brahmap.lbsim.LBSim_InvNoiseCovLO_UnCorr

Bases: BlockDiagInvNoiseCovLO

A block-diagonal linear operator representing the inverse of an uncorrelated noise covariance matrix \(N^{-1}\).

It assumes that for a given MPI process, all observations contain the same set of detectors.

Parameters:

Name	Type	Description	Default
obs	Observation | List[Observation]	An instance of the Observation class or a list of the same	required
noise_variance	dict | float | None	The expected variance of the noise for the given detectors, by default None. It can be a dictionary that maps the detector name to their noise variance OR a single value that is used for all detectors. If set as None, inverse noise variance is set to 1 for each detector for the entire observation duration	None
dtype	DTypeFloat	The data type of the operator, by default np.float64	float64

Methods:

Name	Description
reset_counters	Resets matrix-vector product counter to zero.
dot	Numpy-like dot() method.
matvec	Matrix-vector multiplication method.
to_array	Returns the dense form of the linear operator as a 2D NumPy array.
get_inverse	Returns the inverse block-diagonal covariance operator.

Attributes:

Name	Type	Description
dtype	DTypeLike	The data type of the operator.
nargin	int	Size of the input vector \(x\), i.e. the number of columns of the operator
nargout	int	Size of the output vector \(A(x)\), i.e. the number of rows of the operator
symmetric	bool	Indicates whether the operator is symmetric or not
shape	tuple[int, int]	A tuple (nargout, nargin) representing the shape of the operator
nMatvec	int	The number of matrix-vector multiplications computed so far
T	LinearOperator	The transpose operator
H	LinearOperator	The adjoint operator
block_list	list[LinearOperator]	A list of linear operators representing the individual diagonal blocks.
num_blocks	int	The total number of diagonal blocks in the operator.
row_size	NDArray[integer]	Array containing the number of rows for each block.
col_size	NDArray[integer]	Array containing the number of columns for each block.
size	int	Array containing the number of rows/columns for each block
diag	NDArray[number]	Array containing the diagonal of the operator

Source code in brahmap/lbsim/lbsim_noise_operators.py

class LBSim_InvNoiseCovLO_UnCorr(BlockDiagInvNoiseCovLO):
    """A block-diagonal linear operator representing the inverse of an
    uncorrelated noise covariance matrix $N^{-1}$.

    It assumes that for a given MPI process, all observations contain the
    same set of detectors.

    Parameters
    ----------
    obs : lbs.Observation | List[lbs.Observation]
        An instance of the `Observation` class or a list of the same
    noise_variance : dict | float | None, optional
        The expected variance of the noise for the given detectors, by
        default `None`. It can be a dictionary that maps the detector
        name to their noise variance OR a single value that is used for
        all detectors. If set as `None`, inverse noise variance is set to
        1 for each detector for the entire observation duration
    dtype : DTypeFloat, optional
        The data type of the operator, by default `np.float64`
    """

    # Keep a note of the hard-coded factor of 1e4

    def __init__(
        self,
        obs: lbs.Observation | List[lbs.Observation],
        noise_variance: dict | float | None = None,
        dtype: DTypeFloat = np.float64,
    ) -> None:
        if isinstance(obs, lbs.Observation):
            obs_list = [obs]
        else:
            obs_list = obs

        if noise_variance is None:
            noise_var_dict: dict = dict(
                zip(
                    obs_list[0].name,
                    lbs.mapmaking.common.get_map_making_weights(obs_list[0]) / 1.0e4,
                )
            )
        elif isinstance(noise_variance, numbers.Number):
            noise_var_dict = dict(
                zip(
                    obs_list[0].name,
                    [noise_variance] * len(obs_list[0].name),
                )
            )
        else:
            noise_var_dict = cast(dict, noise_variance)

