示例#1
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def romberg(f,a,b,tol=1.0e-6):
    def richardson(r,k):
        for j in range(k-1,0,-1):
            const = 4.0**(k-j)
            r[j] = (const*r[j+1] - r[j])/(const - 1.0)
        return r
    r = np.zeros(21)
    r[1] = trapezoid(f,a,b,0.0,1)
    r_old = r[1]
    for k in range(2,21):
        r[k] = trapezoid(f,a,b,r[k-1],k)
        r = richardson(r,k)
        if abs(r[1]-r_old) < tol*max(abs(r[1]),1.0):
            return r[1],2**(k-1)
        r_old = r[1]
    print("Romberg quadrature did not converge")
示例#2
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def romberg(f,a,b,tol=1.0e-6):
    
    def richardson(r,k):
        for j in range(k-1,0,-1):
            const = 4.0**(k-j)
            r[j] = (const*r[j+1] - r[j])/(const - 1.0)
        return r
     
    r = zeros((21),type=Float64)
    r[1] = trapezoid(f,a,b,0.0,1)
    r_old = r[1]
    for k in range(2,21):
        r[k] = trapezoid(f,a,b,r[k-1],k)
        r = richardson(r,k)
        if abs(r[1]-r_old) < tol*max(abs(r[1]),1.0):
            return r[1],2**(k-1)
        r_old = r[1]
    print "Romberg quadrature did not converge"
示例#3
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def problem22(): 
    Iold = 0.0
    a = 0.0 
    b = 1.0
    integral, npan = romberg(f2, 0, 4)
    print("n", "\t", "h", "\t", "T_h(f)", "\t", "e_h", "\t", "e_2h/e_h")
    for k in range(1,9):
        Inew = trapezoid(f1, a, b, Iold, k)
        if (k > 1) and (abs(Inew - Iold)) < 1.0e-10: break
        eh2 = ((integral - Iold) / (integral - Inew))
        Iold = Inew
        n1 = (2**(k-1))
        print(2**(k-1), "\t", '{0:.4f}'.format(((b-a)/n1)), "\t", '{0:.4f}'.format(Iold), "\t",'{0:.4f}'.format(math.fabs(integral - Iold)), "\t", '{0:.4f}'.format((eh2)), "\n")
示例#4
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## example6_4
from math import sqrt, cos, pi
from trapezoid import *


def f(x):
    return sqrt(x) * cos(x)


Iold = 0.0
for k in range(1, 21):
    Inew = trapezoid(f, 0.0, pi, Iold, k)
    if (k > 1) and (abs(Inew - Iold)) < 1.0e-6: break
    Iold = Inew
print "Integral =", Inew
print "nPanels =", 2**(k - 1)
raw_input("\nPress return to exit")
示例#5
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while True:  
    go=win.getMouse()
    if go.x>120 and go.x<230:
        #Trapezoid
        if go.y>200 and go.y<275:
            from trapezoid import *
            def f(x): return eval(fninput.getText())
            print(type(f))
            Iold=0.0
            a=eval(lower.getText())
            print(type(a))
            b=eval(upper.getText())
            print(type(b))
            for k in range(1,21):
                Inew=trapezoid(f,a,b,Iold,k)
                if (k>1) and (abs(Inew-Iold))<1.0e-6: break
                Iold=Inew
            print("Trapezoidal Integral =",Inew)
            answer=Inew
            showAnswer()

        #Romberg
        if go.y>310 and go.y<385:
            from romberg import *
            def f(x): return eval(fninput.getText())
            print(type(f))

            I,n=romberg(f,eval(lower.getText()),eval(upper.getText()))
            print("Romberg Integral =",I)
            answer=I
示例#6
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from math import *
import matplotlib.pyplot as plt

#true=exp(1.0)-1.0
#print true
#while n1 % 2 != 0 :
#   n1 = int(raw_input( "Enter number of intervals desired for trapezoidal rule (must be even)" ))

n = []
d1 = []
d2 = []

for n1 in range(100, 1100, 100):
    a = 0.0
    b = 1.0
    ans1 = trapezoid(exp, a, b, n1)
    diff1 = abs(true - ans1)
    print 'Trapezoidal rule = ' + str(ans1)
    print 'Difference between the result and the true value:', diff1
    d1.append(diff1)

    ans2 = simpson(exp, a, b, n1)
    print 'Simpson = ' + str(ans2)
    diff2 = abs(true - ans2)
    print diff2
    d2.append(diff2)
    n.append(n1)
dl1 = []
dl2 = []
for x in d1:
    dl1.append(log10(x))
示例#7
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## example6_4
from math import sqrt,cos,pi
from trapezoid import *

def f(x): return sqrt(x)*cos(x)

Iold = 0.0
for k in range(1,21):
    Inew = trapezoid(f,0.0,pi,Iold,k)
    if (k > 1) and (abs(Inew - Iold)) < 1.0e-6: break
    Iold = Inew
print "Integral =",Inew
print "nPanels =",2**(k-1)
raw_input("\nPress return to exit")
示例#8
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import numpy as np

func = lambda x: np.sqrt(x) * np.cos(x)

## Recursive Trapezoidal Rule
from trapezoid import *

Iold = 0.0
a = 0.0
b = np.pi

for k in range(1, 10):
    Inew = trapezoid(func, a, b, Iold, k)
    Iold = Inew

    print('Inew : ', Inew, '    Panel : ', 2**(k - 1))

## Romberg Integration
from romberg import *
print(romberg(func, a, b, tol=1.0e-06))
示例#9
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from trapezoid import *
from simpson import *
from math import *



n1 = 1
n2 = 0

while n1 % 2 != 0 :
    n1 = int(raw_input( "Enter number of intervals desired for trapezoidal rule (must be even)" ))

a = 0
b = 2 * atan(1.0)

ans1 = trapezoid(sin, a, b, n1)
print 'Trapezoidal rule = ' + str(ans1)

ans2 = adaptive_trapezoid(sin, a, b, 0.0001)
print 'Adaptive trapezoidal rule = ' + str(ans2)
示例#10
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from trapezoid import *
from simpson import *
from math import *

n1 = 1
n2 = 0

while n1 % 2 != 0:
    n1 = int(
        raw_input(
            "Enter number of intervals desired for trapezoidal rule (must be even)"
        ))

a = 0
b = 2 * atan(1.0)
ans1 = trapezoid(sin, a, b, n1)
print 'Trapezoidal rule = ' + str(ans1)

ans2 = adaptive_trapezoid(sin, a, b, 0.0001)
print 'Adaptive trapezoidal rule = ' + str(ans2)