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Update galaxy shapes for covariance info #93

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Jan 10, 2025
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Update galaxy shapes for covariance info #93

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36 changes: 33 additions & 3 deletions content/notebooks/measuring_galaxy_shapes/measuring_galaxy_shapes.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -643,7 +643,7 @@
"metadata": {},
"outputs": [],
"source": [
"err_img = file.err[ymin:ymax, xmin:xmax].value.flatten()"
"err_img = file.err[ymin:ymax, xmin:xmax].flatten()"
]
},
{
Expand Down Expand Up @@ -741,7 +741,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Our fit looks really good. In fact, despite the presence of another bright source in the cutout, `scipy.curve_fit` did a good job of fitting the model to the data. Let's take a quick look at the statistics of the fit residuals:"
"Our fit looks really good. Let's take a quick look at the statistics of the fit residuals:"
]
},
{
Expand Down Expand Up @@ -894,7 +894,37 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Comparing these values with our earlier fit, we find that the median and standard deviation of the residuals of both fits are identical to within four decimal places despite differences in the input and best-fit model parameters. "
"Comparing these values with our earlier fit, we find that the median and standard deviation of the residuals of both fits are identical to within four decimal places despite differences in the input and best-fit model parameters.\n",
"\n",
"From `scipy.optimize.curve_fit()`, we also have the estimated approximate covariance information for each of the fitted parameters. From the `scipy` [documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html), we can use that information to compute the 1-$\\sigma$ uncertainties on the fitted parameters:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"perr = np.sqrt(np.diag(pcov))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where `pcov` is the covariance of the fit (recall that `pout` is the fitted values above). Now we can print the fitted values with the uncertainties:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"labels = ('n', 'hlr', 'flux', 'pa', 'x0', 'y0', 'q')\n",
"\n",
"for i, _ in enumerate(p0):\n",
" print(f'{labels[i]} = {pout[i]:.5f} +/- {perr[i]:.5f}')"
]
},
{
Expand Down
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