def random_multi_indices(shape):
'''
Return a random variable uniformly distributed on I1 x ... x Id.
If shape contains integers, the intervals are defined as
Ij = np.arange(shape[j-1]), j = 1, ..., len(shape).
Parameters
----------
shape : list or numpy.ndarray
The number of elements of each interval, or the interval themselves.
Returns
-------
tensap.RandomVector
The random variable uniformly distributed on I1 x ... x Id.
'''
order = len(shape)
if np.all([isinstance(x, (list, np.ndarray)) for x in shape]):
ind = shape
else:
ind = []
for dim in range(order):
ind.append(np.arange(shape[dim]))
for dim in range(order):
ind[dim] = tensap.DiscreteRandomVariable(ind[dim])
return tensap.RandomVector(ind)
def tensorized_function_functional_bases(self, h=1):
'''
Return a tensap.FunctionalBases object associated with the provided
basis or basis function(s) and the Tensorizer object.
Parameters
----------
h : tensap.FunctionalBases or tensap.FunctionalBasis or function or
list or scalar, optional
The function used to generate the basis. The default is the
function 1.
Returns
-------
tensap.FunctionalBases
The functional bases.
'''
#if isinstance(h, (np.ndarray, list)) or np.isscalar(h):
# h = lambda y, h=h: h*np.ones(np.shape(y))
if hasattr(h, '__call__'):
h = tensap.UserDefinedFunctionalBasis([h])
h.measure = self.Y.random_variables[0]
if isinstance(h, tensap.FunctionalBasis):
h = tensap.FunctionalBases.duplicate(h, self.dim)
if np.isscalar(h):
h = [tensap.PolynomialFunctionalBasis(y.orthonormal_polynomials(),
range(h+1)) for y in self.Y.random_variables]
h = tensap.FunctionalBases(h)
assert isinstance(h, tensap.FunctionalBases), \
'Wrong type of argument for h.'
p = tensap.DiscretePolynomials(tensap.DiscreteRandomVariable(
np.reshape(np.arange(self.b), [-1, 1])))
p = tensap.PolynomialFunctionalBasis(p, np.arange(self.b))
bases = [p]*self.d*self.dim + list(h.bases)
return tensap.FunctionalBases(bases)
def random(self, n=1):
'''
Generate n random numbers according to the probability distribution
obtained by rescaling the DiscreteMeasure.
Parameters
----------
n : int, optional
The number of random numbers generated. The default is 1.
Returns
-------
numpy.ndarray
The n generated random numbers.
'''
Y = tensap.DiscreteRandomVariable(
np.reshape(np.arange(self.weights.size), [-1, 1]),
self.weights / np.sum(self.weights))
ind = Y.icdf(np.random.rand(n)).astype(int)
return self.values[ind, :]
def discretize(self, n):
'''
Return a discrete random variable taking n possible values x1, ..., xn,
these values being the quantiles of self of probability 1/(2n) + i/n,
i=0n ..., n-1 and such that P(Xn >= xn) = 1/n.
Parameters
----------
n : int
The number of possible values the discrete random variable can
take.
Returns
-------
tensap.DiscreteRandomVariable
The obtained discrete random variable.
'''
u = np.linspace(1 / (2 * n), 1 - 1 / (2 * n), n)
x = self.icdf(u)
return tensap.DiscreteRandomVariable(x)
# %% Patch reshape of the data: the patches are consecutive entries of the data
PS = [4, 4] # Patch size
DATA = np.array([
np.concatenate([
np.ravel(
np.reshape(DATA[k, :], [8] * 2)[PS[0] * i:PS[0] * i + PS[0],
PS[1] * j:PS[1] * j + PS[1]])
for i in range(int(8 / PS[0])) for j in range(int(8 / PS[1]))
]) for k in range(DATA.shape[0])
])
DIM = int(int(DATA.shape[1] / np.prod(PS)))
# %% Probability measure
print('Dimension %i' % DIM)
X = tensap.RandomVector(tensap.DiscreteRandomVariable(np.unique(DATA)), DIM)
# %% Training and test samples
P_TRAIN = 0.9 # Proportion of the sample used for the training
N = DATA.shape[0]
TRAIN = random.sample(range(N), int(np.round(P_TRAIN * N)))
TEST = np.setdiff1d(range(N), TRAIN)
X_TRAIN = DATA[TRAIN, :]
X_TEST = DATA[TEST, :]
Y_TRAIN = DIGITS.target[TRAIN]
Y_TEST = DIGITS.target[TEST]
# One hot encoding (vector-valued function)
Y_TRAIN = tf.one_hot(Y_TRAIN.astype(int), 10, dtype=tf.float64)
Y_TEST = tf.one_hot(Y_TEST.astype(int), 10, dtype=tf.float64)