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add ode solver, tests and update docs

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Daniel Weschke
2019-05-26 21:54:58 +02:00
parent 184e80269b
commit d0873a36da
33 changed files with 1821 additions and 396 deletions
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tests/test_fit.py Normal file
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import unittest
import os
import sys
sys.path.insert(0, os.path.abspath('../src'))
import fit
class TestFit(unittest.TestCase):
def test_property(self):
self.assertEqual()
if __name__ == '__main__':
unittest.main()

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tests/test_solver.py Normal file
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Numerical solver.
:Date: 2019-05-25
.. module:: solver
:platform: *nix, Windows
:synopsis: Numerical solver.
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
"""
from __future__ import division, print_function
import unittest
import math
from numpy import linspace, allclose
from numpy.linalg import inv
import os
import sys
sys.path.insert(0, os.path.abspath('../src'))
import solver
import solver_model
#### Post processing
from matplotlib.pyplot import figure, subplots, plot, show
from numpy import sqrt, square, concatenate
def plotx1rphi(x, t, title):
"""Plot plane rotation (x, y, phi)
"""
x1 = x[:, 0]
x2 = x[:, 1]
x3 = x[:, 2]
xp1 = x[:, 3]
xp2 = x[:, 4]
xp3 = x[:, 5]
fig, ax1 = subplots()
ax1.set_title(title)
ax1.plot(t, x1, 'b-')
#ax1.plot(t, x3, 'b-')
ax1.set_xlabel('time t in s')
# Make the y-axis label and tick labels match the line color.
ax1.set_ylabel('x_1', color='b')
for tl in ax1.get_yticklabels():
tl.set_color('b')
envelope = sqrt(square(x1)+square(x2))
ax1.plot(t, envelope, 'b--', t, -envelope, 'b--')
ax2 = ax1.twinx()
ax2.plot(t, xp3, 'r')
ax2.set_ylabel('phi', color='r')
for tl in ax2.get_yticklabels():
tl.set_color('r')
if max(xp3) < 2:
ax2.set_ylim([0,2])
f = solver_model.disk
fnm = solver_model.disk_nm
fnmmdk = solver_model.disk_nmmdk
class TestSolver(unittest.TestCase):
Dt = .01 # Delta t
tend = .1 # t_end
#tend = 300
nt = math.ceil(tend/Dt) # number of timesteps
t = linspace(0., tend, nt+1) # time vector
x0 = 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 # initial conditions
p = .01, .002, .015 # parameter of the model
def test_e1(self):
xe1 = solver.e1(f, self.x0, self.t, *self.p)
#plotx1rphi(xe1, self.t, ("Euler (Runge-Kutta 1th order), increments: %d" % self.nt))
#show()
self.assertTrue(allclose(xe1[:, 5],
[0., 0.00015, 0.0003, 0.00045, 0.0006, 0.00075, 0.0009, 0.00105, 0.0012,
0.00135, 0.0015 ]))
Dt_2 = Dt/5.
nt_2 = math.ceil(tend/Dt_2)
t_2 = linspace(0., tend, nt_2+1)
def test_e1_2(self):
xe1_2 = solver.e1(f, self.x0, self.t_2, *self.p)
#plotx1rphi(xe1_2, self.t_2, ("Euler (Runge-Kutta 1th order), increments: %d" % self.nt_2))
#show()
self.assertTrue(allclose(xe1_2[:, 5],
[0.00000000e+00, 3.00000000e-05, 6.00000000e-05, 8.99999998e-05,
1.19999999e-04, 1.49999998e-04, 1.79999995e-04, 2.09999992e-04,
2.39999987e-04, 2.69999980e-04, 2.99999971e-04, 3.29999960e-04,
3.59999947e-04, 3.89999931e-04, 4.19999913e-04, 4.49999891e-04,
4.79999866e-04, 5.09999837e-04, 5.39999804e-04, 5.69999767e-04,
5.99999726e-04, 6.29999681e-04, 6.59999630e-04, 6.89999575e-04,
7.19999514e-04, 7.49999448e-04, 7.79999376e-04, 8.09999298e-04,
8.39999214e-04, 8.69999123e-04, 8.99999026e-04, 9.29998921e-04,
9.59998810e-04, 9.89998691e-04, 1.01999856e-03, 1.04999843e-03,
1.07999829e-03, 1.10999814e-03, 1.13999798e-03, 1.16999781e-03,
1.19999763e-03, 1.22999744e-03, 1.25999725e-03, 1.28999704e-03,
