我对 Matplotlib 的 quiver plot 有一些问题。给定一个速度矢量场，我想在流线顶部绘制速度矢量。向量与预期的流函数不相切。
为了计算流函数，我使用了 Pankratov 博士的 Matlab 代码的 Python 翻译版本，该代码位于http://www-pord.ucsd.edu/~matlab/stream.htm（我的将很快在 GitHub 上可用）。
使用它的结果，我使用以下代码：
import numpy
import pylab
# Regular grid coordineates, velocity field and stream function
x, y = numpy.meshgrid(numpy.arange(0, 21), numpy.arange(0, 11))
u = numpy.array([[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 29, 30],
[ 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29],
[ 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28],
[ 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27],
[ 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26],
[ 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25],
[ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24],
[ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23],
[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22],
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21],
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20]])
v = numpy.array([[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20],
[ -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19],
[ -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18],
[ -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17],
[ -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15, 16],
[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15],
[ -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13, 14],
[ -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12, 13],
[ -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12],
[ -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11],
[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2,
3, 4, 5, 6, 7, 8, 9, 10]])
psi = numpy.array([[ 0. , 0.5, 2. , 4.5, 8. , 12.5, 18. , 24.5,
32. , 40.5, 50. , 60.5, 72. , 84.5, 98. , 112.5,
128. , 144.5, 162. , 180.5, 200. ],
[ -9.5, -10. , -9.5, -8. , -5.5, -2. , 2.5, 8. ,
14.5, 22. , 30.5, 40. , 50.5, 62. , 74.5, 88. ,
102.5, 118. , 134.5, 152. , 170.5],
[ -18. , -19.5, -20. , -19.5, -18. , -15.5, -12. , -7.5,
-2. , 4.5, 12. , 20.5, 30. , 40.5, 52. , 64.5,
78. , 92.5, 108. , 124.5, 142. ],
[ -25.5, -28. , -29.5, -30. , -29.5, -28. , -25.5, -22. ,
-17.5, -12. , -5.5, 2. , 10.5, 20. , 30.5, 42. ,
54.5, 68. , 82.5, 98. , 114.5],
[ -32. , -35.5, -38. , -39.5, -40. , -39.5, -38. , -35.5,
-32. , -27.5, -22. , -15.5, -8. , 0.5, 10. , 20.5,
32. , 44.5, 58. , 72.5, 88. ],
[ -37.5, -42. , -45.5, -48. , -49.5, -50. , -49.5, -48. ,
-45.5, -42. , -37.5, -32. , -25.5, -18. , -9.5, 0. ,
10.5, 22. , 34.5, 48. , 62.5],
[ -42. , -47.5, -52. , -55.5, -58. , -59.5, -60. , -59.5,
-58. , -55.5, -52. , -47.5, -42. , -35.5, -28. , -19.5,
-10. , 0.5, 12. , 24.5, 38. ],
[ -45.5, -52. , -57.5, -62. , -65.5, -68. , -69.5, -70. ,
-69.5, -68. , -65.5, -62. , -57.5, -52. , -45.5, -38. ,
-29.5, -20. , -9.5, 2. , 14.5],
[ -48. , -55.5, -62. , -67.5, -72. , -75.5, -78. , -79.5,
-80. , -79.5, -78. , -75.5, -72. , -67.5, -62. , -55.5,
-48. , -39.5, -30. , -19.5, -8. ],
[ -49.5, -58. , -65.5, -72. , -77.5, -82. , -85.5, -88. ,
-89.5, -90. , -89.5, -88. , -85.5, -82. , -77.5, -72. ,
-65.5, -58. , -49.5, -40. , -29.5],
[ -50. , -59.5, -68. , -75.5, -82. , -87.5, -92. , -95.5,
-98. , -99.5, -100. , -99.5, -98. , -95.5, -92. , -87.5,
-82. , -75.5, -68. , -59.5, -50. ]])
# The plots!
pylab.close('all')
pylab.ion()
pylab.figure(figsize=[8, 8])
pylab.contour(x, y, psi, 20, colors='k', linestyles='-', linewidth=1.0)
pylab.quiver(x, y, u, v, angles='uv', scale_units='xy', scale=10)
ax = pylab.axes()
ax.set_aspect(1.)
产生以下结果来说明我的问题。
显然计算很好，但速度矢量并不像预期的那样与流函数相切。使用准确的保存值，Matlab 会生成一个箭袋图，它准确地显示了我想要的内容。在我的情况下，将纵横比设置为 1 会给我想要的结果，但会强制轴矩形具有特定的纵横比。
ax = pylab.axes()
ax.set_aspect(1.)
我已经尝试过不同的参数，如“单位”、“角度”或“比例”，但均未成功。
有谁知道如何制作适合画布纵横比并且仍然与我的轮廓线相切的颤抖图，正如预期的那样？
我希望得到与此类似的结果（注意向量如何与流线相切）：
非常感谢！