Scipy interpolation how to resize/resample 3x3 matrix to 5x5?
EDIT: Paul has solved this one below. Thanks!
I'm trying to resample (upscale) a 3x3 matrix to 5x5, filling in the intermediate points with either interpolate.interp2d or interpolate.RectBivariateSpline (or whatever works).
If there's a simple, existing function to do this, I'd like to use it, but I haven't found it yet. For example, a function that would work like:
# upscale 2x2 to 4x4
matrixSmall = ([[-1,8],[3,5]])
matrixBig = matrixSmall.resample(4,4,cubic)
So, if I start with a 3x3 matrix / array:
0,-2,0
-2,11,-2
0,-2,0
I want to compute a new 5x5 matrix ("I" meaning interpolated value):
0, I[1,0], -2, I[3,0], 0
I[0,1], I[1,1], I[2,1], I[3,1], I[4,1]
-2, I[1,2], 11, I[3,2], -2
I[0,3], I[1,3], I[2,3], I[3,3], I[4,3]
0, I[1,4], -2, I[3,4], 0
I've been searching and reading up and trying various different test code, but I haven't quite figured out the correct syntax for what I'm trying to do. I'm also not sure if I need to be using meshgrid, mgrid or linspace in certain lines.
EDIT: Fixed and working Thanks to Paul
import numpy, scipy
from scipy import interpolate
kernelIn = numpy.array([[0,-2,0],
[-2,11,-2],
[0,-2,0]])
inKSize = len(kernelIn)
outKSize = 5
kernelOut = numpy.zeros((outKSize,outKSize),numpy.uint8)
x = numpy.array([0,1,2])
y = numpy.array([0,1,2])
z = kernelIn
xx = numpy.linspace(x.min(),x.max(),outKSize)
yy = numpy.linspace(y.min(),y.max(),outKSize)
newKernel = interpolate.RectBivariateSpline(x,y,z, kx=2,ky=2)
kernelOut = newKernel(xx,yy)
print kernelOut
Answer
Only two small problems:
1) Your xx,yy is outside the bounds of x,y (you can extrapolate, but I'm guessing you don't want to.)
2) Your sample size is too small for a kx and ky of 3 (default). Lower it to 2 and get a quadratic fit instead of cubic.
import numpy, scipy
from scipy import interpolate
kernelIn = numpy.array([
[0,-2,0],
[-2,11,-2],
[0,-2,0]])
inKSize = len(kernelIn)
outKSize = 5
kernelOut = numpy.zeros((outKSize),numpy.uint8)
x = numpy.array([0,1,2])
y = numpy.array([0,1,2])
z = kernelIn
xx = numpy.linspace(x.min(),x.max(),outKSize)
yy = numpy.linspace(y.min(),y.max(),outKSize)
newKernel = interpolate.RectBivariateSpline(x,y,z, kx=2,ky=2)
kernelOut = newKernel(xx,yy)
print kernelOut
##[[ 0. -1.5 -2. -1.5 0. ]
## [ -1.5 5.4375 7.75 5.4375 -1.5 ]
## [ -2. 7.75 11. 7.75 -2. ]
## [ -1.5 5.4375 7.75 5.4375 -1.5 ]
## [ 0. -1.5 -2. -1.5 0. ]]