Tibeuleu/FOC_Reduction
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compute debiased integrated polarization degree

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This commit is contained in:
Thibault Barnouin
2025-04-22 17:46:59 +02:00
parent f4fdce3f07
commit 0a8336aea8
5 changed files with 253 additions and 140 deletions
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31
package/FOC_reduction.py
View File

@@ -40,13 +40,13 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
display_crop = False
# Background estimation
error_sub_type = "scott" # sqrt, sturges, rice, scott, freedman-diaconis (default) or shape (example (51, 51))
subtract_error = 0.50
error_sub_type = "freedman-diaconis" # sqrt, sturges, rice, scott, freedman-diaconis (default) or shape (example (51, 51))
subtract_error = 1.33
display_bkg = True
# Data binning
pxsize = 4
pxscale = "px" # pixel, arcsec or full
pxsize = 0.05
pxscale = "arcsec" # pixel, arcsec or full
rebin_operation = "sum" # sum or average
# Alignement
@@ -59,8 +59,8 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
# Smoothing
smoothing_function = "combine" # gaussian_after, weighted_gaussian_after, gaussian, weighted_gaussian or combine
smoothing_FWHM = 1.5 # If None, no smoothing is done
smoothing_scale = "px" # pixel or arcsec
smoothing_FWHM = 0.075 # If None, no smoothing is done
smoothing_scale = "arcsec" # pixel or arcsec
# Rotation
rotate_North = True
@@ -216,28 +216,26 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
# FWHM of FOC have been estimated at about 0.03" across 1500-5000 Angstrom band, which is about 2 detector pixels wide
# see Jedrzejewski, R.; Nota, A.; Hack, W. J., A Comparison Between FOC and WFPC2
# Bibcode : 1995chst.conf...10J
I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_stat = proj_red.compute_Stokes(
I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes = proj_red.compute_Stokes(
data_array, error_array, data_mask, headers, FWHM=smoothing_FWHM, scale=smoothing_scale, smoothing=smoothing_function, transmitcorr=transmitcorr
)
I_bkg, Q_bkg, U_bkg, S_cov_bkg, header_bkg, s_IQU_stat_bkg = proj_red.compute_Stokes(
I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, header_bkg = proj_red.compute_Stokes(
background, background_error, np.array(True).reshape(1, 1), headers, FWHM=None, scale=smoothing_scale, smoothing=smoothing_function, transmitcorr=False
)
# Step 3:
# Rotate images to have North up
if rotate_North:
I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, s_IQU_stat = proj_red.rotate_Stokes(
I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, s_IQU_stat=s_IQU_stat, SNRi_cut=None
I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes = proj_red.rotate_Stokes(
I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes, SNRi_cut=None
)
I_bkg, Q_bkg, U_bkg, S_cov_bkg, data_mask_bkg, header_bkg, s_IQU_stat_bkg = proj_red.rotate_Stokes(
I_bkg, Q_bkg, U_bkg, S_cov_bkg, np.array(True).reshape(1, 1), header_bkg, s_IQU_stat=s_IQU_stat_bkg, SNRi_cut=None
I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, data_mask_bkg, header_bkg = proj_red.rotate_Stokes(
I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, np.array(True).reshape(1, 1), header_bkg, SNRi_cut=None
)
# Compute polarimetric parameters (polarization degree and angle).
P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P = proj_red.compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_stat=s_IQU_stat)
P_bkg, debiased_P_bkg, s_P_bkg, s_P_P_bkg, PA_bkg, s_PA_bkg, s_PA_P_bkg = proj_red.compute_pol(
I_bkg, Q_bkg, U_bkg, S_cov_bkg, header_bkg, s_IQU_stat=s_IQU_stat_bkg
)
P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P = proj_red.compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes)
P_bkg, debiased_P_bkg, s_P_bkg, s_P_P_bkg, PA_bkg, s_PA_bkg, s_PA_P_bkg = proj_red.compute_pol(I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, header_bkg)
