def __call__(self, N):
"""
Sample generator
Parameters
----------
N : int
Upper quadrature order
Returns
-------
samples : np.ndarray
The quadrature nodes with `samples.shape=(D,K)` where
`D=len(dist)` and `K` is the number of nodes.
"""
dim = len(self.dist)
if self.sparse == 0 or self.scheme in (3, 4, 5, 6):
X = self.segment(N)
if self.scheme in (1, 2):
X = combine((X, ) * dim)
out = self.trans(X)
else:
out = []
for i in xrange(be.terms(N - self.sparse, dim), be.terms(N, dim)):
I = be.multi_index(i, dim)
out.append(combine([self.segment(n) for n in I]))
out = self.trans(np.concatenate(out, 0))
return out.T
def __call__(self, N):
"""
Sample generator
Parameters
----------
N : int
Upper quadrature order
Returns
-------
samples : np.ndarray
The quadrature nodes with `samples.shape=(D,K)` where
`D=len(dist)` and `K` is the number of nodes.
"""
dim = len(self.dist)
if self.sparse==0 or self.scheme in (3,4,5,6):
X = self.segment(N)
if self.scheme in (1,2):
X = combine((X,)*dim)
out = self.trans(X)
else:
out = []
for i in xrange(be.terms(N-self.sparse, dim),
be.terms(N, dim)):
I = be.multi_index(i, dim)
out.append(combine([self.segment(n) for n in I]))
out = self.trans(np.concatenate(out, 0))
return out.T
def __init__(self,
dist,
scheme=1,
box=True,
edge=False,
growth=0,
sparse=0):
"""
Parameters
----------
dist : Dist
The domain where the samples are to be generated
Optional parameters
box : int
0 : The samples are mapped onto the domain using an inverse
Rosenblatt transform.
1 : Will only use distribution bounds and evenly
distribute samples inbetween.
2 : Non transformation will be performed.
edge: bool
True : Will include the bounds of the domain in the samples.
If infinite domain, a resonable trunkation will be used.
growth : int
0 : Linear growth rule. Minimizes the number of samples.
1 : Exponential growth rule. Nested for schemes 1 and 2.
2 : Double the number of polynomial terms. Recommended for
schemes 4, 5 and 6.
sparse : int
Defines the sparseness of the samples.
sparse=len(dist) is equivalent to Smolyak sparse grid nodes.
0 : A full tensor product nodes will be used
scheme : int
0 : Gaussian quadrature will be used.
box and edge argument will be ignored.
1 : uniform distributed samples will be used.
2 : The roots of Chebishev polynomials will be used
(Clenshaw-Curtis and Fejer).
3 : Stroud's cubature rule.
Only order 2 and 3 valid,
edge, growth and sparse are ignored.
4 : Latin Hypercube sampling, no edge or sparse.
5 : Classical random sampling, no edge or sparse.
6 : Halton sampling, no edge or sparse
7 : Hammersley sampling, no edge or sparse
8 : Sobol sampling, no edge or sparse
9 : Korobov samples, no edge or sparse
"""
print "Warning: Sampler is depricated. Use samplegen instead"
self.dist = dist
self.scheme = scheme
self.sparse = sparse
# Gausian Quadrature
if scheme == 0:
segment = lambda n: _gw(n, dist)[0]
self.trans = lambda x: x
else:
if box == 0:
self.trans = lambda x: self.dist.inv(x.T).T
elif box == 1:
lo, up = dist.range().reshape(2, len(dist))
self.trans = lambda x: np.array(x) * (up - lo) + lo
elif box == 2:
self.trans = lambda x: x
if scheme == 1:
_segment = lambda n: np.arange(0, n + 1) * 1. / n
elif scheme == 2:
_segment = lambda n: \
.5*np.cos(np.arange(n,-1,-1)*np.pi/n) + .5
if scheme in (1, 2):
if edge:
if growth == 0:
segment = lambda n: _segment(n + 1)
elif growth == 1:
segment = lambda n: _segment(2**n)
elif growth == 2:
segment = lambda n: _segment(2 * be.terms(n, len(dist)))
else:
if growth == 0:
segment = lambda n: _segment(n + 2)[1:-1]
elif growth == 1:
segment = lambda n: _segment(2**(n + 1))[1:-1]
elif growth == 2:
segment = lambda n: _segment(2*be.terms(n, \
len(dist)))[1:-1]
elif scheme == 4:
if growth == 0:
segment = lambda n: latin_hypercube(n + 1, len(dist))
elif growth == 1:
segment = lambda n: latin_hypercube(2**n, len(dist))
elif growth == 2:
segment = lambda n: latin_hypercube(2*be.terms(n, len(dist)), \
len(dist))
elif scheme == 5:
if growth == 0:
segment = lambda n: np.random.random((n + 1, len(dist)))
elif growth == 1:
segment = lambda n: np.random.random((2**n, len(dist)))
elif growth == 2:
segment = lambda n: np.random.random(
(2 * be.terms(n + 1, len(dist)), len(dist)))
elif scheme == 6:
if growth == 0:
segment = lambda n: halton(n + 1, len(dist))
elif growth == 1:
segment = lambda n: halton(2**n, len(dist))
elif growth == 2:
segment = lambda n: halton(2*be.terms(n, len(dist)), \
len(dist))
elif scheme == 7:
if growth == 0:
segment = lambda n: hammersley(n + 1, len(dist))
elif growth == 1:
segment = lambda n: hammersley(2**n, len(dist))
elif growth == 2:
segment = lambda n: hammersley(2*be.terms(n, len(dist)), \
len(dist))
elif scheme == 8:
if growth == 0:
segment = lambda n: sobol(n + 1, len(dist))
elif growth == 1:
segment = lambda n: sobol(2**n, len(dist))
elif growth == 2:
segment = lambda n: sobol(2*be.terms(n, len(dist)), \
len(dist))
elif scheme == 9:
if growth == 0:
segment = lambda n: korobov(n + 1, len(dist))
elif growth == 1:
segment = lambda n: korobov(2**n, len(dist))
elif growth == 2:
segment = lambda n: korobov(2*be.terms(n, len(dist)), \
len(dist))
self.segment = segment
def __init__(self, dist, scheme=1, box=True, edge=False,
growth=0, sparse=0):
"""
Parameters
----------
dist : Dist
The domain where the samples are to be generated
Optional parameters
box : int
0 : The samples are mapped onto the domain using an inverse
Rosenblatt transform.
