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Half working generated interpolation example
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from math import floor | |
from numba import njit | |
#### | |
#### Working | |
#### | |
@njit | |
def native_index_1d(mat, vec): | |
return mat[vec[0]] | |
@njit | |
def native_index_2d(mat, vec): | |
return mat[vec[0], vec[1]] | |
@njit | |
def findex_1d(mat, vec): | |
x = vec[0] | |
N = mat.shape[0] | |
p = floor(x) # such that x ∈ [N-1),(p+1)[] | |
p = max(0, min(p, N-2)) # to extrapolate linearly | |
q = x - p # barycentric coefficient of x | |
res = mat[p]*(1-q) + mat[p+1]*q | |
return res | |
@njit | |
def findex_2d(mat, vec): | |
x = vec[0] | |
y = vec[1] | |
N_0 = mat.shape[0] | |
N_1 = mat.shape[1] | |
p_0 = floor(x) # such that x ∈ [p_0,p_0+1[ | |
p_0 = max(0, min(p_0, N_0-1)) # to extrapolate linearly | |
q_0 = x - p_0 # barycentric coefficient of x | |
p_1 = floor(y) # such that x ∈ [p_1,p_1+1[ | |
p_1 = max(0, min(p_1, N_1-1)) # to extrapolate linearly | |
q_1 = y - p_1 # barycentric coefficient of x | |
res = ( mat[p_0,p_1] *(1-q_0) + mat[p_0+1,p_1] *q_0 ) * (1-q_1) + \ | |
( mat[p_0,p_1+1]*(1-q_0) + mat[p_0+1,p_1+1]*q_0 ) * (q_1) | |
return res | |
from generated import generated | |
from numba import int64, float64 | |
@generated(nopython=True) | |
def findex(t_mat, t_vec): | |
print(t_vec) | |
if t_vec == int64: | |
if t_mat.ndim==1: | |
print("1d") | |
return native_index_1d | |
elif t_mat.ndim==2: | |
return native_index_2d | |
print("2d") | |
elif t_mat.ndim==1: | |
print("mat") | |
return findex_1d | |
else: | |
return findex_2d # function of 3 arguments | |
# example: | |
import numpy | |
xvec = numpy.linspace(0,10,11) | |
yvec = xvec | |
x2vec = (xvec[None,:]+xvec[:,None]).copy() | |
y2vec = x2vec | |
# yvec can be indexed with an integer i s.t. 0<=i<=9 | |
print('yvec[3]: {}'.format(findex(yvec,[3]))) | |
# now, index it with a float | |
print('yvec[3.5]: {}'.format(findex(yvec,[3.5]))) | |
# it also work in 2 dimensions | |
# yvec can be indexed with an integer i s.t. 0<=i<=9 | |
print('yvec[3,4]: {}'.format(findex(y2vec,[3,4]))) | |
# now, index it with a float | |
print('yvec[3.5,4.3]: {}'.format(findex(y2vec,[3.5,4.3]))) | |
xxvec = numpy.linspace(-0.1,10.1,1000) | |
yyvec = numpy.array( [findex_1d(yvec, [x]) for x in xxvec] ) | |
# is equivalent to: | |
yyvec = numpy.array( [findex(yvec, [x]) for x in xxvec] ) | |
exit() | |
#### | |
#### Not working | |
#### | |
@njit | |
def findex_1d(mat, x): | |
# x is now given as argument as a float | |
N = mat.shape[0] | |
p = floor(x) # such that x ∈ [p/(N-1),(p+1)/(N-1)] | |
p = max(0, min(p, N-2)) # to extrapolate linearly | |
q = x # barycentric coefficient of x | |
res = mat[p]*(1-q) + mat[p+1]*q | |
return res | |
@njit | |
def findex_2d(mat, x, y): | |
# x,y are now given as arguments as floats | |
N_0 = mat.shape[0] | |
N_1 = mat.shape[1] | |
p_0 = floor(x) # such that x ∈ [p/(N-1),(p+1)/(N-1)] | |
p_0 = max(0, min(p_0, N_0-1)) # to extrapolate linearly | |
q_0 = x - p # barycentric coefficient of x | |
p_1 = floor(y) # such that x ∈ [p/(N-1),(p+1)/(N-1)] | |
p_1 = max(0, min(p_1, N_1-1)) # to extrapolate linearly | |
q_1 = y - p_1 # barycentric coefficient of x | |
res = ( mat[p_0,p_1] *(1-q_0) + mat[p_0+1,p_1] *q_0 ) * (1-q_1) + \ | |
( mat[p_0,p_1+1]*(1-q_0) + mat[p_0+1,p_1+1]*q_0 ) * (q_1) | |
return res | |
from generated import generated | |
# this doesn't work (don't know why) | |
@generated(nopython=True) | |
def findex(mat, *args): | |
if mat.ndim==1: | |
return findex_1d # function of 2 arguments | |
else: | |
return findex_2d # function of 3 arguments | |
# guvectorize is another matter | |
# it works very well for findex_1d and findex_2d (modulo the issue with scalar args) | |
# the generated functions may have different core dimensions: | |
@generated_guvectorize(nopython=True) | |
def findex(mat, *args): | |
if mat.ndim==1: | |
core = '(d1,d2),()->()' # function of 2 arguments | |
return core, findex_1d | |
else: | |
core = '(d1),(),()->()' # function of 3 arguments | |
return core, findex_2d |
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