| Name | rockit-meco JSON |
| Version |
0.6.2
JSON |
| download |
| home_page | None |
| Summary | Rapid Optimal Control Kit |
| upload_time | 2025-02-25 10:29:40 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.6 |
| license | GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. This version of the GNU Lesser General Public License incorporates the terms and conditions of version 3 of the GNU General Public License, supplemented by the additional permissions listed below. 0. Additional Definitions. As used herein, "this License" refers to version 3 of the GNU Lesser General Public License, and the "GNU GPL" refers to version 3 of the GNU General Public License. "The Library" refers to a covered work governed by this License, other than an Application or a Combined Work as defined below. An "Application" is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library. A "Combined Work" is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the "Linked Version". The "Minimal Corresponding Source" for a Combined Work means the Corresponding Source for the Combined Work, excluding any source code for portions of the Combined Work that, considered in isolation, are based on the Application, and not on the Linked Version. The "Corresponding Application Code" for a Combined Work means the object code and/or source code for the Application, including any data and utility programs needed for reproducing the Combined Work from the Application, but excluding the System Libraries of the Combined Work. 1. Exception to Section 3 of the GNU GPL. You may convey a covered work under sections 3 and 4 of this License without being bound by section 3 of the GNU GPL. 2. Conveying Modified Versions. If you modify a copy of the Library, and, in your modifications, a facility refers to a function or data to be supplied by an Application that uses the facility (other than as an argument passed when the facility is invoked), then you may convey a copy of the modified version: a) under this License, provided that you make a good faith effort to ensure that, in the event an Application does not supply the function or data, the facility still operates, and performs whatever part of its purpose remains meaningful, or b) under the GNU GPL, with none of the additional permissions of this License applicable to that copy. 3. Object Code Incorporating Material from Library Header Files. The object code form of an Application may incorporate material from a header file that is part of the Library. You may convey such object code under terms of your choice, provided that, if the incorporated material is not limited to numerical parameters, data structure layouts and accessors, or small macros, inline functions and templates (ten or fewer lines in length), you do both of the following: a) Give prominent notice with each copy of the object code that the Library is used in it and that the Library and its use are covered by this License. b) Accompany the object code with a copy of the GNU GPL and this license document. 4. Combined Works. You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following: a) Give prominent notice with each copy of the Combined Work that the Library is used in it and that the Library and its use are covered by this License. b) Accompany the Combined Work with a copy of the GNU GPL and this license document. c) For a Combined Work that displays copyright notices during execution, include the copyright notice for the Library among these notices, as well as a reference directing the user to the copies of the GNU GPL and this license document. d) Do one of the following: 0) Convey the Minimal Corresponding Source under the terms of this License, and the Corresponding Application Code in a form suitable for, and under terms that permit, the user to recombine or relink the Application with a modified version of the Linked Version to produce a modified Combined Work, in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source. 1) Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version. e) Provide Installation Information, but only if you would otherwise be required to provide such information under section 6 of the GNU GPL, and only to the extent that such information is necessary to install and execute a modified version of the Combined Work produced by recombining or relinking the Application with a modified version of the Linked Version. (If you use option 4d0, the Installation Information must accompany the Minimal Corresponding Source and Corresponding Application Code. If you use option 4d1, you must provide the Installation Information in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.) 5. Combined Libraries. You may place library facilities that are a work based on the Library side by side in a single library together with other library facilities that are not Applications and are not covered by this License, and convey such a combined library under terms of your choice, if you do both of the following: a) Accompany the combined library with a copy of the same work based on the Library, uncombined with any other library facilities, conveyed under the terms of this License. b) Give prominent notice with the combined library that part of it is a work based on the Library, and explaining where to find the accompanying uncombined form of the same work. 6. Revised Versions of the GNU Lesser General Public License. The Free Software Foundation may publish revised and/or new versions of the GNU Lesser General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Library as you received it specifies that a certain numbered version of the GNU Lesser General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that published version or of any later version published by the Free Software Foundation. If the Library as you received it does not specify a version number of the GNU Lesser General Public License, you may choose any version of the GNU Lesser General Public License ever published by the Free Software Foundation. If the Library as you received it specifies that a proxy can decide whether future versions of the GNU Lesser General Public License shall apply, that proxy's public statement of acceptance of any version is permanent authorization for you to choose that version for the Library. |
| keywords |
ocp
optimal control
casadi
|
| VCS |
|
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
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| coveralls test coverage |
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|
# rockit
[](https://gitlab.kuleuven.be/meco-software/rockit/commits/master)
[](https://meco-software.pages.gitlab.kuleuven.be/rockit/coverage/index.html)
[](http://meco-software.pages.gitlab.kuleuven.be/rockit)
[](http://meco-software.pages.gitlab.kuleuven.be/rockit/documentation-rockit.pdf)
# Description
Rockit (Rapid Optimal Control kit) is a software framework to quickly prototype optimal control problems (aka dynamic optimization) that may arise in engineering: e.g.
