I am working on a software for spectral analyses.
Data consists of a np.array with spectral intensities, and a "wavelength vector" (wlv), i.e. the X-axis, so to speak.
When combining data, not all data has exactly the same wavelength vector, but they might be shifted ever so slightly, say by 0.00002 units or so.
Here is some example data:
a (blue) is the "proper" dataset, while b (red) is slightly shifted:
a's wavelengths are
[0, 1, 2, 3, 4, 5, 6].
b's wavelengths are
[-0.9, 0.1, 1.1, 2.1, 3.1, 4.1, 5.1]
Example
a_intensities = np.array([[2, 4.2, 5.2, 5, 4, 5, 2.8], [5, 5.2, 5.5, 5.4, 5.3, 5.3, 3.7]])
a_wlv = np.array([0, 1, 2, 3, 4, 5, 6])
b_intensities = np.array([[1, 1.1, 1.7, 1.9, 1.8, 1.9, 1.2], [0.1, 0.7, 0.8, 0.6, 0.5, 0.45, 0.31]])
b_wlv = np.array([-0.9, 0.1, 1.1, 2.1, 3.1, 4.1, 5.1])
plt.figure('Spectra')
plt.plot(a_wlv, a_intensities.T, 'bo-', color='blue')
plt.grid()
plt.plot(b_wlv, b_intensities.T, 'bo--', color='red')
plt.xlabel('Wavelength')
plt.ylabel('Intensity')
plt.show()
Example spectra:
Spectra images (updated)
I now want to "shift" b's wavelength vector so that it overlaps with a. The shift needs to be conducted in the direction where the necessary change occurs.
Note that the wavelengths do not need to be identical (i.e. both be 0:7) but it is important that they overlap exactly.
Rounding to three decimals works in some cases, but not always (since I don't want to lose too much data), so I would like to have a way of doing this without rounding.
Therefore, in above's example, I want to shift b so that the bins overlap with a:
Before shifting:
a: [ 0, 1, 2, 3, 4, 5, 6].
b: [-0.9, 0.1, 1.1, 2.1, 3.1, 4.1, 5.1]
After shifting:
a: [ 0, 1, 2, 3, 4, 5, 6].
b: [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
How would you go about this?
I am currently writing a rather lengthy function to do this, but I am afraid I am missing an obvious, much easier way here.
Edit: Some real-world data:
a_intensities = np.array([0.2184649, 0.2201522, 0.2186561, 0.2158286, 0.2134198, 0.2112872, 0.2141369, 0.2177338, 0.2169663, 0.2109826, 0.2084285, 0.2115282])
a_wlv = np.array([800.3474, 802.2759, 804.2045, 806.1331, 808.0616, 809.9902, 811.9187, 813.8472, 815.7758, 817.7043, 819.6329, 821.5615])
b_intensities = np.array([0.02411663, 0.02425605, 0.02463717, 0.02500274, 0.0251241, 0.02488419, 0.0243349, 0.02371608, 0.02327189, 0.023061, 0.023011, 0.02312733])
b_wlv = np.array([800.34744206, 802.27599007, 804.20453808, 806.1330861, 808.06163411, 809.99018212, 811.91873013, 813.84727814, 815.77582616, 817.70437417, 819.63292218, 821.56147019])
plt.plot(a_wlv, a_intensities, 'bo-', color='red')
plt.plot(b_wlv, b_intensities, 'bo-', color='green')
plt.grid()
plt.show()
question from:
https://stackoverflow.com/questions/65879014/align-overlap-two-vectors-that-are-slightly-shifted 
