Decomposition Classes
The Decomposition Classes allow construction and manipulation of QR, complete orthogonal, and singular value decompositions. These classes are contained in Table 7:
Table 7 – The Decomposition Classes 
Class Name
Type
Header File
A permutation and balance transformation performed on a nonsymmetric matrix before computing its eigenvalues.
rw/lapack/bal.h
Encapsulates two transformations: a permutation and balance transformation performed on a nonsymmetric matrix before computing its eigenvalues.
rw/lapack/bal.h
A symmetric tridiagonal decomposition of a symmetric banded matrix A: A=QTQ’ where Q is orthogonal and T is real tridiagonal symmetric.
rw/lapack/td.h
Encapsulates a complete orthogonal decomposition.
rw/lapack/co.h
The symmetric tridiagonal decomposition of a dense symmetric matrix A, where:A: A=QTQ’ and Q is orthogonal and T is real tridiagonal symmetric.
rw/lapack/td.h
Computes the QR decomposition of a matrix using LAPACK function xgeqpf or xgeqrf.
rw/lapack/qrcalc.h
Computes the QR decomposition of a matrix using LAPACK function xgeqp3.
rw/lapack/qrcalcp3.h
Used to construct and work with QR decompositions or to solve linear least squares problems.
rw/lapack/qr.h
A QR decomposition server used to construct instances of the QR decomposition classes,
rw/lapack/qr.h
Computes the singular value decomposition of a matrix.
rw/lapack/svdcalc.h
Computes the singular value decomposition of a matrix using divide-and-conquer.
rw/lapack/svddccalc.h
Used to construct and work with singular value decompositions.
rw/lapack/sv.h
Used to construct instances of the singular value decomposition class.
rw/lapack/sv.h