def _cubic_smooth_coeff(signal, lamb):
rho, omega = _coeff_smooth(lamb)
cs = 1 - 2 * rho * cos(omega) + rho * rho
K = len(signal)
yp = zeros((K, ), signal.dtype.char)
k = arange(K)
yp[0] = (_hc(0, cs, rho, omega) * signal[0] +
add.reduce(_hc(k + 1, cs, rho, omega) * signal))
yp[1] = (_hc(0, cs, rho, omega) * signal[0] +
_hc(1, cs, rho, omega) * signal[1] +
add.reduce(_hc(k + 2, cs, rho, omega) * signal))
for n in range(2, K):
yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] -
rho * rho * yp[n - 2])
y = zeros((K, ), signal.dtype.char)
y[K - 1] = add.reduce(
(_hs(k, cs, rho, omega) + _hs(k + 1, cs, rho, omega)) * signal[::-1])
y[K - 2] = add.reduce(
(_hs(k - 1, cs, rho, omega) + _hs(k + 2, cs, rho, omega)) *
signal[::-1])
for n in range(K - 3, -1, -1):
y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] -
rho * rho * y[n + 2])
return y
def _cubic_smooth_coeff(signal, lamb):
rho, omega = _coeff_smooth(lamb)
cs = 1 - 2 * rho * cos(omega) + rho * rho
K = len(signal)
yp = zeros((K,), signal.dtype.char)
k = arange(K)
yp[0] = (_hc(0, cs, rho, omega) * signal[0] +
add.reduce(_hc(k + 1, cs, rho, omega) * signal))
yp[1] = (_hc(0, cs, rho, omega) * signal[0] +
_hc(1, cs, rho, omega) * signal[1] +
add.reduce(_hc(k + 2, cs, rho, omega) * signal))
for n in range(2, K):
yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] -
rho * rho * yp[n - 2])
y = zeros((K,), signal.dtype.char)
y[K - 1] = add.reduce((_hs(k, cs, rho, omega) +
_hs(k + 1, cs, rho, omega)) * signal[::-1])
y[K - 2] = add.reduce((_hs(k - 1, cs, rho, omega) +
_hs(k + 2, cs, rho, omega)) * signal[::-1])
for n in range(K - 3, -1, -1):
y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] -
rho * rho * y[n + 2])
return y
def _quadratic_coeff(signal):
zi = -3 + 2 * sqrt(2.0)
K = len(signal)
yplus = zeros((K,), signal.dtype.char)
powers = zi ** arange(K)
yplus[0] = signal[0] + zi * add.reduce(powers * signal)
for k in range(1, K):
yplus[k] = signal[k] + zi * yplus[k - 1]
output = zeros((K,), signal.dtype.char)
output[K - 1] = zi / (zi - 1) * yplus[K - 1]
for k in range(K - 2, -1, -1):
output[k] = zi * (output[k + 1] - yplus[k])
return output * 8.0
def _quadratic_coeff(signal):
zi = -3 + 2 * sqrt(2.0)
K = len(signal)
yplus = zeros((K, ), signal.dtype.char)
powers = zi**arange(K)
yplus[0] = signal[0] + zi * add.reduce(powers * signal)
for k in range(1, K):
yplus[k] = signal[k] + zi * yplus[k - 1]
output = zeros((K, ), signal.dtype.char)
output[K - 1] = zi / (zi - 1) * yplus[K - 1]
for k in range(K - 2, -1, -1):
output[k] = zi * (output[k + 1] - yplus[k])
return output * 8.0
def trapz(y, x=None, dx=1.0, axis=-1):
"""Integrate y(x) using samples along the given axis and the composite
trapezoidal rule. If x is None, spacing given by dx is assumed.
"""
y = asarray(y)
if x is None:
d = dx
else:
d = diff(x, axis=axis)
nd = len(y.shape)
slice1 = [slice(None)] * nd
slice2 = [slice(None)] * nd
slice1[axis] = slice(1, None)
slice2[axis] = slice(None, -1)
return add.reduce(d * (y[slice1] + y[slice2]) / 2.0, axis)
def trapz(y, x=None, dx=1.0, axis=-1):
"""Integrate y(x) using samples along the given axis and the composite
trapezoidal rule. If x is None, spacing given by dx is assumed.
