`svdappend`

Updates an existing SVD after columns or rows are appended to the matrix.

Syntax

S1 = svdappend(U, S, V, D)

Returns the singular values of [U*S*V' D].

[U1, S1, V1] = svdappend(U, S, V, D)

Returns the economy-size factors of the enlarged matrix.

___ = svdappend(U, S, V, D, 'Shape', 'rows')

Appends the rows of D below the matrix instead of columns beside it.

Description

When data arrives in batches, it is wasteful to decompose the whole matrix again each time. svdappend starts from the factors you already have and returns the economy SVD of the matrix with the new data attached, as a convenient shortcut for the usual update pattern.

The result is the same, up to signs, as calling svd on [U*S*V' D] directly.

Input arguments

U, S, V: Factors of an existing SVD; S may be a matrix or a vector of singular values.
D: New columns (or rows) to append. It needs as many rows as U (or as many columns as V has rows, with the rows option).
'Shape': 'columns' (default) or 'rows'.

Output arguments

S1: With one output, the vector of singular values of the enlarged matrix.
U1, V1: Singular vectors of the enlarged matrix.

Example

Append a column

A = magic(3);
[U, S, V] = svd(A, 'econ');
d = [1; 2; 3];
s1 = svdappend(U, S, V, d)'
s2 = svd([A d])'

Output

s1 = 1×3

   15.3990    7.0620    3.4641
s2 = 1×3

   15.3990    7.0620    3.4641

Notes

In MatLivre, with several outputs S1 comes back as a column vector of singular values, not a diagonal matrix.

svdappend