iterative learning (ILC), model predictive control (NMPC), system identification, and motion planning.
Notably, the software allows free end-time problems and multi-stage optimal problems.
The software is currently focused on direct methods and relies heavily on [CasADi](http://casadi.org).
The software is developed by the [KU Leuven MECO research team](https://www.mech.kuleuven.be/en/pma/research/meco).
# Installation
Install using pip: `pip install rockit-meco`
# Hello world
(Taken from the [example gallery](https://meco-software.pages.gitlab.kuleuven.be/rockit/examples/))
You may try it live in your browser: [](https://mybinder.org/v2/git/https%3A%2F%2Fgitlab.kuleuven.be%2Fmeco-software%2Frockit.git/v0.1.9?filepath=examples%2Fhello_world.ipynb).
Import the project:
```python
from rockit import *
```
Start an optimal control environment with a time horizon of 10 seconds
starting from t0=0s.
_(free-time problems can be configured with `FreeTime(initial_guess))_
```python
ocp = Ocp(t0=0, T=10)
```
Define two scalar states (vectors and matrices also supported)
```python
x1 = ocp.state()
x2 = ocp.state()
```
Define one piecewise constant control input
_(use `order=1` for piecewise linear)_
```
u = ocp.control()
```
Compose time-dependent expressions a.k.a. signals
_(explicit time-dependence is supported with `ocp.t`)_
```python
e = 1 - x2**2
```
Specify differential equations for states
_(DAEs also supported with `ocp.algebraic` and `add_alg`)_
```python
ocp.set_der(x1, e * x1 - x2 + u)
ocp.set_der(x2, x1)
```
Lagrange objective term: signals in an integrand
```python
ocp.add_objective(ocp.integral(x1**2 + x2**2 + u**2))
```
Mayer objective term: signals evaluated at t_f = t0_+T
```python
ocp.add_objective(ocp.at_tf(x1**2))
```
Path constraints
_(must be valid on the whole time domain running from `t0` to `tf`,
grid options available such as `grid='integrator'` or `grid='inf'`)_
```python
ocp.subject_to(x1 >= -0.25)
ocp.subject_to(-1 <= (u <= 1 ))
```
Boundary constraints
```python
ocp.subject_to(ocp.at_t0(x1) == 0)
ocp.subject_to(ocp.at_t0(x2) == 1)
```
Pick an NLP solver backend
_(CasADi `nlpsol` plugin)_
```python
ocp.solver('ipopt')
```
Pick a solution method
such as `SingleShooting`, `MultipleShooting`, `DirectCollocation`
with arguments:
* N -- number of control intervals
* M -- number of integration steps per control interval
* grid -- could specify e.g. UniformGrid() or GeometricGrid(4)
```python
method = MultipleShooting(N=10, intg='rk')
ocp.method(method)
```
Set initial guesses for states, controls and variables.
