def idwt(self, other="haar", wavelet_k=2):
"""
Implements the gsl ``WaveletTransform.backward()`` in
:mod:`~sage.gsl.dwt`.
Assumes the length of the sample is a power of 2. Uses the
GSL function ``gsl_wavelet_transform_backward()``.
INPUT:
- ``other`` -- Must be one of the following:
* ``"haar"``
* ``"daubechies"``
* ``"daubechies_centered"``
* ``"haar_centered"``
* ``"bspline"``
* ``"bspline_centered"``
- ``wavelet_k`` -- For daubechies wavelets, ``wavelet_k`` specifies a
daubechie wavelet with `k/2` vanishing moments.
`k = 4,6,...,20` for `k` even are the only ones implemented.
For Haar wavelets, ``wavelet_k`` must be 2.
For bspline wavelets, ``wavelet_k`` equal to `103,105,202,204,
206,208,301,305,307,309` will give biorthogonal B-spline wavelets
of order `(i,j)` where ``wavelet_k`` equals `100 \cdot i + j`.
EXAMPLES::
sage: J = range(8)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt()
sage: t # random arch dependent output
Indexed sequence: [2.82842712474999, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() # random arch dependent output
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() == s
True
sage: J = range(16)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt("bspline", 103)
sage: t # random arch dependent output
Indexed sequence: [4.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
sage: t.idwt("bspline", 103) == s
True
"""
# elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J) ## must be 1 minus a power of 2
S = self.list()
k = wavelet_k
if other=="haar" or other=="haar_centered":
if k in [2]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError("wavelet_k must be = 2")
if other=="debauchies" or other=="debauchies_centered":
if k in [4,6,8,10,12,14,16,18,20]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError("wavelet_k must be in {4,6,8,10,12,14,16,18,20}")
if other=="bspline" or other=="bspline_centered":
if k in [103,105,202,204,206,208,301,305,307,309]:
a = WaveletTransform(N,other,103)
else:
raise ValueError("wavelet_k must be in {103,105,202,204,206,208,301,305,307,309}")
for i in range(N):
a[i] = S[i]
a.backward_transform()
return IndexedSequence([RR(a[j]) for j in J],J)
def idwt(self,other="haar",wavelet_k=2):
"""
Implements the gsl WaveletTransform.backward in dwt.pyx.
other must be an element of
{"haar", "daubechies", "daubechies_centered",
"haar_centered", "bspline", "bspline_centered"}.
Assumes the length of the sample is a power of 2. Uses the
GSL function gsl_wavelet_transform_backward.
INPUT:
other -- the wavelet_type: the name of the type of wavelet,
valid choices are:
'daubechies','daubechies_centered',
'haar' (default),'haar_centered',
'bspline', and 'bspline_centered'.
wavelet_k -- For daubechies wavelets, wavelet_k specifies a
daubechie wavelet with k/2 vanishing moments.
k = 4,6,...,20 for k even are the only ones implemented.
For Haar wavelets, wavelet_k must be 2.
For bspline wavelets,
wavelet_k = 103,105,202,204,206,208,301,305, 307,309
will give biorthogonal B-spline wavelets of order (i,j) where
wavelet_k=100*i+j.
EXAMPLES:
sage: J = range(8)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt()
sage: t # random arch dependent output
Indexed sequence: [2.82842712474999, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() # random arch dependent output
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() == s
True
sage: J = range(16)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt("bspline", 103)
sage: t # random arch dependent output
Indexed sequence: [4.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
sage: t.idwt("bspline", 103) == s
True
"""
F = self.base_ring() ## elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J) ## must be 1 minus a power of 2
S = self.list()
k = wavelet_k
if other=="haar" or other=="haar_centered":
if k in [2]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError,"wavelet_k must be = 2"
if other=="debauchies" or other=="debauchies_centered":
if k in [4,6,8,10,12,14,16,18,20]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError,"wavelet_k must be in {4,6,8,10,12,14,16,18,20}"
if other=="bspline" or other=="bspline_centered":
if k in [103,105,202,204,206,208,301,305,307,309]:
a = WaveletTransform(N,other,103)
else:
raise ValueError,"wavelet_k must be in {103,105,202,204,206,208,301,305,307,309}"
for i in range(N):
a[i] = S[i]
a.backward_transform()
return IndexedSequence([RR(a[j]) for j in J],J)
def idwt(self, other="haar", wavelet_k=2):
"""
Implements the gsl ``WaveletTransform.backward()`` in
:mod:`~sage.gsl.dwt`.
