pyimcom.lakernel

Linear algebra kernels to solve linear systems.

Classes

_LAKernel: Abstract base class of linear algebra kernels.
EigenKernel: LA kernel using eigendecomposition.
CholKernel: LA kernel using Cholesky decomposition.
IterKernel: LA kernel using iterative method.
EmpirKernel: Fake LA kernel using empirical relation.

Functions

conjugate_gradient: Simplified version of scipy.sparse.linalg.cg.
_extract_submatrix: Extract a submatrix from a symmetric matrix.
_extract_subvector: Extract a subvector from a vector.
_assign_subvector: Assign values to a subvector of a vector.

Classes

`_LAKernel`	Abstract base class of linear algebra kernels.
`EigenKernel`	LA kernel using eigendecomposition.
`CholKernel`	LA kernel using Cholesky decomposition.
`IterKernel`	LA kernel using iterative method.
`EmpirKernel`	Fake LA kernel using empirical relation.

Functions

`conjugate_gradient`(→ numpy.array)	Simplified version of scipy.sparse.linalg.cg.
`_extract_submatrix`(→ numpy.array)	Extract a submatrix from a symmetric matrix.
`_extract_subvector`(→ numpy.array)	Extract a subvector from a vector.
`_assign_subvector`(→ None)	Assign values to a subvector of a vector.

Module Contents

class _LAKernel(outst)[source]

Abstract base class of linear algebra kernels.

Parameters:: outst (coadd.OutStamp) – Output postage stamp to which this kernel instance is attached.

__init__()[source]: Constructor.

__call__()[source]: Solve linear systems.

outst[source]

n_out[source]

m[source]

n[source]

n2f[source]

kappaC_arr[source]

nv[source]

ucmin[source]

smax[source]

__call__() → None[source]

Solve linear systems.

Return type:: None

Notes

This produces the following arrays for self.outst:

T = coaddition matrix, shape = (n_out, m, n)
UC = fractional squared error in PSF, shape = (n_out, m)
Sigma = output noise amplification, shape = (n_out, m)
kappa = Lagrange multiplier per output pixel, shape = (n_out, m)

class EigenKernel(outst)[source]

Bases: _LAKernel

LA kernel using eigendecomposition.

_call_single_kappa()[source]: Solve linear systems for single kappa node.

_call_multi_kappa()[source]: Solve linear systems for multiple kappa nodes.

_call_single_kappa() → None[source]: Solve linear systems for single kappa node.

_call_multi_kappa(nbis: int = 13) → None[source]

Solve linear systems for multiple kappa nodes.

Parameters:: nbis (int, optional) – Number of bisections.
Return type:: None

Notes

Based on pyimcom_lakernel.CKernelMulti of furry-parakeet. This one generates multiple images. there can be n_out target PSFs.

class CholKernel(outst)[source]

Bases: _LAKernel

LA kernel using Cholesky decomposition.

_cholesky_wrapper()[source]: Wrapper for cholesky (staticmethod)

_call_single_kappa()[source]: Solve linear systems for single kappa node.

_call_multi_kappa()[source]: Solve linear systems for multiple kappa nodes.

static _cholesky_wrapper(AA: numpy.array, di: tuple[numpy.array, numpy.array], A: numpy.array) → numpy.array[source]

Wrapper for cholesky, rectifies negative eigenvalue(s) if needed.

Parameters:

AA (np.array) – System matrix A plus kappa times noise; shape (n,n).
di ((np.array, np.array)) – Indices to main diagonal of AA; each has shape (n,).
A (np.array) – Original system matrix; shape (n,n).

Returns:

L – Cholesky results; shape (n,n).

Return type:

np.array

_call_single_kappa() → None[source]: Solve linear systems for single kappa node.

_call_multi_kappa() → None[source]

Solve linear systems for multiple kappa nodes.