# Step 4:
# Save image to FITS.
@@ -247,6 +245,7 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
Q_stokes,
U_stokes,
Stokes_cov,
Stokes_stat_cov,
P,
debiased_P,
s_P,

25
package/lib/fits.py
View File

@@ -106,7 +106,23 @@ def get_obs_data(infiles, data_folder="", compute_flux=False):
def save_Stokes(
I_stokes, Q_stokes, U_stokes, Stokes_cov, P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P, header_stokes, data_mask, filename, data_folder="", return_hdul=False
I_stokes,
Q_stokes,
U_stokes,
Stokes_cov,
Stokes_stat_cov,
P,
debiased_P,
s_P,
s_P_P,
PA,
s_PA,
s_PA_P,
header_stokes,
data_mask,
filename,
data_folder="",
return_hdul=False,
):
"""
Save computed polarimetry parameters to a single fits file,
@@ -186,11 +202,15 @@ def save_Stokes(
s_PA_P = s_PA_P[vertex[2] : vertex[3], vertex[0] : vertex[1]]
new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape[::-1]))
new_Stokes_stat_cov = np.zeros((*Stokes_stat_cov.shape[:-2], *shape[::-1]))
for i in range(3):
for j in range(3):
Stokes_cov[i, j][(1 - data_mask).astype(bool)] = 0.0
new_Stokes_cov[i, j] = Stokes_cov[i, j][vertex[2] : vertex[3], vertex[0] : vertex[1]]
Stokes_stat_cov[i, j][(1 - data_mask).astype(bool)] = 0.0
new_Stokes_stat_cov[i, j] = Stokes_stat_cov[i, j][vertex[2] : vertex[3], vertex[0] : vertex[1]]
Stokes_cov = new_Stokes_cov
Stokes_stat_cov = new_Stokes_stat_cov
data_mask = data_mask[vertex[2] : vertex[3], vertex[0] : vertex[1]]
data_mask = data_mask.astype(float, copy=False)
@@ -210,6 +230,7 @@ def save_Stokes(
[Q_stokes, "Q_stokes"],
[U_stokes, "U_stokes"],
[Stokes_cov, "IQU_cov_matrix"],
[Stokes_stat_cov, "IQU_stat_cov_matrix"],
[P, "Pol_deg"],
[debiased_P, "Pol_deg_debiased"],
[s_P, "Pol_deg_err"],
@@ -221,7 +242,7 @@ def save_Stokes(
]:
hdu_header = header.copy()
hdu_header["datatype"] = name
if not name == "IQU_cov_matrix":
if not name[-10:] == "cov_matrix":
data[(1 - data_mask).astype(bool)] = 0.0
hdu = fits.ImageHDU(data=data, header=hdu_header)
hdu.name = name

158
package/lib/plots.py
View File

@@ -2079,7 +2079,7 @@ class crop_Stokes(crop_map):
# Crop dataset
for dataset in self.hdul_crop:
if dataset.header["datatype"] == "IQU_cov_matrix":
if dataset.header["datatype"][-10:] == "cov_matrix":
stokes_cov = np.zeros((3, 3, shape[1], shape[0]))
for i in range(3):
for j in range(3):
@@ -2104,16 +2104,22 @@ class crop_Stokes(crop_map):
if self.fig.canvas.manager.toolbar.mode == "":
self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
# Update integrated values
mask = np.logical_and(self.hdul_crop["data_mask"].data.astype(bool), self.hdul_crop[0].data > 0)
I_diluted = self.hdul_crop["i_stokes"].data[mask].sum()
Q_diluted = self.hdul_crop["q_stokes"].data[mask].sum()
U_diluted = self.hdul_crop["u_stokes"].data[mask].sum()
I_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 0][mask]))
Q_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[1, 1][mask]))
U_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[2, 2][mask]))
IQ_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 1][mask] ** 2))
IU_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 2][mask] ** 2))
QU_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[1, 2][mask] ** 2))
mask = np.logical_and(self.hdul_crop["DATA_MASK"].data.astype(bool), self.hdul_crop[0].data > 0)
I_diluted = self.hdul_crop["I_STOKES"].data[mask].sum()
Q_diluted = self.hdul_crop["Q_STOKES"].data[mask].sum()
U_diluted = self.hdul_crop["U_STOKES"].data[mask].sum()
I_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 0][mask]))
Q_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[1, 1][mask]))
U_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[2, 2][mask]))
IQ_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 1][mask] ** 2))
IU_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 2][mask] ** 2))
QU_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[1, 2][mask] ** 2))
I_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 0][mask]))
Q_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[1, 1][mask]))
U_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[2, 2][mask]))
IQ_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 1][mask] ** 2))
