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| import sys
from PyQt5.QtWidgets import QApplication, QMainWindow, QMenu, QVBoxLayout, QSizePolicy, QLabel, QPushButton, QLineEdit
from PyQt5.QtGui import QIcon
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.figure import Figure
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import griddata
import pylab
import time
N1 = 100
tt =15.
l = 2.
h = l/N1
N2 = 100
t=tt/N2
hh=h*h
rr=hh/t
a11=0.03
a12=0.01
p1=0.03
a21=0.03
a22=0.01
p2=-0.03
m1=0.95
m2=1.2
d1=0.7
d2=0.5
c1=0.25
c2=0.65
h1=0.15
b1=0.35
x =np.zeros((N1+1), 'float')
y =np.zeros((N1+1), 'float')
v =np.zeros((N1+1), 'float')
a =np.zeros((N1), 'float')
b =np.zeros((N1), 'float')
z =np.zeros((N1+1), 'float')
class App(QMainWindow):
def __init__(self):
super().__init__()
self.left = 10
self.top = 10
self.title = ''
self.width = 640
self.height = 400
self.initUI()
def initVars(self):
global N1
global tt
global l
global h
global N2
global t
global hh
global rr
global a11
global a12
global p1
global a21
global a22
global p2
global m1
global m2
global d1
global d2
global c1
global c2
global h1
global b1
global x
global y
global v
global a
global b
global z
N1 = int(self.le_N1 .text())
tt = float(self.le_tt .text())
l = float(self.le_l .text())
N2 = int(self.le_N2 .text())
a11 = float(self.le_a11.text())
a12 = float(self.le_a12.text())
p1 = float(self.le_p1 .text())
a21 = float(self.le_a21.text())
a22 = float(self.le_a22.text())
p2 = float(self.le_p2 .text())
m1 = float(self.le_m1 .text())
m2 = float(self.le_m2 .text())
d1 = float(self.le_d1 .text())
d2 = float(self.le_d2 .text())
c1 = float(self.le_c1 .text())
c2 = float(self.le_c2 .text())
h1 = float(self.le_h1 .text())
b1 = float(self.le_b1 .text())
h = l/N1
t=tt/N2
hh=h*h
rr=hh/t
x = np.zeros((N1+1), 'float')
y = np.zeros((N1+1), 'float')
v = np.zeros((N1+1), 'float')
a = np.zeros((N1), 'float')
b = np.zeros((N1), 'float')
z = np.zeros((N1+1), 'float')
self.m.plot()
def initUI(self):
self.setWindowTitle(self.title)
self.setGeometry(self.left, self.top, self.width, self.height)
self.m = PlotCanvas(self, width=5, height=4)
self.m.move(0,0)
y = 0
label = QLabel('N1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('tt:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('l:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('N2:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('a11:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('a12:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('p1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('a21:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('a22:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('p2:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('m1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('m2:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('d1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('d2:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('c1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('c2:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('h1:', self)
label.move(510, y)
label.resize(50, 20)
y += 20
label = QLabel('b1:', self)
label.move(510, y)
label.resize(50, 20)
y = 0
self.le_N1 = QLineEdit('10', self)
self.le_N1.move(550, y)
self.le_N1.resize(50, 20)
y += 20
self.le_tt = QLineEdit('15', self)
self.le_tt.move(550, y)
self.le_tt.resize(50, 20)
y += 20
self.le_l = QLineEdit('2',self)
self.le_l.move(550, y)
self.le_l.resize(50, 20)
y += 20
self.le_N2 = QLineEdit('10',self)
self.le_N2.move(550, y)
self.le_N2.resize(50, 20)
y += 20
self.le_a11 = QLineEdit('0.03',self)
self.le_a11.move(550, y)
self.le_a11.resize(50, 20)
y += 20
self.le_a12 = QLineEdit('0.01',self)
self.le_a12.move(550, y)
self.le_a12.resize(50, 20)
y += 20
self.le_p1 = QLineEdit('0.03',self)
self.le_p1.move(550, y)
self.le_p1.resize(50, 20)
