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utils.py
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import numpy as np
def infnorm(a):
return np.max(np.absolute(a))
def trilerp(u, i, j, k, fx, fy, fz):
return (1-fz) * ((1-fy) * ((1-fx)*u[i, j, k] + fx*u[i+1, j, k])
+ fy * ((1-fx)*u[i, j+1, k] + fx*u[i+1, j+1, k])) \
+ fz * ((1-fy) * ((1-fx)*u[i, j, k+1] + fx*u[i+1, j, k+1])
+ fy * ((1-fx)*u[i, j+1, k+1] + fx*u[i+1, j+1, k+1]))
# ===== trilinear interpolation ===== #
def bary_x(x, h):
overh = 1 / h
sx = x * overh
i = int(sx)
fx = sx - np.floor(sx)
return i, fx
def bary_x_center(x, h, nx):
overh = 1 / h
sx = x * overh
i = int(sx)
fx = sx - np.floor(sx)
if i < 0:
i, fx = 0, 0.0
elif i > nx - 2:
i = nx - 2
fx = 1.0
return i, fx
def bary_y(y, h):
overh = 1 / h
sy = y * overh
j = int(sy)
fy = sy - np.floor(sy)
return j, fy
def bary_y_center(y, h, ny):
overh = 1 / h
sy = y * overh
j = int(sy)
fy = sy - np.floor(sy)
if j < 0:
j, fy = 0, 0.0
elif j > ny - 2:
j = ny - 2
fy = 1.0
return j, fy
def bary_z(z, h):
overh = 1 / h
sz = z * overh
k = int(sz)
fz = sz - np.floor(sz)
return k, fz
def bary_z_center(z, h, nz):
overh = 1 / h
sz = z * overh
k = int(sz)
fz = sz - np.floor(sz)
if k < 0:
k, fz = 0, 0.0
elif k > nz - 2:
k = nz - 2
fz = 1.0
return k, fz