IU_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 2][mask] ** 2))
QU_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[1, 2][mask] ** 2))
P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
P_diluted_err = (1.0 / I_diluted) * np.sqrt(
@@ -2122,6 +2128,18 @@ class crop_Stokes(crop_map):
- 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
- 2.0 * (U_diluted / I_diluted) * IU_diluted_err
)
P_diluted_stat_err = (
P_diluted
/ I_diluted
* np.sqrt(
I_diluted_stat_err
- 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+ 1.0
/ (I_diluted**2 * P_diluted**4)
* (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
)
)
debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
@@ -2131,7 +2149,7 @@ class crop_Stokes(crop_map):
for dataset in self.hdul_crop:
if dataset.header["FILENAME"][-4:] != "crop":
dataset.header["FILENAME"] += "_crop"
dataset.header["P_int"] = (P_diluted, "Integrated polarization degree")
dataset.header["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
dataset.header["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
dataset.header["PA_int"] = (PA_diluted, "Integrated polarization angle")
dataset.header["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
@@ -2961,6 +2979,10 @@ class pol_map(object):
def IQU_cov(self):
return self.Stokes["IQU_COV_MATRIX"].data
@property
def IQU_stat_cov(self):
return self.Stokes["IQU_STAT_COV_MATRIX"].data
@property
def P(self):
return self.Stokes["POL_DEG_DEBIASED"].data
@@ -3283,27 +3305,26 @@ class pol_map(object):
s_I = np.sqrt(self.IQU_cov[0, 0])
I_reg = self.I.sum()
I_reg_err = np.sqrt(np.sum(s_I**2))
P_reg = self.Stokes[0].header["P_int"]
debiased_P_reg = self.Stokes[0].header["P_int"]
P_reg_err = self.Stokes[0].header["sP_int"]
PA_reg = self.Stokes[0].header["PA_int"]
PA_reg_err = self.Stokes[0].header["sPA_int"]
s_I = np.sqrt(self.IQU_cov[0, 0])
s_Q = np.sqrt(self.IQU_cov[1, 1])
s_U = np.sqrt(self.IQU_cov[2, 2])
s_IQ = self.IQU_cov[0, 1]
s_IU = self.IQU_cov[0, 2]
s_QU = self.IQU_cov[1, 2]
I_cut = self.I[self.cut].sum()
Q_cut = self.Q[self.cut].sum()
U_cut = self.U[self.cut].sum()
I_cut_err = np.sqrt(np.sum(s_I[self.cut] ** 2))
Q_cut_err = np.sqrt(np.sum(s_Q[self.cut] ** 2))
U_cut_err = np.sqrt(np.sum(s_U[self.cut] ** 2))
IQ_cut_err = np.sqrt(np.sum(s_IQ[self.cut] ** 2))
IU_cut_err = np.sqrt(np.sum(s_IU[self.cut] ** 2))
QU_cut_err = np.sqrt(np.sum(s_QU[self.cut] ** 2))
I_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 0][self.cut]))
Q_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 1][self.cut]))
U_cut_err = np.sqrt(np.sum(self.IQU_cov[2, 2][self.cut]))
IQ_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 1][self.cut] ** 2))
IU_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 2][self.cut] ** 2))
QU_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 2][self.cut] ** 2))
I_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][self.cut]))
Q_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][self.cut]))
U_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][self.cut]))
IQ_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][self.cut] ** 2))
IU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][self.cut] ** 2))
QU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][self.cut] ** 2))
with np.errstate(divide="ignore", invalid="ignore"):
P_cut = np.sqrt(Q_cut**2 + U_cut**2) / I_cut
@@ -3316,6 +3337,18 @@ class pol_map(object):
)
/ I_cut
)
P_cut_stat_err = (
P_cut
/ I_cut
* np.sqrt(
I_cut_stat_err
- 2.0 / (I_cut * P_cut**2) * (Q_cut * IQ_cut_stat_err + U_cut * IU_cut_stat_err)
+ 1.0 / (I_cut**2 * P_cut**4) * (Q_cut**2 * Q_cut_stat_err + U_cut**2 * U_cut_stat_err + 2.0 * Q_cut * U_cut * QU_cut_stat_err)
)
)
mask = P_cut**2 > P_cut_stat_err
debiased_P_cut = np.zeros(P_cut.shape)
debiased_P_cut[mask] = np.sqrt(P_cut[mask] ** 2 - P_cut_stat_err[mask] ** 2)
PA_cut = princ_angle((90.0 / np.pi) * np.arctan2(U_cut, Q_cut))
PA_cut_err = (90.0 / (np.pi * (Q_cut**2 + U_cut**2))) * np.sqrt(
@@ -3323,22 +3356,21 @@ class pol_map(object):
)
else:
s_I = np.sqrt(self.IQU_cov[0, 0])
s_Q = np.sqrt(self.IQU_cov[1, 1])
s_U = np.sqrt(self.IQU_cov[2, 2])
s_IQ = self.IQU_cov[0, 1]
s_IU = self.IQU_cov[0, 2]