y += 20
self.le_a21 = QLineEdit('0.03',self)
self.le_a21.move(550, y)
self.le_a21.resize(50, 20)
y += 20
self.le_a22 = QLineEdit('0.01',self)
self.le_a22.move(550, y)
self.le_a22.resize(50, 20)
y += 20
self.le_p2 = QLineEdit('-0.03',self)
self.le_p2.move(550, y)
self.le_p2.resize(50, 20)
y += 20
self.le_m1 = QLineEdit('0.95',self)
self.le_m1.move(550, y)
self.le_m1.resize(50, 20)
y += 20
self.le_m2 = QLineEdit('1.2',self)
self.le_m2.move(550, y)
self.le_m2.resize(50, 20)
y += 20
self.le_d1 = QLineEdit('0.7',self)
self.le_d1.move(550, y)
self.le_d1.resize(50, 20)
y += 20
self.le_d2 = QLineEdit('0.5',self)
self.le_d2.move(550, y)
self.le_d2.resize(50, 20)
y += 20
self.le_c1 = QLineEdit('0.25',self)
self.le_c1.move(550, y)
self.le_c1.resize(50, 20)
y += 20
self.le_c2 = QLineEdit('0.65',self)
self.le_c2.move(550, y)
self.le_c2.resize(50, 20)
y += 20
self.le_h1 = QLineEdit('0.15',self)
self.le_h1.move(550, y)
self.le_h1.resize(50, 20)
y += 20
self.le_b1 = QLineEdit('0.35',self)
self.le_b1.move(550, y)
self.le_b1.resize(50, 20)
y += 20
button = QPushButton('Start', self)
button.move(500,y)
button.resize(50,25)
button.clicked.connect(self.initVars)
self.show()
class PlotCanvas(FigureCanvas):
def e1(self,u,v):
return a11+a12*u*v
def e2(self,u,v):
return a21+a22*u*v
def f1(self,u,v):
return u*(m1-d1)+v*d1-c1*u*u-h1*u-b1
def f2(self,u,v):
return v*(m2-d2)+u*d2-c2*v*v
def __init__(self, parent=None, width=5, height=4, dpi=100):
fig = Figure(figsize=(width, height), dpi=dpi)
self.axes = fig.add_subplot(111)
FigureCanvas.__init__(self, fig)
self.setParent(parent)
FigureCanvas.setSizePolicy(self,
QSizePolicy.Expanding,
QSizePolicy.Expanding)
FigureCanvas.updateGeometry(self)
def plot(self):
self.axes.cla()
plt = self.figure.add_subplot(111)
global N1
global tt
global l
global h
global N2
global t
global hh
global rr
global a11
global a12
global p1
global a21
global a22
global p2
global m1
global m2
global d1
global d2
global c1
global c2
global h1
global b1
global x
global y
global v
global a
global b
global z
tst = time.clock()
a[0]=0.
b[0]=0.
for i in range(0,N1+1):
x[i]=i*h
if i*h<0.62: y[i] = 0.
elif i*h<1.27: y[i]=-35.502*(i*h)*(i*h)+67.098*(i*h)-27.954
else: y[i]=0.
if i*h<1.32: v[i] = 0.
elif i*h<1.96: v[i]=-35.502*(i*h)*(i*h)+116.09*(i*h)-91.154
else: v[i]=0.0
plt.axis([0.,l,0.0,3.5])
plt.plot(x,y, 'b-',label='$u^0(x)$')
plt.plot(x,v, 'g--',label='$v^0(x)$')
plt.legend(loc=0)
plt.set_xlabel('$x$')
plt.set_ylabel('$u,v$')
plt.grid(True)
#pylab.ion()
x = np.linspace(0, l, N1+1)
for j in range(1,N2+1):
for i in range(1,N1):
e11=(self.e1(y[i],v[i])+self.e1(y[i+1],v[i+1]))/2.
e12=(self.e1(y[i],v[i])+self.e1(y[i-1],v[i-1]))/2.
aa=e12/rr
bb=e11/rr
cc=aa+bb+1
r12 = p1/rr
a[i]=bb/(cc-aa*a[i-1])
d=t*self.f1(y[i],v[i])-r12*0.5*((y[i]+y[i+1])*(v[i+1]-v[i])-(y[i]+y[i-1])*(v[i]-v[i-1]))+y[i]
b[i]=(aa*b[i-1]+d)/(cc-aa*a[i-1])
for ii in range(1,N1+1):
i=N1-ii
y[i] = a[i]*y[i+1]+b[i]
for i in range(0,N1+1):
if y[i]<0: y[i]=0
for i in range(1,N1):
e21=(self.e2(y[i],v[i])+self.e2(y[i+1],v[i+1]))/2.
e22=(self.e2(y[i],v[i])+self.e2(y[i-1],v[i-1]))/2.
aa=e22/rr
bb=e21/rr
cc=aa+bb+1
r12 = p2/rr
a[i]=bb/(cc-aa*a[i-1])
d=t*self.f2(y[i],v[i])-r12*0.5*((v[i]+v[i+1])*(y[i+1]-y[i])-(v[i]+v[i-1])*(y[i]-y[i-1]))+v[i]
b[i]=(aa*b[i-1]+d)/(cc-aa*a[i-1])
for ii in range(1,N1+1):
i=N1-ii
v[i] = a[i]*v[i+1]+b[i]
for i in range(0,N1+1):
if v[i]<0: v[i]=0
pylab.clf()
pylab.plot(x,y, 'b-')
pylab.plot(x,v, 'g--')
plt.grid(True)
plt.axis([0.,l,0.0,3.5])
pylab.draw()
pylab.draw()
plt.axis([0.,l,0.0,3.5])
plt.plot(x,y, 'b-',label='$u$')
plt.plot(x,v, 'g--',label='$v$')
plt.legend(loc=0)
plt.set_xlabel('$x$')
plt.set_ylabel('$u,v$')
self.draw()
dt = time.clock() - tst
print ("N2 = %i, N1 = %i, time solution = %1.3e, h = %1.3e" % (N2, N1, dt, h))
if __name__ == '__main__':
app = QApplication(sys.argv)
ex = App()
sys.exit(app.exec_()) |
(
