Hier ist eine einfache Klasse Intergrid die Karten/Skalen ungleichmäßig einheitliche Gitter, dann map_coordinates tut.
Auf einem 4d test case läuft es bei etwa 1 μ Sekunden pro Abfragepunkt. HTML-Dokument ist here.
""" interpolate data given on an Nd rectangular grid, uniform or non-uniform.
Purpose: extend the fast N-dimensional interpolator
`scipy.ndimage.map_coordinates` to non-uniform grids, using `np.interp`.
Background: please look at
http://en.wikipedia.org/wiki/Bilinear_interpolation
https://stackoverflow.com/questions/6238250/multivariate-spline-interpolation-in-python-scipy
http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.ndimage.interpolation.map_coordinates.html
Example
-------
Say we have rainfall on a 4 x 5 grid of rectangles, lat 52 .. 55 x lon -10 .. -6,
and want to interpolate (estimate) rainfall at 1000 query points
in between the grid points.
# define the grid --
griddata = np.loadtxt(...) # griddata.shape == (4, 5)
lo = np.array([ 52, -10 ]) # lowest lat, lowest lon
hi = np.array([ 55, -6 ]) # highest lat, highest lon
# set up an interpolator function "interfunc()" with class Intergrid --
interfunc = Intergrid(griddata, lo=lo, hi=hi)
# generate 1000 random query points, lo <= [lat, lon] <= hi --
query_points = lo + np.random.uniform(size=(1000, 2)) * (hi - lo)
# get rainfall at the 1000 query points --
query_values = interfunc(query_points) # -> 1000 values
What this does:
for each [lat, lon] in query_points:
1) find the square of griddata it's in,
e.g. [52.5, -8.1] -> [0, 3] [0, 4] [1, 4] [1, 3]
2) do bilinear (multilinear) interpolation in that square,
using `scipy.ndimage.map_coordinates` .
Check:
interfunc(lo) -> griddata[0, 0],
interfunc(hi) -> griddata[-1, -1] i.e. griddata[3, 4]
Parameters
----------
griddata: numpy array_like, 2d 3d 4d ...
lo, hi: user coordinates of the corners of griddata, 1d array-like, lo < hi
maps: a list of `dim` descriptors of piecewise-linear or nonlinear maps,
e.g. [[50, 52, 62, 63], None] # uniformize lat, linear lon
copy: make a copy of query_points, default True;
copy=False overwrites query_points, runs in less memory
verbose: default 1: print a 1-line summary for each call, with run time
order=1: see `map_coordinates`
prefilter: 0 or False, the default: smoothing B-spline
1 or True: exact-fit interpolating spline (IIR, not C-R)
1/3: Mitchell-Netravali spline, 1/3 B + 2/3 fit
(prefilter is only for order > 1, since order = 1 interpolates)
Non-uniform rectangular grids
-----------------------------
What if our griddata above is at non-uniformly-spaced latitudes,
say [50, 52, 62, 63] ? `Intergrid` can "uniformize" these
before interpolation, like this:
lo = np.array([ 50, -10 ])
hi = np.array([ 63, -6 ])
maps = [[50, 52, 62, 63], None] # uniformize lat, linear lon
interfunc = Intergrid(griddata, lo=lo, hi=hi, maps=maps)
This will map (transform, stretch, warp) the lats in query_points column 0
to array coordinates in the range 0 .. 3, using `np.interp` to do
piecewise-linear (PWL) mapping:
50 51 52 53 54 55 56 57 58 59 60 61 62 63 # lo[0] .. hi[0]
0 .5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 3
`maps[1] None` says to map the lons in query_points column 1 linearly:
-10 -9 -8 -7 -6 # lo[1] .. hi[1]
0 1 2 3 4
More doc: https://denis-bz.github.com/docs/intergrid.html
"""
# split class Gridmap ?
from __future__ import division
from time import time
# warnings
import numpy as np
from scipy.ndimage import map_coordinates, spline_filter
__version__ = "2014-01-15 jan denis" # 15jan: fix bug in linear scaling
__author_email__ = "[email protected]" # comments welcome, testcases most welcome
#...............................................................................
