Examples

Eleven example scripts demonstrate the main eigensystem analysis routines. Run each from the packages/eigensystems directory:

python examples/example_imsl_evlrg.py
python examples/example_imsl_evcrg.py
python examples/example_imsl_evlsf.py
python examples/example_imsl_svd.py
python examples/example_imsl_cholesky.py
python examples/example_imsl_condition_number.py
python examples/example_imsl_generalized_eigen.py
python examples/example_imsl_complex_eigen.py
python examples/example_imsl_all_generalized.py
python examples/example_imsl_matrix_analysis.py
python examples/example_imsl_matrix_utils.py

Example scripts

Script	Primary topic	Output SVG
example_imsl_evlrg.py	Companion matrix eigenvalues (EVLRG)	example_imsl_evlrg.svg
example_imsl_evcrg.py	Eigenvectors of symmetric matrix (EVCRG)	example_imsl_evcrg.svg
example_imsl_evlsf.py	Toeplitz matrix eigenvalues (EVLSF)	example_imsl_evlsf.svg
example_imsl_svd.py	SVD low-rank approximation	example_imsl_svd.svg
example_imsl_cholesky.py	Cholesky / LU / QR decompositions	example_imsl_cholesky.svg
example_imsl_condition_number.py	Condition number and solve stability	example_imsl_condition_number.svg
example_imsl_generalized_eigen.py	Generalized eigenvalues — vibration (GVCSF)	example_imsl_generalized_eigen.svg
example_imsl_complex_eigen.py	Complex eigenvalues — EVLCG/EVCCG/EVLCH/EVCCH/EVLRH	example_imsl_complex_eigen.svg
example_imsl_all_generalized.py	All generalized eigenvalue forms — GVLRG/GVCRG/GVLSF/EVCSF	example_imsl_all_generalized.svg
example_imsl_matrix_analysis.py	Matrix analysis — det/trace/rank/Frobenius/SVD/Schur	example_imsl_matrix_analysis.svg
example_imsl_matrix_utils.py	Matrix utilities — symmetrize/orthogonalize/pseudo_inverse	example_imsl_matrix_utils.svg

• EVLRG Example — Companion Matrix Eigenvalues
• EVCRG Example — Eigenvectors of a Symmetric Matrix
• EVLSF Example — Toeplitz Matrix Eigenvalues
• SVD Example — Low-Rank Approximation
• Cholesky Example — Matrix Decompositions
• Condition Number Example — Matrix Conditioning and Stability
• Generalized Eigenvalue Example — Mechanical Vibration
• Complex Eigenvalue Problems — EVLCG, EVCCG, EVLCH, EVCCH, EVLRH
• All Generalized Eigenvalue Forms — GVLRG, GVCRG, GVLSF, EVCSF
• Matrix Analysis Functions — DET, TRACE, RANK, FROBENIUS, SVD_VALUES, SCHUR
• Matrix Utility Functions — IS_SYMMETRIC, IS_POSITIVE_DEFINITE, SYMMETRIZE, ORTHOGONALIZE, PSEUDO_INVERSE