lit: Non-linear structure formation

Slides from F. van den Bosch, from a talk given at Jerusalem Winter School.
A Gaussian random field is completely specified by either the two-point correlation function ξ(r), or, equivalently, the power spectrum P(k)

Centering and clipping image, sigma-clipping (ds9 like) in Matplotlib

I wanted to cut out the galaxies I ran Galfit on, then clip the pixel values and save to an image (which is picked up by LaTeX). Here's the source.

Creating a discrete Gaussian kernel with Python

Discrete Gaussian kernels are often used for convolution in signal processing, or, in my case, weighting. I used some hardcoded values before, but here's a recipe for making it on-the-fly.

def gauss_kern(size, sizey=None):
    """ Returns a normalized 2D gauss kernel array for convolutions """
    size = int(size)
    if not sizey:
        sizey = size
    else:
        sizey = int(sizey)
    x, y = mgrid[-size:size+1, -sizey:sizey+1]
    g = exp(-(x**2/float(size)+y**2/float(sizey)))
    return g / g.sum()

Note that 'size' here refers to (shape[0]/2 - 1), i.e. the resulting kernel side is size*2 + 1 long. I need to use a kernel with a central value of 1, so I adjusted the normalisation accordingly:

def gauss_kern(size, sizey=None):
    """ Returns a normalized 2D gauss kernel array for convolutions """
    size = int(size)
    if not sizey:
        sizey = size
    else:
        sizey = int(sizey)
    x, y = scipy.mgrid[-size:size+1, -sizey:sizey+1]
    g = scipy.exp(-(x**2/float(size)+y**2/float(sizey)))
    return g / g.max()