Default: zero
```python
ocp.set_initial(x2, 0) # Constant
ocp.set_initial(x1, ocp.t/10) # Function of time
ocp.set_initial(u, linspace(0, 1, 10)) # Array
```
Solve:
```python
sol = ocp.solve()
```
In case the solver fails, you can still look at the solution:
_(you may need to wrap the solve line in try/except to avoid the script aborting)_
```python
sol = ocp.non_converged_solution
```
Show structure:
```python
ocp.spy()
```
Post-processing:
```python
tsa, x1a = sol.sample(x1, grid='control')
tsb, x1b = sol.sample(x1, grid='integrator')
tsc, x1c = sol.sample(x1, grid='integrator', refine=100)
plot(tsa, x1a, '-')
plot(tsb, x1b, 'o')
plot(tsc, x1c, '.')
```
# Matlab interface
Rockit comes with a (almost) feature-complete interface to Matlab.
Installation steps:
1. [Check](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/support/sysreq/files/python-support.pdf) which Python versions your Matlab installation supports, e.g. `Python 3.6`
2. Open up a compatible Python environment in a terminal (if you don't have one, consider [miniconda](https://docs.conda.io/en/latest/miniconda.html) and create an environment by performing commands `conda create --name myspace python=3.6` and `conda activate myspace` inside the Anaconda Prompt).
3. Perform `pip install "rockit-meco>=0.1.12" "casadi>=3.5.5"` in that teminal
4. Launch Matlab from that same terminal (Type the full path+name of the Matlab executable. In Windows you may find the Matlab executable by right-clicking the icon from the start menu; use quotes (") to encapsulate the full name if it contains spaces. e.g. `"C:\Program Files\Matlab\bin\matlab.exe"`)
5. Install CasADi for Matlab from https://github.com/casadi/casadi/releases/tag/3.5.5: pick the latest applicable matlab archive, unzip it, and add it to the Matlab path (without subdirectories)
6. Make sure you remove any other CasADi version from the Matlab path.
7. Only for Matlab >=2019b: make sure you do have in-process ExecutionMode for speed `pyenv('ExecutionMode','InProcess')`
8. Add rockit to the matlab path: `addpath(char(py.rockit.matlab_path))`
9. Run the `hello_world` example from the [example directory](https://gitlab.kuleuven.be/meco-software/rockit/-/tree/master/examples)
Debugging:
* Check if the correct CasADi Python is found: py.imp.find_module('casadi')
* Check if the correct CasADi Matlab is found: `edit casadi.SerializerBase`, should have a method called 'connect'
* Matlab error "Conversion to double from py.numpy.ndarray is not possible." -> Consult your Matlab release notes to verify that your Python version is supported
* Matlab error "Python Error: RuntimeError: .../casadi/core/serializing_stream.hpp:171: Assertion "false" failed:" -> May occur on Linux for some configurations. Consult rockit authors
# External interfaces
In the long run, we aim to add a bunch of interfaces to [third-party dynamic optimization solvers](https://github.com/meco-group/dynamic_optimization_inventory/blob/main/list.csv).
At the moment, the following solvers are interfaced:
* [acados](https://github.com/acados/acados) -- [examples](https://gitlab.kuleuven.be/meco-software/rockit/-/tree/master/rockit/external/acados/examples)
* [grampc](https://sourceforge.net/projects/grampc/) -- [examples](https://gitlab.kuleuven.be/meco-software/rockit-plugin-grampc/-/tree/main/examples)
Installation when using rockit from git
* `git submodule update --init --recursive`
* Windows only: install Visual Studio (supported: 2017,2019,2022) with the following components: `C++ Desktop Development` workload, and verify that the following components are also installed: `MSBuild`,`MSVC C++ x64/x86 build tools`,`C++ Cmake tools`,`C++/CLI support`
# Presentations
* Benelux 2020: [Effortless modeling of optimal control problems with rockit](https://youtu.be/dS4U_k6B904)
* Demo @ FM symposium: [Rockit: optimal motion planning made easy](https://github.com/meco-group/rockit_demo)
# Citing
Gillis, Joris ; Vandewal, Bastiaan ; Pipeleers, Goele ; Swevers, Jan
"Effortless modeling of optimal control problems with rockit", 39th Benelux Meeting on Systems and Control 2020, Elspeet, The Netherlands
Raw data
{
"_id": null,
"home_page": null,
"name": "rockit-meco",
"maintainer": null,
"docs_url": null,
"requires_python": ">=3.6",
"maintainer_email": null,
"keywords": "OCP, optimal control, casadi",
