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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:
- 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. The corresponding routine names in the Fortran 95 interface are without the first symbol.
Operation |
Real matrices |
Complex matrices |
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Compute the CS decomposition of an orthogonal/unitary matrix in bidiagonal-block form |
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Simultaneously bidiagonalize the blocks of a partitioned orthogonal matrix |
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Simultaneously bidiagonalize the blocks of a partitioned unitary matrix |