s_QU = self.IQU_cov[1, 2]
I_reg = self.I[self.region].sum()
Q_reg = self.Q[self.region].sum()
U_reg = self.U[self.region].sum()
I_reg_err = np.sqrt(np.sum(s_I[self.region] ** 2))
Q_reg_err = np.sqrt(np.sum(s_Q[self.region] ** 2))
U_reg_err = np.sqrt(np.sum(s_U[self.region] ** 2))
IQ_reg_err = np.sqrt(np.sum(s_IQ[self.region] ** 2))
IU_reg_err = np.sqrt(np.sum(s_IU[self.region] ** 2))
QU_reg_err = np.sqrt(np.sum(s_QU[self.region] ** 2))
I_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 0][self.region]))
Q_reg_err = np.sqrt(np.sum(self.IQU_cov[1, 1][self.region]))
U_reg_err = np.sqrt(np.sum(self.IQU_cov[2, 2][self.region]))
IQ_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 1][self.region] ** 2))
IU_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 2][self.region] ** 2))
QU_reg_err = np.sqrt(np.sum(self.IQU_cov[1, 2][self.region] ** 2))
I_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][self.region]))
Q_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][self.region]))
U_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][self.region]))
IQ_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][self.region] ** 2))
IU_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][self.region] ** 2))
QU_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][self.region] ** 2))
conf = PCconf(QN=Q_reg / I_reg, QN_ERR=Q_reg_err / I_reg, UN=U_reg / I_reg, UN_ERR=U_reg_err / I_reg)
if 1.0 - conf > 1e-3:
@@ -3355,6 +3387,16 @@ class pol_map(object):
)
/ I_reg
)
P_reg_stat_err = (
P_reg
/ I_reg
* np.sqrt(
I_reg_stat_err
- 2.0 / (I_reg * P_reg**2) * (Q_reg * IQ_reg_stat_err + U_reg * IU_reg_stat_err)
+ 1.0 / (I_reg**2 * P_reg**4) * (Q_reg**2 * Q_reg_stat_err + U_reg**2 * U_reg_stat_err + 2.0 * Q_reg * U_reg * QU_reg_stat_err)
)
)
debiased_P_reg = np.sqrt(P_reg**2 - P_reg_stat_err**2) if P_reg**2 > P_reg_stat_err**2 else 0.0
PA_reg = princ_angle((90.0 / np.pi) * np.arctan2(U_reg, Q_reg))
PA_reg_err = (90.0 / (np.pi * (Q_reg**2 + U_reg**2))) * np.sqrt(
@@ -3365,12 +3407,18 @@ class pol_map(object):
I_cut = self.I[new_cut].sum()
Q_cut = self.Q[new_cut].sum()
U_cut = self.U[new_cut].sum()
I_cut_err = np.sqrt(np.sum(s_I[new_cut] ** 2))
Q_cut_err = np.sqrt(np.sum(s_Q[new_cut] ** 2))
U_cut_err = np.sqrt(np.sum(s_U[new_cut] ** 2))
IQ_cut_err = np.sqrt(np.sum(s_IQ[new_cut] ** 2))
IU_cut_err = np.sqrt(np.sum(s_IU[new_cut] ** 2))
QU_cut_err = np.sqrt(np.sum(s_QU[new_cut] ** 2))
I_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 0][new_cut]))
Q_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 1][new_cut]))
U_cut_err = np.sqrt(np.sum(self.IQU_cov[2, 2][new_cut]))
IQ_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 1][new_cut] ** 2))
IU_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 2][new_cut] ** 2))
QU_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 2][new_cut] ** 2))
I_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][new_cut]))
Q_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][new_cut]))
U_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][new_cut]))
IQ_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][new_cut] ** 2))
IU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][new_cut] ** 2))
QU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][new_cut] ** 2))
with np.errstate(divide="ignore", invalid="ignore"):
P_cut = np.sqrt(Q_cut**2 + U_cut**2) / I_cut
@@ -3383,6 +3431,18 @@ class pol_map(object):
)
/ I_cut
)
P_cut_stat_err = (
P_cut
/ I_cut
* np.sqrt(
I_cut_stat_err
- 2.0 / (I_cut * P_cut**2) * (Q_cut * IQ_cut_stat_err + U_cut * IU_cut_stat_err)
+ 1.0 / (I_cut**2 * P_cut**4) * (Q_cut**2 * Q_cut_stat_err + U_cut**2 * U_cut_stat_err + 2.0 * Q_cut * U_cut * QU_cut_stat_err)
)
)
mask = P_cut**2 > P_cut_stat_err
debiased_P_cut = np.zeros(P_cut.shape)
debiased_P_cut[mask] = np.sqrt(P_cut[mask] ** 2 - P_cut_stat_err[mask] ** 2)
PA_cut = princ_angle((90.0 / np.pi) * np.arctan2(U_cut, Q_cut))
PA_cut_err = (90.0 / (np.pi * (Q_cut**2 + U_cut**2))) * np.sqrt(
@@ -3403,7 +3463,7 @@ class pol_map(object):
self.pivot_wav, sci_not(I_reg * self.map_convert, I_reg_err * self.map_convert, 2)
)
+ "\n"
