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Made interpolation more general and faster in TKDE._eval_grid_fast

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master
Per.Andreas.Brodtkorb 13 years ago
parent 9dceca985e
commit 3257d675d8
2 changed files with 57 additions and 113 deletions
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161
pywafo/src/wafo/kdetools.py
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@ -142,6 +142,9 @@ class _KDE(object):
arg_0,arg_1,... arg_d-1 : vectors
Alternatively, if no vectors is passed in then
arg_i = linspace(self.xmin[i], self.xmax[i], self.inc)
output : string optional
'value' if value output
'data' if object output
Returns
-------
@ -149,6 +152,11 @@ class _KDE(object):
The values evaluated at meshgrid(*args).
"""
if len(args) == 0:
args = []
for i in range(self.d):
args.append(np.linspace(self.xmin[i], self.xmax[i], self.inc))
self.args = args
return self._eval_grid_fun(self._eval_grid_fast, *args, **kwds)
def _eval_grid_fast(self, *args):
@ -162,9 +170,9 @@ class _KDE(object):
arg_0,arg_1,... arg_d-1 : vectors
Alternatively, if no vectors is passed in then
arg_i = linspace(self.xmin[i], self.xmax[i], self.inc)
output : string
output : string optional
'value' if value output
'wafodata' if object output
'data' if object output
Returns
-------
@ -172,15 +180,15 @@ class _KDE(object):
The values evaluated at meshgrid(*args).
"""
return self._eval_grid_fun(self._eval_grid, *args, **kwds)
def _eval_grid(self, *args):
pass
def _eval_grid_fun(self, eval_grd, *args, **kwds):
if len(args) == 0:
args = []
for i in range(self.d):
args.append(np.linspace(self.xmin[i], self.xmax[i], self.inc))
self.args = args
return self._eval_grid_fun(self._eval_grid, *args, **kwds)
def _eval_grid(self, *args):
pass
def _eval_grid_fun(self, eval_grd, *args, **kwds):
f = eval_grd(*args)
if kwds.get('output', 'value') == 'value':
return f
@ -189,6 +197,7 @@ class _KDE(object):
kwds2 = dict(title=titlestr)
kwds2['plot_kwds'] = dict(plotflag=1)
kwds2.update(**kwds)
args = self.args
if self.d == 1:
args = args[0]
wdata = WafoData(f, args, **kwds2)
@ -390,6 +399,9 @@ class TKDE(_KDE):
arg_0,arg_1,... arg_d-1 : vectors
Alternatively, if no vectors is passed in then
arg_i = gauss2dat(linspace(dat2gauss(self.xmin[i]), dat2gauss(self.xmax[i]), self.inc))
output : string optional
'value' if value output
'data' if object output
Returns
-------
@ -397,17 +409,18 @@ class TKDE(_KDE):
The values evaluated at meshgrid(*args).
