def C1(n):
""" integral related to first order finite Larmor radius effect
"""
c1 = poly2cheb([0, 0, 0, 0, -1.5, 0, 2])
c2 = nthpoly(2 * n)
kernel = chebmul(c1, c2)
cint = chebint(kernel)
return chebval(1, cint)
def C0(n):
""" integral related to zero'th order finite Larmor radius effect
"""
c1 = poly2cheb([0, 1, 0, -2])
c2 = nthpoly(2 * n)
kernel = chebmul(c1, c2)
cint = chebint(kernel)
return chebval(1, cint)
def test_chebmul(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
tgt = np.zeros(i + j + 1)
tgt[i + j] += .5
tgt[abs(i - j)] += .5
res = cheb.chebmul([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebmul(self):
for i in range(5):
for j in range(5):
msg = "At i=%d, j=%d" % (i, j)
tgt = np.zeros(i + j + 1)
tgt[i + j] += .5
tgt[abs(i - j)] += .5
res = cheb.chebmul([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebdiv(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
ci = [0]*i + [1]
cj = [0]*j + [1]
tgt = cheb.chebadd(ci, cj)
quo, rem = cheb.chebdiv(tgt, ci)
res = cheb.chebadd(cheb.chebmul(quo, ci), rem)
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebdiv(self):
for i in range(5):
for j in range(5):
msg = "At i=%d, j=%d" % (i, j)
ci = [0]*i + [1]
cj = [0]*j + [1]
tgt = cheb.chebadd(ci, cj)
quo, rem = cheb.chebdiv(tgt, ci)
res = cheb.chebadd(cheb.chebmul(quo, ci), rem)
assert_equal(trim(res), trim(tgt), err_msg=msg)
def gegenbauerReconstruction(self, A, N):
# np.set_printoptions(precision=3, suppress=True)
entireA = np.hstack((A[1:][::-1], A))
n = np.size(entireA)
x = self.chebNodes(n=N)
k = np.arange(-A.size + 1, A.size)
xx, kk = np.meshgrid(x, k)
M = np.exp(1j * kk * np.pi * xx).T
fx = M.dot(entireA)
cfx = self.chebTransform(fx)
# gamma = 1
# print(gamma)
l = N
# l = 4.5
xx, NN = np.meshgrid(x, np.arange(N))
gx = special.eval_gegenbauer(NN, l, xx)
# print(gx)
cgx = (self.chebTransform(gx.T)).T
# print(cgx)
wx = np.power(1 - x * x, l - 0.5)
cwx = self.chebTransform(wx)
cIx = []
for i in range(gx.shape[0]):
cIx.append(np_cheb.chebmul(cwx, cgx[i, :]))
# print(cgx[i, :])
cIx = np.asarray(cIx)
I = []
h = np.sqrt(np.pi) * special.eval_gegenbauer(np.arange(N), l, 1) * special.gamma(l + 0.5) / special.gamma(l) / (
N + l)
for it in cIx:
I.append(np.real(self.integrate(it, cfx)))
I /= h
# print(np.array(I))
# print(gx)
plt.plot(x, (gx.T).dot(I))
plt.show()
def chebmul(c1, c2):
from numpy.polynomial.chebyshev import chebmul
return chebmul(c1, c2)
def chebmul(c1, c2):
from numpy.polynomial.chebyshev import chebmul
return chebmul(c1, c2)
