python - Python 3.x 在矩阵中查找鞍点

Question

这是我的矩阵：

1  1  2  5  6  1     
5  6  8  5  6  7
10 12 10 12 11 11
8 10  5  6  8  9
6  5 10 12 15 19

我想找到它的鞍点。

鞍点的坐标应该是：

2 0 
2 2
0 4

所以我的问题是。有人可以告诉我，如何用 Python 做这个吗？:)

Answer 1

这是一种 Python 方法，它组装所有行/列最小值和最大值的索引列表，然后使用集合操作来查找它们的交集：

def allSaddles(matrix):
    rowmins = []
    rowmaxs = []
    colmins = []
    colmaxs = []

    for i,row in enumerate(matrix):
        m = min(row)
        M = max(row)
        for j,x in enumerate(row):
            if x == m: rowmins.append((i,j))
            if x == M: rowmaxs.append((i,j))

    t = [list(column) for column in zip(*matrix)] #transpose of matrix

    for j,col in enumerate(t): 
        m = min(col)
        M = max(col)
        for i,x in enumerate(col):
            if x == m: colmins.append((i,j))
            if x == M: colmaxs.append((i,j))

    return (set(rowmins) & set(colmaxs)) | (set(rowmaxs) & set(colmins))

M = [[1,1,2,5,6,1],    
[5,6,8,5,6,7],
[10,12,10,12,11,11],
[8,10,5,6,8,9],
[6,5,10,12,15,19]]

print(allSaddles(M))

输出：{(0, 4), (2, 0), (2, 2)}

Answer 2

这是我在 python 中的鞍点查找器

import numpy as np


def is_saddle(row, column, *args):
    index = 0
    size = row * column
    matrix = np.arange(size).reshape(row, column)
    for i in range(row):
        for j in range(column):
            matrix[i][j] = args[0][index]
            index = index + 1
    print(matrix)
    for item_row in matrix:
        column_number = 0
        min_item = np.amin(item_row)
        for i in range(len(item_row)):
            if min_item == item_row[i]:
                row_number = i
                reversed_matrix = matrix.transpose()
                max_item = np.amax(reversed_matrix[row_number])
                if max_item == min_item:
                    print("saddle point found : {}".format(min_item))

    return matrix


row = input("enter row")
column = input("enter column")
matrix = input("enter the matrix items")
is_saddle(row, column, matrix)

输入样本：行 = 2，列 = 3，矩阵 = (1,2,3,4,5,6)

Answer 3

这是一种不同的制作方法。请注意，输入矩阵是 a np.ndarray：

def saddles(mat : np.ndarray) -> list:

    """
    returns the list of all saddle points of the input matrix

    """


    (N, M) = mat.shape

    jMax = np.argmax(mat, axis = 1) # index of col for max in each row
    iMin = np.argmin(mat, axis = 0) # index of row for min in each col

    IJMax = [(i,jMax[i]) for i in range(N)] # list of indexes of max of each row
    IJMin = [(iMin[j],j) for j in range(M)] # list of indexes of min of each col

    maxRowMinCol = list(set(IJMax) & set(IJMin)) # max of row, min of col


    iMax = np.argmax(mat, axis = 0) # index of row for max in each col
    jMin = np.argmin(mat, axis = 1) # index of col for min in each row

    IJMax = [(iMax[j],j) for j in range(M)] # list of indexes of max of each col
    IJMin = [(i,jMin[i]) for i in range(N)] # list of indexes of min of each row

    minRowMaxCol = list(set(IJMax) & set(IJMin)) # min of row, max of col


    return maxRowMinCol + minRowMaxCol