def _init_function(self, r):
if isinstance(self.function, str):
self.function = self.function.lower()
_mapped = {
'inverse': 'inverse_multiquadric',
'inverse multiquadric': 'inverse_multiquadric',
'thin-plate': 'thin_plate'
}
if self.function in _mapped:
self.function = _mapped[self.function]
func_name = "_h_" + self.function
if hasattr(self, func_name):
self._function = getattr(self, func_name)
else:
functionlist = [
x[3:] for x in dir(self) if x.startswith('_h_')
]
raise ValueError("function must be a callable or one of " +
", ".join(functionlist))
self._function = getattr(self, "_h_" + self.function)
elif callable(self.function):
allow_one = False
if hasattr(self.function, 'func_code') or \
hasattr(self.function, '__code__'):
val = self.function
allow_one = True
elif hasattr(self.function, "im_func"):
val = get_method_function(self.function)
elif hasattr(self.function, "__call__"):
val = get_method_function(self.function.__call__)
else:
raise ValueError(
"Cannot determine number of arguments to function")
argcount = get_function_code(val).co_argcount
if allow_one and argcount == 1:
self._function = self.function
elif argcount == 2:
if sys.version_info[0] >= 3:
self._function = self.function.__get__(self, Rbf_poly_bias)
else:
import new
self._function = new.instancemethod(
self.function, self, Rbf_poly_bias)
else:
raise ValueError(
"Function argument must take 1 or 2 arguments.")
a0 = self._function(r)
if a0.shape != r.shape:
raise ValueError(
"Callable must take array and return array of the same shape")
return a0
def _init_function(self, r):
if isinstance(self.function, str):
self.function = self.function.lower()
_mapped = {'inverse': 'inverse_multiquadric',
'inverse multiquadric': 'inverse_multiquadric',
'thin-plate': 'thin_plate'}
if self.function in _mapped:
self.function = _mapped[self.function]
func_name = "_h_" + self.function
if hasattr(self, func_name):
self._function = getattr(self, func_name)
else:
functionlist = [x[3:] for x in dir(self)
if x.startswith('_h_')]
raise ValueError("function must be a callable or one of " +
", ".join(functionlist))
self._function = getattr(self, "_h_"+self.function)
elif callable(self.function):
allow_one = False
if hasattr(self.function, 'func_code') or \
hasattr(self.function, '__code__'):
val = self.function
allow_one = True
elif hasattr(self.function, "im_func"):
val = get_method_function(self.function)
elif hasattr(self.function, "__call__"):
val = get_method_function(self.function.__call__)
else:
raise ValueError("Cannot determine number of arguments to "
"function")
argcount = get_function_code(val).co_argcount
if allow_one and argcount == 1:
self._function = self.function
elif argcount == 2:
if sys.version_info[0] >= 3:
self._function = self.function.__get__(self, Rbf)
else:
import new
self._function = new.instancemethod(self.function, self,
Rbf)
else:
raise ValueError("Function argument must take 1 or 2 "
"arguments.")
a0 = self._function(r)
if a0.shape != r.shape:
raise ValueError("Callable must take array and return array of "
"the same shape")
return a0
class Rbf(object):
"""
Rbf(*args)
A class for radial basis function approximation/interpolation of
n-dimensional scattered data.
Parameters
----------
*args : arrays
x, y, z, ..., d, where x, y, z, ... are the coordinates of the nodes
and d is the array of values at the nodes
function : str or callable, optional
The radial basis function, based on the radius, r, given by the norm
(default is Euclidean distance); the default is 'multiquadric'::
'multiquadric': sqrt((r/self.epsilon)**2 + 1)
'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
'gaussian': exp(-(r/self.epsilon)**2)
'linear': r
'cubic': r**3
'quintic': r**5
'thin_plate': r**2 * log(r)
If callable, then it must take 2 arguments (self, r). The epsilon
parameter will be available as self.epsilon. Other keyword
arguments passed in will be available as well.
epsilon : float, optional
Adjustable constant for gaussian or multiquadrics functions
- defaults to approximate average distance between nodes (which is
a good start).
smooth : float, optional
Values greater than zero increase the smoothness of the
approximation. 0 is for interpolation (default), the function will
always go through the nodal points in this case.
norm : callable, optional
A function that returns the 'distance' between two points, with
inputs as arrays of positions (x, y, z, ...), and an output as an
array of distance. E.g, the default::
def euclidean_norm(x1, x2):
return sqrt( ((x1 - x2)**2).sum(axis=0) )
which is called with x1=x1ndims,newaxis,:] and
x2=x2ndims,:,newaxis] such that the result is a matrix of the
distances from each point in x1 to each point in x2.
Examples
--------
>>> from scipy.interpolate import Rbf
>>> x, y, z, d = np.random.rand(4, 50)
>>> rbfi = Rbf(x, y, z, d) # radial basis function interpolator instance
>>> xi = yi = zi = np.linspace(0, 1, 20)
>>> di = rbfi(xi, yi, zi) # interpolated values
>>> di.shape
(20,)
"""
def _euclidean_norm(self, x1, x2):
return np.sqrt(((x1 - x2)**2).sum(axis=0))
def _h_multiquadric(self, r):
return np.sqrt((1.0/self.epsilon*r)**2 + 1)
def _h_inverse_multiquadric(self, r):
return 1.0/np.sqrt((1.0/self.epsilon*r)**2 + 1)
def _h_gaussian(self, r):
return np.exp(-(1.0/self.epsilon*r)**2)
def _h_linear(self, r):
return r
def _h_cubic(self, r):
return r**3
def _h_quintic(self, r):
return r**5
def _h_thin_plate(self, r):
return xlogy(r**2, r)
# Setup self._function and do smoke test on initial r
def _init_function(self, r):
if isinstance(self.function, str):
self.function = self.function.lower()
_mapped = {'inverse': 'inverse_multiquadric',
'inverse multiquadric': 'inverse_multiquadric',
'thin-plate': 'thin_plate'}
if self.function in _mapped:
self.function = _mappedself.function]
func_name = "_h_" + self.function
if hasattr(self, func_name):
self._function = getattr(self, func_name)
else:
functionlist = x3:] for x in dir(self) if x.startswith('_h_')]
raise ValueError("function must be a callable or one of " +
", ".join(functionlist))
self._function = getattr(self, "_h_"+self.function)
elif callable(self.function):
allow_one = False
if hasattr(self.function, 'func_code') or \
hasattr(self.function, '__code__'):
val = self.function
allow_one = True
elif hasattr(self.function, "im_func"):
val = get_method_function(self.function)
elif hasattr(self.function, "__call__"):
val = get_method_function(self.function.__call__)
else:
raise ValueError("Cannot determine number of arguments to function")
argcount = get_function_code(val).co_argcount
if allow_one and argcount == 1:
self._function = self.function
elif argcount == 2:
if sys.version_info0] >= 3:
self._function = self.function.__get__(self, Rbf)
else:
import new
self._function = new.instancemethod(self.function, self,
Rbf)