箭头图箭头纵横比

我在使用Matplotlib的箭袋情节时遇到了一些问题 . 给定速度矢量场，我想在流线上绘制速度矢量 . 矢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http://www-pord.ucsd.edu/~matlab/stream.htm（我的很快将在GitHub上提供） .

使用其结果，我使用此代码：

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，但速度矢量与流函数不相符，正如预期的那样 . 使用精确的保存值，Matlab会生成一个箭头图，可以准确显示我想要的内容 . 在我的例子中，将宽高比设置为1可以得到所需的结果，但强制轴矩形具有特定的宽高比 .

ax = pylab.axes()
ax.set_aspect(1.)

我已经尝试过不同的参数，例如'units'，'angles'或'scale' .

是否有人知道如何制作适应画布宽高比并且仍然与我的轮廓线相切的箭头图，如预期的那样？

我期望得到与此类似的结果（注意向量与流线相切的方式）：

非常感谢！