The LQ decomposition of a rectangular matrix A is a representation of the matrix as the product A = LQ, where L - lower triangular (or trapezoid) matrix, Q - orthogonal square matrix.

The LQ decomposition of matrix A is equal to the QR decomposition of matrix A ^T. However it is more effective to use the special algorithm for the LQ decomposition than apply algorithm of QR decomposition to a transposed matrix.

The algorithm of the LQ decomposition is similar to the algorithm of QR decomposition. As with QR decomposition, the module contains 3 subroutines. The first subroutine, RMatrixLQ, performs the LQ decomposition and returns the result in compact form. The second subroutine, RMatrixLQUnpackQ, unpacks the Q. The third subroutine, RMatrixLQUnpackL, unpacks the L.

The subroutine functioning is described in more details in the program comments.

This algorithm is transferred from the LAPACK library.

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C#

C# 1.0 source.
lq.csharp.zip - LQ decomposition of a rectangular matrix

C++

C++ source.
lq.cpp.zip - LQ decomposition of a rectangular matrix
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.
lq.mpfr.zip - LQ decomposition of a rectangular matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
lq.delphi.zip - LQ decomposition of a rectangular matrix

Visual Basic 6

Visual Basic 6 source.
lq.vb6.zip - LQ decomposition of a rectangular matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
lq.zonnon.zip - LQ decomposition of a rectangular matrix