Cosine-Sine Decomposition: LAPACK Computational
Routines
This
topic
describes LAPACK computational routines for computing the
cosine-sine decomposition (CS
decomposition) of a partitioned unitary/orthogonal matrix. The algorithm
computes a complete 2-by-2 CS decomposition, which requires simultaneous
diagonalization of all the four blocks of a unitary/orthogonal matrix
partitioned into a 2-by-2 block structure.
The computation has the following phases:
- The matrix is reduced to a bidiagonal block form.
- The blocks are simultaneously diagonalized using techniques from the bidiagonal SVD algorithms.
Table
"Computational Routines for Cosine-Sine
Decomposition (CSD)"
lists LAPACK routines that perform CS
decomposition of matrices.
Operation
| Real matrices
| Complex matrices
|
---|---|---|