+ r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+ r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+ "\n"
+ r"$\theta_{{P}}^{{int}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_reg, np.ceil(PA_reg_err * 10.0) / 10.0)
+ str_conf
@@ -3415,7 +3475,7 @@ class pol_map(object):
# self.pivot_wav, sci_not(I_cut * self.map_convert, I_cut_err * self.map_convert, 2)
# )
# + "\n"
# + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
# + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
# + "\n"
# + r"$\theta_{{P}}^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_cut, np.ceil(PA_cut_err * 10.0) / 10.0)
# )
@@ -3439,7 +3499,7 @@ class pol_map(object):
self.pivot_wav, sci_not(I_reg * self.map_convert, I_reg_err * self.map_convert, 2)
)
+ "\n"
+ r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+ r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+ "\n"
+ r"$\theta_{{P}}^{{int}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_reg, np.ceil(PA_reg_err * 10.0) / 10.0)
+ str_conf
@@ -3451,7 +3511,7 @@ class pol_map(object):
# self.pivot_wav, sci_not(I_cut * self.map_convert, I_cut_err * self.map_convert, 2)
# )
# + "\n"
# + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
# + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
# + "\n"
# + r"$\theta_{{P}}^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_cut, np.ceil(PA_cut_err * 10.0) / 10.0)
# )

175
package/lib/reduction.py
View File

@@ -1310,12 +1310,12 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
# Statistical error: Poisson noise is assumed
sigma_flux = np.array([np.sqrt(flux / head["exptime"]) for flux, head in zip(pol_flux, pol_headers)])
s_IQU_stat = np.zeros(Stokes_cov.shape)
Stokes_stat_cov = np.zeros(Stokes_cov.shape)
for i in range(Stokes_cov.shape[0]):
s_IQU_stat[i, i] = np.sum([coeff_stokes[i, k] ** 2 * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
Stokes_stat_cov[i, i] = np.sum([coeff_stokes[i, k] ** 2 * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
for j in [k for k in range(3) if k > i]:
s_IQU_stat[i, j] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
s_IQU_stat[j, i] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
Stokes_stat_cov[i, j] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
Stokes_stat_cov[j, i] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
# Compute the derivative of each Stokes parameter with respect to the polarizer orientation
dIQU_dtheta = np.zeros(Stokes_cov.shape)
@@ -1368,19 +1368,19 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
)
# Compute the uncertainty associated with the polarizers' orientation (see Kishimoto 1999)
s_IQU_axis = np.zeros(Stokes_cov.shape)
Stokes_axis_cov = np.zeros(Stokes_cov.shape)
for i in range(Stokes_cov.shape[0]):
s_IQU_axis[i, i] = np.sum([dIQU_dtheta[i, k] ** 2 * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0)
Stokes_axis_cov[i, i] = np.sum([dIQU_dtheta[i, k] ** 2 * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0)
for j in [k for k in range(3) if k > i]:
s_IQU_axis[i, j] = np.sum(
Stokes_axis_cov[i, j] = np.sum(
[abs(dIQU_dtheta[i, k] * dIQU_dtheta[j, k]) * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0
)
s_IQU_axis[j, i] = np.sum(
Stokes_axis_cov[j, i] = np.sum(
[abs(dIQU_dtheta[i, k] * dIQU_dtheta[j, k]) * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0
)
# Add quadratically the uncertainty to the Stokes covariance matrix
Stokes_cov += s_IQU_axis + s_IQU_stat
Stokes_cov += Stokes_axis_cov + Stokes_stat_cov
# Save values to single header
header_stokes = pol_headers[0]
@@ -1414,8 +1414,8 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
for i in range(3):
Stokes_cov[i, i] = np.sum([exp**2 * cov for exp, cov in zip(all_exp, all_Stokes_cov[:, i, i])], axis=0) / all_exp.sum() ** 2
for j in [x for x in range(3) if x != i]:
Stokes_cov[i, j] = np.sqrt(np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, i, j])], axis=0) / all_exp.sum() ** 2)
Stokes_cov[j, i] = np.sqrt(np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, j, i])], axis=0) / all_exp.sum() ** 2)
Stokes_cov[i, j] = np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, i, j])], axis=0) / all_exp.sum() ** 2
