{ "cells": [ { "cell_type": "markdown", "id": "4211e79f", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 1, "id": "62858fc1", "metadata": { "load": "myst_code_init.py", "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading pyMOR defaults from file /builds/pymor/pymor/docs/source/pymor_defaults.py\n" ] } ], "source": [ "import warnings\n", "\n", "import matplotlib as mpl\n", "from IPython import get_ipython\n", "\n", "import pymor.tools.random\n", "\n", "ip = get_ipython()\n", "if ip is not None:\n", " ip.run_line_magic('matplotlib', 'inline')\n", "\n", "warnings.filterwarnings('ignore', category=UserWarning, module='torch')\n", "\n", "pymor.tools.random._default_random_state = None\n", "\n", "mpl.rcParams['figure.facecolor'] = (1.0, 1.0, 1.0, 0.0)\n" ] }, { "cell_type": "markdown", "id": "04becf6c", "metadata": {}, "source": [ "# Tutorial: Linear time-invariant systems\n", "\n", "In this tutorial,\n", "we discuss finite-dimensional, continuous-time, linear time-invariant (LTI)\n", "systems of the form\n", "\n", "```{math}\n", "\\begin{align}\n", " E \\dot{x}(t) & = A x(t) + B u(t), \\\\\n", " y(t) & = C x(t) + D u(t).\n", "\\end{align}\n", "```\n", "\n", "where\n", "{math}`u` is the input,\n", "{math}`x` the state, and\n", "{math}`y` the output of the system,\n", "and {math}`A, B, C, D, E` are matrices of appropriate dimensions\n", "(more details can be found in {cite}`A05`).\n", "In pyMOR, these models are captured by `LTIModels`,\n", "which contain the matrices {math}`A, B, C, D, E` as `Operators`.\n", "We start by building an `LTIModel` and then demonstrate some of its properties,\n", "using a discretized heat equation as the example.\n", "\n", "We focus on a non-parametric example,\n", "but parametric LTI systems can be handled similarly\n", "by constructing {math}`A, B, C, D, E` as parametric `Operators` and\n", "passing `parameter_values` via the `mu` argument to the methods of the\n", "`LTIModel`.\n", "\n", "::: {note}\n", "\n", "Discrete-time LTI systems can be constructed by passing positive values for the\n", "`sampling_time` to any constructor of an `LTIModel`.\n", "\n", ":::\n", "\n", "## Building a model\n", "\n", "We consider the following one-dimensional heat equation over {math}`(0, 1)` with\n", "two inputs {math}`u_1, u_2` and three outputs {math}`y_1, y_2, y_2`:\n", "\n", "```{math}\n", "\\begin{align}\n", " \\partial_t T(\\xi, t) & = \\partial_{\\xi \\xi} T(\\xi, t) + u_1(t),\n", " & 0 < \\xi < 1,\\ t > 0, \\\\\n", " -\\partial_\\xi T(0, t) & = -T(0, t) + u_2(t),\n", " & t > 0, \\\\\n", " \\partial_\\xi T(1, t) & = -T(1, t),\n", " & t > 0, \\\\\n", " y_k(t) & = 3 \\int_{\\frac{k - 1}{3}}^{\\frac{k}{3}} T(\\xi, t) \\, \\mathrm{d}\\xi,\n", " & t > 0,\\ k = 1, 2, 3.\n", "\\end{align}\n", "```\n", "\n", "There are many ways of building an `LTIModel`.\n", "Here, we show how to build one from custom matrices,\n", "instead of using a discretizer as in {doc}`tutorial_builtin_discretizer`\n", "(and the `to_lti` method of\n", "`InstationaryModel` to obtain an `LTIModel`).\n", "In particular, we will use the\n", "`from_matrices` method of `LTIModel`,\n", "which instantiates an `LTIModel` from NumPy or SciPy matrices.