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mindspore2022/tests/st/ops/gpu/test_tensordot_op.py

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  1. # Copyright 2020-2021 Huawei Technologies Co., Ltd

  2. #

  3. # Licensed under the Apache License, Version 2.0 (the "License");

  4. # you may not use this file except in compliance with the License.

  5. # You may obtain a copy of the License at

  6. #

  7. # http://www.apache.org/licenses/LICENSE-2.0

  8. #

  9. # Unless required by applicable law or agreed to in writing, software

  10. # distributed under the License is distributed on an "AS IS" BASIS,

  11. # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

  12. # See the License for the specific language governing permissions and

  13. # limitations under the License.

  14. # ============================================================================

  15. 

  16. import pytest

  17. import numpy as np

  18. 

  19. import mindspore

  20. from mindspore import Tensor

  21. import mindspore.nn as nn

  22. import mindspore.context as context

  23. from mindspore.ops import composite as C

  24. 

  25. 

  26. class NetTensorDot(nn.Cell):

  27.     def __init__(self, axes):

  28.         super(NetTensorDot, self).__init__()

  29.         self.axes = axes

  30. 

  31.     def construct(self, x, y):

  32.         return C.tensor_dot(x, y, self.axes)

  33. 

  34. 

  35. class GradNetwork(nn.Cell):

  36.     def __init__(self, network):

  37.         super(GradNetwork, self).__init__()

  38.         self.grad = C.GradOperation(get_all=True, sens_param=True)

  39.         self.network = network

  40. 

  41.     def construct(self, input_data_a, input_data_b, sens):

  42.         gout = self.grad(self.network)(input_data_a, input_data_b, sens)

  43.         return gout

  44. 

  45. 

  46. @pytest.mark.level0

  47. @pytest.mark.platform_x86_gpu_training

  48. @pytest.mark.env_onecard

  49. def test_tensor_dot_fp32():

  50.     context.set_context(mode=context.PYNATIVE_MODE, device_target="GPU")

  51.     np.random.seed(12876)

  52.     shape_x1 = (1, 3, 9, 7)

  53.     shape_x2 = (9, 7, 3, 1)

  54.     axes = ((1, 3), (2, 1))

  55.     x1 = np.random.random(shape_x1).astype(np.float32)

  56.     x2 = np.random.random(shape_x2).astype(np.float32)

  57.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  58.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  59. 

  60.     network = NetTensorDot(axes)

  61.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  62.     np_result = np.tensordot(x1, x2, axes)

  63.     np.testing.assert_array_almost_equal(ms_result_np, np_result)

  64. 

  65.     # 1D

  66.     shape_x1 = (200)

  67.     shape_x2 = (200)

  68.     axes = 1

  69.     x1 = np.random.random(shape_x1).astype(np.float32)

  70.     x2 = np.random.random(shape_x2).astype(np.float32)

  71.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  72.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  73. 

  74.     network = NetTensorDot(axes)

  75.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  76.     np_result = np.tensordot(x1, x2, axes)

  77.     np.allclose(ms_result_np, np_result)

  78. 

  79.     # 2D

  80.     shape_x1 = (100, 300)

  81.     shape_x2 = (300, 700)

  82.     axes = ([1], [0])

  83.     x1 = np.random.random(shape_x1).astype(np.float32)

  84.     x2 = np.random.random(shape_x2).astype(np.float32)

  85.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  86.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  87. 

  88.     network = NetTensorDot(axes)

  89.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  90.     np_result = np.tensordot(x1, x2, axes)

  91.     np.allclose(ms_result_np, np_result)

  92. 

  93.     # 3D

  94.     shape_x1 = (110, 30, 900)

  95.     shape_x2 = (900, 70, 30)

  96.     axes = ((1, 2), (2, 0))

  97.     x1 = np.random.random(shape_x1).astype(np.float32)

  98.     x2 = np.random.random(shape_x2).astype(np.float32)

  99.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  100.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  101. 

  102.     network = NetTensorDot(axes)

  103.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  104.     np_result = np.tensordot(x1, x2, axes)

  105.     np.allclose(ms_result_np, np_result)

  106. 

