我正在寻找一种Pythonic的方法来获取表示为列表的（正方形）矩阵的所有对角线。
假设我有以下矩阵：
matrix = [[-2, 5, 3, 2],
[ 9, -6, 5, 1],
[ 3, 2, 7, 3],
[-1, 8, -4, 8]]
然后处理大对角线就容易了：
l = len(matrix[0])
print([matrix[i][i] for i in range(l)]) # [-2, -6, 7, 8]
print([matrix[l-1-i][i] for i in range(l-1,-1,-1)]) # [ 2, 5, 2, -1]
但我不知道如何生成所有的对角线。我需要的输出结果是：
[[-2], [9, 5], [3,-6, 3], [-1, 2, 5, 2], [8, 7, 1], [-4, 3], [8],
[2], [3,1], [5, 5, 3], [-2, -6, 7, 8], [9, 2, -4], [3, 8], [-1]]
可能有更好的方法在NumPy中实现，但我还不太熟悉它：
import numpy as np
matrix = np.array(
[[-2, 5, 3, 2],
[ 9, -6, 5, 1],
[ 3, 2, 7, 3],
[-1, 8, -4, 8]])
diags = [matrix[::-1,:].diagonal(i) for i in range(-3,4)]
diags.extend(matrix.diagonal(i) for i in range(3,-4,-1))
print [n.tolist() for n in diags]
[[-2], [9, 5], [3, -6, 3], [-1, 2, 5, 2], [8, 7, 1], [-4, 3], [8], [2], [3, 1], [5, 5, 3], [-2, -6, 7, 8], [9, 2, -4], [3, 8], [-1]]
编辑：更新为适用于任何矩阵大小的通用方法。
import numpy as np
# Alter dimensions as needed
x,y = 3,4
# create a default array of specified dimensions
a = np.arange(x*y).reshape(x,y)
print a
print
# a.diagonal returns the top-left-to-lower-right diagonal "i"
# according to this diagram:
#
# 0 1 2 3 4 ...
# -1 0 1 2 3
# -2 -1 0 1 2
# -3 -2 -1 0 1
# :
#
# You wanted lower-left-to-upper-right and upper-left-to-lower-right diagonals.
#
# The syntax a[slice,slice] returns a new array with elements from the sliced ranges,
# where "slice" is Python's [start[:stop[:step]] format.
# "::-1" returns the rows in reverse. ":" returns the columns as is,
# effectively vertically mirroring the original array so the wanted diagonals are
# lower-right-to-uppper-left.
#
# Then a list comprehension is used to collect all the diagonals. The range
# is -x+1 to y (exclusive of y), so for a matrix like the example above
# (x,y) = (4,5) = -3 to 4.
diags = [a[::-1,:].diagonal(i) for i in range(-a.shape[0]+1,a.shape[1])]
# Now back to the original array to get the upper-left-to-lower-right diagonals,
# starting from the right, so the range needed for shape (x,y) was y-1 to -x+1 descending.
diags.extend(a.diagonal(i) for i in range(a.shape[1]-1,-a.shape[0],-1))
