问题

I can provide a translation of the code-related portions:

我有一个名为```res```的函数，它以某个```omega```变量的复杂值作为输入，并返回一个连分数残差的绝对值（也是复杂的）。

我想要测试```res```函数对各种omega值的反应，并查看哪些值产生最接近零的残差值。因此，我想要查看哪个omega对应于残差连分数的根。因此，我生成了以下omega列表：

```python
N = 400

omega = [complex(np.random.uniform(0.001, 15), np.random.uniform(0, 2)) for i in range(N)]

然后，我将每个omega[i]值应用于res函数。对于omega列表：

omega = [(8.89186304186803+1.8580361935398448j), (4.250554058118386+0.34692636983137204j),(13.77975011058525+0.4067498913305867j), (11.848491447761512+1.1353493824887473j), (5.368197310760776+1.603262808639006j), (7.953834937525846+0.31087387982821735j),
 (12.589975089023985+1.9010925629632527j),(0.8533967396680111+0.9083830823882479j),
 (11.966071152073017+1.7535358294965886j), (6.723597895069045+0.5943732982185757j)]

我得到了相应残差的绝对值：

list_res = [2.1663149855057022, 12.202467603015915, 13.105388388645999, 3.524702335556132, 5.007101216080126, 2.1989779961023457, 4.6753139694285775, 1.82871868615581, 3.8247209107872857, 2.977690850044372]

我想生成一个颜色图或密度图，其中包含omega值和相应残差的绝对值。我的目标是找到局部最小点（残差最接近零的点）。

我尝试使用spb库的plot_complex，但显然只能绘制符号函数。

我想制作一个类似下面的图。其中黑点是res最小的值。

Color plot

<details>
<summary>英文:</summary>

I have a ```res``` function that takes as input complex value of a certain ```omega``` variable and returns the absolute value of the residue (also complex) of a continued fraction.

I&#39;d like to test the ```res``` function for various omega values and see which of those values yields a residual value closest to zero. So I would see which omega corresponds, which would be, in a sense, the root of the equation for the residue of the continued function. Therefore, I generated a list of omegas as follows:

N = 400

omega = [complex(np.random.uniform(0.001, 15), np.random.uniform(0, 2)) for i in range(N)]

And I imposed each ```omega[i]``` value on the ```res``` function. Truncating the lists, for the omega list

omega = [(8.89186304186803+1.8580361935398448j), (4.250554058118386+0.34692636983137204j),(13.77975011058525+0.4067498913305867j), (11.848491447761512+1.1353493824887473j), (5.368197310760776+1.603262808639006j), (7.953834937525846+0.31087387982821735j),
(12.589975089023985+1.9010925629632527j),(0.8533967396680111+0.9083830823882479j),
(11.966071152073017+1.7535358294965886j), (6.723597895069045+0.5943732982185757j)]

I got the following the absolute value of the corresponding residuals

list_res = [2.1663149855057022, 12.202467603015915, 13.105388388645999, 3.524702335556132, 5.007101216080126, 2.1989779961023457, 4.6753139694285775, 1.82871868615581, 3.8247209107872857, 2.977690850044372]

I want to generate a color plot or density plot with the omega values and the respective absolute values of the residual. The idea is to locate the local minimum points (the points where the residual is closest to zero)



I tried using ```plot_comples``` from the ```spb``` library. But apparently you can only plot symbolic functions.

I would like to make a plot similar to the plot below. Where the black dots are the values ​​where ```res``` is minimum.

[Color plot][1]


  [1]: https://i.stack.imgur.com/dDK3b.png

</details>


# 答案1
**得分**: 1

这是[`spb`](https://sympy-plot-backends.readthedocs.io/en/latest/)创建这种类型的可视化的方式：

1. 在复平面中创建一组角速度（omega）值的网格。
2. 在该复杂网格上评估函数。
3. 计算结果的幅值，其范围从0到（可能）无穷大。通常数值范围很大，因此绘制幅值不是一个好主意，因为会得到难以理解的图像...
4. 相反，我们使用以下公式计算亮度：`b = m / (m + 1)`，其中`m`是幅值。请注意，当`m=0`时，`b`为零，当`m`趋近于无穷大时，`b`趋近于一。
5. 绘制亮度。

这是一个示例：

```py
import numpy as np
import matplotlib.pyplot as plt

func = lambda w: np.sin(w**2)
n = 200j
re_w, im_w = np.mgrid[-3:3:n, -3:3:n]
w = re_w + 1j * im_w
res = func(w)
mag = np.absolute(res)
brightness = mag / (mag + 1)

fig, ax = plt.subplots()
img = ax.imshow(brightness, cmap="gray", vmin=brightness.min(), vmax=brightness.max())
cbar = fig.colorbar(img, label="brightness")

import numpy as np
import matplotlib.pyplot as plt

func = lambda w: np.sin(w**2)
n = 200j
re_w, im_w = np.mgrid[-3:3:n, -3:3:n]
w = re_w + 1j * im_w
res = func(w)
mag = np.absolute(res)
brightness = mag / (mag + 1)

fig, ax = plt.subplots()
img = ax.imshow(brightness, cmap="gray", vmin=brightness.min(), vmax=brightness.max())
cbar = fig.colorbar(img, label="brightness")