Stokes_cov[j, i] = np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, j, i])], axis=0) / all_exp.sum() ** 2
# Save values to single header
header_stokes = all_header_stokes[0]
@@ -1430,6 +1430,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
Q_stokes[np.isnan(Q_stokes)] = 0.0
U_stokes[np.isnan(U_stokes)] = 0.0
Stokes_cov[np.isnan(Stokes_cov)] = fmax
Stokes_stat_cov[np.isnan(Stokes_cov)] = fmax
if integrate:
# Compute integrated values for P, PA before any rotation
@@ -1443,6 +1444,12 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
IQ_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 1][mask] ** 2))
IU_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 2][mask] ** 2))
QU_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 2][mask] ** 2))
I_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 0][mask]))
Q_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 1][mask]))
U_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[2, 2][mask]))
IQ_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 1][mask] ** 2))
IU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 2][mask] ** 2))
QU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 2][mask] ** 2))
P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
P_diluted_err = np.sqrt(
@@ -1451,21 +1458,33 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
- 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
- 2.0 * (U_diluted / I_diluted) * IU_diluted_err
)
P_diluted_stat_err = (
P_diluted
/ I_diluted
* np.sqrt(
I_diluted_stat_err
- 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+ 1.0
/ (I_diluted**2 * P_diluted**4)
* (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
)
)
debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
U_diluted**2 * Q_diluted_err**2 + Q_diluted**2 * U_diluted_err**2 - 2.0 * Q_diluted * U_diluted * QU_diluted_err
)
header_stokes["P_int"] = (P_diluted, "Integrated polarization degree")
header_stokes["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
header_stokes["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
header_stokes["PA_int"] = (PA_diluted, "Integrated polarization angle")
header_stokes["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
return I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_stat
return I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes
def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_stat=None):
def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes):
"""
Compute the polarization degree (in %) and angle (in deg) and their
respective errors from given Stokes parameters.
@@ -1540,45 +1559,34 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_s
s_P[np.isnan(s_P)] = fmax
s_PA[np.isnan(s_PA)] = fmax
# Compute the total exposure time so that
# I_stokes*exp_tot = N_tot the total number of events
N_obs = I_stokes * float(header_stokes["exptime"])
# Errors on P, PA supposing Poisson noise
s_P_P = np.ones(I_stokes.shape) * fmax
s_PA_P = np.ones(I_stokes.shape) * fmax
maskP = np.logical_and(mask, P > 0.0)
if s_IQU_stat is not None:
# If IQU covariance matrix containing only statistical error is given propagate to P and PA
# Catch Invalid value in sqrt when diagonal terms are big
s_P_P[maskP] = (
P[maskP]
/ I_stokes[maskP]
* np.sqrt(
s_IQU_stat[0, 0][maskP]
- 2.0 / (I_stokes[maskP] * P[maskP] ** 2) * (Q_stokes[maskP] * s_IQU_stat[0, 1][maskP] + U_stokes[maskP] * s_IQU_stat[0, 2][maskP])
+ 1.0
/ (I_stokes[maskP] ** 2 * P[maskP] ** 4)
* (
Q_stokes[maskP] ** 2 * s_IQU_stat[1, 1][maskP]
+ U_stokes[maskP] ** 2 * s_IQU_stat[2, 2][maskP]
+ 2.0 * Q_stokes[maskP] * U_stokes[maskP] * s_IQU_stat[1, 2][maskP]
)
)
)
s_PA_P[maskP] = (
90.0
/ (np.pi * I_stokes[maskP] ** 2 * P[maskP] ** 2)
s_P_P[maskP] = (
P[maskP]
/ I_stokes[maskP]
* np.sqrt(
Stokes_stat_cov[0, 0][maskP]
- 2.0 / (I_stokes[maskP] * P[maskP] ** 2) * (Q_stokes[maskP] * Stokes_stat_cov[0, 1][maskP] + U_stokes[maskP] * Stokes_stat_cov[0, 2][maskP])
+ 1.0
/ (I_stokes[maskP] ** 2 * P[maskP] ** 4)
* (
Q_stokes[maskP] ** 2 * s_IQU_stat[2, 2][maskP]
+ U_stokes[maskP] * s_IQU_stat[1, 1][maskP]
- 2.0 * Q_stokes[maskP] * U_stokes[maskP] * s_IQU_stat[1, 2][maskP]
Q_stokes[maskP] ** 2 * Stokes_stat_cov[1, 1][maskP]