        # setting the `noise_variance` to 1 for the detectors whose noise variance is
        # not provided in the dictionary
        det_no_variance = np.setdiff1d(obs_list[0].name, list(noise_var_dict.keys()))
        for detector in det_no_variance:
            noise_var_dict[detector] = 1.0

        block_size = []

        if len(set(noise_var_dict.values())) == 1:
            # That is, when all values in noise variance is the same
            block_input_dict: dict = {}
            for obs in obs_list:
                for det_idx in range(obs.n_detectors):
                    block_size.append(obs.n_samples)
                    if obs.n_samples not in block_input_dict:
                        block_input_dict[obs.n_samples] = noise_var_dict[obs.name[0]]
            block_input = block_input_dict
        else:
            block_input = []
            for obs in obs_list:
                for det_idx in range(obs.n_detectors):
                    block_size.append(obs.n_samples)
                    block_input.append(noise_var_dict[obs.name[det_idx]])

        super(LBSim_InvNoiseCovLO_UnCorr, self).__init__(
            InvNoiseCovLO_Diagonal,
            block_size=block_size,
            block_input=block_input,
            input_type="covariance",
            dtype=dtype,
        )

Attributes

dtype: npt.DTypeLike property writable

The data type of the operator.

Returns:

Type	Description
DTypeLike	The NumPy data type of the operator

nargin: int property

Size of the input vector \(x\), i.e. the number of columns of the operator

Returns:

Type	Description
int	The number of input columns

nargout: int property

Size of the output vector \(A(x)\), i.e. the number of rows of the operator

Returns:

Type	Description
int	The number of output rows

symmetric: bool property

Indicates whether the operator is symmetric or not

Returns:

Type	Description
bool	True if symmetric, False otherwise

shape: Tuple[int, int] property

A tuple (nargout, nargin) representing the shape of the operator

Returns:

Type	Description
tuple[int, int]	A tuple (nrows, ncols)

nMatvec: int property

The number of matrix-vector multiplications computed so far

Returns:

Type	Description
int	The number of matrix-vector multiplications performed

T: LinearOperator property

The transpose operator

Returns:

Type	Description
LinearOperator	The transpose of this linear operator

H: LinearOperator property

The adjoint operator

Returns:

Type	Description
LinearOperator	The Hermitian adjoint of this linear operator

block_list: List[LinearOperator] property

A list of linear operators representing the individual diagonal blocks.

Returns:

Type	Description
list[LinearOperator]	A list of linear operators representing the individual diagonal blocks

num_blocks: int property

The total number of diagonal blocks in the operator.

Returns:

Type	Description
int	The total number of diagonal blocks in the operator

row_size: npt.NDArray[np.integer] property

Array containing the number of rows for each block.

Returns:

Type	Description
NDArray[integer]	Array containing the number of rows for each block

col_size: npt.NDArray[np.integer] property

Array containing the number of columns for each block.

Returns:

Type	Description
NDArray[integer]	Array containing the number of columns for each block

size: int property

Array containing the number of rows/columns for each block

Returns:

Type	Description
int	Array containing the number of rows/columns for each block

diag: npt.NDArray[np.number] property

Array containing the diagonal of the operator

Returns:

Type	Description
NDArray[number]	Array containing the diagonal of the operator

Functions

reset_counters() -> None

Resets matrix-vector product counter to zero.

Source code in brahmap/base/linop.py

def reset_counters(self) -> None:
    """Resets matrix-vector product counter to zero."""
    self._nMatvec = 0

dot(x) -> npt.NDArray[np.number]

Numpy-like dot() method.

Parameters:

Name	Type	Description	Default
x	Any	The input vector or object to multiply with.	required

Returns:

Type	Description
NDArray[number]	The result of the dot product.

Source code in brahmap/base/linop.py

def dot(self, x) -> npt.NDArray[np.number]:
    """Numpy-like dot() method.

    Parameters
    ----------
    x : Any
        The input vector or object to multiply with.
    Returns
    -------
    npt.NDArray[np.number]
        The result of the dot product.
    """
    return self.__mul__(x)

matvec(x) -> npt.NDArray[np.number]

Matrix-vector multiplication method.