  107. 

  108. @pytest.mark.level2

  109. @pytest.mark.platform_x86_gpu_training

  110. @pytest.mark.env_onecard

  111. def test_tensor_dot_fp16():

  112.     context.set_context(mode=context.PYNATIVE_MODE, device_target="GPU")

  113.     np.random.seed(41329)

  114.     shape_x1 = (1, 3, 4, 1)

  115.     shape_x2 = (4, 1, 7, 5)

  116.     axes = 2  # select first N from

  117.     x1 = np.random.random(shape_x1).astype(np.float16)

  118.     x2 = np.random.random(shape_x2).astype(np.float16)

  119.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  120.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  121. 

  122.     network = NetTensorDot(axes)

  123.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  124.     np_result = np.tensordot(x1, x2, axes)

  125.     np.testing.assert_array_almost_equal(ms_result_np, np_result)

  126. 

  127.     # 1D

  128.     shape_x1 = (300)

  129.     shape_x2 = (300)

  130.     axes = 1

  131.     x1 = np.random.random(shape_x1).astype(np.float16)

  132.     x2 = np.random.random(shape_x2).astype(np.float16)

  133.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  134.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  135. 

  136.     network = NetTensorDot(axes)

  137.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  138.     np_result = np.tensordot(x1, x2, axes)

  139.     np.testing.assert_array_almost_equal(ms_result_np, np_result)

  140. 

  141.     # 2D

  142.     shape_x1 = (100, 300)

  143.     shape_x2 = (300, 100)

  144.     axes = ([1], [0])

  145.     x1 = np.random.random(shape_x1).astype(np.float16)

  146.     x2 = np.random.random(shape_x2).astype(np.float16)

  147.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  148.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  149. 

  150.     network = NetTensorDot(axes)

  151.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  152.     np_result = np.tensordot(x1, x2, axes)

  153.     assert np.allclose(ms_result_np, np_result, rtol=1e-3, atol=1e-3)

  154. 

  155.     # 3D

  156.     shape_x1 = (60, 30, 450)

  157.     shape_x2 = (450, 90, 30)

  158.     axes = ((1, 2), (2, 0))

  159.     x1 = np.random.random(shape_x1).astype(np.float16)

  160.     x2 = np.random.random(shape_x2).astype(np.float16)

  161.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  162.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  163. 

  164.     network = NetTensorDot(axes)

  165.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  166.     np_result = np.tensordot(x1, x2, axes)

  167.     assert np.allclose(ms_result_np, np_result, rtol=1e-3, atol=6e0)

  168. 

  169. 

  170. @pytest.mark.level0

  171. @pytest.mark.platform_x86_gpu_training

  172. @pytest.mark.env_onecard

  173. def test_tensor_dot_outer():

  174.     context.set_context(mode=context.GRAPH_MODE, device_target="GPU")

  175.     np.random.seed(2746)

  176.     shape_x1 = (1, 2, 3)  # incompatible dims for x1 and x2

  177.     shape_x2 = (4, 5, 6)

  178.     axes = 0  # outer product does not require multiplicable dims

  179.     x1 = np.random.random(shape_x1).astype(np.float32)

  180.     x2 = np.random.random(shape_x2).astype(np.float32)

  181.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  182.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  183. 

  184.     network = NetTensorDot(axes)

  185. 

  186.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  187.     np_result = np.tensordot(x1, x2, axes)

  188.     np.testing.assert_array_almost_equal(ms_result_np, np_result)

  189. 

  190. 

  191. @pytest.mark.level0

  192. @pytest.mark.platform_x86_gpu_training

  193. @pytest.mark.env_onecard

  194. def test_tensor_dot_reverse_axes():

  195.     context.set_context(mode=context.GRAPH_MODE, device_target="GPU")

  196.     np.random.seed(2746)

  197.     shape_x1 = (1, 2, 3)

  198.     shape_x2 = (1, 2, 3)

  199.     axes = ((1, 0), (0, 1))

  200.     x1 = np.random.random(shape_x1).astype(np.float32)

  201.     x2 = np.random.random(shape_x2).astype(np.float32)

  202.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  203.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  204. 