+ U_stokes[maskP] ** 2 * Stokes_stat_cov[2, 2][maskP]
+ 2.0 * Q_stokes[maskP] * U_stokes[maskP] * Stokes_stat_cov[1, 2][maskP]
)
)
else:
# Approximate Poisson error for P and PA
s_P_P[mask] = np.sqrt(2.0 / N_obs[mask])
s_PA_P[maskP] = s_P_P[maskP] / P[maskP] * 90.0 / np.pi
)
s_PA_P[maskP] = (
90.0
/ (np.pi * I_stokes[maskP] ** 2 * P[maskP] ** 2)
* (
Q_stokes[maskP] ** 2 * Stokes_stat_cov[2, 2][maskP]
+ U_stokes[maskP] * Stokes_stat_cov[1, 1][maskP]
- 2.0 * Q_stokes[maskP] * U_stokes[maskP] * Stokes_stat_cov[1, 2][maskP]
)
)
# Catch expected "OverflowWarning" as wrong pixel have an overflowing error
with warnings.catch_warnings(record=True) as _:
@@ -1600,7 +1608,7 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_s
return P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P
def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, s_IQU_stat=None, SNRi_cut=None):
def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes, SNRi_cut=None):
"""
Use scipy.ndimage.rotate to rotate I_stokes to an angle, and a rotation
matrix to rotate Q, U of a given angle in degrees and update header
@@ -1617,7 +1625,11 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
Image (2D floats) containing the Stokes parameters accounting for
+45/-45deg linear polarization intensity
Stokes_cov : numpy.ndarray
Covariance matrix of the Stokes parameters I, Q, U.
Covariance matrix containing all uncertainties of the Stokes
parameters I, Q, U.
Stokes_stat_cov : numpy.ndarray
Covariance matrix containing statistical uncertainty of the Stokes
parameters I, Q, U.
data_mask : numpy.ndarray
2D boolean array delimiting the data to work on.
header_stokes : astropy.fits.header.Header
@@ -1639,6 +1651,8 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
accounting for +45/-45deg linear polarization intensity.
new_Stokes_cov : numpy.ndarray
Updated covariance matrix of the Stokes parameters I, Q, U.
new_Stokes_stat_cov : numpy.ndarray
Updated statistical covariance matrix of the Stokes parameters I, Q, U.
new_header_stokes : astropy.fits.header.Header
Updated Header file associated with the Stokes fluxes accounting
for the new orientation angle.
@@ -1670,11 +1684,9 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
Q_stokes = zeropad(Q_stokes, shape)
U_stokes = zeropad(U_stokes, shape)
data_mask = zeropad(data_mask, shape)
Stokes_cov = zeropad(Stokes_cov, [*Stokes_cov.shape[:-2], *shape])
new_I_stokes = np.zeros(shape)
new_Q_stokes = np.zeros(shape)
new_U_stokes = np.zeros(shape)
new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape))
# Rotate original images using scipy.ndimage.rotate
new_I_stokes = sc_rotate(I_stokes, ang, order=1, reshape=False, cval=0.0)
@@ -1683,6 +1695,10 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
new_data_mask = sc_rotate(data_mask.astype(float) * 10.0, ang, order=1, reshape=False, cval=0.0)
new_data_mask[new_data_mask < 1.0] = 0.0
new_data_mask = new_data_mask.astype(bool)
# Rotate covariance matrix
Stokes_cov = zeropad(Stokes_cov, [*Stokes_cov.shape[:-2], *shape])
new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape))
for i in range(3):
for j in range(3):
new_Stokes_cov[i, j] = sc_rotate(Stokes_cov[i, j], ang, order=1, reshape=False, cval=0.0)
@@ -1693,16 +1709,16 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
new_I_stokes[i, j], new_Q_stokes[i, j], new_U_stokes[i, j] = np.dot(mrot, np.array([new_I_stokes[i, j], new_Q_stokes[i, j], new_U_stokes[i, j]])).T
new_Stokes_cov[:, :, i, j] = np.dot(mrot, np.dot(new_Stokes_cov[:, :, i, j], mrot.T))
if s_IQU_stat is not None:
s_IQU_stat = zeropad(s_IQU_stat, [*s_IQU_stat.shape[:-2], *shape])
new_s_IQU_stat = np.zeros((*s_IQU_stat.shape[:-2], *shape))
for i in range(3):
for j in range(3):
new_s_IQU_stat[i, j] = sc_rotate(s_IQU_stat[i, j], ang, order=1, reshape=False, cval=0.0)
new_s_IQU_stat[i, i] = np.abs(new_s_IQU_stat[i, i])
for i in range(shape[0]):
for j in range(shape[1]):
new_s_IQU_stat[:, :, i, j] = np.dot(mrot, np.dot(new_s_IQU_stat[:, :, i, j], mrot.T))
# Rotate statistical covariance matrix
Stokes_stat_cov = zeropad(Stokes_stat_cov, [*Stokes_stat_cov.shape[:-2], *shape])
