If the symmetric matrix A is represented by its LDLT-decomposition A = LDL ^T (or A = UDU ^T), then its determinant is equal to the determinant of a block-diagonal matrix D.

As LDLT-decomposition is twice as fast as LU-decomposition which is used to calculate general matrix determinants, it is recommended to use LDLT-decomposition when calculating a determinant of a symmetric matrix. In order to calculate the determinant of a symmetric positive definite matrix algorithm on the basis of Cholesky decomposition can be used.

Subroutine description

There are two subroutines in this module. The first subroutine, SMatrixLDLTDet, calculates the determinant of a matrix whose LDLT-decomposition has already been generated. The second subroutine, SMatrixDet, works with symmetric matrices whose LDLT-decomposition hasn't been generated yet.

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C#

C# 1.0 source.
sdet.csharp.zip - Determinant of a symmetric indefinite matrix

C++

C++ source.
sdet.cpp.zip - Determinant of a symmetric indefinite 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.
sdet.mpfr.zip - Determinant of a symmetric indefinite matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
sdet.delphi.zip - Determinant of a symmetric indefinite matrix

Visual Basic 6

Visual Basic 6 source.
sdet.vb6.zip - Determinant of a symmetric indefinite matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
sdet.zonnon.zip - Determinant of a symmetric indefinite matrix