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# cython: profile=True
import numpy as np
cimport numpy as cnp
import cython
# Time evolution for the inner part of the grid
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cpdef evolve_inner(cnp.ndarray[cnp.double_t, ndim=2]u,
cnp.ndarray[cnp.double_t, ndim=2]u_previous,
double a, double dt, double dx2, double dy2):
"""Explicit time evolution.
u: new temperature field
u_previous: previous field
a: diffusion constant
dt: time step. """
cdef int nx = u.shape[0] - 2
cdef int ny = u.shape[1] - 2
cdef int i,j
# Multiplication is more efficient than division
cdef double dx2inv = 1. / dx2
cdef double dy2inv = 1. / dy2
for i in range(2, nx):
for j in range(2, ny):
u[i, j] = u_previous[i, j] + a * dt * ( \
(u_previous[i+1, j] - 2*u_previous[i, j] + \
u_previous[i-1, j]) * dx2inv + \
(u_previous[i, j+1] - 2*u_previous[i, j] + \
u_previous[i, j-1]) * dy2inv )
# Time evolution for the edges of the grid
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cpdef evolve_edges(cnp.ndarray[cnp.double_t, ndim=2]u,
cnp.ndarray[cnp.double_t, ndim=2]u_previous,
double a, double dt, double dx2, double dy2):
"""Explicit time evolution.
u: new temperature field
u_previous: previous field
a: diffusion constant
dt: time step
dx2: grid spacing squared, i.e. dx^2
dy2: -- "" -- , i.e. dy^2"""
cdef int nx = u.shape[0] - 2
cdef int ny = u.shape[1] - 2
cdef int i,j
# Multiplication is more efficient than division
cdef double dx2inv = 1. / dx2
cdef double dy2inv = 1. / dy2
j = 1
for i in range(1, nx+1):
u[i, j] = u_previous[i, j] + a * dt * ( \
(u_previous[i+1, j] - 2*u_previous[i, j] + \
u_previous[i-1, j]) * dx2inv + \
(u_previous[i, j+1] - 2*u_previous[i, j] + \
u_previous[i, j-1]) * dy2inv )
j = ny
for i in range(1, nx+1):
u[i, j] = u_previous[i, j] + a * dt * ( \
(u_previous[i+1, j] - 2*u_previous[i, j] + \
u_previous[i-1, j]) * dx2inv + \
(u_previous[i, j+1] - 2*u_previous[i, j] + \
u_previous[i, j-1]) * dy2inv )
i = 1
for j in range(1, ny+1):
u[i, j] = u_previous[i, j] + a * dt * ( \
(u_previous[i+1, j] - 2*u_previous[i, j] + \
u_previous[i-1, j]) * dx2inv + \
(u_previous[i, j+1] - 2*u_previous[i, j] + \
u_previous[i, j-1]) * dy2inv )
i = nx
for j in range(1, ny+1):
u[i, j] = u_previous[i, j] + a * dt * ( \
(u_previous[i+1, j] - 2*u_previous[i, j] + \
u_previous[i-1, j]) * dx2inv + \
(u_previous[i, j+1] - 2*u_previous[i, j] + \
u_previous[i, j-1]) * dy2inv )