def shift(x, a, period=None, _cache=_cache):
""" shift(x, a, period=2*pi) -> y
Shift periodic sequence x by a: y(u) = x(u+a).
If x_j and y_j are Fourier coefficients of periodic functions x
and y, respectively, then
y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
Optional input:
period
The period of the sequences x and y. Default period is 2*pi.
"""
tmp = asarray(x)
if iscomplexobj(tmp):
return shift(tmp.real, a, period) + 1j * shift(tmp.imag, a, period)
if period is not None:
a = a * 2 * pi / period
n = len(x)
omega = _cache.get((n, a))
if omega is None:
if len(_cache) > 20:
while _cache:
_cache.popitem()
def kernel_real(k, a=a):
return cos(a * k)
def kernel_imag(k, a=a):
return sin(a * k)
omega_real = convolve.init_convolution_kernel(n,
kernel_real,
d=0,
zero_nyquist=0)
omega_imag = convolve.init_convolution_kernel(n,
kernel_imag,
d=1,
zero_nyquist=0)
_cache[(n, a)] = omega_real, omega_imag
else:
omega_real, omega_imag = omega
overwrite_x = _datacopied(tmp, x)
return convolve.convolve_z(tmp,
omega_real,
omega_imag,
overwrite_x=overwrite_x)
def shift(x, a, period=None, _cache=_cache):
"""
Shift periodic sequence x by a: y(u) = x(u+a).
If x_j and y_j are Fourier coefficients of periodic functions x
and y, respectively, then::
y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
Parameters
----------
x : array_like
The array to take the pseudo-derivative from.
a : float
Defines the parameters of the sinh/sinh pseudo-differential
period : float, optional
The period of the sequences x and y. Default period is ``2*pi``.
"""
tmp = asarray(x)
if iscomplexobj(tmp):
return shift(tmp.real,a,period)+1j*shift(tmp.imag,a,period)
if period is not None:
a = a*2*pi/period
n = len(x)
omega = _cache.get((n,a))
if omega is None:
if len(_cache)>20:
while _cache: _cache.popitem()
def kernel_real(k,a=a): return cos(a*k)
def kernel_imag(k,a=a): return sin(a*k)
omega_real = convolve.init_convolution_kernel(n,kernel_real,d=0,
zero_nyquist=0)
omega_imag = convolve.init_convolution_kernel(n,kernel_imag,d=1,
zero_nyquist=0)
_cache[(n,a)] = omega_real,omega_imag
else:
omega_real,omega_imag = omega
overwrite_x = _datacopied(tmp, x)
return convolve.convolve_z(tmp,omega_real,omega_imag,
overwrite_x=overwrite_x)
def shift(x, a, period=None,
_cache = _cache):
""" shift(x, a, period=2*pi) -> y
Shift periodic sequence x by a: y(u) = x(u+a).
If x_j and y_j are Fourier coefficients of periodic functions x
and y, respectively, then
y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
Optional input:
period
The period of the sequences x and y. Default period is 2*pi.
"""
tmp = asarray(x)
if iscomplexobj(tmp):
return shift(tmp.real,a,period)+1j*shift(tmp.imag,a,period)
if period is not None:
a = a*2*pi/period
n = len(x)
omega = _cache.get((n,a))
if omega is None:
if len(_cache)>20:
while _cache: _cache.popitem()
def kernel_real(k,a=a): return cos(a*k)
def kernel_imag(k,a=a): return sin(a*k)
omega_real = convolve.init_convolution_kernel(n,kernel_real,d=0,
zero_nyquist=0)
omega_imag = convolve.init_convolution_kernel(n,kernel_imag,d=1,
zero_nyquist=0)
_cache[(n,a)] = omega_real,omega_imag
else:
omega_real,omega_imag = omega
overwrite_x = _datacopied(tmp, x)
return convolve.convolve_z(tmp,omega_real,omega_imag,
overwrite_x=overwrite_x)
