Covariance

class spizzle.Covariance(out_shape, radius=None, dtype=<class 'numpy.float32'>, fillval=nan)

Bases: object

Covariance between nearby pixels of the image of drizzled exposures.

Add the same operators as to Coadd, each with the variance of its exposure’s data (for example the sum of its variance planes); the image is Coadd.out_img. The covariance is kept for the offsets (dy, dx) with |dy|, |dx| <= radius, for half of them, listed in offsets: (0, 0), then (0, 1) to (0, radius), then (dy, -radius) to (dy, radius) for dy from 1 to radius. The others follow from Cov(img[y, x], img[y - dy, x - dx]) = covariance(k)[y - dy, x - dx].

Pixels farther apart than an input pixel’s footprint share no input pixel and have no covariance; Operator.reach is that distance. By default the radius is the reach of the first operator added. An operator that reaches farther than the radius gives a warning, as the covariance beyond the radius is left out.

The sums take 2 * radius * (radius + 1) + 1 output-sized images of dtype; each exposure’s contribution is computed in float64 before it is added. Output pixels that no exposure reaches are not written, so the system does not give them memory until the results are made. The results are made one image at a time.

Parameters:

out_shapetuple of int

(ny_out, nx_out).

radiusint, optional

Largest offset kept, in output pixels, in y and in x; by default the reach of the first operator added.

dtype{numpy.float32, numpy.float64}

Type of the sums and of the results.

fillvalfloat

Value where the pixel or its neighbor has no weight or variance, or the neighbor is outside the output grid.

Attributes Summary

noise_factor	ndarray, shape out_shape: covariance of each pixel with every pixel, over its variance.
out_cov	ndarray, shape (n_offsets,) + out_shape: covariance for every offset, all in memory at once.
out_var	ndarray, shape out_shape: variance of the image, covariance at offset (0, 0).

Methods Summary

add(W, var[, iscale])	Add one exposure.
correlation(k)	Correlation coefficient of each pixel with its neighbor at offsets[k].
covariance(k)	Covariance of each pixel with its neighbor at offsets[k].
write_correlation(path[, overwrite])	Write the correlation of each pixel with its neighbors to a FITS file.

Attributes Documentation

noise_factor

ndarray, shape out_shape: covariance of each pixel with every pixel, over its variance.

The variance of a sum over an area much larger than an input pixel’s footprint is the sum of the variances of its pixels times this factor, so sqrt(var * noise_factor) is the uncertainty of each pixel for such sums, where sqrt(var) is that of the pixel alone. For evenly dithered exposures it is the square of the noise ratio R of Casertano et al. (2000). fillval where the pixel has no weight or variance.

out_cov

ndarray, shape (n_offsets,) + out_shape: covariance for every offset, all in memory at once.

out_var

ndarray, shape out_shape: variance of the image, covariance at offset (0, 0).

Methods Documentation

add(W, var, iscale=1.0)

Add one exposure.

Parameters:

WOperator or scipy.sparse array

The exposure’s operator, as for Coadd.add. A sparse array records no reach, so it needs the radius to be set.

varndarray, shape (ny, nx)

Variance of the exposure’s data.

iscalefloat

Factor applied to the data; its square is applied to var.

correlation(k)

Correlation coefficient of each pixel with its neighbor at offsets[k].

Parameters:

kint

Returns:

ndarray, shape out_shape

Cov(img[o], img[o']) / sqrt(Var(img[o]) Var(img[o'])); fillval where either pixel has no variance or the neighbor is off the grid.

covariance(k)

Covariance of each pixel with its neighbor at offsets[k].

Parameters:

kint

Returns:

ndarray, shape out_shape

Cov(img[y, x], img[y + dy, x + dx]); fillval where either pixel has no weight or the neighbor is off the grid.

write_correlation(path, overwrite=False)

Write the correlation of each pixel with its neighbors to a FITS file.

Extension CORR is a float32 cube of shape (n_offsets - 1,) + out_shape whose plane k - 1 is correlation for offsets[k], k from 1, and extension OFFSETS a table of their dy and dx; the primary header has the radius. The planes are made and written one at a time. Needs astropy.

Parameters:

pathstr or os.PathLike

overwritebool

Replace an existing file.