# Another list comp to convert back to Python lists from numpy arrays,
# so it prints what you requested.
print [n.tolist() for n in diags]
[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
[[0], [4, 1], [8, 5, 2], [9, 6, 3], [10, 7], [11], [3], [2, 7], [1, 6, 11], [0, 5, 10], [4, 9], [8]]
Column = x Row = y F-Diag = x+y B-Diag = x-y B-Diag` = x-y-MIN
| 0 1 2 | 0 1 2 | 0 1 2 | 0 1 2 | 0 1 2
--|--------- --|--------- --|--------- --|--------- --|---------
0 | 0 1 2 0 | 0 0 0 0 | 0 1 2 0 | 0 1 2 0 | 2 3 4
1 | 0 1 2 1 | 1 1 1 1 | 1 2 3 1 |-1 0 1 1 | 1 2 3
2 | 0 1 2 2 | 2 2 2 2 | 2 3 4 2 |-2 -1 0 2 | 0 1 2
test = [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
max_col = len(test[0])
max_row = len(test)
cols = [[] for _ in range(max_col)]
rows = [[] for _ in range(max_row)]
fdiag = [[] for _ in range(max_row + max_col - 1)]
bdiag = [[] for _ in range(len(fdiag))]
min_bdiag = -max_row + 1
for x in range(max_col):
for y in range(max_row):
cols[x].append(test[y][x])
rows[y].append(test[y][x])
fdiag[x+y].append(test[y][x])
bdiag[x-y-min_bdiag].append(test[y][x])
print(cols)
print(rows)
print(fdiag)
print(bdiag)
这将打印
[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
[[1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12]]
[[1], [2, 4], [3, 5, 7], [6, 8, 10], [9, 11], [12]]
[[10], [7, 11], [4, 8, 12], [1, 5, 9], [2, 6], [3]]
from collections import defaultdict
def groups(data, func):
grouping = defaultdict(list)
for y in range(len(data)):
for x in range(len(data[y])):
grouping[func(x, y)].append(data[y][x])
return list(map(grouping.get, sorted(grouping)))
test = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
cols = groups(test, lambda x, y: x)
rows = groups(test, lambda x, y: y)
fdiag = groups(test, lambda x, y: x + y)
bdiag = groups(test, lambda x, y: x - y)
从上向右倾斜的对角线开始。
如果 (x,y) 是矩阵内的一个矩形坐标，您需要将其转换为/从一个坐标系 (p,q)，其中 p 是对角线的数量，q 是沿对角线的索引。 (因此，p=0 是 [-2] 对角线，p=1 是 [9,5] 对角线，p=2 是 [3,-6,3] 对角线，依此类推。)
要将 (p,q) 转换为 (x,y)，可以使用以下公式:
x = q
y = p - q
尝试输入p和q的值，以查看它是如何工作的。
现在，您只需循环... 对于从0到2N-1的p和从max(0,p-N+1)到min(p,N-1)的q。将p、q转换为x、y并打印出来。
然后对于其他对角线，重复循环但使用不同的转换：
x = N - 1 - q
y = p - q
(这实际上只是将矩阵左右翻转。)
抱歉，我并没有在Python中编写这个代码。 :-)
我首先编写了简单的函数来复制任何矩形矩阵的行或列。
def get_rows(grid):
return [[c for c in r] for r in grid]
def get_cols(grid):
return zip(*grid)
通过这两个函数，我可以通过在每行的开头/结尾添加递增/递减的缓冲区来得到对角线。然后我获取该缓冲网格的列，然后在每个列上移除缓冲区。
1 2 3 |X|X|1|2|3| | | |1|2|3|
4 5 6 => |X|4|5|6|X| => | |4|5|6| | => [[7],[4,8],[1,5,9],[2,6],[3]]
7 8 9 |7|8|9|X|X| |7|8|9| | |
.
def get_backward_diagonals(grid):
b = [None] * (len(grid) - 1)
grid = [b[i:] + r + b[:i] for i, r in enumerate(get_rows(grid))]
return [[c for c in r if c is not None] for r in get_cols(grid)]
def get_forward_diagonals(grid):
b = [None] * (len(grid) - 1)
grid = [b[:i] + r + b[i:] for i, r in enumerate(get_rows(grid))]
return [[c for c in r if c is not None] for r in get_cols(grid)]
最近我不得不重新发明这个轮子。以下是一种易于重用/扩展的方法，用于查找正方形列表中的对角线：
def get_diagonals(grid, bltr = True):
dim = len(grid)
assert dim == len(grid[0])
return_grid = [[] for total in xrange(2 * len(grid) - 1)]
for row in xrange(len(grid)):
for col in xrange(len(grid[row])):
if bltr: return_grid[row + col].append(grid[col][row])
else: return_grid[col - row + (dim - 1)].append(grid[row][col])
return return_grid
那么设置00 01 02 03
10 11 12 13
20 21 22 23