"""
y = asarray(y)
if x is None:
d = dx
else:
d = diff(x,axis=axis)
nd = len(y.shape)
slice1 = [slice(None)]*nd
slice2 = [slice(None)]*nd
slice1[axis] = slice(1,None)
slice2[axis] = slice(None,-1)
return add.reduce(d * (y[slice1]+y[slice2])/2.0,axis)
def average(a, axis=None, weights=None, returned=False):
"""Average the array over the given axis. If the axis is None,
average over all dimensions of the array. Equivalent to
a.mean(axis) and to
a.sum(axis) / size(a, axis)
If weights are given, result is:
sum(a * weights,axis) / sum(weights,axis),
where the weights must have a's shape or be 1D with length the
size of a in the given axis. Integer weights are converted to
Float. Not specifying weights is equivalent to specifying
weights that are all 1.
If 'returned' is True, return a tuple: the result and the sum of
the weights or count of values. The shape of these two results
will be the same.
Raises ZeroDivisionError if appropriate. (The version in MA does
not -- it returns masked values).
"""
if axis is None:
a = array(a).ravel()
if weights is None:
n = add.reduce(a)
d = len(a) * 1.0
else:
w = array(weights).ravel() * 1.0
n = add.reduce(multiply(a, w))
d = add.reduce(w)
else:
a = array(a)
ash = a.shape
if ash == ():
a.shape = (1, )
if weights is None:
n = add.reduce(a, axis)
d = ash[axis] * 1.0
if returned:
d = ones(n.shape) * d
else:
w = array(weights, copy=False) * 1.0
wsh = w.shape
if wsh == ():
wsh = (1, )
if wsh == ash:
n = add.reduce(a * w, axis)
d = add.reduce(w, axis)
elif wsh == (ash[axis], ):
ni = ash[axis]
r = [newaxis] * ni
r[axis] = slice(None, None, 1)
w1 = eval("w[" + repr(tuple(r)) + "]*ones(ash, float)")
n = add.reduce(a * w1, axis)
d = add.reduce(w1, axis)
else:
raise ValueError, 'averaging weights have wrong shape'
if not isinstance(d, ndarray):
if d == 0.0:
raise ZeroDivisionError, 'zero denominator in average()'
if returned:
return n / d, d
else:
return n / d
def average(a, axis=None, weights=None, returned=False):
"""average(a, axis=None weights=None, returned=False)
Average the array over the given axis. If the axis is None,
average over all dimensions of the array. Equivalent to
a.mean(axis) and to
a.sum(axis) / size(a, axis)
If weights are given, result is:
sum(a * weights,axis) / sum(weights,axis),
where the weights must have a's shape or be 1D with length the
size of a in the given axis. Integer weights are converted to
Float. Not specifying weights is equivalent to specifying
weights that are all 1.
If 'returned' is True, return a tuple: the result and the sum of
the weights or count of values. The shape of these two results
will be the same.
Raises ZeroDivisionError if appropriate. (The version in MA does
not -- it returns masked values).
"""
if axis is None:
a = array(a).ravel()
if weights is None:
n = add.reduce(a)
d = len(a) * 1.0
else:
w = array(weights).ravel() * 1.0
n = add.reduce(multiply(a, w))
d = add.reduce(w)
else:
a = array(a)
ash = a.shape
if ash == ():
a.shape = (1,)
if weights is None:
n = add.reduce(a, axis)
d = ash[axis] * 1.0
if returned:
d = ones(n.shape) * d
else:
w = array(weights, copy=False) * 1.0
wsh = w.shape
if wsh == ():
wsh = (1,)
if wsh == ash:
n = add.reduce(a*w, axis)
d = add.reduce(w, axis)
elif wsh == (ash[axis],):
ni = ash[axis]
r = [newaxis]*ni
r[axis] = slice(None, None, 1)
w1 = eval("w["+repr(tuple(r))+"]*ones(ash, float)")
n = add.reduce(a*w1, axis)
d = add.reduce(w1, axis)
else:
raise ValueError, 'averaging weights have wrong shape'
if not isinstance(d, ndarray):
if d == 0.0:
raise ZeroDivisionError, 'zero denominator in average()'
if returned:
return n/d, d
else:
return n/d