The Hermitian matrix A could be represented as A=Q·T·Q ^H, where Q is an unitary matrix, and T is a real tridiagonal matrix. We can say that matrix A is reduced to a tridiagonal matrix via a similarity transformation: Q ^H·A·Q = T.

As a result of HMatrixTD subroutine, matrix A is replaced by the tridiagonal matrix T and a sequence of reflections transformations stored in a compact form. The format of the matrix and the subroutine parameters are described in detail in the subroutine comments; there we can note an analogy with QR-decomposition, that uses the lower triangular part of the matrix R to store the matrix Q and utilizes a very similar data storage format. As with QR decomposition, a subroutine for "unpacking" the matrix Q is presented: HMatrixTDUnpackQ.

This algorithm is transferred from the LAPACK library.

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C#

C# 1.0 source.
htridiagonal.csharp.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.

C++

C++ source.
htridiagonal.cpp.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

C++, multiple precision arithmetic

C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
htridiagonal.mpfr.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
htridiagonal.delphi.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.

Visual Basic 6

Visual Basic 6 source.
htridiagonal.vb6.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
htridiagonal.zonnon.zip - Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.