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classes.py
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classes.py
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import numpy as np
from .logsumexp import lse_scaled, lse_implicit
def max_affine(x, ba):
"""
Evaluates max affine function at values of x, given a set of
max affine fit parameters.
Arguments
---------
x: 2D array [nPoints x nDim]
Independent variable data
ba: 2D array
max affine fit parameters
[[b1, a11, ... a1k]
[ ...., ]
[bk, ak1, ... akk]]
Returns
-------
y: 1D array [nPoints]
Max affine output
dydba: 2D array [nPoints x (nDim + 1)*K]
dydba
"""
npt, dimx = x.shape
K = ba.size // (dimx + 1)
ba = np.reshape(ba, (dimx + 1, K), order="F") # 'F' gives Fortran indexing
X = np.hstack((np.ones((npt, 1)), x)) # augment data with column of ones
y, partition = np.dot(X, ba).max(1), np.dot(X, ba).argmax(1)
dydba = np.zeros((npt, (dimx + 1)*K))
for k in range(K):
inds = np.equal(partition, k)
indadd = (dimx + 1)*k
ixgrid = np.ix_(inds.nonzero()[0], indadd + np.arange(dimx + 1))
dydba[ixgrid] = X[inds, :]
return y, dydba
# pylint: disable=too-many-locals
def softmax_affine(x, params):
"""
Evaluates softmax affine function at values of x, given a set of
SMA fit parameters.
Arguments:
----------
x: Independent variable data
2D numpy array [nPoints x nDimensions]
params: Fit parameters
1D numpy array [(nDim + 2)*K,]
[b1, a11, .. a1d, b2, a21, .. a2d, ...
bK, aK1, aK2, .. aKd, alpha]
Returns:
--------
y: SMA approximation to log transformed data
1D numpy array [nPoints]
dydp: Jacobian matrix
"""
npt, dimx = x.shape
ba = params[0:-1]
softness = params[-1]
alpha = 1/softness
if alpha <= 0:
return np.inf*np.ones((npt, 1)), np.nan
K = np.size(ba) // (dimx + 1)
ba = ba.reshape(dimx + 1, K, order="F")
X = np.hstack((np.ones((npt, 1)), x)) # augment data with column of ones
z = np.dot(X, ba) # compute affine functions
y, dydz, dydsoftness = lse_scaled(z, alpha)
dydsoftness = -dydsoftness*(alpha**2)
nrow, ncol = dydz.shape
repmat = np.tile(dydz, (dimx + 1, 1)).reshape(nrow, ncol*(dimx + 1), order="F")
dydba = repmat*np.tile(X, (1, K))
dydsoftness.shape = (dydsoftness.size, 1)
dydp = np.hstack((dydba, dydsoftness))
return y, dydp
# pylint: disable=too-many-locals
def implicit_softmax_affine(x, params):
"""
Evaluates implicit softmax affine function at values of x, given a set of
ISMA fit parameters.
Arguments:
----------
x: Independent variable data
2D numpy array [nPoints x nDimensions]
params: Fit parameters
1D numpy array [(nDim + 2)*K,]
[b1, a11, .. a1d, b2, a21, .. a2d, ...
bK, aK1, aK2, .. aKd, alpha1, alpha2, ... alphaK]
Returns:
--------
y: ISMA approximation to log transformed data
1D numpy array [nPoints]
dydp: Jacobian matrix
"""
npt, dimx = x.shape
K = params.size // (dimx + 2)
ba = params[0:-K]
alpha = params[-K:]
if any(alpha <= 0):
return np.inf*np.ones((npt, 1)), np.nan
ba = ba.reshape(dimx + 1, K, order="F") # reshape ba to matrix
X = np.hstack((np.ones((npt, 1)), x)) # augment data with column of ones
z = np.dot(X, ba) # compute affine functions
y, dydz, dydalpha = lse_implicit(z, alpha)
nrow, ncol = dydz.shape
repmat = np.tile(dydz, (dimx + 1, 1)).reshape(nrow, ncol*(dimx + 1), order="F")
dydba = repmat*np.tile(X, (1, K))
dydp = np.hstack((dydba, dydalpha))
return y, dydp