from math import cos
def exact_S_solution(t):
return g * (1 - cos(t))
def check_S(S, t, step):
error = exact_S_solution(t) - S[step]
print 't=%.2f S[%d]=%+g error=%g' % (t, step, S[step], error)
# Fixed values for a test
from math import pi
m = 1
b = 2
L = 10
k = 1
beta = 0
S0 = 0
dt = 2 * pi / 40
g = 9.81
N = 200
def w(t):
return 0
S = solve(m, k, beta, S0, dt, g, w, N, user_action=check_S)
m = 1
b = 2
L = 10
k = 1
beta = 0
S0 = 0
dt = 2 * pi / 40
g = 9.81
N = 200
def w(t):
return 0
S = solve(m, k, beta, S0, dt, g, w, N)
# Plot S and the exact solution
from scitools.std import *
tcoor = linspace(0, N * dt, len(S))
exact = exact_S_solution(tcoor)
plot(tcoor,
S,
'r',
tcoor,
exact,
'b',
xlabel='time',
ylabel='S',
legend=('computed S(t)', 'exact S(t)'),
savefig='tmp_S.pdf')
dt = 2 * pi / 40
g = 9.81
w_formula = '0'
N = 200
m, b, L, k, beta, S0, dt, g, w, N = \
init_prms(m, b, L, k, beta, S0, dt, g, w_formula, N)
# Vectorize the StringFunction w
w_formula = str(w) # keep this to see if w=0 later
if ' else ' in w_formula:
w = vectorize(w) # general vectorization
else:
w.vectorize(globals()) # more efficient (when no if)
S = solve(m, k, beta, S0, dt, g, w, N, user_action=plot_S)
# First make a hardcopy of the the last plot of Y
savefig('tmp_Y.pdf')
# Make plots of several additional interesting quantities
tcoor = linspace(0, N * dt, N + 1)
S = array(S)
plots = 2 # number of rows of plots
if beta != 0:
plots += 1
if w_formula != '0':
plots += 1
# Position Y(t)
from boxspring import init_prms, solve
from math import cos
def exact_S_solution(t):
return g*(1 - cos(t))
# Fixed values for a test
from math import pi
m = 1; b = 2; L = 10; k = 1; beta = 0; S0 = 0;
dt = 2*pi/40; g = 9.81; N = 200;
def w(t):
return 0
S = solve(m, k, beta, S0, dt, g, w, N)
# Plot S and the exact solution
from scitools.std import *
tcoor = linspace(0, N*dt, len(S))
exact = exact_S_solution(tcoor)
plot(tcoor, S, 'r', tcoor, exact, 'b',
xlabel='time', ylabel='S',
legend=('computed S(t)', 'exact S(t)'),
savefig='tmp_S.pdf')
# Plot the error
figure() # new plot window
S = array(S) # turn list into NumPy array for computations
error = exact - S
plot(tcoor, error, xlabel='time', ylabel='error',
savefig='tmp_error.pdf')
from boxspring import init_prms, solve
from scitools.std import *
def plot_S(S, t, step):
if step == 0: # nothing to plot yet
return
tstart = 0
tstop = N*dt
tcoor = linspace(0, t, step)
S = array(S[:len(tcoor)])
Y = w(tcoor) - L - S - b/2. # (w, L, b are global vars.)
plot(tcoor, Y)
# Default values
m = 1; b = 2; L = 10; k = 1; beta = 0; S0 = 1;
dt = 2*pi/40; g = 9.81; w_formula = '0'; N = 200;
m, b, L, k, beta, S0, dt, g, w, N = \
init_prms(m, b, L, k, beta, S0, dt, g, w_formula, N)
w.vectorize(globals()) # w must work with arrays in plot_S
S = solve(m, k, beta, S0, dt, g, w, N, user_action=plot_S)
# Make hardcopy of last plot of S
savefig('tmp_S.pdf')
from boxspring import init_prms, solve
import sys, time, os
# make sure that we find the boxspring_figure module in ../oo:
#sys.path.insert(0, '../oo')
# better:
sys.path.insert(0, os.path.join(os.pardir, 'oo'))
from boxspring_figure import draw, set_figure_size
def animate_figure(S, t, step):
draw(L, w(t+dt), S[step], box_size)
time.sleep(0.1)
# Default values
from math import pi
m = 1; b = 2; L = 10; k = 1; beta = 0; S0 = 1;
dt = 2*pi/40; g = 9.81; w_formula = '0'; N = 80;
box_size = 4
w_max = 0
S_max = 15
set_figure_size(L, w_max, S_max, box_size)
m, b, L, k, beta, S0, dt, g, w, N = \
init_prms(m, b, L, k, beta, S0, dt, g, w_formula, N)
S = solve(m, k, beta, S0, dt, g, w, N,
user_action=animate_figure)
from boxspring import init_prms, solve
from math import cos
def exact_S_solution(t):
return g*(1 - cos(t))
def check_S(S, t, step):
error = exact_S_solution(t) - S[step]
print 't=%.2f S[%d]=%+g error=%g' % (t, step, S[step], error)
# Fixed values for a test
from math import pi
m = 1; b = 2; L = 10; k = 1; beta = 0; S0 = 0
dt = 2*pi/40; g = 9.81; N = 200
def w(t):
return 0
S = solve(m, k, beta, S0, dt, g, w, N, user_action=check_S)
sys.path.insert(0, os.path.join(os.pardir, 'oo'))
from boxspring_figure import draw, set_figure_size
def animate_figure(S, t, step):
draw(L, w(t + dt), S[step], box_size)
time.sleep(0.1)
# Default values
from math import pi
m = 1
b = 2
L = 10
k = 1
beta = 0
S0 = 1
dt = 2 * pi / 40
g = 9.81
w_formula = '0'
N = 80
box_size = 4
w_max = 0
S_max = 15
set_figure_size(L, w_max, S_max, box_size)
m, b, L, k, beta, S0, dt, g, w, N = \
init_prms(m, b, L, k, beta, S0, dt, g, w_formula, N)
S = solve(m, k, beta, S0, dt, g, w, N, user_action=animate_figure)