  205.     network = NetTensorDot(axes)

  206. 

  207.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  208.     expected_result = np.array([[0.58561826, 0.21897982, 0.906598],

  209.                                 [0.19630799, 0.10731681, 0.2680981],

  210.                                 [0.8003185, 0.457294, 1.0721111]]).astype(np.float32)

  211.     np.testing.assert_array_almost_equal(ms_result_np, expected_result)

  212. 

  213. 

  214.     np.random.seed(1526)

  215.     shape_x1 = (1, 2, 3, 4, 5)

  216.     shape_x2 = (1, 2, 3)

  217.     axes = ((0, 2), (2, 0))

  218.     x1 = np.random.random(shape_x1).astype(np.float32)

  219.     x2 = np.random.random(shape_x2).astype(np.float32)

  220.     x1_tensor = Tensor(x1, dtype=mindspore.float32)

  221.     x2_tensor = Tensor(x2, dtype=mindspore.float32)

  222. 

  223.     network = NetTensorDot(axes)

  224.     ms_result_np = network(x1_tensor, x2_tensor).asnumpy()

  225.     expected_result = np.array([[[[1.106365, 0.9736746],

  226.                                   [0.91042125, 0.7814131],

  227.                                   [0.5576207, 0.327488],

  228.                                   [0.93404585, 0.7108171],

  229.                                   [1.078351, 0.87405884]],

  230.                                  [[1.1720579, 0.9948833],

  231.                                   [1.1594493, 1.0185612],

  232.                                   [0.7251004, 0.60322404],

  233.                                   [0.4724398, 0.2930961],

  234.                                   [0.9711088, 0.8482977]],

  235.                                  [[1.4110168, 1.1171235],

  236.                                   [0.81948525, 0.778057],

  237.                                   [0.7914786, 0.78767675],

  238.                                   [0.77509344, 0.6020987],

  239.                                   [0.8986199, 0.7100061]],

  240.                                  [[0.7270926, 0.35752398],

  241.                                   [0.5529937, 0.31682697],

  242.                                   [0.73876995, 0.48478222],

  243.                                   [0.96520174, 0.73099715],

  244.                                   [0.96569407, 0.8556314]]],

  245.                                 [[[1.2093457, 0.90222925],

  246.                                   [1.3758272, 0.8189213],

  247.                                   [1.2997738, 1.045748],

  248.                                   [1.1460838, 0.67475325],

  249.                                   [0.95835257, 0.67791444]],

  250.                                  [[0.84732395, 0.8058369],

  251.                                   [1.1979935, 0.57202166],

  252.                                   [0.2577264, 0.22021212],

  253.                                   [0.8855853, 0.5440637],

  254.                                   [0.8993537, 0.4622679]],

  255.                                  [[0.6797033, 0.58302796],

  256.                                   [0.7820443, 0.49587217],

  257.                                   [0.64423263, 0.5469],

  258.                                   [1.0270302, 0.5271675],

  259.                                   [1.0278721, 0.9446807]],

  260.                                  [[1.2069539, 1.0113767],

  261.                                   [0.86160654, 0.7664283],

  262.                                   [0.9797001, 0.7087945],

  263.                                   [0.47638205, 0.4660839],

  264.                                   [0.6920749, 0.36285543]]]]).astype(np.float32)

  265.     np.testing.assert_array_almost_equal(ms_result_np, expected_result)

  266. 

  267. 

  268. @pytest.mark.level0

  269. @pytest.mark.platform_x86_gpu_training

  270. @pytest.mark.env_onecard

  271. def test_tensor_dot_backprop():

  272.     context.set_context(mode=context.GRAPH_MODE, device_target="GPU")

  273.     # TEST 1

  274.     shape_x1 = (2, 4, 2)

  275.     shape_x2 = (3, 2, 3)

  276.     axes = ((0,), (1,))  # select first N from

  277.     network = NetTensorDot(axes)

  278. 