\n", "\n", "First, we do the necessary imports and some matplotlib style choices." ] }, { "cell_type": "code", "execution_count": 2, "id": "47504bf9", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.sparse as sps\n", "from pymor.models.iosys import LTIModel\n", "\n", "plt.rcParams['axes.grid'] = True" ] }, { "cell_type": "markdown", "id": "1ebb4433", "metadata": {}, "source": [ "Next, we can assemble the matrices based on a centered finite difference\n", "approximation using standard methods of NumPy and SciPy." ] }, { "cell_type": "code", "execution_count": 3, "id": "7cb78cd0", "metadata": { "load": "heat_equation.py" }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.sparse as sps\n", "\n", "k = 50\n", "n = 2 * k + 1\n", "\n", "E = sps.eye(n, format='lil')\n", "E[0, 0] = E[-1, -1] = 0.5\n", "E = E.tocsc()\n", "\n", "d0 = n * [-2 * (n - 1)**2]\n", "d1 = (n - 1) * [(n - 1)**2]\n", "A = sps.diags([d1, d0, d1], [-1, 0, 1], format='lil')\n", "A[0, 0] = A[-1, -1] = -n * (n - 1)\n", "A = A.tocsc()\n", "\n", "B = np.zeros((n, 2))\n", "B[:, 0] = 1\n", "B[0, 0] = B[-1, 0] = 0.5\n", "B[0, 1] = n - 1\n", "\n", "C = np.zeros((3, n))\n", "C[0, :n//3] = C[1, n//3:2*n//3] = C[2, 2*n//3:] = 1\n", "C /= C.sum(axis=1)[:, np.newaxis]\n" ] }, { "cell_type": "markdown", "id": "c7aec38f", "metadata": {}, "source": [ "Then, we can create an `LTIModel` from NumPy and SciPy matrices `A`, `B`, `C`,\n", "`E`." ] }, { "cell_type": "code", "execution_count": 4, "id": "55f55b90", "metadata": {}, "outputs": [], "source": [ "fom = LTIModel.from_matrices(A, B, C, E=E)" ] }, { "cell_type": "markdown", "id": "385d92bd", "metadata": {}, "source": [ "We can take a look at the internal representation of the `LTIModel` `fom`." ] }, { "cell_type": "code", "execution_count": 5, "id": "85c24e05", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LTIModel(\n", " NumpyMatrixOperator(<101x101 sparse, 301 nnz>, solver=ScipySpSolveSolver(check_finite=True)),\n", " NumpyMatrixOperator(<101x2 dense>, solver=ScipyLUSolveSolver(check_finite=True)),\n", " NumpyMatrixOperator(<3x101 dense>, solver=ScipyLUSolveSolver(check_finite=True)),\n", " D=ZeroOperator(NumpyVectorSpace(3), NumpyVectorSpace(2)),\n", " E=NumpyMatrixOperator(<101x101 sparse, 101 nnz>, solver=ScipySpSolveSolver(check_finite=True)),\n", " presets={})" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom" ] }, { "cell_type": "markdown", "id": "a0b8d35e", "metadata": {}, "source": [ "From this, we see that the matrices were wrapped in `NumpyMatrixOperators`,\n", "while the default value was chosen for the {math}`D` matrix\n", "(`ZeroOperator`).\n", "The operators in an `LTIModel` can be accessed via its attributes, e.g.,\n", "`fom.A` is the `Operator` representing the {math}`A` matrix.\n", "\n", "We can also see some basic information from `fom`'s string representation" ] }, { "cell_type": "code", "execution_count": 6, "id": "2c62e7d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LTIModel\n", " class: LTIModel\n", " number of equations: 101\n", " number of inputs: 2\n", " number of outputs: 3\n", " continuous-time\n", " linear time-invariant\n", " solution_space: NumpyVectorSpace(101)\n" ] } ], "source": [ "print(fom)" ] }, { "cell_type": "markdown", "id": "1e793640", "metadata": {}, "source": [ "which gives the dimensions of the underlying system more directly,\n", "together with some of its properties.\n", "\n", "## Time-domain simulation\n", "\n", "The `solve` and `output` methods can be used to respectively compute the\n", "solution and output trajectories.\n", "For this, it is necessary to set the final time and the time-stepper.\n", "This could have been done in the `from_matrices` call.