1 : Will only use distribution bounds and evenly
distribute samples inbetween.
2 : Non transformation will be performed.
edge: bool
True : Will include the bounds of the domain in the samples.
If infinite domain, a resonable trunkation will be used.
growth : int
0 : Linear growth rule. Minimizes the number of samples.
1 : Exponential growth rule. Nested for schemes 1 and 2.
2 : Double the number of polynomial terms. Recommended for
schemes 4, 5 and 6.
sparse : int
Defines the sparseness of the samples.
sparse=len(dist) is equivalent to Smolyak sparse grid nodes.
0 : A full tensor product nodes will be used
scheme : int
0 : Gaussian quadrature will be used.
box and edge argument will be ignored.
1 : uniform distributed samples will be used.
2 : The roots of Chebishev polynomials will be used
(Clenshaw-Curtis and Fejer).
3 : Stroud's cubature rule.
Only order 2 and 3 valid,
edge, growth and sparse are ignored.
4 : Latin Hypercube sampling, no edge or sparse.
5 : Classical random sampling, no edge or sparse.
6 : Halton sampling, no edge or sparse
7 : Hammersley sampling, no edge or sparse
8 : Sobol sampling, no edge or sparse
9 : Korobov samples, no edge or sparse
"""
print "Warning: Sampler is depricated. Use samplegen instead"
self.dist = dist
self.scheme = scheme
self.sparse = sparse
# Gausian Quadrature
if scheme==0:
segment = lambda n: _gw(n,dist)[0]
self.trans = lambda x:x
else:
if box==0:
self.trans = lambda x: self.dist.inv(x.T).T
elif box==1:
lo, up = dist.range().reshape(2, len(dist))
self.trans = lambda x: np.array(x)*(up-lo) + lo
elif box==2:
self.trans = lambda x: x
if scheme==1:
_segment = lambda n: np.arange(0, n+1)*1./n
elif scheme==2:
_segment = lambda n: \
.5*np.cos(np.arange(n,-1,-1)*np.pi/n) + .5
if scheme in (1,2):
if edge:
if growth==0:
segment = lambda n: _segment(n+1)
elif growth==1:
segment = lambda n: _segment(2**n)
elif growth==2:
segment = lambda n: _segment(2*be.terms(n, len(dist)))
else:
if growth==0:
segment = lambda n: _segment(n+2)[1:-1]
elif growth==1:
segment = lambda n: _segment(2**(n+1))[1:-1]
elif growth==2:
segment = lambda n: _segment(2*be.terms(n, \
len(dist)))[1:-1]
elif scheme==4:
if growth==0:
segment = lambda n: latin_hypercube(n+1, len(dist))
elif growth==1:
segment = lambda n: latin_hypercube(2**n, len(dist))
elif growth==2:
segment = lambda n: latin_hypercube(2*be.terms(n, len(dist)), \
len(dist))
elif scheme==5:
if growth==0:
segment = lambda n: np.random.random((n+1, len(dist)))
elif growth==1:
segment = lambda n: np.random.random((2**n, len(dist)))
elif growth==2:
segment = lambda n: np.random.random((2*be.terms(n+1,
len(dist)), len(dist)))
elif scheme==6:
if growth==0:
segment = lambda n: halton(n+1, len(dist))
elif growth==1:
segment = lambda n: halton(2**n, len(dist))
elif growth==2:
segment = lambda n: halton(2*be.terms(n, len(dist)), \
len(dist))
elif scheme==7:
if growth==0:
segment = lambda n: hammersley(n+1, len(dist))
elif growth==1:
segment = lambda n: hammersley(2**n, len(dist))
elif growth==2:
segment = lambda n: hammersley(2*be.terms(n, len(dist)), \
len(dist))
elif scheme==8:
if growth==0:
segment = lambda n: sobol(n+1, len(dist))
elif growth==1:
segment = lambda n: sobol(2**n, len(dist))
elif growth==2:
segment = lambda n: sobol(2*be.terms(n, len(dist)), \
len(dist))
elif scheme==9:
if growth==0:
segment = lambda n: korobov(n+1, len(dist))
elif growth==1:
segment = lambda n: korobov(2**n, len(dist))
elif growth==2:
segment = lambda n: korobov(2*be.terms(n, len(dist)), \
len(dist))
self.segment = segment