pylops.signalprocessing.Bilinear

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

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

iavalist or numpy.ndarray

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

dimslist

Number of samples for each dimension

dtypestr, optional

Type of elements in input array.

namestr, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

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

shapetuple

Operator shape

explicitbool

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

Methods

__init__(iava, dims[, dtype, name])
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.
reset_count()	Reset counters
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()

Examples using pylops.signalprocessing.Bilinear

Bilinear Interpolation

Bilinear Interpolation