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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:
  1. The matrix is reduced to a bidiagonal block form.
  2. 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.
Computational Routines for Cosine-Sine Decomposition (CSD)
Operation
Real matrices
Complex matrices
Compute the CS decomposition of an orthogonal/unitary matrix in bidiagonal-block form
Simultaneously bidiagonalize the blocks of a partitioned orthogonal matrix
Simultaneously bidiagonalize the blocks of a partitioned unitary matrix

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