pg_utils.eigen

Solving the eigenvalue problem.

This file contains the code for solving an eigenvalue problem in the framework of PG model.

Functions

apply_bg_to_eq(fname, eq, bg_map[, mode, ...])	Apply background field equation-wise
apply_bg_to_set(eqs, bg[, mode, verbose])	Apply background field to a set of equations
assemble_forcing(eqs, *args[, timescale, ...])	Assemble components of the forcing in the PG system
collect_matrix_elements(read_from, ...[, ...])	Eigensolver step II: collect matrix elements in symbolic forms
compute_eigen(read_from[, read_fmt, ...])	Eigensolver step IV: compute eigenvalues and eigenvectors from matrices
compute_eigen_mp(read_from, save_to[, diag, ...])	Compute eigenvalue problem to multiple precision
compute_matrix_numerics(read_from, ...[, ...])	Eigensolver step III: computation of matrix elements
equations_to_matrices(eqs, xpd_recipe[, ...])	Collect matrix elements
form_equations([eq_mode, components, ...])	Eigensolver step I: form set of equations
process_matrix_element(element, map_trial, ...)	Process matrix elements to desired form
reduce_dimensions(read_from[, save_to, ...])	Eigensolver step Ib: reduce dimension of the system
reduce_eqsys_to_force_form(eqsys_old[, verbose])	Reduce a system of equations to streamfunction-force formulation, thus drastically reducing the dimensionality of the dynamical system
reduce_eqsys_to_psi(eqsys_old[, verbose])	Reduce a system of eqs to 2nd-order formulation in stream function
to_fd_ode_pg(eq_sys, dyn_var)	A convenient function to convert equations to Fourier domain for PG vars
to_fd_ode_psi(eq[, psi_var, verbose])	Reduce an eq of psi to ODE form in cylindrical radius s