"author": null,
"author_email": "MECO-Group <joris.gillis@kuleuven.be>",
"download_url": null,
"platform": null,
"description": "# rockit\n[](https://gitlab.kuleuven.be/meco-software/rockit/commits/master)\n[](https://meco-software.pages.gitlab.kuleuven.be/rockit/coverage/index.html)\n[](http://meco-software.pages.gitlab.kuleuven.be/rockit)\n[](http://meco-software.pages.gitlab.kuleuven.be/rockit/documentation-rockit.pdf)\n\n# Description\n\n\n\nRockit (Rapid Optimal Control kit) is a software framework to quickly prototype optimal control problems (aka dynamic optimization) that may arise in engineering: e.g.\niterative learning (ILC), model predictive control (NMPC), system identification, and motion planning.\n\nNotably, the software allows free end-time problems and multi-stage optimal problems.\nThe software is currently focused on direct methods and relies heavily on [CasADi](http://casadi.org).\nThe software is developed by the [KU Leuven MECO research team](https://www.mech.kuleuven.be/en/pma/research/meco).\n\n# Installation\nInstall using pip: `pip install rockit-meco`\n\n# Hello world\n(Taken from the [example gallery](https://meco-software.pages.gitlab.kuleuven.be/rockit/examples/))\n\nYou may try it live in your browser: [](https://mybinder.org/v2/git/https%3A%2F%2Fgitlab.kuleuven.be%2Fmeco-software%2Frockit.git/v0.1.9?filepath=examples%2Fhello_world.ipynb).\n\nImport the project:\n```python\nfrom rockit import *\n```\n\nStart an optimal control environment with a time horizon of 10 seconds\nstarting from t0=0s.\n_(free-time problems can be configured with `FreeTime(initial_guess))_\n```python\nocp = Ocp(t0=0, T=10)\n```\n\nDefine two scalar states (vectors and matrices also supported)\n```python\nx1 = ocp.state()\nx2 = ocp.state()\n```\n\nDefine one piecewise constant control input\n_(use `order=1` for piecewise linear)_\n```\nu = ocp.control()\n```\n\nCompose time-dependent expressions a.k.a. signals\n_(explicit time-dependence is supported with `ocp.t`)_\n```python\ne = 1 - x2**2\n```\nSpecify differential equations for states\n_(DAEs also supported with `ocp.algebraic` and `add_alg`)_\n```python\nocp.set_der(x1, e * x1 - x2 + u)\nocp.set_der(x2, x1)\n```\n\nLagrange objective term: signals in an integrand\n```python\nocp.add_objective(ocp.integral(x1**2 + x2**2 + u**2))\n```\nMayer objective term: signals evaluated at t_f = t0_+T\n```python\nocp.add_objective(ocp.at_tf(x1**2))\n```\n\nPath constraints\n_(must be valid on the whole time domain running from `t0` to `tf`,\n grid options available such as `grid='integrator'` or `grid='inf'`)_\n```python\nocp.subject_to(x1 >= -0.25)\nocp.subject_to(-1 <= (u <= 1 ))\n```\n\nBoundary constraints\n```python\nocp.subject_to(ocp.at_t0(x1) == 0)\nocp.subject_to(ocp.at_t0(x2) == 1)\n```\n\nPick an NLP solver backend\n_(CasADi `nlpsol` plugin)_\n```python\nocp.solver('ipopt')\n```\n\nPick a solution method\nsuch as `SingleShooting`, `MultipleShooting`, `DirectCollocation`\nwith arguments:\n * N -- number of control intervals\n * M -- number of integration steps per control interval\n * grid -- could specify e.g. UniformGrid() or GeometricGrid(4)\n```python\nmethod = MultipleShooting(N=10, intg='rk')\nocp.method(method)\n```\n\nSet initial guesses for states, controls and variables.\nDefault: zero\n```python\nocp.set_initial(x2, 0) # Constant\nocp.set_initial(x1, ocp.t/10) # Function of time\nocp.set_initial(u, linspace(0, 1, 10)) # Array\n```\n\nSolve:\n```python\nsol = ocp.solve()\n```\n\nIn case the solver fails, you can still look at the solution:\n_(you may need to wrap the solve line in try/except to avoid the script aborting)_\n```python\nsol = ocp.non_converged_solution\n```\n\nShow structure:\n```python\nocp.spy()\n```\n\n\n\nPost-processing:\n```python\ntsa, x1a = sol.sample(x1, grid='control')\ntsb, x1b = sol.sample(x1, grid='integrator')\ntsc, x1c = sol.sample(x1, grid='integrator', refine=100)\nplot(tsa, x1a, '-')\nplot(tsb, x1b, 'o')\nplot(tsc, x1c, '.')\n```\n\n\n\n# Matlab interface\n\nRockit comes with a (almost) feature-complete interface to Matlab.