\n", "Instead of creating a new model using `from_matrices`,\n", "we can redefine `fom` using its `with_` method." ] }, { "cell_type": "code", "execution_count": 7, "id": "44168f18", "metadata": {}, "outputs": [], "source": [ "from pymor.algorithms.timestepping import ImplicitEulerTimeStepper\n", "fom = fom.with_(T=4, time_stepper=ImplicitEulerTimeStepper(200))" ] }, { "cell_type": "markdown", "id": "4bb586dd", "metadata": {}, "source": [ "With this done, we can compute the output for some given input and plot it." ] }, { "cell_type": "code", "execution_count": 8, "id": "7948065b", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "25b59e8208a24db89274b61dae5680de", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Y = fom.output(input='[sin(4 * t[0]), sin(6 * t[0])]')\n", "fig, ax = plt.subplots()\n", "for i, y in enumerate(Y):\n", " ax.plot(np.linspace(0, fom.T, fom.time_stepper.nt + 1), y, label=f'$y_{i+1}(t)$')\n", "_ = ax.set(xlabel='$t$', ylabel='$y(t)$', title='Output')\n", "_ = ax.legend()" ] }, { "cell_type": "markdown", "id": "8f6e55f5", "metadata": {}, "source": [ "Additionally, there are the `impulse_resp` and `step_resp` methods for computing\n", "the impulse and step responses, respectively.\n", "\n", "Impulse response for continuous-time LTI systems is given by\n", "\n", "```{math}\n", "h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t),\n", "```\n", "\n", "where {math}`\\delta` is the Dirac function.\n", "\n", "For computations, we ignore the {math}`D` term and compute the first part by\n", "integrating the ODE system\n", "\n", "```{math}\n", "E \\dot{x}_i(t) = A x_i(t),\\ x_i(0) = E^{-1} B e_i\n", "```\n", "\n", "for canonical basis vectors {math}`e_i` to get the {math}`i`-th column of\n", "{math}`h_i(t) = C x_i(t)`." ] }, { "cell_type": "code", "execution_count": 9, "id": "6103fbb9", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "431b3e1213be4f85a9c29ab0d075aa21", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_impulse = fom.impulse_resp()\n", "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n", "for i in range(fom.dim_output):\n", " for j in range(fom.dim_input):\n", " ax[i, j].plot(np.linspace(0, fom.T, y_impulse.shape[1]), y_impulse[i, :, j])\n", "for i in range(fom.dim_output):\n", " ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n", "for j in range(fom.dim_input):\n", " ax[0, j].set_title(f'Input {j + 1}')\n", " ax[-1, j].set_xlabel('Time')\n", "_ = fig.suptitle('Impulse response')" ] }, { "cell_type": "markdown", "id": "c007b008", "metadata": {}, "source": [ "Step response for continuous-time LTI systems is the output corresponding to the\n", "zero initial condition and inputs {math}`u_i(t) = e_i`." ] }, { "cell_type": "code", "execution_count": 10, "id": "8df49a70", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "18bbe58053c94332adab82635d9d2731", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_step = fom.step_resp()\n", "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n", "for i in range(fom.dim_output):\n", " for j in range(fom.dim_input):\n", " ax[i, j].plot(np.linspace(0, fom.T, y_step.shape[1]), y_step[i, :, j])\n", "for i in range(fom.dim_output):\n", " ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n", "for j in range(fom.dim_input):\n", " ax[0, j].set_title(f'Input {j + 1}')\n", " ax[-1, j].set_xlabel('Time')\n", "_ = fig.suptitle('Step response')" ] }, { "cell_type": "markdown", "id": "0482a086", "metadata": {}, "source": [ "## Transfer function evaluation\n", "\n", "The transfer function {math}`H` is the function such that\n", "{math}`Y(s) = H(s) U(s)`,\n", "where {math}`U` and {math}`Y` are respectively the Laplace transforms of\n", "the input {math}`u` and the output {math}`y`,\n", "assuming zero initial condition ({math}`x(0) = 0`).\n", "The expression for {math}`H` can be found by applying the Laplace transform\n", "to the system equations to obtain\n", "\n", "```{math}\n", "\\begin{align}\n", " s E X(s) & = A X(s) + B U(s), \\\\\n", " Y(s) & = C X(s) + D U(s).\n", "\\end{align}\n", "```\n", "\n", "using that {math}`s X(s)` is the Laplace transform of {math}`\\dot{x}(t)`.\n", "Eliminating {math}`X(s)` leads to\n", "\n", "```{math}\n", "Y(s) = \\left( C (s E - A)^{-1} B + D \\right) U(s),\n", "```\n", "\n", "i.e., {math}`H(s) = C (s E - A)^{-1} B + D`.