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alternative_implementations.py
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alternative_implementations.py
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'''
Run 'python alternative_implementations.py` (no external dependences).
We compare several variants of the code to interpolate cubic splines based on the automatically generated one. They are all included below.
- eval_cubic_spline_3 and eval_cubic_spline_3: the first interpolates at one point and the second repeatedly calls it
- vec_eval_cubic_spline_3_inlined: everything is copied in the loop manually
- vec_eval_cubic_spline_3_inlined_columns: same as above (but points are ordered differently)
- kernel and vec_eval_cubic_spline_3_kernel: the kernel is called repeatedly (it takes all arrays and an index)
- vec_eval_cubic_spline_3_lesswork: fully inlined version which does not rescale and does not interpolate (for comparisons with interpolations.jl)
The benchmark test consists in interpolating random coefficients from a 50x50x50 grid on N=10^6 points. Here are the results:
Repeated calls: 0.24852252006530762
Manually inlined (points in rows): 0.123809814453125
Manually inlined (points in columns): 0.12022709846496582
cuda-like kernel: 0.22097206115722656
No extrap / no rescale: 0.0850365161895752
Cythonized (not shown): 0.11784672737121582
It seems that inlining is not efficient in this case or that it doesn't get enabled.
The performance without extrapolation/rescaling are very similar to those of interpolations.jl which also uses llvm. The penalty cost of those operations seem hard to interpret. (rescaling seems pretty trivial and extrapolation doesn't seem to cost anything).
The Cython version (in eval_cubic_spines_cython.pyx run from main.py) is only slightly faster than numba's.
'''
from numba import njit
from math import floor
from numpy import array, zeros
Ad = array([
# t^3 t^2 t 1
[-1.0/6.0, 3.0/6.0, -3.0/6.0, 1.0/6.0],
[ 3.0/6.0, -6.0/6.0, 0.0/6.0, 4.0/6.0],
[-3.0/6.0, 3.0/6.0, 3.0/6.0, 1.0/6.0],
[ 1.0/6.0, 0.0/6.0, 0.0/6.0, 0.0/6.0]
])
dAd = zeros((4,4))
for i in range(1,4):
dAd[:,i] = Ad[:,i-1]*(4-i)
d2Ad = zeros((4,4))
for i in range(1,4):
d2Ad[:,i] = dAd[:,i-1]*(4-i)
@njit(cache=True)
def eval_cubic_spline_3(a, b, orders, coefs, point, Ad, dAd):
M0 = orders[0]
start0 = a[0]
dinv0 = (orders[0]-1.0)/(b[0]-a[0])
M1 = orders[1]
start1 = a[1]
dinv1 = (orders[1]-1.0)/(b[1]-a[1])
M2 = orders[2]
start2 = a[2]
dinv2 = (orders[2]-1.0)/(b[2]-a[2])
x0 = point[0]
x1 = point[1]
x2 = point[2]
u0 = (x0 - start0)*dinv0
i0 = int( floor( u0 ) )
i0 = max( min(i0,M0-2), 0 )
t0 = u0-i0
u1 = (x1 - start1)*dinv1
i1 = int( floor( u1 ) )
i1 = max( min(i1,M1-2), 0 )
t1 = u1-i1
u2 = (x2 - start2)*dinv2
i2 = int( floor( u2 ) )
i2 = max( min(i2,M2-2), 0 )
t2 = u2-i2
tp0_0 = t0*t0*t0; tp0_1 = t0*t0; tp0_2 = t0; tp0_3 = 1.0;
tp1_0 = t1*t1*t1; tp1_1 = t1*t1; tp1_2 = t1; tp1_3 = 1.0;
tp2_0 = t2*t2*t2; tp2_1 = t2*t2; tp2_2 = t2; tp2_3 = 1.0;
Phi0_0 = 0
Phi0_1 = 0
Phi0_2 = 0
Phi0_3 = 0
if t0 < 0:
Phi0_0 = dAd[0,3]*t0 + Ad[0,3]
Phi0_1 = dAd[1,3]*t0 + Ad[1,3]
Phi0_2 = dAd[2,3]*t0 + Ad[2,3]
Phi0_3 = dAd[3,3]*t0 + Ad[3,3]
elif t0 > 1:
Phi0_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t0-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi0_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t0-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi0_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t0-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi0_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t0-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi0_0 = (Ad[0,0]*tp0_0 + Ad[0,1]*tp0_1 + Ad[0,2]*tp0_2 + Ad[0,3]*tp0_3)
Phi0_1 = (Ad[1,0]*tp0_0 + Ad[1,1]*tp0_1 + Ad[1,2]*tp0_2 + Ad[1,3]*tp0_3)
Phi0_2 = (Ad[2,0]*tp0_0 + Ad[2,1]*tp0_1 + Ad[2,2]*tp0_2 + Ad[2,3]*tp0_3)
Phi0_3 = (Ad[3,0]*tp0_0 + Ad[3,1]*tp0_1 + Ad[3,2]*tp0_2 + Ad[3,3]*tp0_3)
Phi1_0 = 0
Phi1_1 = 0
Phi1_2 = 0
Phi1_3 = 0
if t1 < 0:
Phi1_0 = dAd[0,3]*t1 + Ad[0,3]
Phi1_1 = dAd[1,3]*t1 + Ad[1,3]
Phi1_2 = dAd[2,3]*t1 + Ad[2,3]
Phi1_3 = dAd[3,3]*t1 + Ad[3,3]
elif t1 > 1:
