pylops.signalprocessing.Bilinear

class pylops.signalprocessing.Bilinear(iava, dims, dtype='float64')

Bilinear interpolation operator.

Apply bilinear interpolation onto fractionary positions iava along the first two axes of a n-dimensional array.

Note

The vector iava should contain unique pais. If the same pair is repeated twice an error will be raised.

Parameters:

iava : list or numpy.ndarray

Array of size \([2 \times n_\text{ava}]\) containing pairs of floating indices of locations of available samples for interpolation.

dims : list

Number of samples for each dimension

dtype : str, optional

Type of elements in input array.

Raises:

ValueError

If the vector iava contains repeated values.

Notes

Bilinear interpolation of a subset of \(N\) values at locations iava from an input n-dimensional vector \(\mathbf{x}\) of size \([m_1 \times m_2 \times ... \times m_{ndim}]\) can be expressed as:

\[y_{\mathbf{i}} = (1-w^0_{i}) (1-w^1_{i}) x_{l^{l,0}_i, l^{l,1}_i} + w^0_{i} (1-w^1_{i}) x_{l^{r,0}_i, l^{l,1}_i} + (1-w^0_{i}) w^1_{i} x_{l^{l,0}_i, l^{r,1}_i} + w^0_{i} w^1_{i} x_{l^{r,0}_i, l^{r,1}_i} \quad \forall i=1,2,\ldots,M\]

where \(\mathbf{l^{l,0}}=[\lfloor l_1^0 \rfloor, \lfloor l_2^0 \rfloor, ..., \lfloor l_N^0 \rfloor]\), \(\mathbf{l^{l,1}}=[\lfloor l_1^1 \rfloor, \lfloor l_2^1 \rfloor, ..., \lfloor l_N^1 \rfloor]\), \(\mathbf{l^{r,0}}=[\lfloor l_1^0 \rfloor + 1, \lfloor l_2^0 \rfloor + 1, ..., \lfloor l_N^0 \rfloor + 1]\), \(\mathbf{l^{r,1}}=[\lfloor l_1^1 \rfloor + 1, \lfloor l_2^1 \rfloor + 1, ..., \lfloor l_N^1 \rfloor + 1]\), are vectors containing the indices of the original array at which samples are taken, and \(\mathbf{w^j}=[l_1^i - \lfloor l_1^i \rfloor, l_2^i - \lfloor l_2^i \rfloor, ..., l_N^i - \lfloor l_N^i \rfloor]\) (\(\forall j=0,1\)) are the bilinear interpolation weights.

Attributes:

shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(iava, dims[, dtype])	Initialize this LinearOperator.
adjoint()	Hermitian adjoint.
apply_columns(cols)	Apply subset of columns of operator
cond([uselobpcg])	Condition number of linear operator.
conj()	Complex conjugate operator
div(y[, niter, densesolver])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x)	Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
matmat(X)	Matrix-matrix multiplication.
matvec(x)	Matrix-vector multiplication.
rmatmat(X)	Matrix-matrix multiplication.
rmatvec(x)	Adjoint matrix-vector multiplication.
todense([backend])	Return dense matrix.
toimag([forw, adj])	Imag operator
toreal([forw, adj])	Real operator
tosparse()	Return sparse matrix.
trace([neval, method, backend])	Trace of linear operator.
transpose()	Transpose this linear operator.

Examples using pylops.signalprocessing.Bilinear

Bilinear Interpolation