Return type:: None

Notes

Based on pyimcom_lakernel.get_coadd_matrix_discrete of furry-parakeet: alternative to CKernelMulti, almost same functionality but has a range of kappa.

conjugate_gradient(A: numpy.array, b: numpy.array, rtol: float = 0.0015, maxiter: int = 30) → numpy.array[source]

Simplified version of scipy.sparse.linalg.cg.

Parameters:

A (np.array) – System matrix A, shape (n,n)
b (np.array) – Column vector b, shape (n,).
rtol (float, optional) – Relative tolerance.
maxiter (int, optional) – Maximum number of iterations.

Returns:

x – Solution vector b, shape (n,).

Return type:

np.array

_extract_submatrix(mat_orig: numpy.array, selection: numpy.array) → numpy.array[source]

Extract a submatrix from a symmetric matrix.

Parameters:

mat_orig (np.array) – Symmetric matrix to be extracted, shape (n,n).
selection (np.array) – Integer array of indices of rows and columns to extract, shape (n,).

Returns:

mat_copy – Extracted submatrix. Shape (n_,n_), where n_ is number of selected rows or columns.

Return type:

np.array

_extract_subvector(vec_orig: numpy.array, selection: numpy.array) → numpy.array[source]

Extract a subvector from a vector.

Parameters:

vec_orig (np.array) – Vector to be extracted, shape (n,).
selection (np.array) – Integer array of indices of elements to extract, shape (n,).

Returns:

vec_copy – Extracted subvector. Shape (n_,) where n_ is number of selected elements.

Return type:

np.array

_assign_subvector(vec_left: numpy.array, vec_right: numpy.array, selection: numpy.array) → None[source]

Assign values to a subvector of a vector.

Parameters:

vec_left (np.array) – Vector to be assigned to.
vec_right (np.array) – Subvector of values to assign.
selection (np.array) – Integer array of indices of elements to assign to; same length as vec_left.

Return type:

None

class IterKernel(outst)[source]

Bases: _LAKernel

LA kernel using iterative method.

_iterative_wrapper()[source]: Wrapper for iterative method (staticmethod).

_call_single_kappa()[source]: Solve linear systems for single kappa node.

_call_multi_kappa()[source]: Solve linear systems for multiple kappa nodes.

static _iterative_wrapper(AA: numpy.array, mBhalf: numpy.array, relevant_matrix: numpy.array, rtol: float = 0.0015, maxiter: int = 30) → numpy.array[source]

Wrapper for conjugate gradient method.

Parameters:

AA (np.array) – System matrix A plus kappa times noise. Shape (n,n).
mBhalf (np.array) – System matrix -B/2 (for a single target PSF). Shape (n,n).
relevant_matrix (np.array) – Boolean array indicating whether to use an input pixel for an output pixel. Shape (m,n).
rtol (float, optional) – Relative tolerance.
maxiter (int, optional) – Maximum number of iteration.

Returns:

Output T matrix (for a single target PSF). Shape (m,n).

Return type:

np.array

_call_single_kappa(exact_UC: bool = False) → None[source]

Solve linear systems for single kappa node.

Parameters:: exact_UC (bool, optional) – Whether to use exact expression for U/C. The default is False, as this is slow and the gain is very small.
Return type:: None

_call_multi_kappa(exact_UC: bool = True) → None[source]

Solve linear systems for multiple kappa nodes.

Parameters:: exact_UC (bool, optional) – Whether to use exact expression for U/C. The default is True, as the approximation does not work. KC: Please avoid this whenever possible as this is SUPER slow.
Return type:: None

class EmpirKernel(outst)[source]

Bases: _LAKernel

Fake LA kernel using empirical relation.

_call_single_kappa()[source]: Produce the T matrix without solving linear systems.

_call_multi_kappa()[source]: Pathway to _call_single_kappa.

_call_single_kappa() → None[source]: Produce the T matrix without solving linear systems.

_call_multi_kappa() → None[source]: Pathway to _call_single_kappa, since the empirical kernel doesn’t use kappa.