def ftwindow(x, xmin=None, xmax=None, dx=1, dx2=None,
window='hanning', _larch=None, **kws):
"""
create a Fourier transform window array.
Parameters:
-------------
x: 1-d array array to build window on.
xmin: starting x for FT Window
xmax: ending x for FT Window
dx: tapering parameter for FT Window
dx2: second tapering parameter for FT Window (=dx)
window: name of window type
Returns:
----------
1-d window array.
Notes:
-------
Valid Window names:
hanning cosine-squared taper
parzen linear taper
welch quadratic taper
gaussian Gaussian (normal) function window
sine sine function window
kaiser Kaiser-Bessel function-derived window
"""
if window is None:
window = VALID_WINDOWS[0]
nam = window.strip().lower()[:3]
if nam not in VALID_WINDOWS:
raise RuntimeError("invalid window name %s" % window)
dx1 = dx
if dx2 is None: dx2 = dx1
if xmin is None: xmin = min(x)
if xmax is None: xmax = max(x)
xstep = (x[-1] - x[0]) / (len(x)-1)
xeps = 1.e-4 * xstep
x1 = max(min(x), xmin - dx1 / 2.0)
x2 = xmin + dx1 / 2.0 + xeps
x3 = xmax - dx2 / 2.0 - xeps
x4 = min(max(x), xmax + dx2 / 2.0)
if nam == 'fha':
if dx1 < 0: dx1 = 0
if dx2 > 1: dx2 = 1
x2 = x1 + xeps + dx1*(xmax-xmin)/2.0
x3 = x4 - xeps - dx2*(xmax-xmin)/2.0
elif nam == 'gau':
dx1 = max(dx1, xeps)
def asint(val): return int((val+xeps)/xstep)
i1, i2, i3, i4 = asint(x1), asint(x2), asint(x3), asint(x4)
i1, i2 = max(0, i1), max(0, i2)
i3, i4 = min(len(x)-1, i3), min(len(x)-1, i4)
if i2 == i1: i1 = max(0, i2-1)
if i4 == i3: i3 = max(i2, i4-1)
x1, x2, x3, x4 = x[i1], x[i2], x[i3], x[i4]
if x1 == x2: x2 = x2+xeps
if x3 == x4: x4 = x4+xeps
# initial window
fwin = zeros(len(x))
if i3 > i2:
fwin[i2:i3] = ones(i3-i2)
# now finish making window
if nam in ('han', 'fha'):
fwin[i1:i2+1] = sin((pi/2)*(x[i1:i2+1]-x1) / (x2-x1))**2
fwin[i3:i4+1] = cos((pi/2)*(x[i3:i4+1]-x3) / (x4-x3))**2
elif nam == 'par':
fwin[i1:i2+1] = (x[i1:i2+1]-x1) / (x2-x1)
fwin[i3:i4+1] = 1 - (x[i3:i4+1]-x3) / (x4-x3)
elif nam == 'wel':
fwin[i1:i2+1] = 1 - ((x[i1:i2+1]-x2) / (x2-x1))**2
fwin[i3:i4+1] = 1 - ((x[i3:i4+1]-x3) / (x4-x3))**2
elif nam in ('kai', 'bes'):
cen = (x4+x1)/2
wid = (x4-x1)/2
arg = 1 - (x-cen)**2 / (wid**2)
arg[where(arg<0)] = 0
if nam == 'bes': # 'bes' : ifeffit 1.0 implementation of kaiser-bessel
fwin = bessel_i0(dx* sqrt(arg)) / bessel_i0(dx)
fwin[where(x<=x1)] = 0
fwin[where(x>=x4)] = 0
else: # better version
scale = max(1.e-10, bessel_i0(dx)-1)
fwin = (bessel_i0(dx * sqrt(arg)) - 1) / scale
elif nam == 'sin':
fwin[i1:i4+1] = sin(pi*(x4-x[i1:i4+1]) / (x4-x1))
elif nam == 'gau':
cen = (x4+x1)/2
fwin = exp(-(((x - cen)**2)/(2*dx1*dx1)))
return fwin
def ftwindow(x,
xmin=None,
xmax=None,
dx=1,
dx2=None,
window='hanning',
_larch=None,
**kws):
"""
create a Fourier transform window array.
Parameters:
-------------
x: 1-d array array to build window on.
xmin: starting x for FT Window
xmax: ending x for FT Window
dx: tapering parameter for FT Window
dx2: second tapering parameter for FT Window (=dx)
window: name of window type
Returns:
----------
1-d window array.
