mprod.decompositions.svdm¶

mprod.decompositions.svdm(tens_a: numpy.ndarray, fun_m: Callable[numpy.ndarray, numpy.ndarray], inv_m: Callable[numpy.ndarray, numpy.ndarray], hats: bool = False) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray][source]¶

The svdm function is a helper function for computing the tsvdmII. This function does the FULL tsvdm decomposition: u,s,b = tsvdm(tensor_a, m, inv_m) where u,v are of shapes (m,m,n) and (p,p,n), M-orthogonal tensors and s is f-diagonal tensor of shape (m,p,n)

Parameters

tens_a: np.ndarray: Tensor of shape (m,p,n)
fun_m: MatrixTensorProduct: Invertible mat-vec operation for transforming tens_a tube fibers
inv_m: MatrixTensorProduct: Invertible mat-vec operation for transforming tens_a tube fibers. This operation is the inverse of fun_m
hats: bool: Setting this to True will cause the function to return the tsvdm factors in the tensor domain transform.

Returns

tens_u: np.ndarray: M-orthogonal tensor of shape (m,m,n)
tens_s: np.ndarray: f-diagonal tensor of shape (m,p,n)
tens_v: np.ndarray: M-orthogonal Tensor of shape (p,p,n)