Interpolate

from smpl import plot
from smpl import stat
from smpl import data
from smpl import interpolate
import numpy as np

from smpl import interpolate as interp
from uncertainties import unumpy as unp

Interpolate 1d

x = np.linspace(2,100,20)
y = stat.noisy(x)
plot.data(x,y,interpolate=True)
plot.show()
plot.data(x,y,interpolate=True,also_data=False)
plot.show()

x = np.linspace(2,100,20)
y = stat.poisson_dist(stat.noisy(x))
plot.data(x,y,interpolate=True,sigmas=1,show=True)
plot.data(x,y,interpolate=True,sigmas=1,also_data=False)
plot.data(x,y,interpolate=True,sigmas=1,also_data=False,init=False,interpolator='linear')
""

/__w/smpl/smpl/smpl/plot.py:852: UserWarning: The figure layout has changed to tight
  plt.tight_layout()

''

x = np.linspace(2,100,10)
y = np.exp(-stat.noisy(x,std=0.05))

ff1=plot.data(x,y,interpolate=True,also_data=False,interpolator='linear',logy=True,interpolate_label="linear")
ff2=plot.data(x,y,interpolate=True,also_data=False,interpolator='exp',logy=True,init=False,interpolate_label="exp")


f1 = interp.interpolate(x,y,interpolator="exp")
f2 = lambda x_ : np.exp(interp.interpolate(x,unp.log(y),interpolator="linear")(x_))
x2 = np.linspace(2,100,100)

plot.data(x2,np.exp(-x2),logy=True,init=False,label="true data")
plot.data(x,f2(x),logy=True,init=False,label="shifted interpolate data")
plot.show()

print("lin Chi2:" + str(stat.Chi2(ff1[0](x2),np.exp(-x2))))
print("exp Chi2:" + str(stat.Chi2(ff2[0](x2),np.exp(-x2))))

lin Chi2:0.0409399227046771
exp Chi2:1.6965498479422644e-05

Interpolate 2d

xvalues = np.linspace(-10,10,5)
yvalues = np.linspace(-10,10,5)
xx, yy = data.flatmesh(xvalues, yvalues)
zz=xx**2+yy**2+10*xx+10*yy
print(zz)
plot.plot2d(xx,yy,zz,fill_missing=False,style='scatter',logz=False)
plot.title("interpolate data")
f=interp.interpolate(xx,yy,zz)
print(f(xx,yy))
xvalues = np.linspace(-10,10,11)
yvalues = np.linspace(-10,10,11)
xx, yy = data.flatmesh(xvalues, yvalues)
plot.plot2d(xx,yy,f(xx,yy),fill_missing=False,style='scatter',logz=False)
plot.title("interpolated data")

[  0. -25.   0.  75. 200. -25. -50. -25.  50. 175.   0. -25.   0.  75.
 200.  75.  50.  75. 150. 275. 200. 175. 200. 275. 400.]
[ 1.49435089e-15 -2.50000000e+01 -3.55271368e-14  7.50000000e+01
  2.00000000e+02 -2.50000000e+01 -5.00000000e+01 -2.50000000e+01
  5.00000000e+01  1.75000000e+02  7.10542736e-15 -2.50000000e+01
  3.37507799e-14  7.50000000e+01  2.00000000e+02  7.50000000e+01
  5.00000000e+01  7.50000000e+01  1.50000000e+02  2.75000000e+02
  2.00000000e+02  1.75000000e+02  2.00000000e+02  2.75000000e+02
  4.00000000e+02]

Text(0.5, 1.0, 'interpolated data')

xvalues = np.linspace(-10,10,10)
yvalues = xvalues*2
xx = xvalues
yy = yvalues
xx = np.append(xx,xx)
yy = np.append(yy,-yy)
zz = xx**2+yy**2
f_cub=interp.interpolate(xx,yy,zz)
f_lin=interp.interpolate(xx,yy,zz,interpolator='linear')
f_lind=interp.interpolate(xx,yy,zz,interpolator='linearnd')
f_bi=interp.interpolate(xx,yy,zz,interpolator='bivariatespline')
plot.plot2d(xx,yy,xx**2+yy**2,style='scatter',fill_missing=True,logz=False)
plot.title("interpolate data")
xvalues = np.linspace(-10,10,11)
yvalues = np.linspace(-20,20,11)
xx, yy = data.flatmesh(xvalues, yvalues)
plot.plot2d(xx,yy,f_cub(xx,yy),fill_missing=False,style='scatter',logz=False)
plot.title("cubic interpolated data")
plot.plot2d(xx,yy,f_lin(xx,yy),fill_missing=False,style='scatter',logz=False)
plot.title("linear interpolated data")
plot.plot2d(xx,yy,f_lind(xx,yy),fill_missing=False,style='scatter',logz=False)
plot.title("linearnd interpolated data")
plot.plot2d(xx,yy,f_bi(xx,yy),fill_missing=False,style='scatter',logz=False)
plot.title("bivariatespline interpolated data")

