Cosine-Sine Decomposition

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 (FORTRAN 77 interface) that perform CS decomposition of matrices. Respective routine names in Fortran 95 interface are without the first symbol (see Routine Naming Conventions).

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

sbbcsd/dbbcsd

cbbcsd/zbbcsd

Simultaneously bidiagonalize the blocks of a partitioned orthogonal matrix

?orbdb

Simultaneously bidiagonalize the blocks of a partitioned unitary matrix

?unbdb
Parent topic: Computational Routines

See Also

CS Driver Routine

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