class Intergrid:
__doc__ = globals()["__doc__"]
def __init__(self, griddata, lo, hi, maps=[], copy=True, verbose=1,
order=1, prefilter=False):
griddata = np.asanyarray(griddata)
dim = griddata.ndim # - (griddata.shape[-1] == 1) # ??
assert dim >= 2, griddata.shape
self.dim = dim
if np.isscalar(lo):
lo *= np.ones(dim)
if np.isscalar(hi):
hi *= np.ones(dim)
self.loclip = lo = np.asarray_chkfinite(lo).copy()
self.hiclip = hi = np.asarray_chkfinite(hi).copy()
assert lo.shape == (dim,), lo.shape
assert hi.shape == (dim,), hi.shape
self.copy = copy
self.verbose = verbose
self.order = order
if order > 1 and 0 < prefilter < 1: # 1/3: Mitchell-Netravali = 1/3 B + 2/3 fit
exactfit = spline_filter(griddata) # see Unser
griddata += prefilter * (exactfit - griddata)
prefilter = False
self.griddata = griddata
self.prefilter = (prefilter == True)
self.maps = maps
self.nmap = 0
if len(maps) > 0:
assert len(maps) == dim, "maps must have len %d, not %d" % (
dim, len(maps))
# linear maps (map None): Xcol -= lo *= scale -> [0, n-1]
# nonlinear: np.interp e.g. [50 52 62 63] -> [0 1 2 3]
self._lo = np.zeros(dim)
self._scale = np.ones(dim)
for j, (map, n, l, h) in enumerate(zip(maps, griddata.shape, lo, hi)):
## print "test: j map n l h:", j, map, n, l, h
if map is None or callable(map):
self._lo[j] = l
if h > l:
self._scale[j] = (n - 1)/(h - l) # _map lo -> 0, hi -> n - 1
else:
self._scale[j] = 0 # h <= l: X[:,j] -> 0
continue
self.maps[j] = map = np.asanyarray(map)
self.nmap += 1
assert len(map) == n, "maps[%d] must have len %d, not %d" % (
j, n, len(map))
mlo, mhi = map.min(), map.max()
if not (l <= mlo <= mhi <= h):
print "Warning: Intergrid maps[%d] min %.3g max %.3g " \
"are outside lo %.3g hi %.3g" % (
j, mlo, mhi, l, h)
#...............................................................................
def _map_to_uniform_grid(self, X):
""" clip, map X linear/nonlinear inplace """
np.clip(X, self.loclip, self.hiclip, out=X)
# X nonlinear maps inplace --
for j, map in enumerate(self.maps):
if map is None:
continue
if callable(map):
X[:,j] = map(X[:,j]) # clip again ?
else:
# PWL e.g. [50 52 62 63] -> [0 1 2 3] --
X[:,j] = np.interp(X[:,j], map, np.arange(len(map)))
# linear map the rest, inplace (nonlinear _lo 0, _scale 1: noop)
if self.nmap < self.dim:
X -= self._lo
X *= self._scale # (griddata.shape - 1)/(hi - lo)
## print "test: _map_to_uniform_grid", X.T
#...............................................................................
def __call__(self, X, out=None):
""" query_values = Intergrid(...) (query_points npt x dim)
"""
X = np.asanyarray(X)
assert X.shape[-1] == self.dim, ("the query array must have %d columns, "
"but its shape is %s" % (self.dim, X.shape))
Xdim = X.ndim
if Xdim == 1:
X = np.asarray([X]) # in a single point -> out scalar
if self.copy:
X = X.copy()
assert X.ndim == 2, X.shape
npt = X.shape[0]
if out is None:
out = np.empty(npt, dtype=self.griddata.dtype)
t0 = time()
self._map_to_uniform_grid(X) # X inplace
#...............................................................................
map_coordinates(self.griddata, X.T,
order=self.order, prefilter=self.prefilter,
mode="nearest", # outside -> edge
# test: mode="constant", cval=np.NaN,
output=out)
if self.verbose:
print "Intergrid: %.3g msec %d points in a %s grid %d maps order %d" % (
(time() - t0) * 1000, npt, self.griddata.shape, self.nmap, self.order)
return out if Xdim == 2 else out[0]
at = __call__
# end intergrid.py
Das war genau das, was ich brauchte. Prost, Jaime! –