\n", "Note that {math}`H` is a matrix-valued rational function\n", "(each component is a rational function).\n", "\n", "The transfer function of a given `LTIModel` is stored as the attribute\n", "`transfer_function`.\n", "It can be evaluated using its\n", "`eval_tf` method.\n", "The result is a NumPy array." ] }, { "cell_type": "code", "execution_count": 11, "id": "4a3fb85e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.56266667 0.61333333]\n", " [0.620175 0.50166667]\n", " [0.564075 0.38833333]]\n", "[[0.35516035 0.42800414]\n", " [0.39053974 0.30625375]\n", " [0.35602872 0.21798312]]\n", "[[0.41916591-0.24498821j 0.49022668-0.21786001j]\n", " [0.46133002-0.27112399j 0.36609293-0.23081817j]\n", " [0.42019995-0.24562591j 0.26612665-0.20191321j]]\n" ] } ], "source": [ "print(fom.transfer_function.eval_tf(0))\n", "print(fom.transfer_function.eval_tf(1))\n", "print(fom.transfer_function.eval_tf(1j))" ] }, { "cell_type": "markdown", "id": "17ec9bd1", "metadata": {}, "source": [ "Similarly, the derivative of the transfer function can be computed using the\n", "`eval_dtf` method.\n", "The result is again a NumPy array." ] }, { "cell_type": "code", "execution_count": 12, "id": "0b6b3621", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.32905051 -0.28965578]\n", " [-0.36417571 -0.31024153]\n", " [-0.32990749 -0.27380581]]\n", "[[-0.13086074 -0.11936496]\n", " [-0.14479475 -0.12300531]\n", " [-0.1312008 -0.10527819]]\n", "[[-0.1198173 +0.21367653j -0.11093146+0.18362116j]\n", " [-0.13256763+0.23652374j -0.11255455+0.20186916j]\n", " [-0.12012849+0.21423385j -0.09488566+0.18167128j]]\n" ] } ], "source": [ "print(fom.transfer_function.eval_dtf(0))\n", "print(fom.transfer_function.eval_dtf(1))\n", "print(fom.transfer_function.eval_dtf(1j))" ] }, { "cell_type": "markdown", "id": "89716a6e", "metadata": {}, "source": [ "To evaluate the transfer function over a sequence of points on the imaginary\n", "axis,\n", "the `freq_resp` method\n", "can be used.\n", "A typical use case is plotting the transfer function,\n", "which is discussed in the next section.\n", "\n", "## Magnitude and Bode plots\n", "\n", "It is known that if the input is chosen as\n", "{math}`u(t) = a e^{\\xi t} \\sin(\\omega t + \\varphi) e_j`\n", "(where {math}`e_j` is the {math}`j`-th canonical vector),\n", "then\n", "\n", "```{math}\n", "\\lim_{t \\to \\infty}\n", "\\left(\n", " y_i(t)\n", " - a \\lvert H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega) \\rvert e^{\\xi t}\n", " \\sin(\\omega t + \\varphi + \\arg(H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega)))\n", "\\right)\n", "= 0.\n", "```\n", "\n", "In words, if the input is a pure exponential,\n", "the frequency is preserved in the output,\n", "the amplitude is multiplied by the amplitude of the transfer function, and\n", "the phase is shifted by the argument of the transfer function.\n", "In particular, if the input is sinusoidal, i.e., {math}`\\xi = 0`,\n", "then the output is also sinusoidal.\n", "\n", "It is of interest to plot the transfer function over the imaginary axis to\n", "visualize how the LTI system responds to each frequency in the input.\n", "Since the transfer function is complex-valued (and matrix-valued),\n", "there are multiple ways to plot it.\n", "\n", "One way is the \"magnitude plot\", a visualization of the mapping\n", "{math}`\\omega \\mapsto \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert`,\n", "using the `mag_plot`\n", "method." ] }, { "cell_type": "code", "execution_count": 13, "id": "7ea09975", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w = (1e-2, 1e3)\n", "_ = fom.transfer_function.mag_plot(w)" ] }, { "cell_type": "markdown", "id": "3abe35f8", "metadata": {}, "source": [ "Note that `mag_plot`\n", "computes the Frobenius norm of {math}`H(\\boldsymbol{\\imath} \\omega)` by default,\n", "just as `scipy.linalg.norm`.