def runtests(p, problem, parallel=False, tol=None):
from nodepy import rk, ivp, conv
import numpy as np
from nodepy import loadmethod
if tol is None:
tol = [10.**(-m) for m in range(2, 11)]
# Load methods
print 'constructing Ex-Euler'
ex = rk.extrap_pair(p)
print 'constructing Ex-midpoint'
exm = rk.extrap_pair(p / 2, 'midpoint')
print 'constructing DC-Euler'
dc = rk.DC_pair(p - 1)
if p == 6:
ork = rk.loadRKM('CMR6')
elif p == 8:
ork = rk.loadRKM('DP8')
elif p == 10:
ork = loadmethod.load_rkpair_from_file('rk108curtis.txt')
elif p == 12:
ork = loadmethod.load_rkpair_from_file('rk129hiroshi.txt')
if problem == 'suite':
myivp = ivp.detest_suite_minus()
else:
myivp = ivp.detest(problem)
methods = [ork, ex, exm, dc]
[work, err] = conv.ptest(methods,
myivp,
tol,
verbosity=1,
parallel=parallel)
plot_efficiency(methods, err, work)
fname = 'eff_' + problem + '_' + str(p)
if parallel:
fname = fname + '_par'
plt.ylabel('Sequential derivative evaluations')
plt.savefig(fname + '.pdf')
def run_tolerances(tols, p=8):
from nodepy import rk
from nodepy import loadmethod
err = np.zeros((4, len(tols)))
work = np.zeros((4, len(tols)))
rkm = rk.loadRKM("BS5").__num__()
q_ref, dx, iwork = stegoton(rkm, tol=1.0e-13)
rkm = rk.extrap_pair(p / 2, "midpoint").__num__()
rke = rk.extrap_pair(p).__num__()
rkd = rk.DC_pair(p - 1, grid="cheb").__num__()
if p == 6:
ork = rk.loadRKM("CMR6")
elif p == 8:
ork = rk.loadRKM("DP8")
elif p == 10:
ork = loadmethod.load_rkpair_from_file("rk108curtis.txt")
elif p == 12:
ork = loadmethod.load_rkpair_from_file("rk129hiroshi.txt")
for i, tol in enumerate(tols):
q, dx, iwork = stegoton(ork, tol)
err[0, i] = np.linalg.norm(q - q_ref, 1) * dx
work[0, i] = iwork * len(rkm)
q, dx, iwork = stegoton(rke, tol)
err[2, i] = np.linalg.norm(q - q_ref, 1) * dx
work[2, i] = iwork * len(rke)
q, dx, iwork = stegoton(rkm, tol)
err[1, i] = np.linalg.norm(q - q_ref, 1) * dx
work[1, i] = iwork * len(rkm)
q, dx, iwork = stegoton(rkd, tol)
err[3, i] = np.linalg.norm(q - q_ref, 1) * dx
work[3, i] = iwork * len(rkd)
return err, work, ork
def run_tolerances(tols, p=8):
from nodepy import rk
from nodepy import loadmethod
err = np.zeros((4, len(tols)))
work = np.zeros((4, len(tols)))
rkm = rk.loadRKM('BS5').__num__()
q_ref, dx, iwork = stegoton(rkm, tol=1.e-13)
rkm = rk.extrap_pair(p / 2, 'midpoint').__num__()
rke = rk.extrap_pair(p).__num__()
rkd = rk.DC_pair(p - 1, grid='cheb').__num__()
if p == 6:
ork = rk.loadRKM('CMR6')
elif p == 8:
ork = rk.loadRKM('DP8')
elif p == 10:
ork = loadmethod.load_rkpair_from_file('rk108curtis.txt')
elif p == 12:
ork = loadmethod.load_rkpair_from_file('rk129hiroshi.txt')
for i, tol in enumerate(tols):
q, dx, iwork = stegoton(ork, tol)
err[0, i] = np.linalg.norm(q - q_ref, 1) * dx
work[0, i] = iwork * len(rkm)
q, dx, iwork = stegoton(rke, tol)
err[2, i] = np.linalg.norm(q - q_ref, 1) * dx
work[2, i] = iwork * len(rke)
q, dx, iwork = stegoton(rkm, tol)
err[1, i] = np.linalg.norm(q - q_ref, 1) * dx
work[1, i] = iwork * len(rkm)
q, dx, iwork = stegoton(rkd, tol)
err[3, i] = np.linalg.norm(q - q_ref, 1) * dx
work[3, i] = iwork * len(rkd)
return err, work, ork
def runtests(p,problem,parallel=False,tol=None):
from nodepy import rk, ivp, conv
import numpy as np
from nodepy import loadmethod
if tol is None:
tol = [10.**(-m) for m in range(2,11)]
# Load methods
print 'constructing Ex-Euler'
ex = rk.extrap_pair(p);
print 'constructing Ex-midpoint'
exm = rk.extrap_pair(p/2,'midpoint');
print 'constructing DC-Euler'
dc = rk.DC_pair(p-1);
if p == 6:
ork = rk.loadRKM('CMR6')
elif p == 8:
ork = rk.loadRKM('DP8')
elif p == 10:
ork = loadmethod.load_rkpair_from_file('rk108curtis.txt')
elif p == 12:
ork = loadmethod.load_rkpair_from_file('rk129hiroshi.txt')
if problem == 'suite':
myivp = ivp.detest_suite_minus()
else:
myivp = ivp.detest(problem);
methods = [ork,ex,exm,dc]
[work,err] = conv.ptest(methods,myivp,tol,verbosity=1,parallel=parallel);
plot_efficiency(methods, err, work)
fname = 'eff_'+problem+'_'+str(p)
if parallel:
fname = fname + '_par'
plt.ylabel('Sequential derivative evaluations')
plt.savefig(fname+'.pdf')
if p == 6:
ork = rk.loadRKM('CMR6')
elif p == 8:
ork = rk.loadRKM('DP8')
elif p == 10:
ork = loadmethod.load_rkpair_from_file('rk108curtis.txt')
elif p == 12:
ork = loadmethod.load_rkpair_from_file('rk129hiroshi.txt')
pp,q = ork.stability_function()
I_R[0,i] = stability_function.real_stability_interval(pp,q)
I_I[0,i] = stability_function.imaginary_stability_interval(pp,q)
I_R_scaled[0,i] = I_R[0,i]/len(ork)
I_I_scaled[0,i] = I_I[0,i]/len(ork)
exe = rk.extrap_pair(p)
pp,q = exe.stability_function()
I_R[1,i] = stability_function.real_stability_interval(pp,q)
I_I[1,i] = stability_function.imaginary_stability_interval(pp,q)
I_R_scaled[1,i] = I_R[1,i]/len(exe)
I_I_scaled[1,i] = I_I[1,i]/len(exe)
if p%2==0:
exm = rk.extrap_pair(p/2,'midpoint')
pp,q = exm.stability_function()
I_R[2,i] = stability_function.real_stability_interval(pp,q)
I_I[2,i] = stability_function.imaginary_stability_interval(pp,q)
I_R_scaled[2,i] = I_R[2,i]/len(exm)
I_I_scaled[2,i] = I_I[2,i]/len(exm)
dc = rk.DC_pair(p-1)