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LSST Data Management Base Package
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Functions | |
covar_to_ellipse (sigma_x_sq, sigma_y_sq, cov_xy, degrees=False) | |
gauss2dint (xdivsigma) | |
lsst.gauss2d.utils.covar_to_ellipse | ( | sigma_x_sq, | |
sigma_y_sq, | |||
cov_xy, | |||
degrees = False ) |
Convert covariance matrix terms to ellipse major axis, axis ratio and position angle representation. Parameters ---------- sigma_x_sq, sigma_y_sq : `float` or array-like x- and y-axis squared standard deviations of a 2-dimensional normal distribution (diagonal terms of its covariance matrix). Must be scalar or identical length array-likes. cov_xy : `float` or array-like x-y covariance of a of a 2-dimensional normal distribution (off-diagonal term of its covariance matrix). Must be scalar or identical length array-likes. degrees : `bool` Whether to return the position angle in degrees instead of radians. Returns ------- r_major, axrat, angle : `float` or array-like Converted major-axis radius, axis ratio and position angle (counter-clockwise from the +x axis) of the ellipse defined by each set of input covariance matrix terms. Notes ----- The eigenvalues from the determinant of a covariance matrix are: |a-m b| |b c-m| det = (a-m)(c-m) - b^2 = ac - (a+c)m + m^2 - b^2 = m^2 - (a+c)m + (ac-b^2) Solving: m = ((a+c) +/- sqrt((a+c)^2 - 4(ac-b^2)))/2 ...or equivalently: m = ((a+c) +/- sqrt((a-c)^2 + 4b^2))/2 Unfortunately, the latter simplification is not as well-behaved in floating point math, leading to square roots of negative numbers when one of a or c is very close to zero. The values from this function should match those from `Ellipse.make_ellipse_major` to within rounding error, except in the special case of sigma_x == sigma_y == 0, which returns a NaN axis ratio here by default. This function mainly intended to be more convenient (and possibly faster) for array-like inputs.
Definition at line 25 of file utils.py.
lsst.gauss2d.utils.gauss2dint | ( | xdivsigma | ) |
Return the fraction of the total surface integral of a 2D Gaussian contained with a given multiple of its dispersion. Parameters ---------- xdivsigma : `float` The multiple of the dispersion to integrate to. Returns ------- frac : `float` The fraction of the surface integral contained within an ellipse of size `xdivsigma`. Notes ----- This solution can be computed as follows: https://www.wolframalpha.com/input/?i= Integrate+2*pi*x*exp(-x%5E2%2F(2*s%5E2))%2F(s*sqrt(2*pi))+dx+from+0+to+r
Definition at line 81 of file utils.py.