  279.     np.random.seed(115)

  280.     x1 = np.random.random(shape_x1).astype(np.float16)

  281.     np.random.seed(1467)

  282.     x2 = np.random.random(shape_x2).astype(np.float16)

  283.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  284.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  285. 

  286.     np.random.seed(157)

  287.     grad = np.random.random((4, 2, 3, 3))

  288.     grad_tensor = Tensor(grad, dtype=mindspore.float16)

  289.     grad_network = GradNetwork(network)

  290.     dx1, dx2 = grad_network(x1_tensor, x2_tensor, grad_tensor)

  291.     dx1, dx2 = dx1.asnumpy(), dx2.asnumpy()

  292. 

  293.     # precomputed

  294.     expect_dx1 = np.array([[[2.0293, 2.4473],

  295.                             [2.9727, 1.4873],

  296.                             [1.7910, 3.4727],

  297.                             [2.4160, 1.7227]],

  298.                            [[2.5547, 2.5039],

  299.                             [3.4062, 2.3320],

  300.                             [2.6270, 3.1543],

  301.                             [2.1406, 1.7666]]])

  302.     expect_dx2 = np.array([[[2.1523, 2.9199, 0.8350],

  303.                             [2.0254, 2.7734, 1.3213]],

  304.                            [[2.6836, 2.4707, 1.0156],

  305.                             [2.9746, 3.0254, 1.9199]],

  306.                            [[1.8545, 1.7803, 1.3457],

  307.                             [2.2676, 2.1797, 1.2764]]])

  308.     np.allclose(dx1, expect_dx1)

  309.     np.allclose(dx2, expect_dx2)

  310. 

  311.     # TEST 2

  312.     shape_x1 = (10, 35)

  313.     shape_x2 = (20, 10)

  314.     axes = ((0,), (1,))  # select first N from

  315.     network = NetTensorDot(axes)

  316. 

  317.     np.random.seed(215)

  318.     x1 = np.random.random(shape_x1).astype(np.float16)

  319.     np.random.seed(2467)

  320.     x2 = np.random.random(shape_x2).astype(np.float16)

  321.     x1_tensor = Tensor(x1, dtype=mindspore.float16)

  322.     x2_tensor = Tensor(x2, dtype=mindspore.float16)

  323. 

  324.     np.random.seed(257)

  325.     grad = np.random.random((35, 20))

  326.     grad_tensor = Tensor(grad, dtype=mindspore.float16)

  327.     grad_network = GradNetwork(network)

  328.     dx1, dx2 = grad_network(x1_tensor, x2_tensor, grad_tensor)

  329.     dx1, dx2 = dx1.asnumpy(), dx2.asnumpy()

  330. 

  331.     # precomputed

  332.     expect_dx1 = np.array([[5.9727, 4.6484, 5.1836, 4.3906, 5.1641, 5.1406, 5.1211, 6.5352, 4.9922,

  333.                             4.4297, 4.4648, 6.5469, 6.2305, 4.8789, 6.8320, 5.3906, 4.7383, 6.0352,

  334.                             4.7383, 4.4844, 5.3711, 6.2617, 4.6484, 5.8672, 4.7500, 6.0234, 3.6387,

  335.                             5.3789, 5.9727, 5.7227, 6.0234, 4.9609, 5.0117, 5.4141, 5.1406],

  336.                            [5.2305, 4.0078, 4.6328, 3.9238, 4.2773, 4.2539, 4.6797, 5.1289, 3.7910,

  337.                             3.8887, 3.2930, 5.5898, 5.4219, 3.6211, 5.5234, 3.5391, 4.8516, 4.7539,

  338.                             4.2500, 2.9785, 4.8867, 5.4648, 5.0195, 6.0195, 4.7109, 3.9727, 3.4922,

  339.                             4.1484, 4.7969, 5.3555, 4.9414, 5.2969, 3.1992, 5.2031, 4.4648],

  340.                            [5.2266, 5.2617, 5.3750, 4.7930, 4.9062, 5.4102, 4.9336, 6.9414, 4.4961,

  341.                             4.4023, 4.7344, 5.8125, 4.9180, 4.7891, 5.9805, 5.2383, 4.6445, 6.1172,

