear')\n",
    "data = data.rename('To').to_frame()\n",
    "\n",
    "# indoor auxiliary heat\n",
    "data['Qa'] = 0 * np.ones(data.shape[0])\n",
    "\n",
    "# input vector\n",
    "u = data[['To', 'Qa']]\n",
    "\n",
    "# initial conditions\n",
    "θ_exp = 15 * np.ones([As.shape[0], u.shape[0]])\n",
    "θ_imp = 15 * np.ones([As.shape[0], u.shape[0]])\n",
    "\n",
    "# time integration: Euler explicit & implicit\n",
    "n_states = As.shape[0]\n",
    "I = np.eye(n_states)\n",
    "\n",
    "for k in range(u.shape[0] - 1):\n",
    "    θ_exp[:, k + 1] = (I + Δt * As) @ θ_exp[:, k]\\\n",
    "        + Δt * Bs @ u.iloc[k, :]\n",
    "    θ_imp[:, k + 1] = np.linalg.inv(I - Δt * As) @\\\n",
    "        (θ_imp[:, k] + Δt * Bs @ u.iloc[k, :])\n",
    "\n",
    "data['θi_exp'] = θ_exp[-1, :]\n",
    "data['θi_imp'] = θ_imp[-1, :]\n",
    "\n",
    "ax = data[['To', 'θi_exp']].plot()\n",
    "ax.legend(['Outdoor temperature', 'Indoor temperature'])\n",
    "ax.set(xlabel='Time',\n",
    "       ylabel='Air temperature, $θ$ / °C',\n",
    "       title='Explicit Euler')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ee5618-d909-4cb4-904c-182e5245fe2c",
   "metadata": {},
   "source": [
    "> Figure 7. Simulation of wall response to the variation of the outdoor temperature obtained with Euler **explicit** method for integration in time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "3090cd6f-bd93-40eb-9f62-b2baef8c085b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = data[['To', 'θi_imp']].plot()\n",
    "ax.legend(['Outdoor temperature', 'Indoor temperature'])\n",
    "ax.set(xlabel='Time',\n",
    "       ylabel='Air temperature, $θ$ / °C',\n",
    "       title='Implicit Euler')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b793f148-dd06-42c9-937d-b92c4a8d7ee3",
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   "source": [
    "> Figure 8. Simulation of wall response to the variation of the outdoor temperature obtained with Euler **implicit** method for integration in time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6276fa9-5935-405d-ab0f-461628ed5b5c",
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   "source": [
    "## Discussion\n",
    "\n",
    "- Change the time step to do it slightly larger than the maximum time step. Compare the results of obtained with Euler explicit and Euler implicit methods.\n",
    "- Interchnage the materials  of the layers so that layer 1 to be insulation and layer 2 to be concrete. Discuss the step responses and the simuation for weather. Give arguments for the advantages and the disadvanted of indoor and outdoor insulation. Explain the difference in the maximum time step for numerical integration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "352c7f79-4e5f-4d20-ba5a-a5bb80681fcc",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## References\n",
    "\n",
    "Ghiaus, C. (2013) Causality issue in the heat balance method for calculating the design heating and cooling loads, *Energy* 50: 292-301, https://doi.org/10.1016/j.energy.2012.10.024, [hal-03605823](https://hal.archives-ouvertes.fr/hal-03605823/document)\n",
    "\n",
    "C. Ghiaus (2021). Dynamic Models for Energy Control of Smart Homes, in *S. Ploix M. Amayri, N. Bouguila (eds.) Towards Energy Smart Homes*, Online ISBN: 978-3-030-76477-7, Print ISBN: 978-3-030-76476-0, Springer, pp. 163-198 (ref.)\n",
    "[DOI 10.1007/978-3-030-76477-7_5](https://doi.org/10.1007/978-3-030-76477-7_5), [HAL 03578578](https://hal.archives-ouvertes.fr/hal-03578578/document)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "003e5b45-2181-4715-858a-ae4a8382eb5a",
   "metadata": {},
   "source": [
    "# [Thermal circuit and state-space representation for a thermal circuit with capacities in some nodes: cubic building](03CubicBuilding.ipynb)\n",
    "\n",
    "# [Thermal circuits assembling](04AssemblingCircuits.ipynb)\n",
    "\n",
    "# [Switch between models: heating & cooling and free-running](05SwitchModels.ipynb)\n",
    "\n",
    "# [Control input: heating & cooling and free-running](06Control_Input.ipynb)\n",
    "\n",
    "# [Radiation coupled with convection](07Coupled_rad_convection.ipynb)\n",
    "\n",
    "# [Sensible thermal load in steady-state](08Thermal_load.ipynb)\n",
    "\n",
    "# [Air flow by ventilation](09Air_flow_ventilation.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dec76f9-0f69-43e0-bc37-70def7f12668",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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