\n", "Likewise, the choice of the norm {math}`\\lVert \\cdot \\rVert` can be controlled\n", "using the `ord` parameter.\n", "\n", "Another visualization is the Bode plot,\n", "which shows the magnitude and phase of each component of the transfer function.\n", "More specifically,\n", "{math}`\\omega \\mapsto \\lvert H_{ij}(\\boldsymbol{\\imath} \\omega) \\rvert`\n", "is in subplot {math}`(2 i - 1, j)` and\n", "{math}`\\omega \\mapsto \\arg(H_{ij}(\\boldsymbol{\\imath} \\omega))`\n", "is in subplot {math}`(2 i, j)`." ] }, { "cell_type": "code", "execution_count": 14, "id": "be197946", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(6, 2, figsize=(8, 10), sharex=True, constrained_layout=True)\n", "_ = fom.transfer_function.bode_plot(w, ax=axs)" ] }, { "cell_type": "markdown", "id": "c7be958e", "metadata": {}, "source": [ "To restrict which inputs and outputs are plotted by `bode_plot`,\n", "its parameters `input_indices` and `output_indices` can be used.\n", "The following restricts the plot to the second input {math}`u_2` and the first output {math}`y_1`." ] }, { "cell_type": "code", "execution_count": 15, "id": "0cb55590", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2, 1, figsize=(8, 10), sharex=True, constrained_layout=True)\n", "_ = fom.transfer_function.bode_plot(w, ax=axs, input_indices=[1], output_indices=[0])" ] }, { "cell_type": "markdown", "id": "475caaba", "metadata": {}, "source": [ "Note the change in the `axs` shape compared to the first call to `bode_plot`.\n", "\n", "## System poles\n", "\n", "The poles of an LTI system are the poles of its transfer function.\n", "From the form of the transfer function\n", "it follows that the poles are eigenvalues of {math}`E^{-1} A`,\n", "assuming that {math}`E` is invertible.\n", "Conversely, the eigenvalues of {math}`E^{-1} A` are the poles of the system\n", "in the generic case\n", "(more precisely, if the system is minimal, i.e., controllable and observable;\n", "see {cite}`A05`).\n", "\n", "The poles of an `LTIModel` can be obtained using its\n", "`poles` method\n", "(assuming the system is minimal)." ] }, { "cell_type": "code", "execution_count": 16, "id": "9a3d6b21", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "poles = fom.poles()\n", "fig, ax = plt.subplots()\n", "ax.plot(poles.real, poles.imag, '.')\n", "_ = ax.set_title('Poles')" ] }, { "cell_type": "markdown", "id": "014f0ec1", "metadata": {}, "source": [ ":::{note}\n", "\n", "The `poles` method uses a dense\n", "eigenvalue solver,\n", "which is applicable only up to medium-sized problems.\n", "\n", ":::\n", "\n", "## System Gramians\n", "\n", "The controllability and observability Gramians of an asymptotically stable\n", "system with invertible {math}`E` are respectively\n", "\n", "```{math}\n", "\\begin{align*}\n", " P & =\n", " \\int_0^\\infty\n", " e^{t E^{-1} A} E^{-1} B\n", " B^{\\operatorname{T}} E^{-\\!\\operatorname{T}}\n", " e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n", " \\operatorname{d}\\!t, \\text{ and} \\\\\n", " E^{\\operatorname{T}} Q E & =\n", " \\int_0^\\infty\n", " e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n", " C^{\\operatorname{T}} C\n", " e^{t E^{-1} A}\n", " \\operatorname{d}\\!t.\n", "\\end{align*}\n", "```\n", "\n", "From this,\n", "it is clear that {math}`P` and {math}`Q` are symmetric positive semidefinite.