py__cvt_adj_pdaf()

The adjoint control variable transformation.

Here, this function performs \(\mathbf{U}^\mathrm{T} \mathbf{v}_h\). Here, the input vector can be \(\mathbf{v}_h = \mathbf{H}^\mathrm{T}\mathbf{R}^{-1}\delta \mathbf{x}\) with \(\delta \mathbf{x}\) the innovation vector.

The control vector transform is given by \(\mathbf{U}\mathbf{v}\) with \(\mathbf{v}\) the control vector and \(\mathbf{U}\) the transformation matrix, which can be \(\mathbf{B}^\frac{1}{2}\).

This function is used in 3DVar and hybrid 3DVar.

Parameters

iter: int

Current optimisation iteration number.

dim_p: int

Dimension of the state vector.

dim_cvec: int

Dimension of the control vector.

vcv_p: np.ndarray[np.float, dim=1]

\(\mathbf{v}_h\). shape: (dim_p, )

cv_p: np.ndarray[np.float, dim=1]

\(\mathbf{U}^\mathrm{T} \mathbf{v}_h\). shape: (dim_cvec, )

Returns

cv_p: np.ndarray[np.float, dim=1]

\(\mathbf{U}^\mathrm{T} \mathbf{v}_h\). shape: (dim_cvec, )