python - 伊辛模型 : How to shorten simulation time?

Question

我正在模拟 Ising Model使用简单的编码结构来处理尺寸大于 3 的铁磁体，但在效率方面存在一些问题。在我的代码中，有一个特定的函数是瓶颈。

在模拟过程中，需要找到所谓的给定站点的最近邻居。例如，在 2D Ising 模型中，自旋占据每个点的晶格，用两个数字表示:(x,y)。 (x,y)处的点的最近邻就是四个相邻的值，即(x+1,y),(x-1,y),(x,y+1),(x,y-1) .在 5D 中，某些格点的自旋具有坐标 (a,b,c,d,e) 和 10 个最近的邻居，形式与以前相同，但元组中的每个点。

现在这是给出以下输入的代码:

"site_i is a random value between 0 and n-1 denoting the site of the ith spin"
"coord is an array of size (n**dim,dim) that contains the coordinates of ever spin"
"spins is an array of shape (n**dim,1) that contains the spin values (-1 or 1)"
"n is the lattice size and dim is the dimensionality"
"neighbor_coupling is the number that tells the function to return the neighbor spins that are one spacing away, two spacing away, etc."

def calc_neighbors(site_i,coord,spins,n,dim,neighbor_coupling):
    # Extract all nearest neighbors
    # Obtain the coordinates of each nearest neighbor
    # How many neighbors to extract
    num_NN = 2*dim
    # Store the results in a result array 
    result_coord = np.zeros((num_NN,dim))
    result_spins = np.zeros((num_NN,1))
    # Get the coordinates of the ith site
    site_coord = coord[site_i]
    # Run through the + and - for each scalar value in the vector in site_coord
    count = 0
    for i in range(0,dim):
        assert count <= num_NN, "Accessing more than nearest neighbors values."
        site_coord_i = site_coord[i]
        plus = site_coord_i + neighbor_coupling
        minus = site_coord_i - neighbor_coupling

        # Implement periodic boundaries
        if (plus > (n-1)): plus = plus - n
        if (minus < 0): minus = n - np.abs(minus)

        # Store the coordinates
        result_coord[count] = site_coord
        result_coord[count][i] = minus
        # Store the spin value
        spin_index = np.where(np.all(result_coord[count]==coord,axis=1))[0][0]
        result_spins[count] = spins[spin_index]
        count = count + 1

        # Store the coordinates
        result_coord[count] = site_coord
        result_coord[count][i] = plus
        # Store the spin value
        spin_index = np.where(np.all(result_coord[count]==coord,axis=1))[0][0]
        result_spins[count] = spins[spin_index]
        count = count + 1 

我真的不知道如何才能让它更快，但它会有很大帮助。也许是一种不同的存储方式？

Answer 1

不是答案，只是一些纠正的建议:当您尝试记录计算的每一步时，会进行大量复制。在不牺牲这一点的情况下，您可以删除 site_coord_i，然后

    # New coords, implement periodic boundaries
    plus = (site_coord[i] + neighbor_coupling) % n
    minus = (site_coord[i] - neighbor_coupling + n) % n

这避免了中间步骤(“如果...”)。另一个建议是推迟使用子数组，直到您真正需要它为止:

    # Store the coordinates
    rcc = site_coord
    rcc[i] = plus
    # Store the spin value
    spin_index = np.where(np.all(rcc==coord,axis=1))[0][0]
    result_spins[count] = spins[spin_index]
    result_coord[count] = rcc
    count += 1

目标是减少比较中使用的变量的维数，并优先使用局部变量。