\nInstallation steps:\n 1. [Check](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/support/sysreq/files/python-support.pdf) which Python versions your Matlab installation supports, e.g. `Python 3.6`\n 2. Open up a compatible Python environment in a terminal (if you don't have one, consider [miniconda](https://docs.conda.io/en/latest/miniconda.html) and create an environment by performing commands `conda create --name myspace python=3.6` and `conda activate myspace` inside the Anaconda Prompt).\n 3. Perform `pip install \"rockit-meco>=0.1.12\" \"casadi>=3.5.5\"` in that teminal\n 4. Launch Matlab from that same terminal (Type the full path+name of the Matlab executable. In Windows you may find the Matlab executable by right-clicking the icon from the start menu; use quotes (\") to encapsulate the full name if it contains spaces. e.g. `\"C:\\Program Files\\Matlab\\bin\\matlab.exe\"`)\n 5. Install CasADi for Matlab from https://github.com/casadi/casadi/releases/tag/3.5.5: pick the latest applicable matlab archive, unzip it, and add it to the Matlab path (without subdirectories)\n 6. Make sure you remove any other CasADi version from the Matlab path.\n 7. Only for Matlab >=2019b: make sure you do have in-process ExecutionMode for speed `pyenv('ExecutionMode','InProcess')`\n 8. Add rockit to the matlab path: `addpath(char(py.rockit.matlab_path))`\n 9. Run the `hello_world` example from the [example directory](https://gitlab.kuleuven.be/meco-software/rockit/-/tree/master/examples)\n\nDebugging:\n * Check if the correct CasADi Python is found: py.imp.find_module('casadi')\n * Check if the correct CasADi Matlab is found: `edit casadi.SerializerBase`, should have a method called 'connect'\n * Matlab error \"Conversion to double from py.numpy.ndarray is not possible.\" -> Consult your Matlab release notes to verify that your Python version is supported\n * Matlab error \"Python Error: RuntimeError: .../casadi/core/serializing_stream.hpp:171: Assertion \"false\" failed:\" -> May occur on Linux for some configurations. Consult rockit authors\n\n# External interfaces\nIn the long run, we aim to add a bunch of interfaces to [third-party dynamic optimization solvers](https://github.com/meco-group/dynamic_optimization_inventory/blob/main/list.csv).\nAt the moment, the following solvers are interfaced:\n * [acados](https://github.com/acados/acados) -- [examples](https://gitlab.kuleuven.be/meco-software/rockit/-/tree/master/rockit/external/acados/examples)\n * [grampc](https://sourceforge.net/projects/grampc/) -- [examples](https://gitlab.kuleuven.be/meco-software/rockit-plugin-grampc/-/tree/main/examples)\n\nInstallation when using rockit from git\n * `git submodule update --init --recursive`\n * Windows only: install Visual Studio (supported: 2017,2019,2022) with the following components: `C++ Desktop Development` workload, and verify that the following components are also installed: `MSBuild`,`MSVC C++ x64/x86 build tools`,`C++ Cmake tools`,`C++/CLI support`\n\n \n# Presentations\n\n * Benelux 2020: [Effortless modeling of optimal control problems with rockit](https://youtu.be/dS4U_k6B904)\n * Demo @ FM symposium: [Rockit: optimal motion planning made easy](https://github.com/meco-group/rockit_demo)\n\n# Citing\nGillis, Joris ; Vandewal, Bastiaan ; Pipeleers, Goele ; Swevers, Jan\n\"Effortless modeling of optimal control problems with rockit\", 39th Benelux Meeting on Systems and Control 2020, Elspeet, The Netherlands\n",
"bugtrack_url": null,
"license": "GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. This version of the GNU Lesser General Public License incorporates the terms and conditions of version 3 of the GNU General Public License, supplemented by the additional permissions listed below. 0. Additional Definitions. As used herein, \"this License\" refers to version 3 of the GNU Lesser General Public License, and the \"GNU GPL\" refers to version 3 of the GNU General Public License. \"The Library\" refers to a covered work governed by this License, other than an Application or a Combined Work as defined below. An \"Application\" is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library. A \"Combined Work\" is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the \"Linked Version\". The \"Minimal Corresponding Source\" for a Combined Work means the Corresponding Source for the Combined Work, excluding any source code for portions of the Combined Work that, considered in isolation, are based on the Application, and not on the Linked Version. The \"Corresponding Application Code\" for