# split class Gridmap ?
import collections
from time import time
# warnings
import numpy as np
from scipy.ndimage import map_coordinates, spline_filter
__version__ = "2013-07-01 jul denis"
__author_email__ = "denis-bz-py@t-online.de"
[docs]class Intergrid:
""" interpolate data given on an Nd rectangular grid, uniform or non-uniform.
documentation and original website:
https://denis-bz.github.io/docs/intergrid.html
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
http://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
Parameters
----------
griddata: numpy array_like,
2d 3d 4d ...
lo: numpy array_like,
hi: numpy array_like,
user coordinates of the corners of griddata, 1d array-like, lo < hi
maps: list
a list of `dim` descriptors of piecewise-linear or nonlinear maps,
e.g. [[50, 52, 62, 63], None] # uniformize lat, linear lon
copy: bool, default True;
make a copy of query_points
copy=False overwrites query_points, runs in less memory
verbose: bool, default True
print a 1-line summary for each call, with run time
order: int, default 1
see `map_coordinates`
prefilter: bool, default 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)
Examples
--------
1) For regular grid:
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]
2) For 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([ 60, -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
"""
def __init__( self, griddata, lo, hi, maps=[], copy=True, verbose=True,
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)
assert lo.shape == (dim,), lo.shape
assert hi.shape == (dim,), hi.shape
self.loclip = lo = np.asarray_chkfinite( lo ).copy()
self.hiclip = hi = np.asarray_chkfinite( hi ).copy()
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.nmap = 0
if maps != []: # sanity check maps --
assert len(maps) == dim, "maps must have len %d, not %d" % (
dim, len(maps))
for j, (map, n, l, h) in enumerate( zip( maps, griddata.shape, lo, hi )):
if map is None or isintance(map, collections.Callable):
lo[j], hi[j] = 0, 1
continue
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 ))
self.maps = maps
self._lo = lo # caller's lo for linear, 0 nonlinear maps
shape_1 = np.array( self.griddata.shape, float ) - 1
self._linearmap = shape_1 / np.where( hi > lo, hi - lo, np.inf ) # 25jun
#...............................................................................
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()
np.clip( X, self.loclip, self.hiclip, out=X ) # inplace
# X nonlinear maps inplace --
for j, map in enumerate(self.maps):
if map is None:
continue
if isinstance(map, collections.Callable):
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 (affine_transform ?)
if self.nmap < self.dim:
X -= self._lo
X *= self._linearmap # (griddata.shape - 1) / (hi - lo)
## print "test X:", X[0]
#...............................................................................
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