regresidual()#
- TikhonovDecoupledSolver.regresidual(Ohat: ndarray) ndarray[source]#
Compute the residual of the regularized regression objective for each row of the given operator matrix.
Specifically, given a potential \(\Ohat\), compute
\[\|\D\ohat_i - \z_i\|_2^2 + \|\bfGamma_i(\ohat_i-\ohat_i^{(0)})\|_2^2, \quad i = 1, \ldots, r,\]where \(\ohat_i\) and \(\z_i\) are the \(i\)-th rows of \(\Ohat\) and \(\Z\), respectively, and \(\bfGamma_i\) is the corresponding symmetric-positive-definite regularization matrix. The \(\ohat_i^{(0)}\) are the rows of the initial guess provided during the initialization (defaulted to zero).
- Parameters:
- Ohat(r, d) ndarray
Operator matrix \(\Ohat\).
- Returns:
- residuals(r,) ndarray
\(2\)-norm residuals for each row of the operator matrix.