Prochaine révision | Révision précédente |
teaching:methcalchim:eigenvalues_and_eigenvectors [2018/11/27 05:32] – créée villersd | teaching:methcalchim:eigenvalues_and_eigenvectors [2021/06/11 12:15] (Version actuelle) – villersd |
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===== Applications ===== | ===== Applications ===== |
* collisional relaxation | * collisional relaxation |
* population dynamics, evolution (stationary population pyramid) | * //e.g.// [[https://pubs.acs.org/doi/abs/10.1021/ed066p142|Collisional relaxation via eigenfunction-eigenvalue expansion: Analysis of a simple case]] Wendell Forst, J. Chem. Educ., 1989, 66 (2), p 142 DOI: 10.1021/ed066p142 |
| * population dynamics, evolution (stationary [[wp>population pyramid]]) |
| * [[wp>Leslie_matrix|Leslie matrix]] |
| * [[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.7164&rep=rep1&type=pdf|Leslie Matrix Model in Population Dynamics - CiteSeerX]] |
| * [[http://personal.denison.edu/~ludwigl/2011populationdynamicsandma.pdf]],... |
* normal modes analysis (molecular vibrations) | * normal modes analysis (molecular vibrations) |
* PCA (principal component analysis) | * PCA (principal component analysis) |
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===== Python libraries ===== | ===== Python libraries ===== |
| * NumPy (more portability) |
| * [[https://docs.scipy.org/doc/numpy/reference/routines.linalg.html|numpy.linalg]] |
| * [[https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html|linalg.eig(a)]] Compute the eigenvalues and right eigenvectors of a square array |
| * SciPy (more complete wrapper on [[wp>LAPACK|LAPACK]] fortran package) |
| * [[https://docs.scipy.org/doc/scipy/reference/linalg.html|scipy.linalg]] |
| * [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eig.html|scipy.linalg.eig]] Solve an ordinary or generalized eigenvalue problem of a square matrix |
| * [[https://docs.scipy.org/doc/scipy/reference/linalg.html#decompositions|Decompositions]] (LU, QR,...) |
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===== References ===== | ===== References ===== |
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| * Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688 |
| * [[http://numerical.recipes/]] |
| * [[http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf]], chapter 11 Eigensystems p 456... |
| * [[http://apps.nrbook.com/empanel/index.html#]] |
| * Python NumPy vs SciPy : //cf.// [[https://stackoverflow.com/questions/6684238/whats-the-fastest-way-to-find-eigenvalues-vectors-in-python]] |
| * [[https://medium.com/analytics-vidhya/eigenvectors-and-eigenvalues-a-deeper-understanding-c715f8ded4c7|Eigenvectors and Eigenvalues: A deeper understanding]] Muhammad Abdullah Bilal, Analytics Vidhya, Medium, 04/03/2021 |
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