def _interpolate(self, x, z, **kwds):
"""interpolate data (x,z) to generate response function z=f(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,) or (npts, N)
Additional Inputs:
method: string for kind of interpolator
extrap: if True, extrapolate a bounding box (can reduce # of nans)
arrays: if True, return a numpy array; otherwise don't return arrays
axis: int in [0,N], index of z to interpolate (all, by default)
Output:
interpolated response function, where z=f(*x.T)
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear',
'nearest','cubic','inverse','gaussian','quintic','thin_plate').
NOTE:
additional keyword arguments (epsilon, smooth, norm) are avaiable
for use with a Rbf interpolator. See mystic.math.interpolate.Rbf
for more details.
"""
import numpy as np
from mystic.math.interpolate import interpf
with np.warnings.catch_warnings():
np.warnings.filterwarnings('ignore')
f = interpf(x, z, **kwds)
return f
def read(archives): # method?
"""read stored functions from the list of dbs
Args:
archives (list[string]): list of names of function archives
Returns:
a klepto.archive instance
Notes:
The order of the dbs is important, with the index of ``archives``
corresponding to the desired axis. If a db is empty, returns ``None``
for the empty db. Also, a klepto.archive instance can be provided
instead of the ``name`` of the db.
"""
if isinstance(archives, (str, (u'').__class__)):
archives = db(archives)
if type(archives).__module__.startswith('klepto.'):
f = rb.read_func(db(archives))
if f is None:
return f
f = f[0]
if not hasattr(f, '__axis__'):
f.__axis__ = None
return f
from mystic.math.interpolate import interpf
f = interpf([[1, 2], [2, 3]], [[1, 2], [2, 3]], method='thin_plate')
f.__axis__[:] = [(i if i is None else i[0])
for i in map(rb.read_func, map(db, archives))]
return f
def __init__(self, x, z=None, function=None, **kwds):
"""scatter plotter for data (x,z) and response surface function(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,)
function: function f, where z=f(*x.T), or str (interpolation method)
Additional Inputs:
step: int, plot every 'step' points on the grid [default: 200]
scale: float, scaling factor for the z-axis [default: False]
shift: float, additive shift for the z-axis [default: False]
density: int, density of wireframe for the plot surface [default: 9]
axes: tuple, indicies of the axes to plot [default: ()]
vals: list of values (one per axis) for unplotted axes [default: ()]
maxpts: int, maximum number of (x,z) points to use [default: None]
kernel: function transforming x to x', where x' = kernel(x)
vtol: float, maximum distance outside bounds hypercube to plot data
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear',
'nearest','cubic','inverse','gaussian','quintic','thin_plate').
"""
self.x = getattr(x, '_x', x) # params (x)
self.z = x._y if z is None else z # cost (f(x))
if function is None:
function = 'linear'
if type(function) is str:
from mystic.math.interpolate import interpf
function = interpf(self.x, self.z, method=function,
arrays=True) #XXX: kwds?
self.function = function
#self.dim = kwds.pop('dim', None) #XXX: or len(x)?
# interpolator configuration
self.args = dict(step=200, scale=False, shift=False, vtol=None, \
kernel=None, density=9, axes=(), vals=(), maxpts=None)
self.args.update(kwds)
self.maxpts = self.args.pop('maxpts')
return
def __init__(self, x, z=None, function=None, **kwds):
"""scatter plotter for data (x,z) and response surface function(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,)
function: function f, where z=f(*x.T), or str (interpolation method)
Additional Inputs:
step: int, plot every 'step' points on the grid [default: 200]
scale: float, scaling factor for the z-axis [default: False]
shift: float, additive shift for the z-axis [default: False]
density: int, density of wireframe for the plot surface [default: 9]
axes: tuple, indicies of the axes to plot [default: ()]
vals: list of values (one per axis) for unplotted axes [default: ()]
maxpts: int, maximum number of (x,z) points to use [default: None]
kernel: function transforming x to x', where x' = kernel(x)
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear',
'nearest','cubic','inverse','gaussian','quintic','thin_plate').
"""
self.x = getattr(x, '_x', x) # params (x)
self.z = x._y if z is None else z # cost (f(x))
if function is None:
function='linear'
if type(function) is str:
from mystic.math.interpolate import interpf
function = interpf(self.x,self.z, method=function, arrays=True) #XXX: kwds?
self.function = function
#self.dim = kwds.pop('dim', None) #XXX: or len(x)?
# interpolator configuration
self.args = dict(step=200, scale=False, shift=False, \
kernel=None, density=9, axes=(), vals=(), maxpts=None)
self.args.update(kwds)
self.maxpts = self.args.pop('maxpts')
return
def _interpolate(self, x, z, **kwds):
"""interpolate data (x,z) to generate response function z=f(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,)
Additional Inputs:
method: string for kind of interpolator
extrap: if True, extrapolate a bounding box (can reduce # of nans)
arrays: if True, return a numpy array; otherwise don't return arrays
Output:
interpolated response function, where z=f(*x.T)
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear',
'nearest','cubic','inverse','gaussian','quintic','thin_plate').
"""
from mystic.math.interpolate import interpf
return interpf(x, z, **kwds)
def _interpolate(self, x, z, **kwds):
"""interpolate data (x,z) to generate response function z=f(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,)
Additional Inputs:
method: string for kind of interpolator
extrap: if True, extrapolate a bounding box (can reduce # of nans)
arrays: if True, return a numpy array; otherwise don't return arrays
Output:
interpolated response function, where z=f(*x.T)
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear',
'nearest','cubic','inverse','gaussian','quintic','thin_plate').
"""
from mystic.math.interpolate import interpf
return interpf(x, z, **kwds)
test _to_function and _to_objective in cost and gradient calculations
"""
import numpy as np
x = np.random.rand(10,3)
def cost(x):
return sum(np.sin(x)**2) + 1
y = cost(x.T)
import mystic.math.interpolate as ip
fx = ip._to_function(cost)
assert (fx(*x.T) - cost(x.T) ).sum() < 0.0001
f = ip.interpf(x, y, method='linear', arrays=True)
cf = ip._to_objective(f)
assert (f(*x.T) - cf(x.T) ).sum() < 0.0001
assert f(*x[0].T) == cf(x[0].T)
assert fx(*x[0].T) == cost(x[0].T)
assert ip.gradient(x, f, method='linear').shape \
== ip.gradient(x, fx, method='linear').shape
from mystic.models import rosen0der as rosen
y = rosen(x.T)
f = ip.interpf(x, y, method='linear')
fx = ip._to_function(rosen)
test _to_function and _to_objective in cost and gradient calculations
"""
import numpy as np
x = np.random.rand(10,3)
def cost(x):
return sum(np.sin(x)**2) + 1
y = cost(x.T)
import mystic.math.interpolate as ip
fx = ip._to_function(cost)
assert (fx(*x.T) - cost(x.T) ).sum() < 0.0001
f = ip.interpf(x, y, method='linear', arrays=True)
cf = ip._to_objective(f)
assert (f(*x.T) - cf(x.T) ).sum() < 0.0001
assert f(*x[0].T) == cf(x[0].T)
assert fx(*x[0].T) == cost(x[0].T)
assert ip.gradient(x, f, method='linear').shape \
== ip.gradient(x, fx, method='linear').shape
from mystic.models import rosen0der as rosen
y = rosen(x.T)
f = ip.interpf(x, y, method='linear')
fx = ip._to_function(rosen)