Phi1_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t1-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi1_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t1-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi1_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t1-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi1_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t1-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi1_0 = (Ad[0,0]*tp1_0 + Ad[0,1]*tp1_1 + Ad[0,2]*tp1_2 + Ad[0,3]*tp1_3)
Phi1_1 = (Ad[1,0]*tp1_0 + Ad[1,1]*tp1_1 + Ad[1,2]*tp1_2 + Ad[1,3]*tp1_3)
Phi1_2 = (Ad[2,0]*tp1_0 + Ad[2,1]*tp1_1 + Ad[2,2]*tp1_2 + Ad[2,3]*tp1_3)
Phi1_3 = (Ad[3,0]*tp1_0 + Ad[3,1]*tp1_1 + Ad[3,2]*tp1_2 + Ad[3,3]*tp1_3)
Phi2_0 = 0
Phi2_1 = 0
Phi2_2 = 0
Phi2_3 = 0
if t2 < 0:
Phi2_0 = dAd[0,3]*t2 + Ad[0,3]
Phi2_1 = dAd[1,3]*t2 + Ad[1,3]
Phi2_2 = dAd[2,3]*t2 + Ad[2,3]
Phi2_3 = dAd[3,3]*t2 + Ad[3,3]
elif t2 > 1:
Phi2_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t2-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi2_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t2-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi2_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t2-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi2_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t2-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi2_0 = (Ad[0,0]*tp2_0 + Ad[0,1]*tp2_1 + Ad[0,2]*tp2_2 + Ad[0,3]*tp2_3)
Phi2_1 = (Ad[1,0]*tp2_0 + Ad[1,1]*tp2_1 + Ad[1,2]*tp2_2 + Ad[1,3]*tp2_3)
Phi2_2 = (Ad[2,0]*tp2_0 + Ad[2,1]*tp2_1 + Ad[2,2]*tp2_2 + Ad[2,3]*tp2_3)
Phi2_3 = (Ad[3,0]*tp2_0 + Ad[3,1]*tp2_1 + Ad[3,2]*tp2_2 + Ad[3,3]*tp2_3)
t = Phi0_0*(Phi1_0*(Phi2_0*(coefs[i0+0,i1+0,i2+0]) + Phi2_1*(coefs[i0+0,i1+0,i2+1]) + Phi2_2*(coefs[i0+0,i1+0,i2+2]) + Phi2_3*(coefs[i0+0,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+0,i1+1,i2+0]) + Phi2_1*(coefs[i0+0,i1+1,i2+1]) + Phi2_2*(coefs[i0+0,i1+1,i2+2]) + Phi2_3*(coefs[i0+0,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+0,i1+2,i2+0]) + Phi2_1*(coefs[i0+0,i1+2,i2+1]) + Phi2_2*(coefs[i0+0,i1+2,i2+2]) + Phi2_3*(coefs[i0+0,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+0,i1+3,i2+0]) + Phi2_1*(coefs[i0+0,i1+3,i2+1]) + Phi2_2*(coefs[i0+0,i1+3,i2+2]) + Phi2_3*(coefs[i0+0,i1+3,i2+3]))) + Phi0_1*(Phi1_0*(Phi2_0*(coefs[i0+1,i1+0,i2+0]) + Phi2_1*(coefs[i0+1,i1+0,i2+1]) + Phi2_2*(coefs[i0+1,i1+0,i2+2]) + Phi2_3*(coefs[i0+1,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+1,i1+1,i2+0]) + Phi2_1*(coefs[i0+1,i1+1,i2+1]) + Phi2_2*(coefs[i0+1,i1+1,i2+2]) + Phi2_3*(coefs[i0+1,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+1,i1+2,i2+0]) + Phi2_1*(coefs[i0+1,i1+2,i2+1]) + Phi2_2*(coefs[i0+1,i1+2,i2+2]) + Phi2_3*(coefs[i0+1,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+1,i1+3,i2+0]) + Phi2_1*(coefs[i0+1,i1+3,i2+1]) + Phi2_2*(coefs[i0+1,i1+3,i2+2]) + Phi2_3*(coefs[i0+1,i1+3,i2+3]))) + Phi0_2*(Phi1_0*(Phi2_0*(coefs[i0+2,i1+0,i2+0]) + Phi2_1*(coefs[i0+2,i1+0,i2+1]) + Phi2_2*(coefs[i0+2,i1+0,i2+2]) + Phi2_3*(coefs[i0+2,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+2,i1+1,i2+0]) + Phi2_1*(coefs[i0+2,i1+1,i2+1]) + Phi2_2*(coefs[i0+2,i1+1,i2+2]) + Phi2_3*(coefs[i0+2,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+2,i1+2,i2+0]) + Phi2_1*(coefs[i0+2,i1+2,i2+1]) + Phi2_2*(coefs[i0+2,i1+2,i2+2]) + Phi2_3*(coefs[i0+2,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+2,i1+3,i2+0]) + Phi2_1*(coefs[i0+2,i1+3,i2+1]) + Phi2_2*(coefs[i0+2,i1+3,i2+2]) + Phi2_3*(coefs[i0+2,i1+3,i2+3]))) + Phi0_3*(Phi1_0*(Phi2_0*(coefs[i0+3,i1+0,i2+0]) + Phi2_1*(coefs[i0+3,i1+0,i2+1]) + Phi2_2*(coefs[i0+3,i1+0,i2+2]) + Phi2_3*(coefs[i0+3,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+3,i1+1,i2+0]) + Phi2_1*(coefs[i0+3,i1+1,i2+1]) + Phi2_2*(coefs[i0+3,i1+1,i2+2]) + Phi2_3*(coefs[i0+3,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+3,i1+2,i2+0]) + Phi2_1*(coefs[i0+3,i1+2,i2+1]) + Phi2_2*(coefs[i0+3,i1+2,i2+2]) + Phi2_3*(coefs[i0+3,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+3,i1+3,i2+0]) + Phi2_1*(coefs[i0+3,i1+3,i2+1]) + Phi2_2*(coefs[i0+3,i1+3,i2+2]) + Phi2_3*(coefs[i0+3,i1+3,i2+3])))
return t
@njit(cache=True)
def vec_eval_cubic_spline_3(a, b, orders, coefs, points, values):
N = points.shape[0]
for n in range(N):
point = points[n, :]
values[n] = eval_cubic_spline_3(a, b, orders, coefs, point, Ad, dAd)
@njit(cache=True)
def vec_eval_cubic_spline_3_inlined(a, b, orders, coefs, points, values):
N = points.shape[0]
for n in range(N):
x0 = points[n,0]
x1 = points[n,1]
x2 = points[n,2]