  342.                             4.8477, 3.7578, 4.3047, 5.7969, 4.5859, 6.0273, 4.3438, 4.7305, 4.0938,

  343.                             4.8398, 5.8320, 5.3438, 5.3281, 4.8320, 4.0938, 4.9375, 5.3281],

  344.                            [7.4297, 5.1484, 6.3477, 5.4844, 5.7852, 6.3906, 5.5234, 7.2383, 5.2969,

  345.                             4.9844, 4.5625, 7.3047, 7.3789, 6.4453, 8.2266, 6.6172, 5.5547, 7.0234,

  346.                             4.8594, 4.9531, 6.0469, 6.9258, 6.1055, 6.7539, 6.6953, 6.0430, 4.5117,

  347.                             5.7344, 7.4297, 6.4219, 6.8125, 6.4141, 5.2773, 6.8828, 6.0430],

  348.                            [5.7969, 4.7109, 5.8281, 4.5703, 5.5078, 6.4219, 4.8359, 7.1484, 4.2617,

  349.                             4.8477, 4.2539, 5.6016, 6.4414, 5.7305, 6.4766, 5.4648, 4.5859, 6.5547,

  350.                             5.5156, 3.3848, 5.1523, 5.5352, 4.9531, 6.5938, 5.2969, 4.6055, 5.2109,

  351.                             4.4961, 5.8984, 5.4531, 5.8086, 5.7930, 5.0742, 5.4102, 4.9453],

  352.                            [7.2188, 5.8789, 6.9453, 6.0039, 6.7188, 7.3359, 6.7695, 8.6172, 5.6680,

  353.                             6.4219, 6.1836, 7.7695, 7.5391, 6.5312, 8.2812, 7.5352, 5.8867, 7.7070,

  354.                             6.0039, 5.1172, 6.4844, 7.4297, 5.9219, 7.5078, 6.3125, 6.9805, 5.3750,

  355.                             5.9805, 7.2148, 7.6484, 7.8828, 6.7695, 5.7109, 6.8828, 6.9023],

  356.                            [5.7656, 4.3633, 4.5039, 4.4375, 4.3867, 5.4336, 4.3672, 5.5469, 3.5742,

  357.                             4.0508, 3.7402, 5.9141, 5.7734, 4.5781, 5.6719, 4.5625, 4.5391, 5.1719,

  358.                             4.3945, 3.4844, 4.9297, 5.7227, 4.8203, 5.8125, 4.8633, 4.3125, 3.6641,

  359.                             4.3789, 5.6133, 5.1758, 4.9141, 5.8008, 4.0391, 5.8984, 4.3594],

  360.                            [4.7734, 3.4238, 4.3477, 3.6270, 4.4883, 5.2031, 3.9023, 5.0078, 2.9355,

  361.                             3.8477, 3.4648, 5.1445, 4.8398, 4.4297, 5.1641, 4.2422, 4.2695, 4.6992,

  362.                             4.5039, 2.5176, 4.2500, 5.6680, 4.1875, 5.4141, 3.6094, 3.1758, 3.8398,

  363.                             3.9180, 5.3320, 4.6523, 3.9531, 4.8281, 3.9863, 4.8867, 4.3711],

  364.                            [6.7578, 5.3164, 6.0000, 4.4531, 5.8789, 6.3750, 5.1094, 7.0391, 4.5781,

  365.                             4.8633, 4.5156, 6.6641, 6.3594, 5.5664, 6.9453, 5.5820, 5.1992, 6.9570,

  366.                             5.3242, 3.8574, 5.1445, 6.0547, 5.0273, 6.9180, 5.1914, 4.6914, 4.6445,

  367.                             5.1289, 5.8711, 6.2070, 6.1953, 5.7695, 4.7617, 5.5898, 4.9492],

  368.                            [4.9180, 4.0117, 4.1211, 3.4629, 3.6445, 4.6602, 3.7031, 4.9062, 4.1133,

  369.                             3.0020, 3.2246, 4.6562, 4.4727, 3.3828, 5.2695, 4.0078, 3.2559, 4.9688,