The matvec method encapsulates the matvec routine specified at construct time, to ensure the consistency of the input and output arrays with the operator's shape.

Parameters:

Name	Type	Description	Default
x	NDArray[number]	The input vector \(x\) to be multiplied by the operator	required

Returns:

Type	Description
NDArray[number]	The result of the matrix-vector multiplication \(A(x)\)

Source code in brahmap/base/linop.py

def matvec(self, x) -> npt.NDArray[np.number]:
    """
    Matrix-vector multiplication method.

    The `matvec` method encapsulates the `matvec`
    routine specified at construct time, to ensure the
    consistency of the input and output arrays with the
    operator's shape.

    Parameters
    ----------
    x : npt.NDArray[np.number]
        The input vector $x$ to be multiplied by the operator

    Returns
    -------
    npt.NDArray[np.number]
        The result of the matrix-vector multiplication $A(x)$
    """
    x = np.asanyarray(x, dtype=self.dtype)
    M, N = self.shape

    # check input data consistency
    N = int(N)
    try:
        x = x.reshape(N)
    except ValueError:
        msg = (
            f"The size of the input array is incompatible with the "
            f"dimensions required by the operator\n"
            f"size of the input array: {x.size}\n"
            f"shape of the operator: {self.shape}"
        )
        msg = f"{self.__class__.__name__}: " + msg
        raise ValueError(msg)

    y = self.__matvec(x)

    # check output data consistency
    M = int(M)
    try:
        y = y.reshape(M)
    except ValueError:
        msg = (
            f"The size of the output array is incompatible with the "
            f"dimensions required by the operator\n"
            f"size of the output array: {y.size}\n"
            f"shape of the operator: {self.shape}"
        )
        msg = f"{self.__class__.__name__}: " + msg
        raise ValueError(msg)

    return y

to_array() -> npt.NDArray[np.number]

Returns the dense form of the linear operator as a 2D NumPy array.

Warning

This method first allocates a NumPy array of shape self.shape and data-type self.dtype, and then fills them with numbers. As such, for a large linear operator, it can occupy an enormous amount of memory and crash your system. Don't use it unless you understand the risk!

Returns:

Type	Description
NDArray[number]	The dense 2D array representation of the linear operator

Source code in brahmap/base/linop.py

def to_array(self) -> npt.NDArray[np.number]:
    """Returns the dense form of the linear operator as a 2D NumPy array.

    !!! Warning

        This method first allocates a NumPy array of shape `self.shape`
        and data-type `self.dtype`, and then fills them with numbers. As
        such, for a large linear operator, it can occupy an enormous
        amount of memory and crash your system. Don't use it unless you
        understand the risk!

    Returns
    -------
    npt.NDArray[np.number]
        The dense 2D array representation of the linear operator
    """
    n, m = self.shape
    H = np.empty((n, m), dtype=self.dtype)
    ej = np.zeros(m, dtype=self.dtype)
    for j in range(m):
        ej[j] = 1.0
        H[:, j] = self * ej
        ej[j] = 0.0
    return H

get_inverse() -> BaseBlockDiagInvNoiseCovLinearOperator

Returns the inverse block-diagonal covariance operator.

Returns:

Type	Description
BaseBlockDiagInvNoiseCovLinearOperator	The inverse block-diagonal covariance operator

Source code in brahmap/base/noise_ops.py

def get_inverse(self) -> "BaseBlockDiagInvNoiseCovLinearOperator":
    """Returns the inverse block-diagonal covariance operator.

    Returns
    -------
    BaseBlockDiagInvNoiseCovLinearOperator
        The inverse block-diagonal covariance operator
    """
    inverse_list = [
        cast(NoiseCovLinearOperator, block).get_inverse()
        for block in self.block_list
    ]
    return BaseBlockDiagInvNoiseCovLinearOperator(
        block_list=inverse_list,
    )