1.31999682e-03, 1.34999660e-03, 1.37999636e-03, 1.40999611e-03,
1.43999585e-03, 1.46999558e-03, 1.49999530e-03]
))
maxIterations = 1000
tol = 1e-9 # against residuum
def test_e2(self):
xe2 = solver.e2(f, self.x0, self.t, *self.p)
#plotx1rphi(xe2, self.t, ("Runge-Kutta 2th order, increments: %d" % self.nt))
#show()
self.assertTrue(allclose(xe2[:, 5],
[0., 0.00015, 0.0003, 0.00045, 0.0006, 0.00075, 0.0009, 0.00105, 0.0012,
0.00135, 0.0015 ]))
def test_e4(self):
xe4 = solver.e4(f, self.x0, self.t, *self.p)
#plotx1rphi(xe4, self.t, ("Runge-Kutta 4th order, increments: %d" % self.nt))
#show()
self.assertTrue(allclose(xe4[:, 5],
[0., 0.00015, 0.0003, 0.00045, 0.0006, 0.00075, 0.0009, 0.00105, 0.0012,
0.00135, 0.0015 ]))
def test_i1(self):
xi1, iterations = solver.i1(f, self.x0, self.t, *self.p, self.maxIterations, self.tol)
#plotx1rphi(xi1, self.t, ("Backward Euler, increments: %d, iterations: %d" % (self.nt, sum(iterations))))
#show()
self.assertTrue(allclose(xi1[:, 5],
[0., 0.00015, 0.0003, 0.00045, 0.0006, 0.00075, 0.0009, 0.00105, 0.0012,
0.00135, 0.0015 ]))
gamma = .5 # newmark parameter for velocity
beta = .25 # newmark parameter for displacement
def test_nm(self):
xnm, xpnm, xppnm, iterations = solver.newmark_newtonraphson(fnm,
(0,0,0), (0,0,0), (0,0,0), self.t, *self.p,
self.gamma, self.beta, 1, self.tol)
#print(xnm)
#print(xpnm)
x = concatenate((xnm, xpnm), axis=1)
#plotx1rphi(x, self.t, ("Newmark, increments: %d, iterations: %d" % (self.nt, sum(iterations))))
#show()
self.assertTrue(allclose(x[:, 5],
[0.00000000e+00, 7.49999925e-05, 2.24999951e-04, 3.74999839e-04,
5.24999621e-04, 6.74999269e-04, 8.24998752e-04, 9.74998039e-04,
1.12499710e-03, 1.27499591e-03, 1.42499444e-03]
))
def test_nm_2(self):
xnm, xpnm, xppnm, iterations = solver.newmark_newtonraphson(fnm,
(0,0,0), (0,0,0), (0,0,0), self.t, *self.p,
self.gamma, self.beta, self.maxIterations, self.tol)
#print(xnm)
#print(xpnm)
x = concatenate((xnm, xpnm), axis=1)
#plotx1rphi(x, self.t, ("Newmark, increments: %d, iterations: %d" % (self.nt, sum(iterations))))
#show()
self.assertTrue(allclose(x[:, 5],
[0.00000000e+00, 7.49999925e-05, 2.24999951e-04, 3.74999839e-04,
5.24999621e-04, 6.74999269e-04, 8.24998752e-04, 9.74998039e-04,
1.12499710e-03, 1.27499591e-03, 1.42499444e-03]
))
def test_nmmdk(self):
xnm, xpnm, xppnm, iterations = solver.newmark_newtonraphson_rdk(fnmmdk,
(0,0,0), (0,0,0), (0,0,0), self.t, *self.p,
self.gamma, self.beta, 1, self.tol)
#print(xnm)
#print(xpnm)
x = concatenate((xnm, xpnm), axis=1)
#plotx1rphi(x, self.t, ("Newmark, increments: %d, iterations: %d" % (self.nt, sum(iterations))))
#show()
self.assertTrue(allclose(x[:, 5],
[0.00000000e+00, 7.49999963e-05, 2.24999974e-04, 3.74999906e-04,
5.24999764e-04, 6.74999516e-04, 8.24999134e-04, 9.74998586e-04,
1.12499784e-03, 1.27499688e-03, 1.42499566e-03]
))
def test_nmmdk_2(self):
xnm, xpnm, xppnm, iterations = solver.newmark_newtonraphson_rdk(fnmmdk,
(0,0,0), (0,0,0), (0,0,0), self.t, *self.p,
self.gamma, self.beta, 100, self.tol)
#print(xnm)
#print(xpnm)
x = concatenate((xnm, xpnm), axis=1)
#plotx1rphi(x, self.t, ("Newmark, increments: %d, iterations: %d" % (self.nt, sum(iterations))))
#show()
self.assertTrue(allclose(x[:, 5],
[0.00000000e+00, 7.49999963e-05, 2.24999974e-04, 3.74999906e-04,
5.24999764e-04, 6.74999516e-04, 8.24999134e-04, 9.74998586e-04,
1.12499784e-03, 1.27499688e-03, 1.42499566e-03]
))
#from scipy.integrate import odeint
#xode = odeint(solver_model.disk, x0, t, p, printmessg=True)
#plotx1rphi(xode, t, ("ODE, Inkremente: %d" % nt))
#show()
if __name__ == '__main__':
unittest.main()