# # a bit faster ?
# x0 = points[0,n]
# x1 = points[1,n]
# x2 = points[2,n]
M0 = orders[0]
start0 = a[0]
dinv0 = (orders[0]-1.0)/(b[0]-a[0])
M1 = orders[1]
start1 = a[1]
dinv1 = (orders[1]-1.0)/(b[1]-a[1])
M2 = orders[2]
start2 = a[2]
dinv2 = (orders[2]-1.0)/(b[2]-a[2])
u0 = (x0 - start0)*dinv0
i0 = int( floor( u0 ) )
i0 = max( min(i0,M0-2), 0 )
t0 = u0-i0
u1 = (x1 - start1)*dinv1
i1 = int( floor( u1 ) )
i1 = max( min(i1,M1-2), 0 )
t1 = u1-i1
u2 = (x2 - start2)*dinv2
i2 = int( floor( u2 ) )
i2 = max( min(i2,M2-2), 0 )
t2 = u2-i2
tp0_0 = t0*t0*t0; tp0_1 = t0*t0; tp0_2 = t0; tp0_3 = 1.0;
tp1_0 = t1*t1*t1; tp1_1 = t1*t1; tp1_2 = t1; tp1_3 = 1.0;
tp2_0 = t2*t2*t2; tp2_1 = t2*t2; tp2_2 = t2; tp2_3 = 1.0;
Phi0_0 = 0
Phi0_1 = 0
Phi0_2 = 0
Phi0_3 = 0
if t0 < 0:
Phi0_0 = dAd[0,3]*t0 + Ad[0,3]
Phi0_1 = dAd[1,3]*t0 + Ad[1,3]
Phi0_2 = dAd[2,3]*t0 + Ad[2,3]
Phi0_3 = dAd[3,3]*t0 + Ad[3,3]
elif t0 > 1:
Phi0_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t0-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi0_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t0-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi0_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t0-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi0_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t0-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi0_0 = (Ad[0,0]*tp0_0 + Ad[0,1]*tp0_1 + Ad[0,2]*tp0_2 + Ad[0,3]*tp0_3)
Phi0_1 = (Ad[1,0]*tp0_0 + Ad[1,1]*tp0_1 + Ad[1,2]*tp0_2 + Ad[1,3]*tp0_3)
Phi0_2 = (Ad[2,0]*tp0_0 + Ad[2,1]*tp0_1 + Ad[2,2]*tp0_2 + Ad[2,3]*tp0_3)
Phi0_3 = (Ad[3,0]*tp0_0 + Ad[3,1]*tp0_1 + Ad[3,2]*tp0_2 + Ad[3,3]*tp0_3)
Phi1_0 = 0
Phi1_1 = 0
Phi1_2 = 0
Phi1_3 = 0
if t1 < 0:
Phi1_0 = dAd[0,3]*t1 + Ad[0,3]
Phi1_1 = dAd[1,3]*t1 + Ad[1,3]
Phi1_2 = dAd[2,3]*t1 + Ad[2,3]
Phi1_3 = dAd[3,3]*t1 + Ad[3,3]
elif t1 > 1:
Phi1_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t1-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi1_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t1-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi1_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t1-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi1_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t1-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi1_0 = (Ad[0,0]*tp1_0 + Ad[0,1]*tp1_1 + Ad[0,2]*tp1_2 + Ad[0,3]*tp1_3)
Phi1_1 = (Ad[1,0]*tp1_0 + Ad[1,1]*tp1_1 + Ad[1,2]*tp1_2 + Ad[1,3]*tp1_3)
Phi1_2 = (Ad[2,0]*tp1_0 + Ad[2,1]*tp1_1 + Ad[2,2]*tp1_2 + Ad[2,3]*tp1_3)
Phi1_3 = (Ad[3,0]*tp1_0 + Ad[3,1]*tp1_1 + Ad[3,2]*tp1_2 + Ad[3,3]*tp1_3)
Phi2_0 = 0
Phi2_1 = 0
Phi2_2 = 0
Phi2_3 = 0
if t2 < 0:
Phi2_0 = dAd[0,3]*t2 + Ad[0,3]
Phi2_1 = dAd[1,3]*t2 + Ad[1,3]
Phi2_2 = dAd[2,3]*t2 + Ad[2,3]
Phi2_3 = dAd[3,3]*t2 + Ad[3,3]
elif t2 > 1:
Phi2_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t2-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi2_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t2-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi2_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t2-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi2_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t2-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi2_0 = (Ad[0,0]*tp2_0 + Ad[0,1]*tp2_1 + Ad[0,2]*tp2_2 + Ad[0,3]*tp2_3)
Phi2_1 = (Ad[1,0]*tp2_0 + Ad[1,1]*tp2_1 + Ad[1,2]*tp2_2 + Ad[1,3]*tp2_3)
Phi2_2 = (Ad[2,0]*tp2_0 + Ad[2,1]*tp2_1 + Ad[2,2]*tp2_2 + Ad[2,3]*tp2_3)
Phi2_3 = (Ad[3,0]*tp2_0 + Ad[3,1]*tp2_1 + Ad[3,2]*tp2_2 + Ad[3,3]*tp2_3)
