fastdtw.ipynb [Emilys Galactic Gits]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
====== Analyzing Astronomical Data with FastDTW ======
=== fastDTW.ipynb ===
This Jupyter Notebook demonstrates the application of the Fast Dynamic Time Warping (FastDTW) algorithm to reconcile and compare astronomical data, specifically focusing on magnitude and color shifts between fiducial lines and isochrones. It includes data loading, preprocessing, and shifting color and magnitude values to find minimal differences, utilizing libraries such as matplotlib for plotting and scipy for calculations. The notebook provides a detailed example of using FastDTW to understand and visualize the alignment and differences in astronomical observations.


```python
import pickle as pkl
import matplotlib.pyplot as plt
from fastdtw import fastdtw
from scipy.spatial.distance import euclidean, hamming
import numpy as np
from mplEasyAnimate import animation
from tqdm import tqdm
import similaritymeasures
from scipy.interpolate import interp1d
```


```python
PATH = "../DebugOutput.pkl"
```


```python
with open(PATH, 'rb') as f:
    debugOutput = pkl.load(f)
isoColor, isoMag, fFid, fiducialLine = debugOutput
corrLists = list()

nMin = 5
nMax = 25
initShift = np.mean(fiducialLine[1]) - np.mean(isoMag)
isoMagOrig = isoMag.copy()
isoMag = isoMag + initShift

f = interp1d(isoMag, isoColor, bounds_error=False, fill_value='extrapolate')
for n in tqdm(range(nMin, nMax), desc="Guessing mu"):
    correlations = list()
    magShifts = np.linspace(-10,10, n)
    fMagEval = np.linspace(fiducialLine[1].min(), fiducialLine[1].max(), n)
    iMagEval = np.linspace(isoMag.min(), isoMag.max(), n)
    dtwX = np.zeros(shape=(n,1))
    dtwY = np.zeros(shape=(n,1))
    fColor = fFid(fMagEval)
    for magShift in magShifts: 
        iColor = f(iMagEval+magShift)


        dtwX[:, 0] = fColor
        dtwY[:, 0] = iColor
        dtw = fastdtw(dtwX, dtwY, dist=euclidean)

        minFiducialColor, maxFiducialColor = min(fMagEval), max(fMagEval)
        dists = list()
        for i, j in dtw[1]:
            if minFiducialColor <= iMagEval[j] <= maxFiducialColor:
                dists.append(np.sqrt((fColor[i] - iColor[j])**2 + (fMagEval[i] - iMagEval[j])**2))
        chi2 = np.sum([x**2 for x in dists])
        chi2nu = chi2/len(dists)
        correlations.append(chi2nu)
    magShift = magShifts[np.argmin(correlations)]
    corrLists.append(magShift)
magShift = np.mean(corrLists)
print(magShift)

n = 100
with plt.style.context(pubStyle):
    fig, axs = plt.subplots(1,2,figsize=(20,7))
    ax = axs[0]
    fMagEval = np.linspace(fiducialLine[1].min(), fiducialLine[1].max(), n)
    iMagEval = np.linspace(isoMag.min(), isoMag.max(), n)

    fColor = fFid(fMagEval)
    isoMagShifted = isoMag - magShift
    isoColorShifted = isoColor
    isoFuncShifted = interp1d(isoMagShifted, isoColorShifted, bounds_error=False, fill_value='extrapolate')
    iColor = isoFuncShifted(fMagEval)
    
    ax.plot(fColor, fMagEval, 'o-', markersize=3)
    ax.plot(iColor, fMagEval, 'o-', markersize=3)

    dtwX = np.zeros(shape=(n,1))
    dtwY = np.zeros(shape=(n,1))

    dtwX[:, 0] = fColor
    dtwY[:, 0] = iColor
    dtw = fastdtw(dtwX, dtwY, dist=euclidean)
    minFiducialColor, maxFiducialColor = min(fMagEval), max(fMagEval)
    dists = list()
    for i, j in dtw[1]:
        # if minFiducialColor <= iMagEval[j] <= maxFiducialColor:
        if ((j < len(iColor)-1) and j != 0) and ((i < len(fColor)-1) and i != 0):
            dists.append(np.sqrt((fColor[i] - iColor[j])**2 + (fMagEval[i] - fMagEval[j])**2))
            ax.plot([fColor[i], iColor[j]], [fMagEval[i], fMagEval[j]], color='black', alpha=0.1)
    chi2 = np.sum([x**2 for x in dists])
    chi2nu = chi2/len(dists)
    ax.invert_yaxis()
    
    axs[1].plot(fiducialLine[0], fiducialLine[1], label="Fiducial Line")
    axs[1].plot(isoColor, isoMagOrig, label="Isochrone")
    axs[1].legend(frameon=False)
    axs[1].invert_yaxis()
    
    axs[1].set_facecolor("#F0F1EB")
    axs[0].set_facecolor("#F0F1EB")
    fig.set_facecolor("#F0F1EB")
    
    axs[0].set_xlabel("F275W - F814W", fontsize=25)
    axs[1].set_xlabel("F275W - F814W", fontsize=25)
    axs[0].set_ylabel("F814W", fontsize=25)
    axs[1].set_ylabel("F814W", fontsize=25)
    
    fig.savefig("DTWChi2.png", dpi=200)

    # axs[1].set_xlim(ax.get_xlim())
    # axs[1].set_ylim(ax.get_ylim())
```

    Guessing mu: 100%|███████████████████████████████████████████████████| 20/20 [00:00<00:00, 23.15it/s]


    1.0163341752771688



    
![png](media:7d683abe475cc7d1caec91ca5669654d6cccc609a3a17f90e6e2e617623f588c:output_2_2.png)
    



```python
magShift
```




    -30.0




```python
colorShift
```




    0.7366746325569853




```python
list(range(5, 25))
```




    [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]




```python

```