Notes:
-------
Valid Window names:
hanning cosine-squared taper
parzen linear taper
welch quadratic taper
gaussian Gaussian (normal) function window
sine sine function window
kaiser Kaiser-Bessel function-derived window
"""
if window is None:
window = VALID_WINDOWS[0]
nam = window.strip().lower()[:3]
if nam not in VALID_WINDOWS:
raise RuntimeError("invalid window name %s" % window)
dx1 = dx
if dx2 is None: dx2 = dx1
if xmin is None: xmin = min(x)
if xmax is None: xmax = max(x)
xstep = (x[-1] - x[0]) / (len(x) - 1)
xeps = 1.e-4 * xstep
x1 = max(min(x), xmin - dx1 / 2.0)
x2 = xmin + dx1 / 2.0 + xeps
x3 = xmax - dx2 / 2.0 - xeps
x4 = min(max(x), xmax + dx2 / 2.0)
if nam == 'fha':
if dx1 < 0: dx1 = 0
if dx2 > 1: dx2 = 1
x2 = x1 + xeps + dx1 * (xmax - xmin) / 2.0
x3 = x4 - xeps - dx2 * (xmax - xmin) / 2.0
elif nam == 'gau':
dx1 = max(dx1, xeps)
def asint(val):
return int((val + xeps) / xstep)
i1, i2, i3, i4 = asint(x1), asint(x2), asint(x3), asint(x4)
i1, i2 = max(0, i1), max(0, i2)
i3, i4 = min(len(x) - 1, i3), min(len(x) - 1, i4)
if i2 == i1: i1 = max(0, i2 - 1)
if i4 == i3: i3 = max(i2, i4 - 1)
x1, x2, x3, x4 = x[i1], x[i2], x[i3], x[i4]
if x1 == x2: x2 = x2 + xeps
if x3 == x4: x4 = x4 + xeps
# initial window
fwin = zeros(len(x))
if i3 > i2:
fwin[i2:i3] = ones(i3 - i2)
# now finish making window
if nam in ('han', 'fha'):
fwin[i1:i2 + 1] = sin((pi / 2) * (x[i1:i2 + 1] - x1) / (x2 - x1))**2
fwin[i3:i4 + 1] = cos((pi / 2) * (x[i3:i4 + 1] - x3) / (x4 - x3))**2
elif nam == 'par':
fwin[i1:i2 + 1] = (x[i1:i2 + 1] - x1) / (x2 - x1)
fwin[i3:i4 + 1] = 1 - (x[i3:i4 + 1] - x3) / (x4 - x3)
elif nam == 'wel':
fwin[i1:i2 + 1] = 1 - ((x[i1:i2 + 1] - x2) / (x2 - x1))**2
fwin[i3:i4 + 1] = 1 - ((x[i3:i4 + 1] - x3) / (x4 - x3))**2
elif nam in ('kai', 'bes'):
cen = (x4 + x1) / 2
wid = (x4 - x1) / 2
arg = 1 - (x - cen)**2 / (wid**2)
arg[where(arg < 0)] = 0
if nam == 'bes': # 'bes' : ifeffit 1.0 implementation of kaiser-bessel
fwin = bessel_i0(dx * sqrt(arg)) / bessel_i0(dx)
fwin[where(x <= x1)] = 0
fwin[where(x >= x4)] = 0
else: # better version
scale = max(1.e-10, bessel_i0(dx) - 1)
fwin = (bessel_i0(dx * sqrt(arg)) - 1) / scale
elif nam == 'sin':
fwin[i1:i4 + 1] = sin(pi * (x4 - x[i1:i4 + 1]) / (x4 - x1))
elif nam == 'gau':
cen = (x4 + x1) / 2
fwin = exp(-(((x - cen)**2) / (2 * dx1 * dx1)))
return fwin
def ftwindow(x: ndarray,
x_range: list = [-inf, inf],
dx1: float = 1,
dx2: float = None,
win: str = 'hanning') -> ndarray:
"""Returns a FT window.
Parameters
----------
x
Array for the FT window.
x_range
Range for the FT window. The default is [-:data:`~numpy.inf`, :data:`~numpy.inf`].
dx1
First tapering parameter for FT window. The defaut is 1.
dx2
Second tapering parameter for FT window. If None it will use the same value as dx1.
win
Name of the window type. The default is 'hanning'. See Notes for valid names.
Returns
-------
:
1-d array with the FT window.
Raises
------
ValueError
If ``window`` name is not recognized.
Notes
-----
Valid window names:
- 'hanning' : cosine-squared function window.
- 'parzen' : linear function window.
- 'welch' : quadratic function window.
- 'gaussian' : Gaussian (normal) function window.
- 'sine' : sine function window.
- 'kaiser' : Kaiser-Bessel function-derived window.
