def rbfinterp(d,s,p,rbf,**rbfparms):
"""
yp = rbfinterp(data, surface, evaluation points, rbf, *rbfparms)
Use Radial Basis Functions (rbf) to interpolate using Infinitely Smooth
RBF or Polyharmonic Spline (PHS)
Arguments:
(TYPE ARRAY SHAPE N, 2)
d = data array shape (N,2)
s = surface (curve) to be interpolated array shape (N,1)
p = evaluation points (s is interpolated) array shape (M,2)
*rbfparms = ep', 'm'
ep = shape parameter for RBFs scalar / list shape (N,)
m = exponent for polyharmonic spline (PHS) scalar
Output:
yp = surface interpolated at the evaluation points array shape (M,1)
"""
# Construct the collocation matrices:
# ep = shape parameter
ep = rbfparms.get('shapeparm')
# m = power for PHS
m = rbfparms.get('power')
zoo = {
'linear': linear,
'phs': phs,
'mq': mq,
'gauss': gauss
}
if rbf in zoo:
rbf = zoo[rbf]
else:
raise NameError('RBF not known.')
# IM = interpolation matrix
IM = rbf(d, shapeparm = ep, power = m)
# EM = evaluation matrix
EM = rbf(p, centers = d, shapeparm = ep, power = m)
#***************************************************************************
# Linear Algebra Remarks:
#
# P*w = s is a system of equations where the coefficients, w, are unknown
# This matrix system is called the "collocation problem," i.e. What weights
# are needed so that a linear combination of basis functions and weights
# yeilds a point on the surface?
# Once the weights, w, are determined, they can be used to construct the
# interpolant.
#
# Summary:
# P*w = s => w = inv(P)*s
# EM*w = yp where yp is the interpolant and EM is the matrix with entries
# that are known basis functions at the evaluation points.
#
# Since w = inv(P)*s, EM*w = yp => EM*inv(P)*s
#
return dot(EM,linalg.solve(IM,s))
def gauss(d,**parms):
# gaussian, f(r) = exp(-(ep r)^2)
c = parms.get('centers')
#op = parms.get('operator','interp')
ep = parms.get('shapeparm',1)
DM = dmatrix(d, centers = c)
# eps_r = epsilon*r where epsilon may be an array or scalar
eps_r = dot(ep*eye(DM.shape[0]),DM)
return exp(-(eps_r)**2)
def mq(d,**parms):
# multiquadric, f(r) = sqrt(1 + (ep r)^2)
c = parms.get('centers')
#op = parms.get('operator','interp')
ep = parms.get('shapeparm',1)
DM = dmatrix(d, centers = c)
# eps_r = epsilon*r where epsilon may be an array or scalar
eps_r = dot(ep*eye(DM.shape[0]),DM)
return sqrt(1+(eps_r)**2)
def _icqft(self, V_hat, **kwargs):
"""
::
Inverse constant-Q Fourier transform. Make a signal from a constant-Q transform.
"""
if not self._have_cqft:
return None
fp = self._check_feature_params()
X_hat = P.dot(self.Q.T, V_hat)
if self.verbosity:
print("iCQFT->X_hat")
self._istftm(X_hat, **kwargs)
return self.x_hat
def _mfcc(self):
"""
::
DCT of the Log magnitude CQFT
"""
fp = self._check_feature_params()
if not self._cqft():
return False
self._make_dct()
AA = P.log10(P.clip(self.CQFT, 0.0001, self.CQFT.max()))
self.MFCC = P.dot(self.DCT, AA)
self._have_mfcc = True
if self.verbosity:
print("Extracted MFCC: lcoef=%d, ncoef=%d, intensified=%d" %
(self.lcoef, self.ncoef, self.intensify))
n = self.ncoef
l = self.lcoef
self.X = self.MFCC[l:l + n, :]
return True
def _hcqft(self):
"""
::
Apply high lifter to MFCC and invert to CQFT domain
"""
fp = self._check_feature_params()
if not self._mfcc():
return False
a, b = self.CQFT.shape
n = self.ncoef
l = self.lcoef
AA = self.MFCC[n + l:a, :] # apply Lifter
self.HCQFT = 10**P.dot(self.DCT[n + l:a, :].T, AA)
self._have_hcqft = True
if self.verbosity:
print("Extracted HCQFT: lcoef=%d, ncoef=%d, intensified=%d" %
(self.lcoef, self.ncoef, self.intensify))
self.inverse = self.icqft
self.X = self.HCQFT
return True
print("Calculating error stats...")
ah = 8
a = y.reshape(-1)[:-ah]
ax = x.reshape(-1)
print("VARIANCE")
print(P.var(a))
print("STD")
print(P.std(a))
A = P.vstack([a[i:(i - ah)] for i in range(ah)])
AX = P.vstack([ax[i:(i - 2 * ah)] for i in range(2 * ah)])
A = P.vstack([A, AX, ax[2 * ah:]])
b = a[ah:]
A = A - P.mean(A, 1).reshape(-1, 1)
b = b - P.mean(b)
print("LMMSE with {0} taps".format(ah))
LMMSE = P.mean((b - A.T.dot(P.inv(P.dot(A, A.T)).dot(A.dot(b))))**2)
print(LMMSE)
print("LMRMSE with {0} taps".format(ah))
print(P.sqrt(LMMSE))
def mu_law(a, mu=256, MAX=None):
mu = mu - 1
a = P.array(a)
MAX = a.max() if MAX is None else MAX
a = a / MAX
y = (1 + P.sign(a) * P.log(1 + mu * abs(a)) / P.log(1 + mu)) / 2
inds = P.around(y * mu).astype(P.uint8)
return inds