def ifft(self):
"""
Implements the gsl FastFourierTransform.inverse in fft.pyx.
If the number of sample points in the input is a power of 2
then the wrapper for the GSL function
gsl_fft_complex_radix2_inverse is automatically called.
Otherwise, gsl_fft_complex_inverse is used.
EXAMPLES:
sage: J = range(5)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.fft(); t
Indexed sequence: [5.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft()
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft() == s
1
"""
F = self.base_ring() ## elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J)
S = self.list()
a = FastFourierTransform(N)
for i in range(N):
a[i] = S[i]
a.inverse_transform()
return IndexedSequence([a[j][0]+I*a[j][1] for j in J],J)
def ifft(self):
"""
Implements the gsl ``FastFourierTransform.inverse`` in
:mod:`~sage.gsl.fft`.
If the number of sample points in the input is a power of 2
then the wrapper for the GSL function
``gsl_fft_complex_radix2_inverse()`` is automatically called.
Otherwise, ``gsl_fft_complex_inverse()`` is used.
EXAMPLES::
sage: J = range(5)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.fft(); t
Indexed sequence: [5.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft()
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft() == s
1
"""
from sage.rings.all import I
# elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J)
S = self.list()
a = FastFourierTransform(N)
for i in range(N):
a[i] = S[i]
a.inverse_transform()
return IndexedSequence([a[j][0]+I*a[j][1] for j in J],J)
def ifft(self):
"""
Implements the gsl ``FastFourierTransform.inverse`` in
:mod:`~sage.gsl.fft`.
If the number of sample points in the input is a power of 2
then the wrapper for the GSL function
``gsl_fft_complex_radix2_inverse()`` is automatically called.
Otherwise, ``gsl_fft_complex_inverse()`` is used.
EXAMPLES::
sage: J = list(range(5))
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.fft(); t
Indexed sequence: [5.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft()
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4]
sage: t.ifft() == s
1
"""
from sage.rings.all import CC
I = CC.gen()
# elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J)
S = self.list()
a = FastFourierTransform(N)
for i in range(N):
a[i] = S[i]
a.inverse_transform()
return IndexedSequence([a[j][0] + I * a[j][1] for j in J], J)