Mapping ---------- .. autofunction:: dec.spectral.varphi .. autofunction:: dec.spectral.varphi_inv Helper Functions ------------------ .. autofunction:: dec.spectral.alpha0 .. autofunction:: dec.spectral.beta0 .. autofunction:: dec.spectral.alpha .. autofunction:: dec.spectral.beta .. autofunction:: dec.spectral.rho .. autofunction:: dec.spectral.gamma .. autofunction:: dec.spectral.delta Periodic Basis Functions ---------------------------- .. autofunction:: dec.spectral.phi0 .. autofunction:: dec.spectral.phi1 .. autofunction:: dec.spectral.phid0 .. autofunction:: dec.spectral.phid1 .. plot:: from dec.spectral import * from matplotlib.pyplot import * from dec.plot import plot_bases_1d N = 5 g = Grid_1D_Periodic(N) plot_bases_1d(g, g.xmin, g.xmax, "\phi") Regular Basis Functions ---------------------------- .. autofunction:: dec.spectral.kappa0 .. autofunction:: dec.spectral.kappa1 .. autofunction:: dec.spectral.kappad0 .. autofunction:: dec.spectral.kappad1 Even 0-forms, Odd 1-forms .. plot:: from dec.spectral import * from matplotlib.pyplot import * from dec.plot import plot_bases_1d N = 2 g = Grid_1D_Regular(N) figure() plot_bases_1d(g, g.xmin, g.xmax, "\kappa") N = 5 g = Grid_1D_Regular(N) figure() plot_bases_1d(g, g.xmin, g.xmax, "\kappa") figure() plot_bases_1d(g, -g.xmax, g.xmax, "\kappa") figure() N = 9 g = Grid_1D_Regular(N) plot_bases_1d(g, g.xmin, g.xmax, "\kappa") show() Chebyshev Basis Functions ---------------------------- .. autofunction:: dec.spectral.psi0 .. autofunction:: dec.spectral.psi1 .. autofunction:: dec.spectral.psid0 .. autofunction:: dec.spectral.psid1 .. plot:: from dec.spectral import * from matplotlib.pyplot import * from dec.plot import plot_bases_1d N = 5 g = Grid_1D_Chebyshev(N) plot_bases_1d(g, g.xmin, g.xmax, "\kappa") show() :math:`\psi^0` and :math:`\widetilde{\psi}^0` match the Lagrange polynomials .. autofunction:: dec.spectral.lagrange_polynomials 2D Periodic Basis Function ----------------------------- .. plot:: plot/cheb/basis_forms_2d.py .. plot:: plot/cheb/vector_field_plot.py