\n", "Furthermore,\n", "it can be shown that {math}`P` and {math}`Q` are solutions to Lyapunov equation\n", "\n", "```{math}\n", "\\begin{align*}\n", " A P E^{\\operatorname{T}}\n", " + E P A^{\\operatorname{T}}\n", " + B B^{\\operatorname{T}}\n", " & = 0, \\\\\n", " A^{\\operatorname{T}} Q E\n", " + E^{\\operatorname{T}} Q A\n", " + C^{\\operatorname{T}} C\n", " & = 0.\n", "\\end{align*}\n", "```\n", "\n", "The Gramians can be used to quantify how much does the input influence the state\n", "(controllability) and state the output (observability).\n", "This is used to motivate the balanced truncation method\n", "(see {doc}`tutorial_bt`).\n", "Also, they can be used to compute the {math}`\\mathcal{H}_2` norm (see below).\n", "\n", "To find the \"Gramians\" {math}`P` and {math}`Q` of an `LTIModel`,\n", "the `gramian` method can be used.\n", "Although solutions to Lyapunov equations are generally dense matrices,\n", "they can be often be very well approximated by a low-rank matrix.\n", "With `gramian`,\n", "it is possible to compute the dense solution or only the low-rank Cholesky\n", "factor.\n", "For example, the following computes the low-rank Cholesky factor of the\n", "controllability Gramian as a `VectorArray`:" ] }, { "cell_type": "code", "execution_count": 17, "id": "3af41862", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "NumpyVectorArray(\n", " NumpyVectorSpace(101),\n", " [[-9.67050759e-01 -1.13133419e+00 9.08538963e-01 ... 4.64535560e-20\n", " 2.62086546e-17 1.25694965e-17]\n", " [-9.49603788e-01 -9.59580542e-01 4.58145972e-01 ... -3.92587982e-18\n", " -1.07592314e-15 -5.39959495e-16]\n", " [-9.37818152e-01 -8.43810516e-01 2.24375612e-01 ... 2.06257277e-16\n", " 1.99682583e-14 1.05464247e-14]\n", " ...\n", " [-5.08356138e-01 1.94699113e-01 9.25753046e-02 ... 5.37928373e-10\n", " 6.28508514e-11 1.38207595e-11]\n", " [-5.03442167e-01 1.92880555e-01 9.17614570e-02 ... -1.18731984e-10\n", " -1.14267044e-11 -4.71613277e-12]\n", " [-4.98481264e-01 1.91000976e-01 9.08841977e-02 ... 1.38435047e-11\n", " 1.06280816e-12 6.56771771e-13]],\n", " _len=101)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.gramian('c_lrcf')" ] }, { "cell_type": "markdown", "id": "25b88461", "metadata": {}, "source": [ "## Hankel singular values\n", "\n", "The Hankel singular values of an LTI system are\n", "{math}`\\sigma_i = \\sqrt{\\lambda_i(E^{\\operatorname{T}} Q E P)}`,\n", "where {math}`\\lambda_i` is the {math}`i`-th eigenvalue.\n", "\n", "Plotting the Hankel singular values shows us how well an LTI system can be\n", "approximated by a reduced-order model.\n", "The `hsv` method can be used to compute them." ] }, { "cell_type": "code", "execution_count": 18, "id": "e2b06eb9", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "hsv = fom.hsv()\n", "fig, ax = plt.subplots()\n", "ax.semilogy(range(1, len(hsv) + 1), hsv, '.-')\n", "_ = ax.set_title('Hankel singular values')" ] }, { "cell_type": "markdown", "id": "fd286d2c", "metadata": {}, "source": [ "As expected for a heat equation, the Hankel singular values decay rapidly.\n", "\n", "## System norms\n", "\n", "There are various system norms,\n", "used for quantifying the sensitivity of system's outputs to its inputs.\n", "pyMOR currently has methods for computing:\n", "the {math}`\\mathcal{H}_2` norm,\n", "the {math}`\\mathcal{H}_\\infty` norm, and\n", "the Hankel (semi)norm.\n", "\n", "The {math}`\\mathcal{H}_2` norm is\n", "(if {math}`E` is invertible,\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane, and\n", "{math}`D` is zero)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "=\n", "\\left(\n", " \\frac{1}{2 \\pi}\n", " \\int_{-\\infty}^{\\infty}\n", " \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_{\\operatorname{F}}^2\n", " \\operatorname{d}\\!\\omega\n", "\\right)^{\\frac{1}{2}}.