Assumes the length of the sample is a power of 2. Uses the
GSL function ``gsl_wavelet_transform_backward()``.
INPUT:
- ``other`` -- Must be one of the following:
* ``"haar"``
* ``"daubechies"``
* ``"daubechies_centered"``
* ``"haar_centered"``
* ``"bspline"``
* ``"bspline_centered"``
- ``wavelet_k`` -- For daubechies wavelets, ``wavelet_k`` specifies a
daubechie wavelet with `k/2` vanishing moments.
`k = 4,6,...,20` for `k` even are the only ones implemented.
For Haar wavelets, ``wavelet_k`` must be 2.
For bspline wavelets, ``wavelet_k`` equal to `103,105,202,204,
206,208,301,305,307,309` will give biorthogonal B-spline wavelets
of order `(i,j)` where ``wavelet_k`` equals `100 \cdot i + j`.
EXAMPLES::
sage: J = range(8)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt()
sage: t # random arch dependent output
Indexed sequence: [2.82842712474999, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() # random arch dependent output
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() == s
True
sage: J = range(16)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt("bspline", 103)
sage: t # random arch dependent output
Indexed sequence: [4.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
sage: t.idwt("bspline", 103) == s
True
"""
# elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J) ## must be 1 minus a power of 2
S = self.list()
k = wavelet_k
if other=="haar" or other=="haar_centered":
if k in [2]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError("wavelet_k must be = 2")
if other=="debauchies" or other=="debauchies_centered":
if k in [4,6,8,10,12,14,16,18,20]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError("wavelet_k must be in {4,6,8,10,12,14,16,18,20}")
if other=="bspline" or other=="bspline_centered":
if k in [103,105,202,204,206,208,301,305,307,309]:
a = WaveletTransform(N,other,103)
else:
raise ValueError("wavelet_k must be in {103,105,202,204,206,208,301,305,307,309}")
for i in range(N):
a[i] = S[i]
a.backward_transform()
return IndexedSequence([RR(a[j]) for j in J],J)
def idwt(self,other="haar",wavelet_k=2):
"""
Implements the gsl WaveletTransform.backward in dwt.pyx.
other must be an element of
{"haar", "daubechies", "daubechies_centered",
"haar_centered", "bspline", "bspline_centered"}.
Assumes the length of the sample is a power of 2. Uses the
GSL function gsl_wavelet_transform_backward.
INPUT:
other -- the wavelet_type: the name of the type of wavelet,
valid choices are:
'daubechies','daubechies_centered',
'haar' (default),'haar_centered',
'bspline', and 'bspline_centered'.
wavelet_k -- For daubechies wavelets, wavelet_k specifies a
daubechie wavelet with k/2 vanishing moments.
k = 4,6,...,20 for k even are the only ones implemented.
For Haar wavelets, wavelet_k must be 2.
For bspline wavelets,
wavelet_k = 103,105,202,204,206,208,301,305, 307,309
will give biorthogonal B-spline wavelets of order (i,j) where
wavelet_k=100*i+j.
EXAMPLES:
sage: J = range(8)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt()
sage: t # random arch dependent output
Indexed sequence: [2.82842712474999, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() # random arch dependent output
Indexed sequence: [1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000, 1.00000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7]
sage: t.idwt() == s
True
sage: J = range(16)
sage: A = [RR(1) for i in J]
sage: s = IndexedSequence(A,J)
sage: t = s.dwt("bspline", 103)
sage: t # random arch dependent output
Indexed sequence: [4.00000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000]
indexed by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
sage: t.idwt("bspline", 103) == s
True
"""
F = self.base_ring() ## elements must be coercible into RR
J = self.index_object() ## must be = range(N)
N = len(J) ## must be 1 minus a power of 2
S = self.list()
k = wavelet_k
if other=="haar" or other=="haar_centered":
if k in [2]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError,"wavelet_k must be = 2"
if other=="debauchies" or other=="debauchies_centered":
if k in [4,6,8,10,12,14,16,18,20]:
a = WaveletTransform(N,other,wavelet_k)
else:
raise ValueError,"wavelet_k must be in {4,6,8,10,12,14,16,18,20}"
if other=="bspline" or other=="bspline_centered":
if k in [103,105,202,204,206,208,301,305,307,309]:
a = WaveletTransform(N,other,103)
else:
raise ValueError,"wavelet_k must be in {103,105,202,204,206,208,301,305,307,309}"
for i in range(N):
a[i] = S[i]
a.backward_transform()
return IndexedSequence([RR(a[j]) for j in J],J)