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interpolate.py
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interpolate.py
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import numpy as np
from scipy.interpolate import griddata, interp2d
def fill_nans(m):
""" Fills missing values in 2D numpy array grid """
x = np.arange(0, m.shape[1])
y = np.arange(0, m.shape[0])
#mask invalid values
array = np.ma.masked_invalid(m)
xx, yy = np.meshgrid(x, y)
#get only the valid values
x1 = xx[~array.mask]
y1 = yy[~array.mask]
newarr = array[~array.mask]
with np.errstate(all = 'ignore'):
f = interp2d(x1,y1,newarr,kind='linear')
znew = f(x,y)
return znew
def interpolate2m(mxx, myy, B):
""" Interpolate from grid to markers and return list of values (p.117 eq.8.19)
mxx - numpy 1D array of x coordinates of markers
myy - numpy 1D array of y coordinates of markers
B - numpy 2D array
"""
i_res, j_res = B.shape
mxx_int = mxx.astype(int)
myy_int = myy.astype(int)
mxx_res = mxx - mxx_int
myy_res = myy - myy_int
mxx_res[mxx<0] = 0
myy_res[myy<0] = 0
mxx_int[mxx<0] = 0
myy_int[myy<0] = 0
values = np.zeros(np.shape(mxx_int))
for idx in range(len(mxx_int)):
i = myy_int[idx]
j = mxx_int[idx]
x = mxx_res[idx]
y = myy_res[idx]
if (i > i_res-2) and (j > j_res-2):
values[idx] = B[i,j]
elif i > i_res-2:
values[idx] = B[i,j]*(1-x) + B[i,j+1]*x
elif j > j_res-2:
values[idx] = B[i,j]*(1-y) + B[i+1,j]*y
else:
values[idx] = B[i,j]*(1-x)*(1-y) + B[i,j+1]*x*(1-y) + B[i+1,j]*(1-x)*y + B[i+1,j+1]*x*y
return values
def interpolate2m_vect(mxx, myy, B):
""" Interpolate from grid to markers and return list of values (p.117 eq.8.19)
It is vectorised (faster) version of interpolate2m
mxx - numpy 1D array of x coordinates of markers
myy - numpy 1D array of y coordinates of markers
B - numpy 2D array
"""
i_res, j_res = B.shape
mxx_int = mxx.astype(int)
myy_int = myy.astype(int)
mxx_res = mxx - mxx_int
myy_res = myy - myy_int
mxx_res[mxx<0] = 0
myy_res[myy<0] = 0
mxx_int[mxx<0] = 0
myy_int[myy<0] = 0
values = np.zeros(np.shape(mxx_int))
i = myy_int
j = mxx_int
x = mxx_res
y = myy_res
msk_i = i>i_res-2 # mask for i>i_res-1
msk_j = j>j_res-2 # mask for j>i_res-1
msk_ij_ = np.logical_and(i>i_res-2, j>j_res-2)
msk_ij = np.logical_not(np.logical_and(i>i_res-2, j>j_res-2))
msk_nij = np.logical_not(np.logical_or(msk_i,msk_j))
msk_i = np.logical_and(msk_i,msk_ij)
msk_j = np.logical_and(msk_j,msk_ij)
#values[idx] = B[i,j]
values[msk_ij_] = B[i[msk_ij_],j[msk_ij_]]
#values[idx] = (B[i,j]*(1-x) + B[i,j+1]*x)
values[msk_i] = (B[i[msk_i],j[msk_i]]*(1-x[msk_i]) + B[i[msk_i],j[msk_i]+1]*x[msk_i])
#values[idx] = (B[i,j]*(1-y) + B[i+1,j]*y)
values[msk_j] = (B[i[msk_j],j[msk_j]]*(1-y[msk_j]) + B[i[msk_j]+1,j[msk_j]]*y[msk_j])
#values = B[i,j]*(1-x)*(1-y) + B[i,j+1]*x*(1-y) + B[i+1,j]*(1-x)*y + B[i+1,j+1]*x*y
values[msk_nij] = B[i[msk_nij],j[msk_nij]]*(1-x[msk_nij])*(1-y[msk_nij]) +\
B[i[msk_nij],j[msk_nij]+1]*x[msk_nij]*(1-y[msk_nij]) + \
B[i[msk_nij]+1,j[msk_nij]]*(1-x[msk_nij])*y[msk_nij] + \
B[i[msk_nij]+1,j[msk_nij]+1]*x[msk_nij]*y[msk_nij]
return values
def interpolate(mxx,myy,i_res,j_res, datas):
""" Interpolate from markers to gird using bilineral interpolation
1st order accuray scheme from p.116 eq.8.18
mxx - numpy 1D array of x coordinates of markers
myy - numpy 1D array of y coordinates of markers
i_res - x resolutin of a gird
j_res - y resolutin of a gird
datas - numpy 1D array of marker values
"""
mxx_round = np.round(mxx).astype(int)
myy_round = np.round(myy).astype(int)
mxx_res = np.abs(mxx - mxx_round)
myy_res = np.abs(myy - myy_round)
wm = (1 - mxx_res)*(1-myy_res)
down = np.zeros((i_res,j_res))
values = []
for i in range(len(datas)):
values.append(np.zeros((i_res,j_res)))
np.add.at(down,(myy_round,mxx_round),wm)
for i in range(len(values)):
np.add.at(values[i],(myy_round,mxx_round),wm*datas[i])
values[i] = values[i]/down
return values
def interpolate_harmonic(mxx,myy,i_res,j_res,data):
""" Interpolate from markers to gird using harmonic bilineral interpolation
1st order accuray scheme from p.184 eq.13.10
mxx - numpy 1D array of x coordinates of markers
myy - numpy 1D array of y coordinates of markers
i_res - x resolutin of a gird
j_res - y resolutin of a gird
data - numpy 1D array of marker values
"""
mxx_round = np.round(mxx).astype(int)
myy_round = np.round(myy).astype(int)
mxx_res = np.abs(mxx - mxx_round)
myy_res = np.abs(myy - myy_round)
wm = (1 - mxx_res)*(1-myy_res)
with np.errstate(divide='ignore'):
wm_data = wm/data
down = np.zeros((i_res,j_res))
values = np.zeros((i_res,j_res))
np.add.at(down,(myy_round,mxx_round),wm)
np.add.at(values,(myy_round,mxx_round),wm_data)
values = down/values
return values