home.md

-# PyPK
-PyPK is a collection of p-k methods for solving the flutter equation.
-
-The original p-k method is described in [Rodden, Aerodynamic lag functions, divergence, and the British flutter method](https://doi.org/10.2514/3.44772) and its non-iterative version is described in [van Zyl, Aeroelastic Divergence and Aerodynamic Lag Roots](https://doi.org/10.2514/2.2806). The mode tracking algorithm is described in [van Zyl, Use of eigenvectors in the solution of the flutter equation](https://doi.org/10.2514/3.46380).
-
-## Install and run
-If you only want to use PyPK, you can install it using
-```bash
-python3 -m pip install . [--user]
-```
-and then run a case using
-```bash
-python3 path/to/case.py
-```
-If you need to develop in PyPK before using it, you do not need to install anything, and you can just run your case from the repo folder using
-```bash
-python3 run.py path/to/case.py
-```
-
-## Use
-PyPK is initialized through its API `init_pypk`. Examples can be found under the tests directory. A case file typically contains the following lines
-```python
-# Initialize
-from pypk import init_pypk
-cfg = {...}
-solver = init_pypk(cfg)
-solver.set_matrices(m, k, q)
-# Compute flutter solution
-solver.compute()
-solver.find_flutter()
-solver.save(case_name)
-solver.plot(case_name, show=True, format=fmt)
-# Compute gradients (only available for NIPK)
-solver.compute_gradients()
-```
-where `cfg` is a `dict` defining the configuration of the solution method, `m`, `k` and `q` are the mass, stiffness and aerodynamic force matrices provided as `numpy array`, and `case_name` and `fmt` are `str`. The variables are stored as public attributes of the `solver` and are listed in [`Solution.__init__()`](https://gitlab.uliege.be/am-dept/pypk/-/blob/master/pypk/solution.py).
-PyPK has also been interfaced with OpenMDAO for performing flutter-constrained optimization, see [OMFlut](https://gitlab.uliege.be/am-dept/omflut). Within that context, its builder must be imported using `from pypk.api_om import PypkBuilder`, then initialized with a configuration dictionary and provided to an OMFLut FlutterGroup as `FlutterGroup(..., flutter=PypkBuilder(cfg))`.
-
-The configuration dictionary contains the following entries
-```python
-'k_ref': numpy array, # reference reduced frequencies
-'l_ref': float, # reference length (usually half root chord)
-'mach': float, # freestream Mach number
-'n_modes': int, # number of modes
-'g_struct': float, # structural damping (complex proportional stiffness)
-'rho_ks': float, # aggregation parameter for KS
-'method': str, # method type ('pk' or 'nipk')
-'vrb': int # verbosity level
-'fluid': str, # fluid type ('unmatched' or 'matched_isa')
-# IF 'fluid' is 'unmatched'
-'rho_inf': float, # freesteam density
-'u_idx': numpy array, # velocity index range
-'mu': float, # mass ratio
-'f_ref': float, # frequency of first torsional mode
-# IF 'fluid' is 'mached_isa'
-'alt': numpy array, # altitudes range
+# PyPK
+PyPK is a collection of p-k methods for solving the flutter equation.
+
+The original p-k method is described in [Rodden, Aerodynamic lag functions, divergence, and the British flutter method](https://doi.org/10.2514/3.44772) and its non-iterative version is described in [van Zyl, Aeroelastic Divergence and Aerodynamic Lag Roots](https://doi.org/10.2514/2.2806). The mode tracking algorithm is described in [van Zyl, Use of eigenvectors in the solution of the flutter equation](https://doi.org/10.2514/3.46380). The methodology implemented in PyPk is decribed in this [technical note](https://hdl.handle.net/2268/324281).
+
+## Install and run
+If you only want to use PyPK, you can install it using
+```bash
+python3 -m pip install . [--user]
+```
+and then run a case using
+```bash
+python3 path/to/case.py
+```
+If you need to develop in PyPK before using it, you do not need to install anything, and you can just run your case from the repo folder using
+```bash
+python3 run.py path/to/case.py
+```
+
+## Use
+PyPK is initialized through its API `init_pypk`. Examples can be found under the tests directory. A case file typically contains the following lines
+```python
+# Initialize
+from pypk import init_pypk
+cfg = {...}
+solver = init_pypk(cfg)
+solver.set_matrices(m, k, q)
+# Compute flutter solution
+solver.compute()
+solver.find_flutter()
+solver.save(case_name)
+solver.plot(case_name, show=True, format=fmt)
+# Compute gradients (only available for NIPK)
+solver.compute_gradients()
+```
+where `cfg` is a `dict` defining the configuration of the solution method, `m`, `k` and `q` are the mass, stiffness and aerodynamic force matrices provided as `numpy array`, and `case_name` and `fmt` are `str`. The variables are stored as public attributes of the `solver` and are listed in [`Solution.__init__()`](https://gitlab.uliege.be/am-dept/pypk/-/blob/master/pypk/solution.py).
+PyPK has also been interfaced with OpenMDAO for performing flutter-constrained optimization, see [OMFlut](https://gitlab.uliege.be/am-dept/omflut). Within that context, its builder must be imported using `from pypk.api_om import PypkBuilder`, then initialized with a configuration dictionary and provided to an OMFLut FlutterGroup as `FlutterGroup(..., flutter=PypkBuilder(cfg))`.
+
+The configuration dictionary contains the following entries
+```python
+'k_ref': numpy array, # reference reduced frequencies
+'l_ref': float, # reference length (usually half root chord)
+'mach': float, # freestream Mach number
+'n_modes': int, # number of modes
+'g_struct': float, # structural damping (complex proportional stiffness)
+'rho_ks': float, # aggregation parameter for KS
+'method': str, # method type ('pk' or 'nipk')
+'vrb': int # verbosity level
+'fluid': str, # fluid type ('unmatched' or 'matched_isa')
+# IF 'fluid' is 'unmatched'
+'rho_inf': float, # freesteam density
+'u_idx': numpy array, # velocity index range
+'mu': float, # mass ratio
+'f_ref': float, # frequency of first torsional mode
+# IF 'fluid' is 'mached_isa'
+'alt': numpy array, # altitudes range
 ```
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