/github/home/.cache/pypoetry/virtualenvs/smpl-4sWS420u-py3.8/lib/python3.8/site-packages/scipy/interpolate/_fitpack_impl.py:977: RuntimeWarning: No more knots can be added because the number of B-spline
coefficients already exceeds the number of data points m.
Probable causes: either s or m too small. (fp>s)
        kx,ky=3,3 nx,ny=10,8 m=20 fp=0.000000 s=0.000000
  warnings.warn(RuntimeWarning(_iermess2[ierm][0] + _mess))
/github/home/.cache/pypoetry/virtualenvs/smpl-4sWS420u-py3.8/lib/python3.8/site-packages/scipy/interpolate/_fitpack_impl.py:977: RuntimeWarning: No more knots can be added because the number of B-spline
coefficients already exceeds the number of data points m.
Probable causes: either s or m too small. (fp>s)
        kx,ky=1,1 nx,ny=7,7 m=20 fp=0.000000 s=0.000000
  warnings.warn(RuntimeWarning(_iermess2[ierm][0] + _mess))

Text(0.5, 1.0, 'bivariatespline interpolated data')

scipy vs smpl code

Example taken from https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.LinearNDInterpolator.html

import numpy as np
rng = np.random.default_rng()
x = rng.random(10) - 0.5
y = rng.random(10) - 0.5
z = np.hypot(x, y)
lX = np.linspace(min(x), max(x))
lY = np.linspace(min(y), max(y))
X, Y = np.meshgrid(lX, lY)  # 2D grid for interpolation

scipy code

from scipy.interpolate import LinearNDInterpolator
import matplotlib.pyplot as plt
# interpolate
interp = LinearNDInterpolator(list(zip(x, y)), z)
# evaluate interpoaltion function
Z = interp(X, Y)
# plot it
plt.pcolormesh(X, Y, Z, shading='auto')
plt.plot(x, y, "ok", label="input point")
plt.legend()
plt.colorbar()
plt.axis("equal")
plt.show()

smpl code

from smpl import interpolate as interpol
from smpl import plot,data
f=interpol.interpolate(x,y,z,interpolator='linearnd')
plot.plot2d(X,Y,f(X,Y),logz=False)

Pre and Post transformations

It might turn out that some behaviour/shape of the function is known. Including this into the interpolation improves the result as was seen in previos 1d expolential interpolation section.

import numpy as np
rng = np.random.default_rng()
x = 20*rng.random(50)
y = 20*rng.random(50)
tx = np.linspace(min(x), max(x))
ty = np.linspace(min(y), max(y))
z = np.exp(-stat.noisy(x+y,std=0.05))
X, Y = np.meshgrid(tx, ty)  # 2D grid for interpolation
tz = np.exp(-np.abs(X)-np.abs(Y))

plot.plot2d(X,Y,tz,logz=True)
plt.plot(x, y, "ok", label="input point")
plt.legend()

<matplotlib.legend.Legend at 0x7fcbac300730>

f=interpol.interpolate(x,y,z,interpolator='linearnd')
plot.plot2d(X,Y,f(X,Y),logz=True)
r= f(X,Y).flatten()[~np.isnan(f(X,Y).flatten())]
t = tz.flatten()[~np.isnan(f(X,Y).flatten())]
print("Chi2: " + str(stat.Chi2(r,t)))
print("R2: " + str(stat.R2(r,t)))
print("var: " + str(stat.average_deviation(r,t)))

Chi2: 2.4076022113520867
R2: -0.02938002651941929
var: (1+/-8)e+02

f=interpol.interpolate(x,y,z,interpolator='linearnd',pre=np.log,post=np.exp)
plot.plot2d(X,Y,f(X,Y),logz=True)
r= f(X,Y).flatten()[~np.isnan(f(X,Y).flatten())]
t = tz.flatten()[~np.isnan(f(X,Y).flatten())]
print("Chi2: " + str(stat.Chi2(r,t)))
print("R2: " + str(stat.R2(r,t)))
print("var: " + str(stat.average_deviation(r,t)))

Chi2: 0.00010997392744650321
R2: -0.009412081439635012
var: 0.5+/-0.8