py__cvt_pdaf

py__cvt_pdaf(iter: int, dim_p: int, dim_cvec: int, cv_p: np.ndarray, vv_p: np.ndarray) → np.ndarray

The control variable transformation.

Here, this function performs \(\mathbf{U} \mathbf{v}\) 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.

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

\(\mathbf{v}\). shape: (dim_cvec, )

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

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

Returns

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

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