def test_golden_section():
"""Test golden section method on a simple example"""
import numpy as np
from psecas import golden_section
def f(x):
return (x - 2)**2
tol = 1e-8
(c, d) = golden_section(f, 1, 5, tol)
print(c, d)
np.testing.assert_allclose(c, 2.0, tol)
np.testing.assert_allclose(d, 2.0, tol)
if False:
from psecas import golden_section
def f(kx):
grid = FourierGrid(N=64, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=1.0, kx=kx)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 12) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=False, tol=1e-8)
return -omega.real
a = 3.512831867406509
b = 3.512831875508205
(a, b) = golden_section(f, a, b, tol=1e-8)
# Create initial conditions for Athena simulation
if True:
from psecas import save_system
kxmax = 3.5128319
grid = FourierGrid(N=256, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=1.0, kx=kxmax)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 12) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=True, tol=1e-8)
# Normalize eigenmodes
y = np.vstack([
Using golden_section is much cheaper than calculating the growth rate for
a fine mesh of wave vectors and taking the maximum.
"""
def f(kx, **kwargs):
# Set up a grid
grid = FourierGrid(N=64, zmin=0, zmax=2)
system = KelvinHelmholtzUniform(grid, beta=1e3, nu=0, kx=kx)
if 'nu' in kwargs.keys():
system.nu = kwargs['nu']
# Set up a solver
solver = Solver(grid, system)
# Iteratively solve
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 12) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=False, tol=1e-4)
return -omega.real
(a, b) = golden_section(f, 3.0, 6, tol=1e-3, nu=0.0)
print(a, b, (a + b) / 2, -f((a + b) / 2))
(a, b) = golden_section(f, 3.0, 6, tol=1e-3, nu=1e-2)
print(a, b, (a + b) / 2, -f((a + b) / 2))
(a, b) = golden_section(f, 3.0, 6, tol=1e-3, nu=1e-1)
print(a, b, (a + b) / 2, -f((a + b) / 2))
# Find the kx that gives maximum growth
if False:
from psecas import golden_section
def f(kx):
grid = FourierGrid(N=64, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=0.0, kx=kx)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 20) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=False, tol=1e-8)
return -omega.real
(a, b) = golden_section(f, 5.148550549911674, 5.158147443539172, tol=1e-8)
a = 5.1540899488183065
b = 5.154089957164513
# Create initial conditions for Athena simulation
if True:
from psecas import save_system
kxmax = 5.1540899
grid = FourierGrid(N=256, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=0.0, kx=kxmax)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 20) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=True, tol=1e-10)
# Find the kx that gives maximum growth
if False:
from psecas import golden_section
def f(kx):
grid = FourierGrid(N=64, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=1.0, kx=kx)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 12) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=False, tol=1e-6)
return -omega.real
(a, b) = golden_section(f, 3.512295, 3.513135, tol=1e-5)
# Create initial conditions for Athena simulation
if False:
from psecas import write_athena, save_system
kxmax = 3.5128286141291243
grid = FourierGrid(N=64, zmin=0.0, zmax=2.0)
system = KelvinHelmholtzHydroOnly(grid, u0=1.0, delta=1.0, kx=kxmax)
solver = Solver(grid, system)
Ns = np.hstack((np.arange(1, 5) * 16, np.arange(3, 12) * 32))
omega, v, err = solver.iterate_solver(Ns, verbose=False, tol=1e-6)
# Write files for loading into Athena
# write_athena(system, Nz=256, Lz=2.0)