200 lines
6.8 KiB
Python
Executable File
200 lines
6.8 KiB
Python
Executable File
import numpy as np
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def rot2D(ang):
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"""
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Return the 2D rotation matrix of given angle in degrees
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----------
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Inputs:
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ang : float
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Angle in degrees
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----------
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Returns:
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rot_mat : numpy.ndarray
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2D matrix of shape (2,2) to perform vector rotation at angle "ang".
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"""
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alpha = np.pi * ang / 180
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return np.array([[np.cos(alpha), np.sin(alpha)], [-np.sin(alpha), np.cos(alpha)]])
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def princ_angle(ang):
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"""
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Return the principal angle in the 0° to 180° quadrant as PA is always
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defined at p/m 180°.
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----------
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Inputs:
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ang : float, numpy.ndarray
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Angle in degrees. Can be an array of angles.
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----------
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Returns:
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princ_ang : float, numpy.ndarray
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Principal angle in the 0°-180° quadrant in the same shape as input.
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"""
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if not isinstance(ang, np.ndarray):
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A = np.array([ang])
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else:
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A = np.array(ang)
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while np.any(A < 0.0):
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A[A < 0.0] = A[A < 0.0] + 360.0
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while np.any(A >= 180.0):
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A[A >= 180.0] = A[A >= 180.0] - 180.0
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if type(ang) is type(A):
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return A
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else:
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return A[0]
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def PCconf(QN, UN, QN_ERR, UN_ERR):
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"""
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Compute the confidence level for 2 parameters polarisation degree and
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polarisation angle from the PCUBE analysis.
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----------
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Inputs:
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QN : float, numpy.ndarray
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Normalized Q Stokes flux.
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UN : float, numpy.ndarray
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Normalized U Stokes flux.
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QN_ERR : float, numpy.ndarray
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Normalized error on Q Stokes flux.
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UN_ERR : float, numpy.ndarray
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Normalized error on U Stokes flux.
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----------
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Returns:
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conf : numpy.ndarray
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2D matrix of same shape as input containing the confidence on the polarization
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computation between 0 and 1 for 2 parameters of interest (Q and U Stokes fluxes).
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"""
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mask = np.logical_and(QN_ERR > 0.0, UN_ERR > 0.0)
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conf = np.full(QN.shape, -1.0)
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chi2 = QN**2 / QN_ERR**2 + UN**2 / UN_ERR**2
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conf[mask] = 1.0 - np.exp(-0.5 * chi2[mask])
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return conf
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def CenterConf(mask, PA, sPA):
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"""
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Compute the confidence map for the position of the center of emission.
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----------
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Inputs:
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mask : bool, numpy.ndarray
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Mask of the polarization vectors from which the center of emission should be drawn.
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PA : float, numpy.ndarray
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2D matrix containing the computed polarization angle.
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sPA : float, numpy.ndarray
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2D matrix containing the total uncertainties on the polarization angle.
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----------
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Returns:
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conf : numpy.ndarray
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2D matrix of same shape as input containing the confidence on the polarization
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computation between 0 and 1 for 2 parameters of interest (Q and U Stokes fluxes).