values[n] = Phi0_0*(Phi1_0*(Phi2_0*(coefs[i0+0,i1+0,i2+0]) + Phi2_1*(coefs[i0+0,i1+0,i2+1]) + Phi2_2*(coefs[i0+0,i1+0,i2+2]) + Phi2_3*(coefs[i0+0,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+0,i1+1,i2+0]) + Phi2_1*(coefs[i0+0,i1+1,i2+1]) + Phi2_2*(coefs[i0+0,i1+1,i2+2]) + Phi2_3*(coefs[i0+0,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+0,i1+2,i2+0]) + Phi2_1*(coefs[i0+0,i1+2,i2+1]) + Phi2_2*(coefs[i0+0,i1+2,i2+2]) + Phi2_3*(coefs[i0+0,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+0,i1+3,i2+0]) + Phi2_1*(coefs[i0+0,i1+3,i2+1]) + Phi2_2*(coefs[i0+0,i1+3,i2+2]) + Phi2_3*(coefs[i0+0,i1+3,i2+3]))) + Phi0_1*(Phi1_0*(Phi2_0*(coefs[i0+1,i1+0,i2+0]) + Phi2_1*(coefs[i0+1,i1+0,i2+1]) + Phi2_2*(coefs[i0+1,i1+0,i2+2]) + Phi2_3*(coefs[i0+1,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+1,i1+1,i2+0]) + Phi2_1*(coefs[i0+1,i1+1,i2+1]) + Phi2_2*(coefs[i0+1,i1+1,i2+2]) + Phi2_3*(coefs[i0+1,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+1,i1+2,i2+0]) + Phi2_1*(coefs[i0+1,i1+2,i2+1]) + Phi2_2*(coefs[i0+1,i1+2,i2+2]) + Phi2_3*(coefs[i0+1,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+1,i1+3,i2+0]) + Phi2_1*(coefs[i0+1,i1+3,i2+1]) + Phi2_2*(coefs[i0+1,i1+3,i2+2]) + Phi2_3*(coefs[i0+1,i1+3,i2+3]))) + Phi0_2*(Phi1_0*(Phi2_0*(coefs[i0+2,i1+0,i2+0]) + Phi2_1*(coefs[i0+2,i1+0,i2+1]) + Phi2_2*(coefs[i0+2,i1+0,i2+2]) + Phi2_3*(coefs[i0+2,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+2,i1+1,i2+0]) + Phi2_1*(coefs[i0+2,i1+1,i2+1]) + Phi2_2*(coefs[i0+2,i1+1,i2+2]) + Phi2_3*(coefs[i0+2,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+2,i1+2,i2+0]) + Phi2_1*(coefs[i0+2,i1+2,i2+1]) + Phi2_2*(coefs[i0+2,i1+2,i2+2]) + Phi2_3*(coefs[i0+2,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+2,i1+3,i2+0]) + Phi2_1*(coefs[i0+2,i1+3,i2+1]) + Phi2_2*(coefs[i0+2,i1+3,i2+2]) + Phi2_3*(coefs[i0+2,i1+3,i2+3]))) + Phi0_3*(Phi1_0*(Phi2_0*(coefs[i0+3,i1+0,i2+0]) + Phi2_1*(coefs[i0+3,i1+0,i2+1]) + Phi2_2*(coefs[i0+3,i1+0,i2+2]) + Phi2_3*(coefs[i0+3,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+3,i1+1,i2+0]) + Phi2_1*(coefs[i0+3,i1+1,i2+1]) + Phi2_2*(coefs[i0+3,i1+1,i2+2]) + Phi2_3*(coefs[i0+3,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+3,i1+2,i2+0]) + Phi2_1*(coefs[i0+3,i1+2,i2+1]) + Phi2_2*(coefs[i0+3,i1+2,i2+2]) + Phi2_3*(coefs[i0+3,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+3,i1+3,i2+0]) + Phi2_1*(coefs[i0+3,i1+3,i2+1]) + Phi2_2*(coefs[i0+3,i1+3,i2+2]) + Phi2_3*(coefs[i0+3,i1+3,i2+3])))
@njit(cache=True)
def vec_eval_cubic_spline_3_inlined_columns(a, b, orders, coefs, points, values):
# N = points.shape[0]
N = points.shape[1]
M0 = orders[0]
start0 = a[0]
dinv0 = (orders[0]-1.0)/(b[0]-a[0])
M1 = orders[1]
start1 = a[1]
dinv1 = (orders[1]-1.0)/(b[1]-a[1])
M2 = orders[2]
start2 = a[2]
dinv2 = (orders[2]-1.0)/(b[2]-a[2])
for n in range(N):
# x0 = points[n,0]
# x1 = points[n,1]
# x2 = points[n,2]
# # a bit faster ?
x0 = points[0,n]
x1 = points[1,n]
x2 = points[2,n]
u0 = (x0 - start0)*dinv0
i0 = int( floor( u0 ) )
i0 = max( min(i0,M0-2), 0 )
t0 = u0-i0
u1 = (x1 - start1)*dinv1
i1 = int( floor( u1 ) )
i1 = max( min(i1,M1-2), 0 )
t1 = u1-i1
u2 = (x2 - start2)*dinv2
i2 = int( floor( u2 ) )
i2 = max( min(i2,M2-2), 0 )
t2 = u2-i2
tp0_0 = t0*t0*t0; tp0_1 = t0*t0; tp0_2 = t0; tp0_3 = 1.0;
tp1_0 = t1*t1*t1; tp1_1 = t1*t1; tp1_2 = t1; tp1_3 = 1.0;
tp2_0 = t2*t2*t2; tp2_1 = t2*t2; tp2_2 = t2; tp2_3 = 1.0;
Phi0_0 = 0
Phi0_1 = 0
Phi0_2 = 0
Phi0_3 = 0
if t0 < 0:
Phi0_0 = dAd[0,3]*t0 + Ad[0,3]
Phi0_1 = dAd[1,3]*t0 + Ad[1,3]
Phi0_2 = dAd[2,3]*t0 + Ad[2,3]
Phi0_3 = dAd[3,3]*t0 + Ad[3,3]
elif t0 > 1:
Phi0_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t0-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi0_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t0-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi0_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t0-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi0_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t0-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi0_0 = (Ad[0,0]*tp0_0 + Ad[0,1]*tp0_1 + Ad[0,2]*tp0_2 + Ad[0,3]*tp0_3)
Phi0_1 = (Ad[1,0]*tp0_0 + Ad[1,1]*tp0_1 + Ad[1,2]*tp0_2 + Ad[1,3]*tp0_3)
Phi0_2 = (Ad[2,0]*tp0_0 + Ad[2,1]*tp0_1 + Ad[2,2]*tp0_2 + Ad[2,3]*tp0_3)
Phi0_3 = (Ad[3,0]*tp0_0 + Ad[3,1]*tp0_1 + Ad[3,2]*tp0_2 + Ad[3,3]*tp0_3)
Phi1_0 = 0
Phi1_1 = 0
Phi1_2 = 0
Phi1_3 = 0
if t1 < 0:
Phi1_0 = dAd[0,3]*t1 + Ad[0,3]
Phi1_1 = dAd[1,3]*t1 + Ad[1,3]