a Combined Work means the object code and/or source code for the Application, including any data and utility programs needed for reproducing the Combined Work from the Application, but excluding the System Libraries of the Combined Work. 1. Exception to Section 3 of the GNU GPL. You may convey a covered work under sections 3 and 4 of this License without being bound by section 3 of the GNU GPL. 2. Conveying Modified Versions. If you modify a copy of the Library, and, in your modifications, a facility refers to a function or data to be supplied by an Application that uses the facility (other than as an argument passed when the facility is invoked), then you may convey a copy of the modified version: a) under this License, provided that you make a good faith effort to ensure that, in the event an Application does not supply the function or data, the facility still operates, and performs whatever part of its purpose remains meaningful, or b) under the GNU GPL, with none of the additional permissions of this License applicable to that copy. 3. Object Code Incorporating Material from Library Header Files. The object code form of an Application may incorporate material from a header file that is part of the Library. You may convey such object code under terms of your choice, provided that, if the incorporated material is not limited to numerical parameters, data structure layouts and accessors, or small macros, inline functions and templates (ten or fewer lines in length), you do both of the following: a) Give prominent notice with each copy of the object code that the Library is used in it and that the Library and its use are covered by this License. b) Accompany the object code with a copy of the GNU GPL and this license document. 4. Combined Works. You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following: a) Give prominent notice with each copy of the Combined Work that the Library is used in it and that the Library and its use are covered by this License. b) Accompany the Combined Work with a copy of the GNU GPL and this license document. c) For a Combined Work that displays copyright notices during execution, include the copyright notice for the Library among these notices, as well as a reference directing the user to the copies of the GNU GPL and this license document. d) Do one of the following: 0) Convey the Minimal Corresponding Source under the terms of this License, and the Corresponding Application Code in a form suitable for, and under terms that permit, the user to recombine or relink the Application with a modified version of the Linked Version to produce a modified Combined Work, in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source. 1) Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version. e) Provide Installation Information, but only if you would otherwise be required to provide such information under section 6 of the GNU GPL, and only to the extent that such information is necessary to install and execute a modified version of the Combined Work produced by recombining or relinking the Application with a modified version of the Linked Version. (If you use option 4d0, the Installation Information must accompany the Minimal Corresponding Source and Corresponding Application Code. If you use option 4d1, you must provide the Installation Information in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.) 5. Combined Libraries. You may place library facilities that are a work based on the Library side by side in a single library together with other library facilities that are not Applications and are not covered by this License, and convey such a combined library under terms of your choice, if you do both of the following: a) Accompany the combined library with a copy of the same work based on the Library, uncombined with any other library facilities, conveyed under the terms of this License. b) Give prominent notice with the combined library that part of it is a work based on the Library, and explaining where to find the accompanying uncombined form of the same work. 6. Revised Versions of the GNU Lesser General Public License. The Free Software Foundation may publish revised and/or new versions of the GNU Lesser General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. 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