30 31 32 33
bltr = True（默认值）将返回从左下到右上的对角线，即：00 # row + col == 0
10 01 # row + col == 1
20 11 02 # row + col == 2
30 21 12 03 # row + col == 3
31 22 13 # row + col == 4
32 23 # row + col == 5
33 # row + col == 6
将bltr = False，返回从左下到右上的对角线，即：
30 # (col - row) == -3
20 31 # (col - row) == -2
10 21 32 # (col - row) == -1
00 11 22 33 # (col - row) == 0
01 12 23 # (col - row) == +1
02 13 # (col - row) == +2
03 # (col - row) == +3
from collections import defaultdict
有一种叫做defaultdict的方法，它是从collections模块导入的，用于创建字典，如果你不知道将要拥有的键。
我们在以下情况下使用它：
导入后，您可以运行以下代码并检查。
rows,cols = 3,3
matrix = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
diagonal1 = defaultdict(list) # For the top right to bottom left
diagonal2 = defaultdict(list) # For the top left to bottom right
for i in range(rows):
for j in range(cols):
diagonal1[i-j].append(matrix[i][j])
diagonal2[i+j].append(matrix[i][j])
print(diagonal1,'\n',diagonal2)
list参数将创建一个特定键的值列表。
输出如下：
defaultdict(<class 'list'>, {0: [1, 5, 9], -1: [2, 6], -2: [3], 1: [4, 8], 2: [7]})
defaultdict(<class 'list'>, {0: [1], 1: [2, 4], 2: [3, 5, 7], 3: [6, 8], 4: [9]})
matrix = [[11, 2, 4],[4, 5, 6],[10, 8, -12]]
# only works for diagnoals of equal width and height
def forward_diagonal(matrix):
if not isinstance(matrix, list):
raise TypeError("Must be of type list")
results = []
x = 0
for k, row in enumerate(matrix):
# next diag is (x + 1, y + 1)
for i, elm in enumerate(row):
if i == 0 and k == 0:
results.append(elm)
break
if (x + 1 == i):
results.append(elm)
x = i
break
return results
print 'forward diagnoals', forward_diagonal(matrix)
基于Nemo上面的答案的代码：
def print_diagonals(matrix):
n = len(matrix)
diagonals_1 = [] # lower-left-to-upper-right diagonals
diagonals_2 = [] # upper-left-to-lower-right diagonals
for p in range(2*n-1):
diagonals_1.append([matrix[p-q][q] for q in range(max(0, p - n + 1), min(p, n - 1) + 1)])
diagonals_2.append([matrix[n-p+q-1][q] for q in range(max(0, p - n + 1), min(p, n - 1) + 1)])
print("lower-left-to-upper-right diagonals: ", diagonals_1)
print("upper-left-to-lower-right diagonals: ", diagonals_2)
print_diagonals([
[1, 2, 1, 1],
[1, 1, 4, 1],
[1, 3, 1, 6],
[1, 7, 2, 5],
])
lower-left-to-upper-right diagonals: [[1], [1, 2], [1, 1, 1], [1, 3, 4, 1], [7, 1, 1], [2, 6], [5]]
upper-left-to-lower-right diagonals: [[1], [1, 7], [1, 3, 2], [1, 1, 1, 5], [2, 4, 6], [1, 1], [1]]
matrix = [[-2, 5, 3, 2],
[ 9, -6, 5, 1],
[ 3, 2, 7, 3],
[-1, 8, -4, 8]]
import itertools as it
def show_diagonals(alist):
# get row/col lenght
a = len(alist)
# creating a fliped matrix
rlist = []
for r in alist:
new = r.copy()
new.reverse()
rlist.append(new)
flatten_list = list(it.chain.from_iterable(alist))
flatten_rlist = list(it.chain.from_iterable(rlist))
b = len(flatten_list)
first_diag = list(it.islice(flatten_list, 0, b+1, a+1))
second_diag = list(it.islice(flatten_rlist, 0, b+1, a+1))
return first_diag, second_diag
a, b = show_diagonals(matrix)
mat = [[-2, 5, 3, 2],
[ 9, -6, 5, 1],
[ 3, 2, 7, 3],
[-1, 8, -4, 8]]
dct = dict()
for i in range(len(mat)-1,-len(mat[0]),-1):
dct[i] = []
for i in range(len(mat)):
for j in range(len(mat[0])):
dct[i-j].append(mat[i][j])
print(dct)
输出：
{3: [-1], 2: [3, 8], 1: [9, 2, -4], 0: [-2, -6, 7, 8], -1: [5, 5, 3], -2: [3, 1], -3: [2]}
MIN是B-Diag中最小值的常量。0 - 0 - (-2) == 2。这使您可以在列表上下文中使用基于零的数组索引来排列值。 - flakes