Phi1_2 = dAd[2,3]*t1 + Ad[2,3]
Phi1_3 = dAd[3,3]*t1 + Ad[3,3]
elif t1 > 1:
Phi1_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t1-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi1_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t1-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi1_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t1-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi1_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t1-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi1_0 = (Ad[0,0]*tp1_0 + Ad[0,1]*tp1_1 + Ad[0,2]*tp1_2 + Ad[0,3]*tp1_3)
Phi1_1 = (Ad[1,0]*tp1_0 + Ad[1,1]*tp1_1 + Ad[1,2]*tp1_2 + Ad[1,3]*tp1_3)
Phi1_2 = (Ad[2,0]*tp1_0 + Ad[2,1]*tp1_1 + Ad[2,2]*tp1_2 + Ad[2,3]*tp1_3)
Phi1_3 = (Ad[3,0]*tp1_0 + Ad[3,1]*tp1_1 + Ad[3,2]*tp1_2 + Ad[3,3]*tp1_3)
Phi2_0 = 0
Phi2_1 = 0
Phi2_2 = 0
Phi2_3 = 0
if t2 < 0:
Phi2_0 = dAd[0,3]*t2 + Ad[0,3]
Phi2_1 = dAd[1,3]*t2 + Ad[1,3]
Phi2_2 = dAd[2,3]*t2 + Ad[2,3]
Phi2_3 = dAd[3,3]*t2 + Ad[3,3]
elif t2 > 1:
Phi2_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t2-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi2_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t2-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi2_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t2-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi2_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t2-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi2_0 = (Ad[0,0]*tp2_0 + Ad[0,1]*tp2_1 + Ad[0,2]*tp2_2 + Ad[0,3]*tp2_3)
Phi2_1 = (Ad[1,0]*tp2_0 + Ad[1,1]*tp2_1 + Ad[1,2]*tp2_2 + Ad[1,3]*tp2_3)
Phi2_2 = (Ad[2,0]*tp2_0 + Ad[2,1]*tp2_1 + Ad[2,2]*tp2_2 + Ad[2,3]*tp2_3)
Phi2_3 = (Ad[3,0]*tp2_0 + Ad[3,1]*tp2_1 + Ad[3,2]*tp2_2 + Ad[3,3]*tp2_3)
values[n] = Phi0_0*(Phi1_0*(Phi2_0*(coefs[i0+0,i1+0,i2+0]) + Phi2_1*(coefs[i0+0,i1+0,i2+1]) + Phi2_2*(coefs[i0+0,i1+0,i2+2]) + Phi2_3*(coefs[i0+0,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+0,i1+1,i2+0]) + Phi2_1*(coefs[i0+0,i1+1,i2+1]) + Phi2_2*(coefs[i0+0,i1+1,i2+2]) + Phi2_3*(coefs[i0+0,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+0,i1+2,i2+0]) + Phi2_1*(coefs[i0+0,i1+2,i2+1]) + Phi2_2*(coefs[i0+0,i1+2,i2+2]) + Phi2_3*(coefs[i0+0,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+0,i1+3,i2+0]) + Phi2_1*(coefs[i0+0,i1+3,i2+1]) + Phi2_2*(coefs[i0+0,i1+3,i2+2]) + Phi2_3*(coefs[i0+0,i1+3,i2+3]))) + Phi0_1*(Phi1_0*(Phi2_0*(coefs[i0+1,i1+0,i2+0]) + Phi2_1*(coefs[i0+1,i1+0,i2+1]) + Phi2_2*(coefs[i0+1,i1+0,i2+2]) + Phi2_3*(coefs[i0+1,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+1,i1+1,i2+0]) + Phi2_1*(coefs[i0+1,i1+1,i2+1]) + Phi2_2*(coefs[i0+1,i1+1,i2+2]) + Phi2_3*(coefs[i0+1,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+1,i1+2,i2+0]) + Phi2_1*(coefs[i0+1,i1+2,i2+1]) + Phi2_2*(coefs[i0+1,i1+2,i2+2]) + Phi2_3*(coefs[i0+1,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+1,i1+3,i2+0]) + Phi2_1*(coefs[i0+1,i1+3,i2+1]) + Phi2_2*(coefs[i0+1,i1+3,i2+2]) + Phi2_3*(coefs[i0+1,i1+3,i2+3]))) + Phi0_2*(Phi1_0*(Phi2_0*(coefs[i0+2,i1+0,i2+0]) + Phi2_1*(coefs[i0+2,i1+0,i2+1]) + Phi2_2*(coefs[i0+2,i1+0,i2+2]) + Phi2_3*(coefs[i0+2,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+2,i1+1,i2+0]) + Phi2_1*(coefs[i0+2,i1+1,i2+1]) + Phi2_2*(coefs[i0+2,i1+1,i2+2]) + Phi2_3*(coefs[i0+2,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+2,i1+2,i2+0]) + Phi2_1*(coefs[i0+2,i1+2,i2+1]) + Phi2_2*(coefs[i0+2,i1+2,i2+2]) + Phi2_3*(coefs[i0+2,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+2,i1+3,i2+0]) + Phi2_1*(coefs[i0+2,i1+3,i2+1]) + Phi2_2*(coefs[i0+2,i1+3,i2+2]) + Phi2_3*(coefs[i0+2,i1+3,i2+3]))) + Phi0_3*(Phi1_0*(Phi2_0*(coefs[i0+3,i1+0,i2+0]) + Phi2_1*(coefs[i0+3,i1+0,i2+1]) + Phi2_2*(coefs[i0+3,i1+0,i2+2]) + Phi2_3*(coefs[i0+3,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+3,i1+1,i2+0]) + Phi2_1*(coefs[i0+3,i1+1,i2+1]) + Phi2_2*(coefs[i0+3,i1+1,i2+2]) + Phi2_3*(coefs[i0+3,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+3,i1+2,i2+0]) + Phi2_1*(coefs[i0+3,i1+2,i2+1]) + Phi2_2*(coefs[i0+3,i1+2,i2+2]) + Phi2_3*(coefs[i0+3,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+3,i1+3,i2+0]) + Phi2_1*(coefs[i0+3,i1+3,i2+1]) + Phi2_2*(coefs[i0+3,i1+3,i2+2]) + Phi2_3*(coefs[i0+3,i1+3,i2+3])))