new_Stokes_stat_cov = np.zeros((*Stokes_stat_cov.shape[:-2], *shape))
for i in range(3):
for j in range(3):
new_Stokes_stat_cov[i, j] = sc_rotate(Stokes_stat_cov[i, j], ang, order=1, reshape=False, cval=0.0)
new_Stokes_stat_cov[i, i] = np.abs(new_Stokes_stat_cov[i, i])
for i in range(shape[0]):
for j in range(shape[1]):
new_Stokes_stat_cov[:, :, i, j] = np.dot(mrot, np.dot(new_Stokes_stat_cov[:, :, i, j], mrot.T))
# Update headers to new angle
mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)], [np.sin(-alpha), np.cos(-alpha)]])
@@ -1732,35 +1748,50 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
I_diluted = new_I_stokes[mask].sum()
Q_diluted = new_Q_stokes[mask].sum()
U_diluted = new_U_stokes[mask].sum()
I_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 0][mask]))
Q_diluted_err = np.sqrt(np.sum(new_Stokes_cov[1, 1][mask]))
U_diluted_err = np.sqrt(np.sum(new_Stokes_cov[2, 2][mask]))
IQ_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 1][mask] ** 2))
IU_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 2][mask] ** 2))
QU_diluted_err = np.sqrt(np.sum(new_Stokes_cov[1, 2][mask] ** 2))
I_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 0][mask]))
Q_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 1][mask]))
U_diluted_err = np.sqrt(np.sum(Stokes_cov[2, 2][mask]))
IQ_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 1][mask] ** 2))
IU_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 2][mask] ** 2))
QU_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 2][mask] ** 2))
I_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 0][mask]))
Q_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 1][mask]))
U_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[2, 2][mask]))
IQ_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 1][mask] ** 2))
IU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 2][mask] ** 2))
QU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 2][mask] ** 2))
P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
P_diluted_err = (1.0 / I_diluted) * np.sqrt(
P_diluted_err = np.sqrt(
(Q_diluted**2 * Q_diluted_err**2 + U_diluted**2 * U_diluted_err**2 + 2.0 * Q_diluted * U_diluted * QU_diluted_err) / (Q_diluted**2 + U_diluted**2)
+ ((Q_diluted / I_diluted) ** 2 + (U_diluted / I_diluted) ** 2) * I_diluted_err**2
- 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
- 2.0 * (U_diluted / I_diluted) * IU_diluted_err
)
P_diluted_stat_err = (
P_diluted
/ I_diluted
* np.sqrt(
I_diluted_stat_err
- 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+ 1.0
/ (I_diluted**2 * P_diluted**4)
* (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
)
)
debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
U_diluted**2 * Q_diluted_err**2 + Q_diluted**2 * U_diluted_err**2 - 2.0 * Q_diluted * U_diluted * QU_diluted_err
)
new_header_stokes["P_int"] = (P_diluted, "Integrated polarization degree")
new_header_stokes["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
new_header_stokes["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
new_header_stokes["PA_int"] = (PA_diluted, "Integrated polarization angle")
new_header_stokes["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
if s_IQU_stat is not None:
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_data_mask, new_header_stokes, new_s_IQU_stat
else:
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_data_mask, new_header_stokes
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_Stokes_stat_cov, new_data_mask, new_header_stokes
def rotate_data(data_array, error_array, data_mask, headers):

4
package/src/emission_center.py
View File

@@ -43,7 +43,9 @@ def main(infile, P_cut=0.99, target=None, display="pf", output_dir=None):
if target is None:
target = Stokes[0].header["TARGNAME"]
fig = figure(figsize=(8, 8.5), layout="constrained")
ratiox = max(int(stkI.shape[1] / (stkI.shape[0])), 1)
ratioy = max(int((stkI.shape[0]) / stkI.shape[1]), 1)
fig = figure(figsize=(8 * ratiox, 8 * ratioy), layout="constrained")
fig, ax = polarization_map(Stokes, P_cut=P_cut, step_vec=1, scale_vec=5, display=display, fig=fig, width=0.33, linewidth=0.5)
ax.plot(*Stokescenter, marker="+", color="k", lw=3)