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161 | #!/usr/bin/env python
import pylab
VERBOSE=False
class Polynom:
"""My polynomial calculates:
- function value
- sums of polynomials
- derivatives
- integral
- roots"""
coeff = None
nullstellen = None
# default_x: lower limit, upper limit, steps per interval, tolerance
default_x = [-10.,10.,100,1e-10]
poly_func = lambda x: 0
name = '0'
def __call__(self,x):
"""This one of Python's sepcial methods. Play with this script
to find out, what's so special about this method."""
return self.poly_func(x)
def __init__(self,c):
"""Coefficients are passed as a sequence during init"""
self.coeff = []
if type(c) == type([]) or type(c) == type(()):
for C in c:
self.coeff.append(C)
elif type(c) == type(1) or type(c) == type(1.):
self.coeff.append(c)
else:
raise TypeError, 'Int or sequence of Int expected, got: %s' % str(type(c))
self.set_func()
def __add__(self,other):
"We can add polynomials"
a = self.coeff[::-1]
b = other.coeff[::-1]
print a,b
c = []
al,bl = len(a),len(b)
for i in range(min(al,bl)):
c.append(a[i]+b[i])
if al>bl:
for i in range(bl,al):
c.append(a[i])
elif bl>al:
for i in range(al,bl):
c.append(b[i])
else:
pass
return Polynom(c[::-1])
def __str__(self):
return 'Polynom: %s' % self.name
def get_coeff(self):
return self.coeff
def set_func(self):
"""For mathematics coefficients are converted to a function"""
f = []
for n in range(len(self.coeff)):
f.append('%+.6g * x**%d' % (self.coeff[n],len(self.coeff)-n-1))
self.name = ' '.join(f)
if VERBOSE: print self.name
self.poly_func = eval('lambda x: '+ self.name)
def derive(self,order=1):
for o in range(order):
L = len(self.coeff)
new_coeff = [0 for i in range(L-1)]
for i in range(L-1,-1,-1):
try:
new_coeff[i] = self.coeff[i]*float(L-i-1)
except:
pass
return Polynom(new_coeff)
def integrate(self,order=1,const=0):
for o in range(order):
L = len(self.coeff)
new_coeff = [const for i in range(L+1)]
for i in range(L-1,-1,-1):
#try:
if self.coeff[i] == 0: continue
new_coeff[i] = self.coeff[i]*1/float(L-i)
#except:
#new_coeff[i] = 0
print i, new_coeff[i],L-i
return Polynom(new_coeff)
def find_nullst(self,a,b):
"""Recursive method for determining roots"""
x = a
delta = (b-a)/float(self.default_x[2])
last_y = None
for i in range(self.default_x[2]):
x += delta
y = self.poly_func(x)
#if VERBOSE: print "%05.3f %06.3f" % (x,y)
if last_y:
if (last_y > 0 and y < 0) or (last_y < 0 and y > 0):
if VERBOSE: print "Nullstelle zwischen %05.3f und %05.3f" % (x-delta,x)
if abs(y-last_y)<self.default_x[3]:
return x
else:
if VERBOSE: print "recuring ..."
return self.find_nullst(x-delta,x)
last_y = y
else:
return None
def cal_nullst(self):
"""Default method for determining roots. Returns list of roots."""
if type(self.nullstellen) == type([]):
del self.nullstellen[:]
else:
self.nullstellen = []
nullst = self.default_x[0]
while True:
nullst = self.find_nullst(nullst,self.default_x[1])
if nullst:
self.nullstellen.append(nullst)
else:
if VERBOSE: print "nichts zurueck gegeben!"
break
print "Nullstellen:"
for n in self.nullstellen:
print "%+08e %+08e" % (n, self.poly_func(n))
return self.nullstellen
def show(self):
"Plotting a polynomial is always nice."
x = pylab.arange(self.default_x[0],self.default_x[1],.01)
y = self.poly_func(x)
pylab.plot(x,y)
pylab.grid()
pylab.show()
if __name__ == '__main__':
p = Polynom([3,-12,2,-3])
q = pylab.poly1d([3,-12,2,-3])
print p
print p.integrate()
print pylab.polyint(q)
print p(2.) # here the method __call__ of p is called!
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