\n", "```\n", "\n", "It can be shown that\n", "\n", "```{math}\n", "\\lVert y \\rVert_{\\mathcal{L}_\\infty}\n", "\\leqslant\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "\\lVert u \\rVert_{\\mathcal{L}_2}.\n", "```\n", "\n", "Additionally, for systems with a single input or a single output\n", "(i.e., {math}`u(t) \\in \\mathbb{R}` or {math}`y(t) \\in \\mathbb{R}`),\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "=\n", "\\sup_{u \\neq 0}\n", "\\frac{\\lVert y \\rVert_{\\mathcal{L}_\\infty}}{\\lVert u \\rVert_{\\mathcal{L}_2}}.\n", "```\n", "\n", "The computation of the {math}`\\mathcal{H}_2` norm is based on the system\n", "Gramians\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}^2\n", "= \\operatorname{tr}\\!\\left(C P C^{\\operatorname{T}}\\right)\n", "= \\operatorname{tr}\\!\\left(B^{\\operatorname{T}} Q B\\right).\n", "```\n", "\n", "The `h2_norm` method of an `LTIModel` can be\n", "used to compute it." ] }, { "cell_type": "code", "execution_count": 19, "id": "1b5e5d00", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(1.3148819640649632)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.h2_norm()" ] }, { "cell_type": "markdown", "id": "8cd637e0", "metadata": {}, "source": [ "The {math}`\\mathcal{H}_\\infty` norm is\n", "(if {math}`E` is invertible and\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "= \\sup_{\\omega \\in \\mathbb{R}}\n", "\\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_2.\n", "```\n", "\n", "It is always true that\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "=\n", "\\sup_{u \\neq 0}\n", "\\frac{\\lVert y \\rVert_{\\mathcal{L}_2}}{\\lVert u \\rVert_{\\mathcal{L}_2}},\n", "```\n", "\n", "and, in particular,\n", "\n", "```{math}\n", "\\lVert y \\rVert_{\\mathcal{L}_2}\n", "\\leqslant\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "\\lVert u \\rVert_{\\mathcal{L}_2}.\n", "```\n", "\n", "The `hinf_norm` method uses a dense solver\n", "from [Slycot]() to compute the\n", "{math}`\\mathcal{H}_\\infty` norm." ] }, { "cell_type": "code", "execution_count": 20, "id": "edaff60a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(1.335114722611455)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.hinf_norm()" ] }, { "cell_type": "markdown", "id": "091bf3f2", "metadata": {}, "source": [ "The Hankel norm is\n", "(if {math}`E` is invertible and\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\operatorname{H}}\n", "= \\sigma_1,\n", "```\n", "\n", "i.e., the largest Hankel singular value.\n", "Since it is independent of {math}`D`,\n", "the \"Hankel norm\" is only a seminorm in general.\n", "\n", "It can be shown that the Hankel norm is the norm of the Hankel operator\n", "{math}`\\mathcal{H} \\colon \\mathcal{L}_2(-\\infty, 0) \\to \\mathcal{L}_2(0, \\infty)`\n", "mapping past inputs {math}`u_-` to future outputs {math}`y_+`\n", "\n", "```{math}\n", "y_+(t)\n", "= \\mathcal{H}(u_-)(t)\n", "= \\int_{-\\infty}^0 h(t - \\tau) u_-(\\tau) \\operatorname{d}\\!\\tau,\n", "```\n", "\n", "where {math}`h` is the impulse response\n", "{math}`h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t)`\n", "(i.e., {math}`H` is the Laplace transform of {math}`h`).\n", "Thus,\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\operatorname{H}}\n", "=\n", "\\sup_{u_- \\neq 0}\n", "\\frac{\\lVert y_+ \\rVert_{\\mathcal{L}_2}}{\\lVert u_- \\rVert_{\\mathcal{L}_2}},\n", "```\n", "\n", "The computation of the Hankel norm in\n", "`hankel_norm` relies on the\n", "`hsv` method." ] }, { 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00:04 LTIModel: Computing output of LTIModel for {input: StepFunction(2, 0, 0.0)} ...
00:04 LTIModel: Computing output of LTIModel for {input: StepFunction(2, 1, 0.0)} ...
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