Covariances¶
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class
sacc.covariance.BaseCovariance[source]¶ The abstract base class for covariances in different forms.
The three concrete subclasses that are created are:
FullCovariance - for dense matrices
- BlockDiagonalCovariance - for block diagonal matrices
- (those in which some sub-blocks are dense but without correlation between the blocks
DiagonalCovariance - a covariance where the elements are uncorrelated
Attributes: - cov_type: string
The type of the covariance (class variable)
Methods
from_hdu(hdu)Make a covariance object from an astropy FITS HDU object. make(cov)Make an appropriate covariance object from the matrix info itself. -
classmethod
from_hdu(hdu)[source]¶ Make a covariance object from an astropy FITS HDU object.
The type of the covariance is determined from a keyword in the HDU, and then the corresponding subclass from_hdu method is called.
Parameters: - hdu: astropy.fits.ImageHDU instance
An HDU object with covariance info in it
- Returns: instance
A covariance instance
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classmethod
make(cov)[source]¶ Make an appropriate covariance object from the matrix info itself.
You can pass in a list of covariance blocks for a block-diagonal, covariance a 1D array for a diagonal covariance, or a full matrix.
A different subclass is returned for each of these cases.
Parameters: - cov: list[array] or array
If a list, the total length of all the arrays in it should equal n. If an array, it should be either 1D of length n or 2D of shape (n x n).
- n: int
length of the data vector to which this covariance applies
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class
sacc.covariance.BlockDiagonalCovariance(blocks)[source]¶ A covariance subclass representing block diagonal covariances
Block diagonal covariances have sub-blocks that are full dense matrices, but without correlations between the blocks. This feature can be taken advantage of when doing matrix operations like multiplication or inversion.
Attributes: - blocks: list[arrays]
list of sub-blocks of the matrix
- block_sizes: list[int]
list of sizes n of each the n x n sub-blocks
- size: int
overall total size of the matrix
Methods
from_hdu(hdu)Read a covariance object from a loaded FITS HDU. get_block(self, indices)Read a (not necessarily contiguous) sublock of the matrix inverted(self)Return the inverse of the covariance matrix, as a dense array. make(cov)Make an appropriate covariance object from the matrix info itself. masked(self, mask)Return a new matrix with only the masked elements retained. to_hdu(self)Write a FITS HDU from the data, ready to be saved. -
classmethod
from_hdu(hdu)[source]¶ Read a covariance object from a loaded FITS HDU.
Parameters: - hdu: FITS HDU object as read in by astropy.
Returns: - cov: BlockDiagonalCovariance
Loaded covariance object
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get_block(self, indices)[source]¶ Read a (not necessarily contiguous) sublock of the matrix
Parameters: - indices: array
An array of integer indices, which must be in ascending order
Returns: - cov: array
A full (dense) 2x2 array of the submatrix.
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inverted(self)[source]¶ Return the inverse of the covariance matrix, as a dense array.
Returns: - invC: array
Inverse covariance
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masked(self, mask)[source]¶ Return a new matrix with only the masked elements retained.
This method will try to return another BlockDiagonalCovariance if it can, but otherwise will revert to a full one: if the mask passed in is of a boolean type or if it is integers in it can remain block diagonal
Parameters: - mask: array or list
Either an array or list of integer indices, or a boolean array of the same size (1D) as the matrix. Specifies rows/cols to keep in the new matrix.
Returns: - cov: FullCovariance or BlockDiagonalCovariance
A covariance with only the corresponding data points remaining
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class
sacc.covariance.DiagonalCovariance(variances)[source]¶ A covariance subclass representing covariances that are purely diagonal.
Attributes: - size: int
The size of the matrix
- diag: array
The diagonal terms in the covariance (i.e. the variances)
Methods
from_hdu(hdu)Load a covariance object from the data in the HDU get_block(self, indices)Read a (not necessarily contiguous) sublock of the matrix inverted(self)Return the inverse of the covariance matrix, as a dense array. make(cov)Make an appropriate covariance object from the matrix info itself. masked(self, mask)Return a new DiagonalCovariance with only the masked elements retained. to_hdu(self)Make an astropy FITS HDU object with this covariance in it. -
classmethod
from_hdu(hdu)[source]¶ Load a covariance object from the data in the HDU
Parameters: - hdu: astropy.fits.BinTableHDU instance
Returns: - cov: DiagonalCovariance
Loaded covariance object
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get_block(self, indices)[source]¶ Read a (not necessarily contiguous) sublock of the matrix
Parameters: - indices: array
An array of integer indices, which should be in ascending order (for consistency with the block diagonal interface)
Returns: - cov: array
A full (dense) 2x2 array of the submatrix.
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inverted(self)[source]¶ Return the inverse of the covariance matrix, as a dense array.
Returns: - invC: array
Inverse covariance
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masked(self, mask)[source]¶ Return a new DiagonalCovariance with only the masked elements retained.
Parameters: - mask: array or list
Either an array or list of integer indices, or a boolean array of the same size (1D) as the matrix. Specifies rows/cols to keep in the new matrix.
Returns: - cov: DiagonalCovariance
A covariance with only the corresponding data points remaining
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class
sacc.covariance.FullCovariance(covmat)[source]¶ A covariance subclass representing a full matrix with correlations anywhere. Represented as an n x n matrix.
Attributes: - size: int
the length of the corresponding data vector
- covmat: 2D array
The matrix itself, of shape (size x size)
Methods
from_hdu(hdu)Load a covariance object from the data in the HDU get_block(self, indices)Read a (not necessarily contiguous) sublock of the matrix inverted(self)Return the inverse of the covariance matrix, as a dense array. make(cov)Make an appropriate covariance object from the matrix info itself. masked(self, mask)Return a new matrix with only the masked elements retained. to_hdu(self)Make an astropy FITS HDU object with this covariance in it. -
classmethod
from_hdu(hdu)[source]¶ Load a covariance object from the data in the HDU
Parameters: - hdu: astropy.fits.ImageHDU instance
Returns: - cov: FullCovariance
Loaded covariance object
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get_block(self, indices)[source]¶ Read a (not necessarily contiguous) sublock of the matrix
Parameters: - indices: array
An array of integer indices
Returns: - block: array
a 2D array of the relevant sub-block of the matrix
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inverted(self)[source]¶ Return the inverse of the covariance matrix, as a dense array.
Returns: - invC: array
Inverse covariance
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masked(self, mask)[source]¶ Return a new matrix with only the masked elements retained.
Parameters: - mask: array or list
Either an array or list of integer indices, or a boolean array of the same size (1D) as the matrix. Specifies rows/cols to keep in the new matrix.
Returns: - cov: FullCovariance
A covariance with only the corresponding data points remaining