Cholesky decomposition could be used to invert a symmetric positive definite matrix. This algorithm is able to invert only positive definite matrices. Arbitrary symmetric matrices could be inverted by more general algorithm on the basis of LDLT-decomposition.

Subroutine SPDMatrixCholeskyInverse inverts a symmetric positive definite matrix A whose Cholesky decomposition has already been generated. The subroutine gets an output of subroutine SPDMatrixCholesky - Cholesky decomposition of matrix A (A = U ^TU or A = LL ^T) as an input, and returns the upper or lower triangle of symmetric matrix A ^-1 (depending on which variant of decomposition was returned by SPDMatrixCholesky).

Subroutine SPDMatrixInverse calls subroutine SPDMatrixCholesky to factorize matrix A which is given by its lower or upper triangle, and returns the upper or lower triangle of symmetric matrix A ^-1 (depending on which part of the matrix was input).

This algorithm is transferred from the LAPACK library.

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C#

C# 1.0 source.
spdinverse.csharp.zip - Inverse of a symmetric positive definite matrix

C++

C++ source.
spdinverse.cpp.zip - Inverse of a symmetric positive definite 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.
spdinverse.mpfr.zip - Inverse of a symmetric positive definite matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
spdinverse.delphi.zip - Inverse of a symmetric positive definite matrix

Visual Basic 6

Visual Basic 6 source.
spdinverse.vb6.zip - Inverse of a symmetric positive definite matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
spdinverse.zonnon.zip - Inverse of a symmetric positive definite matrix