"""
f = self._eval_grid_fast(*args)
if kwds.get('output', 'value') == 'value':
return f
else:
args = self.args
titlestr = 'Kernel density estimate (%s)' % self.kernel.name
kwds2 = dict(title=titlestr)
kwds2.update(**kwds)
if self.d == 1:
args = args[0]
return WafoData(f, args, **kwds2)
return self._eval_grid_fun(self._eval_grid_fast, *args, **kwds)
# f = self._eval_grid_fast(*args)
# if kwds.get('output', 'value') == 'value':
# return f
# else:
# args = self.args
# titlestr = 'Kernel density estimate (%s)' % self.kernel.name
# kwds2 = dict(title=titlestr)
# kwds2.update(**kwds)
# if self.d == 1:
# args = args[0]
# return WafoData(f, args, **kwds2)
def _eval_grid_fast(self, *args):
if self.L2 is None:
@ -420,14 +433,18 @@ class TKDE(_KDE):
points = meshgrid(*self.args) if self.d > 1 else self.args
f = self._scale_pdf(tf, points)
if len(args):
if self.d == 1:
pdf = interpolate.interp1d(points[0], f, bounds_error=False, fill_value=0.0)
elif self.d == 2:
pdf = interpolate.interp2d(points[0], points[1], f, bounds_error=False, fill_value=0.0)
#ipoints = meshgrid(*args) if self.d>1 else args
fi = pdf(*args)
ipoints = meshgrid(*args) if self.d>1 else args
#shape0 = points[0].shape
#shape0i = ipoints[0].shape
for i in range(self.d):
points[i].shape = (-1,)
#ipoints[i].shape = (-1,)
points = np.asarray(points).T
#ipoints = np.asarray(ipoints).T
fi = interpolate.griddata(points, f.ravel(), tuple(ipoints), method='linear',
fill_value=0.0)
#fi.shape = shape0i
self.args = args
#fi.shape = ipoints[0].shape
return fi*(fi>0)
return f
def _eval_grid(self, *args):
@ -1636,91 +1653,18 @@ def mkernel(X, kernel):
fun = _MKERNEL_DICT[kernel[:4]]
return fun(np.atleast_2d(X))
def accumsum(accmap, a, size=None, dtype=None):
"""
A sum accumulation function
Parameters
----------
accmap : ndarray
This is the "accumulation map". It maps input (i.e. indices into
`a`) to their destination in the output array. The first `a.ndim`
dimensions of `accmap` must be the same as `a.shape`. That is,
`accmap.shape[:a.ndim]` must equal `a.shape`. For example, if `a`
has shape (15,4), then `accmap.shape[:2]` must equal (15,4). In this
case `accmap[i,j]` gives the index into the output array where
element (i,j) of `a` is to be accumulated. If the output is, say,
a 2D, then `accmap` must have shape (15,4,2). The value in the
last dimension give indices into the output array. If the output is
1D, then the shape of `accmap` can be either (15,4) or (15,4,1)
a : ndarray
The input data to be accumulated.
size : ndarray or None
The size of the output array. If None, the size will be determined
from `accmap`.
dtype : numpy data type, or None
The data type of the output array. If None, the data type of
`a` is used.
Returns
-------
out : ndarray
The accumulated results.
The shape of `out` is `size` if `size` is given. Otherwise the
shape is determined by the (lexicographically) largest indices of
the output found in `accmap`.
Examples
--------
>>> from numpy import array, prod
>>> a = array([[1,2,3],[4,-1,6],[-1,8,9]])
>>> a
array([[ 1, 2, 3],
[ 4, -1, 6],
[-1, 8, 9]])
>>> # Sum the diagonals.
>>> accmap = array([[0,1,2],[2,0,1],[1,2,0]])
>>> s = accum(accmap, a)
>>> s
array([ 9, 7, 15])
>>> # A 2D output, from sub-arrays with shapes and positions like this:
>>> # [ (2,2) (2,1)]
>>> # [ (1,2) (1,1)]
>>> accmap = array([
... [[0,0],[0,0],[0,1]],
... [[0,0],[0,0],[0,1]],
... [[1,0],[1,0],[1,1]]])
>>> # Accumulate using a product.
>>> accum(accmap, a, func=prod, dtype=float)
array([[ -8., 18.],
[ -8., 9.]])
>>> # Same accmap, but create an array of lists of values.
>>> accum(accmap, a, func=lambda x: x, dtype='O')
array([[[1, 2, 4, -1], [3, 6]],
[[-1, 8], [9]]], dtype=object)
"""
