brahmap.base.MatrixLinearOperator

Bases: LinearOperator

A linear operator wrapping a dense or sparse 2D NumPy/SciPy matrix.

While BrahMap typically relies on matrix-free operations for large-scale data, MatrixLinearOperator allows standard explicitly constructed matrices (e.g., small covariance blocks or low-resolution masks) to seamlessly interact with the iterative solvers and operator algebra in the framework. The operator's dtype is the same as the specified matrix argument.

Parameters:

Name	Type	Description	Default
matrix	NDArray[number]	A dense 2D matrix to be wrapped as a LinearOperator	required
**kwargs	Any	Extra keyword arguments	{}

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.

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

Source code in brahmap/base/linop.py

class MatrixLinearOperator(LinearOperator):
    """A linear operator wrapping a dense or sparse 2D NumPy/SciPy matrix.

    While BrahMap typically relies on matrix-free operations for large-scale
    data, `MatrixLinearOperator` allows standard explicitly constructed matrices
    (e.g., small covariance blocks or low-resolution masks) to seamlessly
    interact with the iterative solvers and operator algebra in the framework.
    The operator's dtype is the same as the specified `matrix` argument.

    Parameters
    ----------
    matrix : npt.NDArray[np.number]
        A dense 2D matrix to be wrapped as a LinearOperator
    **kwargs: Any
        Extra keyword arguments

    """

    def __init__(self, matrix: npt.NDArray[np.number], **kwargs: Any) -> None:
        if "symmetric" in kwargs:
            kwargs.pop("symmetric")
        if "matvec" in kwargs:
            kwargs.pop("matvec")
        if "dtype" in kwargs:
            kwargs.pop("dtype")

        if not hasattr(matrix, "shape"):
            matrix = np.asanyarray(matrix)

        if matrix.ndim != 2:
            msg = "matrix must be 2-d (shape can be [M, N], [M, 1] or [1, N])"
            msg = f"{self.__class__.__name__}: " + msg
            raise ValueError(msg)

        matvec = matrix.dot
        iscomplex = np.iscomplexobj(matrix)

        if matrix.shape[0] == matrix.shape[1]:
            symmetric = np.all(matrix == matrix.conj().T)
        else:
            symmetric = False

        if not symmetric:
            rmatvec = matrix.conj().T.dot if iscomplex else matrix.T.dot
        else:
            rmatvec = None

        super(MatrixLinearOperator, self).__init__(
            matrix.shape[1],
            matrix.shape[0],
            symmetric=symmetric,
            matvec=matvec,
            rmatvec=rmatvec,
            dtype=matrix.dtype,
            **kwargs,
        )

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

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