Example
--------
.. plot::
:context: reset
>>> from numpy import arange
>>> import matplotlib.pyplot as plt
>>> from araucaria.xas import ftwindow
>>> from araucaria.plot import fig_xas_template
>>> k = arange(0, 10.1, 0.05)
>>> k_range = [2,8]
>>> windows = ['hanning', 'parzen', 'welch',
... 'gaussian', 'sine', 'kaiser']
>>> dk = 1.0
>>> fig_kws = {'sharex' : True}
>>> fig, axes = fig_xas_template(panels='ee/ee/ee', **fig_kws)
>>> for i, ax in enumerate(axes.flatten()):
... win = ftwindow(k, k_range, dk, win= windows[i])
... line = ax.plot(k, win, label=windows[i])
... for val in k_range:
... line = ax.axvline(val - dk/2, color='gray', ls=':')
... line = ax.axvline(val + dk/2, color='gray', ls=':')
... leg = ax.legend()
... text = ax.set_ylabel('')
... text = ax.set_xlabel('')
>>> fig.tight_layout()
>>> plt.show(block=False)
"""
# available windows
windows = ['han', 'fha', 'gau', 'kai', 'par', 'wel', 'sin', 'bes']
name = win.strip().lower()[:3]
if name not in windows:
raise ValueError("window name %s not recognized." % win)
if dx2 is None:
dx2 = dx1
# asigning values inside the x array
xrange = check_xrange(x_range, x)
xstep = (x[-1] - x[0]) / (len(x) - 1)
xeps = 1.e-4 * xstep
x1 = max(min(x), xrange[0] - dx1 / 2.0)
x2 = xrange[0] + dx1 / 2.0 + xeps
x3 = xrange[1] - dx2 / 2.0 - xeps
x4 = min(max(x), xrange[1] + dx2 / 2.0)
if name == 'fha':
if dx1 < 0: dx1 = 0
if dx2 > 1: dx2 = 1
x2 = x1 + xeps + dx1 * (xrange[1] - xrange[0]) / 2.0
x3 = x4 - xeps - dx2 * (xrange[1] - xrange[0]) / 2.0
elif name == 'gau':
dx1 = max(dx1, xeps)
# return values as integer for indices
def asint(val):
return int((val + xeps) / xstep)
i1 = max(0, asint(x1))
i2 = max(0, asint(x2))
i3 = min(len(x) - 1, asint(x3))
i4 = min(len(x) - 1, asint(x4))
if i2 == i1:
i1 = max(0, i2 - 1)
if i4 == i3:
i3 = max(i2, i4 - 1)
x1, x2, x3, x4 = x[i1], x[i2], x[i3], x[i4]
if x1 == x2: x2 = x2 + xeps
if x3 == x4: x4 = x4 + xeps
# initial window
fwin = zeros(len(x))
if i3 > i2:
fwin[i2:i3] = 1.0
# final window
if name in ('han', 'fha'):
fwin[i1:i2 + 1] = sin((pi / 2) * (x[i1:i2 + 1] - x1) / (x2 - x1))**2
fwin[i3:i4 + 1] = cos((pi / 2) * (x[i3:i4 + 1] - x3) / (x4 - x3))**2
elif name == 'par':
fwin[i1:i2 + 1] = (x[i1:i2 + 1] - x1) / (x2 - x1)
fwin[i3:i4 + 1] = 1 - (x[i3:i4 + 1] - x3) / (x4 - x3)
elif name == 'wel':
fwin[i1:i2 + 1] = 1 - ((x[i1:i2 + 1] - x2) / (x2 - x1))**2
fwin[i3:i4 + 1] = 1 - ((x[i3:i4 + 1] - x3) / (x4 - x3))**2
elif name in ('kai', 'bes'):
cen = (x4 + x1) / 2
wid = (x4 - x1) / 2
arg = 1 - (x - cen)**2 / (wid**2)
arg[where(arg < 0)] = 0
if name == 'bes': # 'bes' : ifeffit 1.0 implementation of kaiser-bessel
fwin = bessel_i0(dx1 * sqrt(arg)) / bessel_i0(dx1)
fwin[where(x <= x1)] = 0
fwin[where(x >= x4)] = 0
else: # better version
scale = max(1.e-10, bessel_i0(dx1) - 1)
fwin = (bessel_i0(dx1 * sqrt(arg)) - 1) / scale
elif name == 'sin':
fwin[i1:i4 + 1] = sin(pi * (x4 - x[i1:i4 + 1]) / (x4 - x1))
elif name == 'gau':
cen = (x4 + x1) / 2
fwin = exp(-(((x - cen)**2) / (2 * dx1**2)))
return fwin
def vis_data_path(realization):
path = os.path.join(vis_data_dir,
'realization_{0}.uvh5'.format(realization))
return path
# Load beam data
omegas_data_path = zdir + '/hera_validation/test-0.1/HERA_dipole_Omegas.h5'
with h5py.File(omegas_data_path, 'r') as h5f:
Omega = h5f['Omega'].value
Omegapp = h5f['Omegapp'].value
# Add a new window function to hera_pspec's aipy instance
kaiser6 = lambda x, L: bessel_i0(np.pi * 6 * np.sqrt(1 - (2 * x / (
L - 1) - 1)**2)) / bessel_i0(np.pi * 6)
hps.pspecdata.aipy.dsp.WINDOW_FUNC['kaiser6'] = kaiser6
def astropyPlanck15_for_hera_pspec():
H0 = 67.74
h = H0 / 100.
Om_b = 0.02230 / h**2.
Om_c = 0.1188 / h**2.
Om_L = 0.6911
Om_k = 1. - (Om_b + Om_c + Om_L)
hps_cosmo = hps.conversions.Cosmo_Conversions(
Om_L=Om_L,
Om_b=Om_b,