def test_multilinear_extrap():
import numpy as np
N = 100000
K = 10
d = 1
a = np.array([0.0] * d)
b = np.array([1.0] * d)
n = np.array([K] * d)
grid_u = ((0.0, 1.0, K), ) * d
from interpolation.cartesian import mlinspace
s = mlinspace(a, b, n)
f = lambda x: (x**2).sum(axis=1)
x = f(s)
v = x.reshape(n)
from interpolation.splines.eval_splines import eval_linear
pp = np.linspace(-0.5, 1.5, 100)[:, None]
from interpolation.splines.option_types import options
xx_ = eval_linear(grid_u, v, pp)
xx_cst = eval_linear(grid_u, v, pp, options.CONSTANT)
xx_lin = eval_linear(grid_u, v, pp, options.LINEAR)
xx_nea = eval_linear(grid_u, v, pp, options.NEAREST)
yy_ = np.array([eval_linear(grid_u, v, p_) for p_ in pp])
yy_cst = np.array(
[eval_linear(grid_u, v, p_, options.CONSTANT) for p_ in pp])
yy_lin = np.array(
[eval_linear(grid_u, v, p_, options.LINEAR) for p_ in pp])
yy_nea = np.array(
[eval_linear(grid_u, v, p_, options.NEAREST) for p_ in pp])
zz_ = xx_.copy() * 0
zz_cst = xx_cst.copy() * 0
zz_lin = xx_lin.copy() * 0
zz_nea = xx_nea.copy() * 0
print("Inplace")
eval_linear(grid_u, v, pp, zz_)
eval_linear(grid_u, v, pp, zz_cst, options.CONSTANT)
eval_linear(grid_u, v, pp, zz_lin, options.LINEAR)
eval_linear(grid_u, v, pp, zz_nea, options.NEAREST)
assert (abs(xx_ - yy_) + (abs(xx_ - zz_))).max() < 1e-10
assert (abs(xx_cst - yy_cst) + (abs(xx_cst - zz_cst))).max() < 1e-10
assert (abs(xx_lin - yy_lin) + (abs(xx_lin - zz_lin))).max() < 1e-10
assert (abs(xx_nea - yy_nea) + (abs(xx_nea - zz_nea))).max() < 1e-10
def nodes(grid):
from interpolation.cartesian import mlinspace
return mlinspace([g[0] for g in grid], [g[1] for g in grid],
[g[2] for g in grid])
from __future__ import division from numpy import * from interpolation.cartesian import mlinspace d = 2 # number of dimension Ng = 1000 # number of points on the grid K = int(Ng**(1 / d)) # nb of points in each dimension N = 10000 # nb of points to evaluate a = array([0.0] * d, dtype=float) b = array([1.0] * d, dtype=float) orders = array([K] * d, dtype=int) grid = mlinspace(a, b, orders) # single valued function to interpolate f = lambda vec: sqrt(vec.sum(axis=1)) # df # # vector valued function # g # single valued function to interpolate vals = f(grid) print(vals) mvals = concatenate([vals[:, None], vals[:, None]], axis=1) print(mvals.shape) # cubic # multilinear
import numpy as np N = 100000 K = 10 d = 1 a = np.array([0.0] * d) b = np.array([1.0] * d) n = np.array([K] * d) grid_u = ((0.0, 1.0, K), ) * d from interpolation.cartesian import mlinspace s = mlinspace(a, b, n) f = lambda x: (x**2).sum(axis=1) x = f(s) v = x.reshape(n) from interpolation.splines.eval_splines import eval_linear pp = np.linspace(-0.5, 1.5, 100)[:, None] from interpolation.splines.option_types import options xx_ = eval_linear(grid_u, v, pp) xx_cst = eval_linear(grid_u, v, pp, options.CONSTANT) xx_lin = eval_linear(grid_u, v, pp, options.LINEAR) xx_nea = eval_linear(grid_u, v, pp, options.NEAREST) yy_ = np.array([eval_linear(grid_u, v, p_) for p_ in pp]) yy_cst = np.array([eval_linear(grid_u, v, p_, options.CONSTANT) for p_ in pp]) yy_lin = np.array([eval_linear(grid_u, v, p_, options.LINEAR) for p_ in pp])
from __future__ import division from numpy import * from interpolation.cartesian import mlinspace d = 2 # number of dimension Ng = 1000 # number of points on the grid K = int(Ng ** (1 / d)) # nb of points in each dimension N = 10000 # nb of points to evaluate a = array([0.0] * d, dtype=float) b = array([1.0] * d, dtype=float) orders = array([K] * d, dtype=int) grid = mlinspace(a, b, orders) # single valued function to interpolate f = lambda vec: sqrt(vec.sum(axis=1)) # df # # vector valued function # g # single valued function to interpolate vals = f(grid) print(vals) mvals = concatenate([vals[:, None], vals[:, None]], axis=1) print(mvals.shape) # cubic