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]

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

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,k,n)

tens_s: np.ndarray

A (k,n) matrix representation of the f-diagonal tensor of shape (k,k,n)

tens_v: np.ndarray

M-orthogonal Tensor of shape (p,k,n)