如何将非矢量化 for 循环转换为矢量化格式？

Question

我正在尝试将 for 循环（如下）转换为矢量化格式，目的是提高计算速度。

a1,b1,c1的值都是常量。

如何将 for 循环转换为矢量化格式？

注：

虽然我知道将 for 循环转换为矢量化格式会提高效率，但我希望通过更改 while 和 for 循环进一步提高速度的指示

如果阅读 material（或其他资源）可以提供将非矢量化代码转换为矢量化代码的背景知识，我将不胜感激

 T = np.zeros((int(time/dt)+2, N+1)) #setting up Temperature - Position array

 n = 0 #setting position equal to 0 (initial position)
 # Initial Condition
 T[n, :] = T0 #setting T = T0 at t=0 for all positions (initial temperature array)
 # Boundary Condition
 T[:, 0] =  T_in #setting all times at n=0 to inlet fluid temperature

 while t <= time: #running simulation until required simulation time
     for i in range(1,N): #solving for temperature at every increment
         T[n+1,i] = T[n,i] + a1*T[n,i+1] - b1*T[n,i] + c1*T[n,i-1] #using three nodes (i-1,i,i+1) at time n to solve for 
                                                                   #temperature at n+1, position i

     T[n+1,-1]  = T[n+1,-2] #setting final position temperature equal to second last temperature
     T[n+1, 0] =  T_in #resetting position 0 as inlet fluid temperature
     n = n + 1 #incrementing position
     t = t + dt #incrementing time

Answer 1

你可以试试这个：

T = np.empty((int(time / dt), N + 1))  #setting up Temperature - Position array

# Initial Condition
T[0, :] = T0  
# Boundary Condition
T[:, 0] = T_in

for n in range(0, T.shape[0] - 1):
    T[n + 1, 1:N] = c1 * T[n, :N - 1] + (1 - b1) * T[n, 1:N] + a1 * T[n, 2:]
    T[n + 1, -1] = T[n + 1, -2]

不需要 while 循环。数组 T 的行数是这样选择的，当您遍历该数组的所有行时，条件 t <= time 将得到满足。我没有看到避免剩余 for 循环的简单方法，因为您正在递归计算每一行。

如何将非矢量化 for 循环转换为矢量化格式？

How to convert non-vectorized for loop to vectorized format?

python

vectorization