@njit(cache=True)
def vec_eval_cubic_spline_3_inlined_lesswork(orders, coefs, points, values, Ad, dAd):
N = points.shape[0]
M0 = orders[0]
# start0 = a[0]
# dinv0 = (orders[0]-1.0)/(b[0]-a[0])
M1 = orders[1]
# start1 = a[1]
# dinv1 = (orders[1]-1.0)/(b[1]-a[1])
M2 = orders[2]
# start2 = a[2]
# dinv2 = (orders[2]-1.0)/(b[2]-a[2])
for n in range(N):
u0 = points[n,0]
u1 = points[n,1]
u2 = points[n,2]
i0 = int( floor( u0 ) )
i0 = max( min(i0,M0-2), 0 )
t0 = u0-i0
i1 = int( floor( u1 ) )
i1 = max( min(i1,M1-2), 0 )
t1 = u1-i1
i2 = int( floor( u2 ) )
i2 = max( min(i2,M2-2), 0 )
t2 = u2-i2
tp0_0 = t0*t0*t0; tp0_1 = t0*t0; tp0_2 = t0; tp0_3 = 1.0;
tp1_0 = t1*t1*t1; tp1_1 = t1*t1; tp1_2 = t1; tp1_3 = 1.0;
tp2_0 = t2*t2*t2; tp2_1 = t2*t2; tp2_2 = t2; tp2_3 = 1.0;
Phi0_0 = (Ad[0,0]*tp0_0 + Ad[0,1]*tp0_1 + Ad[0,2]*tp0_2 + Ad[0,3]*tp0_3)
Phi0_1 = (Ad[1,0]*tp0_0 + Ad[1,1]*tp0_1 + Ad[1,2]*tp0_2 + Ad[1,3]*tp0_3)
Phi0_2 = (Ad[2,0]*tp0_0 + Ad[2,1]*tp0_1 + Ad[2,2]*tp0_2 + Ad[2,3]*tp0_3)
Phi0_3 = (Ad[3,0]*tp0_0 + Ad[3,1]*tp0_1 + Ad[3,2]*tp0_2 + Ad[3,3]*tp0_3)
Phi1_0 = (Ad[0,0]*tp1_0 + Ad[0,1]*tp1_1 + Ad[0,2]*tp1_2 + Ad[0,3]*tp1_3)
Phi1_1 = (Ad[1,0]*tp1_0 + Ad[1,1]*tp1_1 + Ad[1,2]*tp1_2 + Ad[1,3]*tp1_3)
Phi1_2 = (Ad[2,0]*tp1_0 + Ad[2,1]*tp1_1 + Ad[2,2]*tp1_2 + Ad[2,3]*tp1_3)
Phi1_3 = (Ad[3,0]*tp1_0 + Ad[3,1]*tp1_1 + Ad[3,2]*tp1_2 + Ad[3,3]*tp1_3)
Phi2_0 = (Ad[0,0]*tp2_0 + Ad[0,1]*tp2_1 + Ad[0,2]*tp2_2 + Ad[0,3]*tp2_3)
Phi2_1 = (Ad[1,0]*tp2_0 + Ad[1,1]*tp2_1 + Ad[1,2]*tp2_2 + Ad[1,3]*tp2_3)
Phi2_2 = (Ad[2,0]*tp2_0 + Ad[2,1]*tp2_1 + Ad[2,2]*tp2_2 + Ad[2,3]*tp2_3)
Phi2_3 = (Ad[3,0]*tp2_0 + Ad[3,1]*tp2_1 + Ad[3,2]*tp2_2 + Ad[3,3]*tp2_3)
values[n] = Phi0_0*(Phi1_0*(Phi2_0*(coefs[i0+0,i1+0,i2+0]) + Phi2_1*(coefs[i0+0,i1+0,i2+1]) + Phi2_2*(coefs[i0+0,i1+0,i2+2]) + Phi2_3*(coefs[i0+0,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+0,i1+1,i2+0]) + Phi2_1*(coefs[i0+0,i1+1,i2+1]) + Phi2_2*(coefs[i0+0,i1+1,i2+2]) + Phi2_3*(coefs[i0+0,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+0,i1+2,i2+0]) + Phi2_1*(coefs[i0+0,i1+2,i2+1]) + Phi2_2*(coefs[i0+0,i1+2,i2+2]) + Phi2_3*(coefs[i0+0,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+0,i1+3,i2+0]) + Phi2_1*(coefs[i0+0,i1+3,i2+1]) + Phi2_2*(coefs[i0+0,i1+3,i2+2]) + Phi2_3*(coefs[i0+0,i1+3,i2+3]))) + Phi0_1*(Phi1_0*(Phi2_0*(coefs[i0+1,i1+0,i2+0]) + Phi2_1*(coefs[i0+1,i1+0,i2+1]) + Phi2_2*(coefs[i0+1,i1+0,i2+2]) + Phi2_3*(coefs[i0+1,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+1,i1+1,i2+0]) + Phi2_1*(coefs[i0+1,i1+1,i2+1]) + Phi2_2*(coefs[i0+1,i1+1,i2+2]) + Phi2_3*(coefs[i0+1,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+1,i1+2,i2+0]) + Phi2_1*(coefs[i0+1,i1+2,i2+1]) + Phi2_2*(coefs[i0+1,i1+2,i2+2]) + Phi2_3*(coefs[i0+1,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+1,i1+3,i2+0]) + Phi2_1*(coefs[i0+1,i1+3,i2+1]) + Phi2_2*(coefs[i0+1,i1+3,i2+2]) + Phi2_3*(coefs[i0+1,i1+3,i2+3]))) + Phi0_2*(Phi1_0*(Phi2_0*(coefs[i0+2,i1+0,i2+0]) + Phi2_1*(coefs[i0+2,i1+0,i2+1]) + Phi2_2*(coefs[i0+2,i1+0,i2+2]) + Phi2_3*(coefs[i0+2,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+2,i1+1,i2+0]) + Phi2_1*(coefs[i0+2,i1+1,i2+1]) + Phi2_2*(coefs[i0+2,i1+1,i2+2]) + Phi2_3*(coefs[i0+2,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+2,i1+2,i2+0]) + Phi2_1*(coefs[i0+2,i1+2,i2+1]) + Phi2_2*(coefs[i0+2,i1+2,i2+2]) + Phi2_3*(coefs[i0+2,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+2,i1+3,i2+0]) + Phi2_1*(coefs[i0+2,i1+3,i2+1]) + Phi2_2*(coefs[i0+2,i1+3,i2+2]) + Phi2_3*(coefs[i0+2,i1+3,i2+3]))) + Phi0_3*(Phi1_0*(Phi2_0*(coefs[i0+3,i1+0,i2+0]) + Phi2_1*(coefs[i0+3,i1+0,i2+1]) + Phi2_2*(coefs[i0+3,i1+0,i2+2]) + Phi2_3*(coefs[i0+3,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+3,i1+1,i2+0]) + Phi2_1*(coefs[i0+3,i1+1,i2+1]) + Phi2_2*(coefs[i0+3,i1+1,i2+2]) + Phi2_3*(coefs[i0+3,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+3,i1+2,i2+0]) + Phi2_1*(coefs[i0+3,i1+2,i2+1]) + Phi2_2*(coefs[i0+3,i1+2,i2+2]) + Phi2_3*(coefs[i0+3,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+3,i1+3,i2+0]) + Phi2_1*(coefs[i0+3,i1+3,i2+1]) + Phi2_2*(coefs[i0+3,i1+3,i2+2]) + Phi2_3*(coefs[i0+3,i1+3,i2+3])))