# Check for bad arguments and handle the defaults.
if accmap.shape[:a.ndim] != a.shape:
raise ValueError("The initial dimensions of accmap must be the same as a.shape")
def accumsum(accmap, a, size, dtype=None):
if dtype is None:
dtype = a.dtype
adims = tuple(range(a.ndim))
if size is None:
size = 1 + np.squeeze(np.apply_over_axes(np.max, accmap, axes=adims))
size = np.atleast_1d(size)
if len(size)>1:
binx = accmap[:,0]
biny = accmap[:,1]
out = np.asarray(sparse.coo_matrix((a.ravel(), (binx, biny)),shape=size, dtype=dtype).todense()).reshape(size)
out = sparse.coo_matrix((a.ravel(), (binx, biny)),shape=size, dtype=dtype).tocsr()
else:
binx = accmap.ravel()
zero = np.zeros(len(binx))
out = np.asarray(sparse.coo_matrix((a.ravel(), (binx, zero)),shape=(size,1), dtype=dtype).todense()).reshape(size)
out = sparse.coo_matrix((a.ravel(), (binx, zero)),shape=(size,1), dtype=dtype).tocsr()
return out
def accumsum2(accmap, a, size):
@ -2335,8 +2279,8 @@ def gridcount(data, X, use_sparse=False):
abs = np.abs
if d == 1:
x.shape = (-1,)
c = (acfun(binx, (x[binx + 1] - dat), size=[inc, ]) +
acfun(binx+1, (dat - x[binx]), size=[inc, ])) / w
c = np.asarray((acfun(binx, (x[binx + 1] - dat), size=(inc, )) +
acfun(binx+1, (dat - x[binx]), size=(inc, ))) / w).ravel()
# elif d == 2:
# b2 = binx[1]
# b1 = binx[0]
@ -2350,6 +2294,9 @@ def gridcount(data, X, use_sparse=False):
else: # % d>2
Nc = csiz.prod()
# if use_sparse:
# c = sparse.csr_matrix((Nc,1))
# else:
c = np.zeros((Nc,))
fact2 = np.asarray(np.reshape(inc * np.arange(d), (d, -1)), dtype=int)
@ -2368,12 +2315,12 @@ def gridcount(data, X, use_sparse=False):
bt2 = bt0[two] + fact2
b2 = binx + bt2 # linear index to X
c += acfun(b1, abs(np.prod(X1[b2] - dat, axis=0)), size=(Nc,))
c = np.reshape(c / w, csiz, order='F')
# if use_sparse:
# c = c.toarray().ravel()
c = np.reshape(c/w , csiz, order='F')
T = range(d)
T[1], T[0] = T[0], T[1]
#T[-2], T[-1] = T[-1], T[-2]
c = c.transpose(*T) # make sure c is stored in the same way as meshgrid
return c
@ -2477,5 +2424,5 @@ def test_docstrings():
doctest.testmod()
if __name__ == '__main__':
test_docstrings()
#test_docstrings()
kde_demo3()

7
pywafo/src/wafo/test/test_kdetools.py
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@ -224,11 +224,8 @@ def test_gridcount_1D():
>>> x = np.linspace(0, max(data.ravel()) + 1, 10)
>>> dx = x[1] - x[0]
>>> c = wk.gridcount(data, x, use_sparse=False)
>>> c = wk.gridcount(data, x)
>>> c
array([ 0.78762626, 1.77520717, 7.99190087, 4.04054449, 1.67156643,
2.38228499, 1.05933195, 0.29153785, 0. , 0. ])
>>> wk.gridcount(data, x, use_sparse=True)
array([ 0.78762626, 1.77520717, 7.99190087, 4.04054449, 1.67156643,
2.38228499, 1.05933195, 0.29153785, 0. , 0. ])
@ -289,7 +286,7 @@ def test_gridcount_3D():
>>> x = np.linspace(0, max(data.ravel()) + 1, 3)
>>> dx = x[1] - x[0]
>>> X = np.vstack((x, x, x))
>>> c = wk.gridcount(data, X, use_sparse=True)
>>> c = wk.gridcount(data, X)
>>> c
array([[[ 8.74229894e-01, 1.27910940e+00, 1.42033973e-01],
[ 1.94778915e+00, 2.59536282e+00, 3.28213680e-01],

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