用plt在热图上绘制渐变箭头

Question

我正在尝试绘制箭头以可视化热图上的渐变。这是我到目前为止的代码：

import matplotlib.pyplot as plt
import numpy as np
function_to_plot = lambda x, y: x + y ** 2
horizontal_min, horizontal_max, horizontal_stepsize = 0, 3, 0.3
vertical_min, vertical_max, vertical_stepsize = 0, 3, 0.6

xv, yv = np.meshgrid(np.arange(horizontal_min, horizontal_max, horizontal_stepsize), 
                     np.arange(vertical_min, vertical_max, vertical_stepsize))

result_matrix = function_to_plot(xv, yv)
xd, yd = np.gradient(result_matrix)

def func_to_vectorize(x, y, dx, dy, scaling=1):
    plt.arrow(x + horizontal_stepsize/2, y + vertical_stepsize/2, dx*scaling, dy*scaling, fc="k", ec="k", head_width=0.1, head_length=0.1)

vectorized_arrow_drawing = np.vectorize(func_to_vectorize)

plt.imshow(result_matrix, extent=[horizontal_min, horizontal_max, vertical_min, vertical_max])
vectorized_arrow_drawing(xv, yv, xd, yd, 1)
plt.colorbar()
plt.show()

这是结果图：

我期望箭头指向具有最大值的矩形，但事实并非如此。我想念什么？

Answer 1

1. 看起来np.gradient()返回的x值之前的 y值
2. 颜色也似乎不正确，因为图形上下文的y值已反转。因此，我在绘制过程中使用了np.flip(result_matrix,0)
3. 最后，我注意到当stepsize不能均匀划分区域时，绘制箭头时会出现故障，此外，网格未与框的中心对齐。我已经在以下代码中修复了这两个问题：

这是我用来生成图形的代码：

import matplotlib.pyplot as plt
import numpy as np
import math
function_to_plot = lambda x, y: x**2 + y**2
horizontal_min, horizontal_max, horizontal_stepsize = -2, 3, 0.3
vertical_min, vertical_max, vertical_stepsize = -1, 4, 0.5

horizontal_dist = horizontal_max-horizontal_min
vertical_dist = vertical_max-vertical_min

horizontal_stepsize = horizontal_dist / float(math.ceil(horizontal_dist/float(horizontal_stepsize)))
vertical_stepsize = vertical_dist / float(math.ceil(vertical_dist/float(vertical_stepsize)))

xv, yv = np.meshgrid(np.arange(horizontal_min, horizontal_max, horizontal_stepsize),
                     np.arange(vertical_min, vertical_max, vertical_stepsize))
xv+=horizontal_stepsize/2.0
yv+=vertical_stepsize/2.0

result_matrix = function_to_plot(xv, yv)
yd, xd = np.gradient(result_matrix)

def func_to_vectorize(x, y, dx, dy, scaling=0.01):
    plt.arrow(x, y, dx*scaling, dy*scaling, fc="k", ec="k", head_width=0.06, head_length=0.1)

vectorized_arrow_drawing = np.vectorize(func_to_vectorize)

plt.imshow(np.flip(result_matrix,0), extent=[horizontal_min, horizontal_max, vertical_min, vertical_max])
vectorized_arrow_drawing(xv, yv, xd, yd, 0.1)
plt.colorbar()
plt.show()