LAPACK routine for SVD of product of two matrices

Question

I need to find the SVD of $A \times B$ where $A$ is an upper triangular matrix and B is a lower triangular matrix. What is the efficient way to go about and a routine which does this in LAPACK?

Answer 1

I can suggest you the GNU GSL library which can do a lot of matrix algebra, such as SVD decomposition and triangular matrix multiplication very efficiently (and many others!) I think(???) it support even LAPACK

http://www.gnu.org/software/gsl/

Answer 2

As far as I am aware, there is no clever way to compute the SVD of such a product. You simply multiply the matrices, then take the SVD of the resulting matrix.