The algorithm of general complex matrix condition number estimations is similar to algorithm which estimates real matrix condition number, therefore we will not describe the algorithm principles again. You can find a full description by following the link above.

Subroutine description

To avoid an overflow in case of the singular matrix subroutines below do not calculate a condition number but an inverse number - . In case of a singular matrix . If the matrix is ill-conditioned, the value of is close to the value of machine precision.

The subroutines CMatrixRCond1 and CMatrixRCondInf calculate 1-norm and ∞-norm of the condition number, respectively. They require O(N ³) operations to perform the LU decomposition, and O(N ²) to estimate the condition number.

The subroutines CMatrixLURCond1 and CMatrixLURCondInf calculate 1-norm and ∞-norm of the condition number for a matrix given by its LU decomposition. They get as an input the result of subroutine CMatrixLU - matrices L and U in compact form (the permutation table isn't required because the permutations cannot change a condition number), and estimate the condition number in O(N ²) operations.

This algorithm is transferred from the LAPACK library.

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C#

C# 1.0 source.
crcond.csharp.zip - Complex matrix condition number estimate

C++

C++ source.
crcond.cpp.zip - Complex matrix condition number estimate
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.
crcond.mpfr.zip - Complex matrix condition number estimate
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
crcond.delphi.zip - Complex matrix condition number estimate

Visual Basic 6

Visual Basic 6 source.
crcond.vb6.zip - Complex matrix condition number estimate

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
crcond.zonnon.zip - Complex matrix condition number estimate