def genChebzshevPolyGS(n_poly = 3):
"""
Generates Chebyshev Polynomials using GramSchmidt
"""
integr = iL.FivePointIntegrator(10, [-1,1])
polys = []
print '\nGenerating Chebyshev Polynomials using GramSchmidt'
print '-----------------------------------------------------------------------\n'
for n in range(0, n_poly+1):
print ' - generate P%d'%n
Tn = pL.poly([1]*(n+1)) #degree 1 has 2 coefficients, degree 2 has 3, ...
polys.append(Tn)
for m in range(len(Tn())-1):
Tm = polys[m]
#print 'indices',n,m
#print 'Tn', Tn
#print 'Tm', Tm
for i in range(Tm.n):
#print ' n,m,i',n,m,i
#tmp = integr(lambda x:(Tn(x) * Tm(x)) / np.sqrt(1.0-x*x))
#print ' intgr at: ',n,m,i,"int",tmp, Tm[i]
#Tn[i] -= tmp * Tm[i]
#print ' ', Tn, '\n ',Tm
Tn[i] -= integr(lambda x:(Tn(x) * Tm(x)) / np.sqrt(1.0-x*x)) * Tm[i]
polys[n] = norm1(Tn, integr)
return normFinal(polys)
def genChebyshevPolyGCQ(n_poly=3, M_eval=10):
"""
Generates Chebyshev Polynomials using
* Gauss-Chebyshev quadrature for integration
* Gram Schmidt
"""
integr = iL.GaussChebishevQuadrature(M_eval)
polys = []
print '\n\nGenerating Chebyshev Polynomials using Gauss-Chebyshev quadrature'
print '-----------------------------------------------------------------------\n'
for n in range(0, n_poly + 1):
print ' - generate P%d' % n
Tn = pL.poly(
[1] * (n + 1)) #degree 1 has 2 coefficients, degree 2 has 3, ...
polys.append(Tn)
for m in range(len(Tn()) - 1):
Tm = polys[m]
#print 'indices',n,m
#print 'Tn', Tn
#print 'Tm', Tm
for i in range(Tm.n):
#print ' n,m,i',n,m,i
#tmp = integr(lambda x:(Tn(x) * Tm(x)) / np.sqrt(1.0-x*x))
#print ' intgr at: ',n,m,i,"int",tmp, Tm[i]
#Tn[i] -= tmp * Tm[i]
#print ' ', Tn, '\n ',Tm
Tn[i] -= integr(Tn * Tm) * Tm[i]
polys[n] = norm2(Tn, integr)
return normFinal(polys)
def genChebzshevPolyGS(n_poly=3):
"""
Generates Chebyshev Polynomials using GramSchmidt
"""
integr = iL.FivePointIntegrator(10, [-1, 1])
polys = []
print '\nGenerating Chebyshev Polynomials using GramSchmidt'
print '-----------------------------------------------------------------------\n'
for n in range(0, n_poly + 1):
print ' - generate P%d' % n
Tn = pL.poly(
[1] * (n + 1)) #degree 1 has 2 coefficients, degree 2 has 3, ...
polys.append(Tn)
for m in range(len(Tn()) - 1):
Tm = polys[m]
#print 'indices',n,m
#print 'Tn', Tn
#print 'Tm', Tm
for i in range(Tm.n):
#print ' n,m,i',n,m,i
#tmp = integr(lambda x:(Tn(x) * Tm(x)) / np.sqrt(1.0-x*x))
#print ' intgr at: ',n,m,i,"int",tmp, Tm[i]
#Tn[i] -= tmp * Tm[i]
#print ' ', Tn, '\n ',Tm
Tn[i] -= integr(lambda x:
(Tn(x) * Tm(x)) / np.sqrt(1.0 - x * x)) * Tm[i]
polys[n] = norm1(Tn, integr)
return normFinal(polys)
def genChebyshevPolyGCQ(n_poly = 3, M_eval = 10):
"""
Generates Chebyshev Polynomials using
* Gauss-Chebyshev quadrature for integration
* Gram Schmidt
"""
integr = iL.GaussChebishevQuadrature(M_eval)
polys = []
print '\n\nGenerating Chebyshev Polynomials using Gauss-Chebyshev quadrature'
print '-----------------------------------------------------------------------\n'
for n in range(0, n_poly+1):
print ' - generate P%d'%n
Tn = pL.poly([1]*(n+1)) #degree 1 has 2 coefficients, degree 2 has 3, ...
polys.append(Tn)
for m in range(len(Tn())-1):
Tm = polys[m]
#print 'indices',n,m
#print 'Tn', Tn
#print 'Tm', Tm
for i in range(Tm.n):
#print ' n,m,i',n,m,i
#tmp = integr(lambda x:(Tn(x) * Tm(x)) / np.sqrt(1.0-x*x))
#print ' intgr at: ',n,m,i,"int",tmp, Tm[i]
#Tn[i] -= tmp * Tm[i]
#print ' ', Tn, '\n ',Tm
Tn[i] -= integr(Tn * Tm) * Tm[i]
polys[n] = norm2(Tn, integr)
return normFinal(polys)