  370.                             3.5742, 3.1133, 3.8223, 4.7578, 3.7949, 4.8438, 4.0664, 4.4336, 3.0957,

  371.                             4.4375, 4.2969, 4.1758, 4.5234, 4.2930, 3.9434, 4.8281, 3.0703]])

  372.     expect_dx2 = np.array([[6.7930, 7.0000, 8.8203, 9.7031, 8.1250,

  373.                             6.7422, 8.4844, 8.7031, 7.2891, 10.1484],

  374.                            [8.5781, 8.1641, 9.9609, 9.2344, 9.3281,

  375.                             8.1484, 9.8984, 9.0391, 7.9805, 11.0469],

  376.                            [8.1016, 7.0781, 8.9688, 10.0938, 9.6641,

  377.                             7.1523, 8.2969, 8.8594, 8.3047, 10.2578],

  378.                            [7.0938, 7.3477, 9.3594, 8.2422, 7.9141,

  379.                             6.5156, 8.2812, 8.2266, 6.9766, 8.5703],

  380.                            [9.2891, 9.2500, 11.6875, 9.5234, 10.1172,

  381.                             8.8125, 9.5781, 9.5547, 8.9688, 11.2266],

  382.                            [9.3594, 7.7539, 9.2500, 9.2500, 8.1094,

  383.                             8.0859, 8.7344, 8.2031, 8.5859, 10.3203],

  384.                            [8.7344, 7.7227, 10.2578, 10.1641, 9.3984,

  385.                             8.1719, 8.0156, 8.6953, 8.6797, 10.6875],

  386.                            [8.8750, 7.9922, 10.2422, 10.3984, 9.5234,

  387.                             8.5156, 8.7266, 8.8125, 8.2578, 10.2578],

  388.                            [9.5703, 8.9844, 10.0547, 10.3047, 10.4062,

  389.                             8.2422, 10.7031, 9.7891, 9.2969, 11.0078],

  390.                            [9.2891, 9.5391, 10.5938, 10.5078, 9.8203,

  391.                             8.5156, 9.0859, 9.0703, 8.7812, 10.8750],

  392.                            [8.6094, 8.2734, 10.2734, 9.7891, 9.4531,

  393.                             7.5820, 8.4609, 8.6094, 7.7578, 10.3438],

  394.                            [8.2891, 8.7578, 9.3906, 9.6016, 9.4375,

  395.                             7.1016, 8.6875, 8.1875, 8.2188, 9.3672],

  396.                            [7.2969, 6.6953, 9.3984, 8.2422, 8.3438,

  397.                             7.5547, 7.6445, 7.5820, 7.5156, 9.0781],

  398.                            [8.3906, 7.3516, 8.5938, 9.2422, 8.7734,

  399.                             8.0781, 9.1250, 7.8359, 7.7891, 10.9375],

  400.                            [9.9219, 8.8281, 9.4141, 10.2500, 9.8047,

  401.                             8.5234, 8.5391, 8.4609, 8.5859, 11.2422],

  402.                            [6.8984, 6.4570, 8.0000, 6.4688, 7.4609,

  403.                             6.6016, 7.0352, 6.6797, 6.5586, 7.7070],

  404.                            [8.0625, 7.4805, 8.7578, 8.3281, 8.2188,

  405.                             7.4023, 8.5312, 7.5312, 7.1445, 10.3750],

  406.                            [7.7773, 6.6484, 9.1094, 8.0078, 7.8281,

  407.                             7.1016, 8.2422, 8.1562, 6.8828, 10.3281],

  408.                            [8.3281, 8.3672, 9.7656, 10.4922, 8.2500,

  409.                             7.5625, 8.4922, 8.9844, 8.0703, 10.3438],

  410.                            [7.5195, 7.0430, 7.9453, 8.4375, 7.6641,

  411.                             6.9688, 7.7734, 8.7734, 6.3672, 9.4766]])

  412.     np.allclose(dx1, expect_dx1)

  413.     np.allclose(dx2, expect_dx2)