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"""
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chi2 = np.full(PA.shape, np.nan, dtype=np.float64)
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conf = np.full(PA.shape, -1.0, dtype=np.float64)
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yy, xx = np.indices(PA.shape)
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Nobs = np.sum(mask)
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def ideal(c):
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itheta = np.full(PA.shape, np.nan)
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itheta[(xx + 0.5) != c[0]] = np.degrees(np.arctan((yy[(xx + 0.5) != c[0]] + 0.5 - c[1]) / (xx[(xx + 0.5) != c[0]] + 0.5 - c[0])))
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itheta[(xx + 0.5) == c[0]] = PA[(xx + 0.5) == c[0]]
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return princ_angle(itheta)
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def chisq(c):
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return np.sum((princ_angle(PA[mask]) - ideal((c[0], c[1]))[mask]) ** 2 / sPA[mask] ** 2) / (Nobs - 2)
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for x, y in zip(xx[np.isfinite(PA)], yy[np.isfinite(PA)]):
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chi2[y, x] = chisq((x, y))
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from scipy.optimize import minimize
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conf[np.isfinite(PA)] = 0.5 * np.exp(-0.5 * chi2[np.isfinite(PA)])
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c0 = np.unravel_index(np.argmax(conf), conf.shape)[::-1]
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result = minimize(chisq, c0, bounds=[(0, PA.shape[1]), (0.0, PA.shape[0])], method="TNC")
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if result.success:
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print("Center of emission found: reduced chi_squared {0:.2f}/{1:d}={2:.2f}".format(chisq(result.x) * (Nobs - 2), Nobs - 2, chisq(result.x)))
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else:
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print("Center of emission not found", result)
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return conf, result.x
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def sci_not(v, err, rnd=1, out=str):
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"""
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Return the scientific error notation as a string.
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----------
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Inputs:
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v : float
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Value to be transformed into scientific notation.
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err : float
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Error on the value to be transformed into scientific notation.
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rnd : int
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Number of significant numbers for the scientific notation.
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Default to 1.
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out : str or other
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Format in which the notation should be returned. "str" means the notation
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is returned as a single string, "other" means it is returned as a list of "str".
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Default to str.
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----------
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Returns:
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conf : numpy.ndarray
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2D matrix of same shape as input containing the confidence on the polarization
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computation between 0 and 1 for 2 parameters of interest (Q and U Stokes fluxes).
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"""
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power = -int(("%E" % v)[-3:]) + 1
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output = [r"({0}".format(round(v * 10**power, rnd)), round(v * 10**power, rnd)]
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if isinstance(err, list):
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for error in err:
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output[0] += r" $\pm$ {0}".format(round(error * 10**power, rnd))
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output.append(round(error * 10**power, rnd))
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else:
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output[0] += r" $\pm$ {0}".format(round(err * 10**power, rnd))
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output.append(round(err * 10**power, rnd))
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if out is str:
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return output[0] + r")e{0}".format(-power)
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else:
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return *output[1:], -power
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def wcs_CD_to_PC(CD):
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"""
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Return the position angle in degrees to the North direction of a wcs
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from the values of coefficient of its transformation matrix.
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----------
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Inputs:
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CD : np.ndarray
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Value of the WCS matrix CD
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----------
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Returns:
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cdelt : (float, float)
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Scaling factor in arcsec between pixel in X and Y directions.
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orient : float
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Angle in degrees between the North direction and the Up direction of the WCS.
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"""
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det = CD[0, 0] * CD[1, 1] - CD[0, 1] * CD[1, 0]
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sgn = -1.0 if det < 0 else 1.0
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cdelt = np.array([sgn, 1.0]) * np.sqrt(np.sum(CD**2, axis=1))
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rot = np.arctan2(-CD[1, 0], sgn * CD[0, 0])
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rot2 = np.arctan2(sgn * CD[0, 1], CD[1, 1])
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orient = 0.5 * (rot + rot2) * 180.0 / np.pi
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return cdelt, orient
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def wcs_PA(PC, cdelt):
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"""
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Return the position angle in degrees to the North direction of a wcs
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from the values of coefficient of its transformation matrix.
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----------
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Inputs:
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PC : np.ndarray
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Value of the WCS matrix PC
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cdelt : (float, float)
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Scaling factor in arcsec between pixel in X and Y directions.
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----------
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Returns:
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orient : float
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Angle in degrees between the North direction and the Up direction of the WCS.
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"""
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rot = np.pi / 2.0 - np.arctan2(-cdelt[1] * PC[1, 0], abs(cdelt[0]) * PC[0, 0])
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rot2 = np.pi / 2.0 - np.arctan2(abs(cdelt[0]) * PC[0, 1], cdelt[1] * PC[1, 1])
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orient = 0.5 * (rot + rot2) * 180.0 / np.pi
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return orient
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