@njit(cache=True)
def kernel(n, a, b, orders, coefs, points, values):
x0 = points[n,0]
x1 = points[n,1]
x2 = points[n,2]
# common to all units
M0 = orders[0]
start0 = a[0]
dinv0 = (orders[0]-1.0)/(b[0]-a[0])
M1 = orders[1]
start1 = a[1]
dinv1 = (orders[1]-1.0)/(b[1]-a[1])
M2 = orders[2]
start2 = a[2]
dinv2 = (orders[2]-1.0)/(b[2]-a[2])
# locate the point
u0 = (x0 - start0)*dinv0
i0 = int( floor( u0 ) )
i0 = max( min(i0,M0-2), 0 )
t0 = u0-i0
u1 = (x1 - start1)*dinv1
i1 = int( floor( u1 ) )
i1 = max( min(i1,M1-2), 0 )
t1 = u1-i1
u2 = (x2 - start2)*dinv2
i2 = int( floor( u2 ) )
i2 = max( min(i2,M2-2), 0 )
t2 = u2-i2
tp0_0 = t0*t0*t0; tp0_1 = t0*t0; tp0_2 = t0; tp0_3 = 1.0;
tp1_0 = t1*t1*t1; tp1_1 = t1*t1; tp1_2 = t1; tp1_3 = 1.0;
tp2_0 = t2*t2*t2; tp2_1 = t2*t2; tp2_2 = t2; tp2_3 = 1.0;
Phi0_0 = 0
Phi0_1 = 0
Phi0_2 = 0
Phi0_3 = 0
if t0 < 0:
Phi0_0 = dAd[0,3]*t0 + Ad[0,3]
Phi0_1 = dAd[1,3]*t0 + Ad[1,3]
Phi0_2 = dAd[2,3]*t0 + Ad[2,3]
Phi0_3 = dAd[3,3]*t0 + Ad[3,3]
elif t0 > 1:
Phi0_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t0-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi0_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t0-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi0_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t0-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi0_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t0-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi0_0 = (Ad[0,0]*tp0_0 + Ad[0,1]*tp0_1 + Ad[0,2]*tp0_2 + Ad[0,3]*tp0_3)
Phi0_1 = (Ad[1,0]*tp0_0 + Ad[1,1]*tp0_1 + Ad[1,2]*tp0_2 + Ad[1,3]*tp0_3)
Phi0_2 = (Ad[2,0]*tp0_0 + Ad[2,1]*tp0_1 + Ad[2,2]*tp0_2 + Ad[2,3]*tp0_3)
Phi0_3 = (Ad[3,0]*tp0_0 + Ad[3,1]*tp0_1 + Ad[3,2]*tp0_2 + Ad[3,3]*tp0_3)
Phi1_0 = 0
Phi1_1 = 0
Phi1_2 = 0
Phi1_3 = 0
if t1 < 0:
Phi1_0 = dAd[0,3]*t1 + Ad[0,3]
Phi1_1 = dAd[1,3]*t1 + Ad[1,3]
Phi1_2 = dAd[2,3]*t1 + Ad[2,3]
Phi1_3 = dAd[3,3]*t1 + Ad[3,3]
elif t1 > 1:
Phi1_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t1-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi1_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t1-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi1_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t1-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi1_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t1-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi1_0 = (Ad[0,0]*tp1_0 + Ad[0,1]*tp1_1 + Ad[0,2]*tp1_2 + Ad[0,3]*tp1_3)
Phi1_1 = (Ad[1,0]*tp1_0 + Ad[1,1]*tp1_1 + Ad[1,2]*tp1_2 + Ad[1,3]*tp1_3)
Phi1_2 = (Ad[2,0]*tp1_0 + Ad[2,1]*tp1_1 + Ad[2,2]*tp1_2 + Ad[2,3]*tp1_3)
Phi1_3 = (Ad[3,0]*tp1_0 + Ad[3,1]*tp1_1 + Ad[3,2]*tp1_2 + Ad[3,3]*tp1_3)
Phi2_0 = 0
Phi2_1 = 0
Phi2_2 = 0
Phi2_3 = 0
if t2 < 0:
Phi2_0 = dAd[0,3]*t2 + Ad[0,3]
Phi2_1 = dAd[1,3]*t2 + Ad[1,3]
Phi2_2 = dAd[2,3]*t2 + Ad[2,3]
Phi2_3 = dAd[3,3]*t2 + Ad[3,3]
elif t2 > 1:
Phi2_0 = (3*Ad[0,0] + 2*Ad[0,1] + Ad[0,2])*(t2-1) + (Ad[0,0]+Ad[0,1]+Ad[0,2]+Ad[0,3])
Phi2_1 = (3*Ad[1,0] + 2*Ad[1,1] + Ad[1,2])*(t2-1) + (Ad[1,0]+Ad[1,1]+Ad[1,2]+Ad[1,3])
Phi2_2 = (3*Ad[2,0] + 2*Ad[2,1] + Ad[2,2])*(t2-1) + (Ad[2,0]+Ad[2,1]+Ad[2,2]+Ad[2,3])
Phi2_3 = (3*Ad[3,0] + 2*Ad[3,1] + Ad[3,2])*(t2-1) + (Ad[3,0]+Ad[3,1]+Ad[3,2]+Ad[3,3])
else:
Phi2_0 = (Ad[0,0]*tp2_0 + Ad[0,1]*tp2_1 + Ad[0,2]*tp2_2 + Ad[0,3]*tp2_3)
Phi2_1 = (Ad[1,0]*tp2_0 + Ad[1,1]*tp2_1 + Ad[1,2]*tp2_2 + Ad[1,3]*tp2_3)
Phi2_2 = (Ad[2,0]*tp2_0 + Ad[2,1]*tp2_1 + Ad[2,2]*tp2_2 + Ad[2,3]*tp2_3)
Phi2_3 = (Ad[3,0]*tp2_0 + Ad[3,1]*tp2_1 + Ad[3,2]*tp2_2 + Ad[3,3]*tp2_3)
