python - 如何隔离python“for循环”中的函数计算以避免广播形状冲突?
问题描述
我正在尝试计算 IR 光谱中峰值坐标的一系列高斯曲线。在 0 到 4000 1/cm 的频率范围 (X) 上计算单个峰值的脚本正常运行。然而,当我尝试在 75 个频率和强度坐标的范围内进行迭代时,我得到了 4001 个“x”值和 75 个峰值坐标对之间的广播形状冲突。有没有办法隔离计算,使其表现得像一系列独立的计算,从而避免冲突?
这是我的代码和错误回溯:
import numpy as np
def gaussian(intens, mu):
x = np.arange(4001)
sig = 50
return intens*np.exp(-np.power(x-mu, 2.)/(2*np.power(sig, 2.)))
results = np.empty((4001, 1), float)
for i in range(75):
mu = np.array([106.2516, 169.2317, 179.4433, 210.1843, 225.1875, 237.6963, 261.1454,
290.3952, 298.8429, 383.1141, 394.5482, 415.7989, 474.0785, 522.2687,
555.9868, 571.7233, 617.1713, 646.9524, 712.1052, 757.1555, 839.7896,
862.2479, 874.9923, 927.4888, 948.9697, 951.0036, 964.3596, 969.371,
1008.6015, 1039.7932, 1044.8249, 1063.0541, 1107.298, 1127.9082, 1155.2848,
1180.83, 1196.411, 1225.1961, 1234.4729, 1256.5558, 1278.3917, 1284.0116,
1311.6421, 1338.709, 1346.252, 1360.011, 1434.1602, 1439.0059, 1455.3892,
1490.6434, 1512.7327, 1517.3906, 1521.4376, 1525.9011, 1531.1185, 1540.3454,
1546.1395, 1554.7932, 1841.6486, 3045.7824, 3050.0779, 3053.1525, 3064.5046,
3070.2651, 3073.4956, 3094.2865, 3097.3753, 3101.0081, 3107.7236, 3108.5122,
3115.0888, 3117.7676, 3123.2296, 3127.9553, 3141.7127])
intens = np.array([3.609400e+00, 6.870000e-02, 1.425000e-01, 1.908000e-01, 2.848000e-01,
9.040000e-01, 7.114000e-01, 3.850000e-01, 1.899100e+00, 7.697000e-01,
1.484000e-01, 1.223400e+00, 5.366000e-01, 4.554700e+00, 2.007100e+00,
8.798000e-01, 9.361000e-01, 1.767700e+00, 4.380000e-01, 6.543100e+00,
4.705000e-01, 1.423900e+00, 5.475000e-01, 1.230200e+00, 3.059800e+00,
4.872000e-01, 1.293400e+00, 2.782900e+00, 5.430000e-02, 1.592800e+00,
2.582030e+01, 2.047560e+01, 1.544500e+00, 4.941600e+00, 1.135200e+00,
6.229000e-01, 3.967100e+00, 1.082100e+00, 5.126800e+00, 3.136400e+00,
3.190000e-02, 3.438700e+00, 6.669500e+00, 2.266600e+00, 1.033200e+00,
4.739000e+00, 4.292300e+00, 4.469500e+00, 6.858500e+00, 8.952200e+00,
2.593600e+00, 6.386200e+00, 4.342300e+00, 2.799900e+00, 1.920900e+00,
3.788000e-01, 4.900100e+00, 4.086800e+00, 2.093403e+02, 1.231370e+01,
1.935290e+01, 3.692450e+01, 2.791320e+01, 1.315910e+01, 2.868290e+01,
2.371370e+01, 1.425640e+01, 4.406400e+00, 7.293400e+00, 5.097790e+01,
4.594300e+01, 3.229710e+01, 1.685690e+01, 2.933100e+01, 2.938250e+01])
g_calc = map(gaussian(intens, mu), zip(intens, mu))
results = vstack(results, g_calc)
results
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-29-c890381ce491> in <module>()
35 2.371370e+01, 1.425640e+01, 4.406400e+00, 7.293400e+00, 5.097790e+01,
36 4.594300e+01, 3.229710e+01, 1.685690e+01, 2.933100e+01, 2.938250e+01])
---> 37 g_calc = map(gaussian(intens, mu), zip(intens, mu))
38 results = vstack(results, g_calc)
39 results
<ipython-input-29-c890381ce491> in gaussian(intens, mu)
4 x = np.arange(4001)
5 sig = 50
----> 6 return intens*np.exp(-np.power(x-mu, 2.)/(2*np.power(sig, 2.)))
7
8 results = np.empty((4001, 1), float)
ValueError: operands could not be broadcast together with shapes (4001,) (75,)
解决方案
如果我正确理解您的问题,您要计算的是:
(如果这是正确的,我建议重新制定标题,因为这实际上并不是特定于高斯的。)
对于这类操作,我numpy.meshgrid
广泛使用。在这里,它基本上创建二维数组,其中一维是您的频率网格(j
索引),另一维对应于不同的峰值(i
索引)。然后,您可以有效地调用它们上的numpy
数组的所有机制。看看下面的代码是否产生了你期望的输出:
import numpy as np
import matplotlib.pyplot as plt
intens = np.array([0.1, 0.22, 0.13, 0.51, 0.4])
freq_0 = np.array([500.3, 123.4, 1023.6, 2562.45, 3126.2])
sigmaf = np.array([10.3, 20.4, 5.6, 40.5, 26.2])
freq_mesh = np.linspace(0.0,4000.0, num=4001, endpoint=True)
[I, FM] = np.meshgrid(intens, freq_mesh)
[F0,FM] = np.meshgrid(freq_0, freq_mesh)
[SF,FM] = np.meshgrid(sigmaf, freq_mesh)
signal_2d_arr = I*np.exp(-(FM-F0)**2/(2*SF**2))
spectrum = np.sum(signal_2d_arr, axis = 1)
plt.figure()
plt.plot(freq_mesh, spectrum)
plt.show()
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