t = Phi0_0*(Phi1_0*(Phi2_0*(coefs[i0+0,i1+0,i2+0]) + Phi2_1*(coefs[i0+0,i1+0,i2+1]) + Phi2_2*(coefs[i0+0,i1+0,i2+2]) + Phi2_3*(coefs[i0+0,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+0,i1+1,i2+0]) + Phi2_1*(coefs[i0+0,i1+1,i2+1]) + Phi2_2*(coefs[i0+0,i1+1,i2+2]) + Phi2_3*(coefs[i0+0,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+0,i1+2,i2+0]) + Phi2_1*(coefs[i0+0,i1+2,i2+1]) + Phi2_2*(coefs[i0+0,i1+2,i2+2]) + Phi2_3*(coefs[i0+0,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+0,i1+3,i2+0]) + Phi2_1*(coefs[i0+0,i1+3,i2+1]) + Phi2_2*(coefs[i0+0,i1+3,i2+2]) + Phi2_3*(coefs[i0+0,i1+3,i2+3]))) + Phi0_1*(Phi1_0*(Phi2_0*(coefs[i0+1,i1+0,i2+0]) + Phi2_1*(coefs[i0+1,i1+0,i2+1]) + Phi2_2*(coefs[i0+1,i1+0,i2+2]) + Phi2_3*(coefs[i0+1,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+1,i1+1,i2+0]) + Phi2_1*(coefs[i0+1,i1+1,i2+1]) + Phi2_2*(coefs[i0+1,i1+1,i2+2]) + Phi2_3*(coefs[i0+1,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+1,i1+2,i2+0]) + Phi2_1*(coefs[i0+1,i1+2,i2+1]) + Phi2_2*(coefs[i0+1,i1+2,i2+2]) + Phi2_3*(coefs[i0+1,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+1,i1+3,i2+0]) + Phi2_1*(coefs[i0+1,i1+3,i2+1]) + Phi2_2*(coefs[i0+1,i1+3,i2+2]) + Phi2_3*(coefs[i0+1,i1+3,i2+3]))) + Phi0_2*(Phi1_0*(Phi2_0*(coefs[i0+2,i1+0,i2+0]) + Phi2_1*(coefs[i0+2,i1+0,i2+1]) + Phi2_2*(coefs[i0+2,i1+0,i2+2]) + Phi2_3*(coefs[i0+2,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+2,i1+1,i2+0]) + Phi2_1*(coefs[i0+2,i1+1,i2+1]) + Phi2_2*(coefs[i0+2,i1+1,i2+2]) + Phi2_3*(coefs[i0+2,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+2,i1+2,i2+0]) + Phi2_1*(coefs[i0+2,i1+2,i2+1]) + Phi2_2*(coefs[i0+2,i1+2,i2+2]) + Phi2_3*(coefs[i0+2,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+2,i1+3,i2+0]) + Phi2_1*(coefs[i0+2,i1+3,i2+1]) + Phi2_2*(coefs[i0+2,i1+3,i2+2]) + Phi2_3*(coefs[i0+2,i1+3,i2+3]))) + Phi0_3*(Phi1_0*(Phi2_0*(coefs[i0+3,i1+0,i2+0]) + Phi2_1*(coefs[i0+3,i1+0,i2+1]) + Phi2_2*(coefs[i0+3,i1+0,i2+2]) + Phi2_3*(coefs[i0+3,i1+0,i2+3])) + Phi1_1*(Phi2_0*(coefs[i0+3,i1+1,i2+0]) + Phi2_1*(coefs[i0+3,i1+1,i2+1]) + Phi2_2*(coefs[i0+3,i1+1,i2+2]) + Phi2_3*(coefs[i0+3,i1+1,i2+3])) + Phi1_2*(Phi2_0*(coefs[i0+3,i1+2,i2+0]) + Phi2_1*(coefs[i0+3,i1+2,i2+1]) + Phi2_2*(coefs[i0+3,i1+2,i2+2]) + Phi2_3*(coefs[i0+3,i1+2,i2+3])) + Phi1_3*(Phi2_0*(coefs[i0+3,i1+3,i2+0]) + Phi2_1*(coefs[i0+3,i1+3,i2+1]) + Phi2_2*(coefs[i0+3,i1+3,i2+2]) + Phi2_3*(coefs[i0+3,i1+3,i2+3])))
values[n] = t
@njit(cache=True)
def vec_eval_cubic_spline_3_kernel(a, b, orders, coefs, points, values):
N = points.shape[0]
for n in range(N):
kernel(n, a, b, orders, coefs, points, values)
if __name__ == '__main__':
import numpy as np
d = 3
K = 50
N = 10**6
a = np.zeros(3)
b = np.ones(3)
orders = np.array([K for i in range(d)])
coeffs = np.random.random([k+2 for k in orders])
points = np.random.random((N,d)) # each line is a vector
points_c = points.T.copy() # each column is a vector
vals = np.zeros(N)
print("Interpolation comparison (d={}, K={}, N={})" .format(d,K,N))
import time
vec_eval_cubic_spline_3 (a,b,orders,coeffs,points,vals) # warmup
vec_eval_cubic_spline_3_inlined(a,b,orders,coeffs,points,vals) # warmup
vec_eval_cubic_spline_3_inlined_columns(a,b,orders,coeffs,points_c,vals) # warmup
vec_eval_cubic_spline_3_kernel (a,b,orders,coeffs,points,vals) # warmup
vec_eval_cubic_spline_3_inlined_lesswork(orders,coeffs,points,vals,Ad,dAd)
t1 = time.time()
vec_eval_cubic_spline_3(a,b,orders,coeffs,points,vals)
t2 = time.time()
vec_eval_cubic_spline_3_inlined(a,b,orders,coeffs,points,vals)
t3 = time.time()
vec_eval_cubic_spline_3_inlined_columns(a,b,orders,coeffs,points_c,vals)
t4 = time.time()
vec_eval_cubic_spline_3_kernel(a,b,orders,coeffs,points,vals)
t5 = time.time()
vec_eval_cubic_spline_3_inlined_lesswork(orders,coeffs,points,vals,Ad,dAd)
t6 = time.time()
print("one function call per point: {}".format(t2-t1))
print("inlined (points in rows): {}".format(t3-t2))
print("inlined (points in columns): {}".format(t4-t3))
print("kernel: {}".format(t5-t4))
print("less work: {}".format(t6-t5))