OptiVec: MF

MF_det

MD_det

ME_det

MCF_det

MCD_det

MCE_det

Function

determinant of a square matrix

Syntax C/C++	#include <MFstd.h> float MF_det( fMatrix MA, ui len ); float MFb_det( fMatrix MA, ui len, fVector Buf ); fComplex MCF_det( cfMatrix MA, ui len ); fComplex MCFb_det( cfMatrix MA, ui len, cfVector Buf ); ui MFb_det_sizeBuf( ui len ); float MFsym_det( fMatrix MA, ui len );
C++ MatObj	#include <OptiVec.h> T matrix<T>::det(); T matrix<T>::b_det( vector<T>& Buf ); complex<T> matrix<complex<T>>::det(); complex<T> matrix<complex<T>>::b_det( vector<complex<T>>& Buf ); ui matrix<T>::b_det_sizeBuf( const ui len ); T matrix<T>::sym_det();
Pascal/Delphi	uses MFstd; function MF_det( MA:fMatrix; len:UIntSize ):Single; function MFb_det( MA:fMatrix; len:UIntSize; Buf:fVector ):Single; function MCF_det( MA:cfMatrix; len:UIntSize ):fComplex; function MCFb_det( MA:cfMatrix; len:UIntSize; Buf:cfVector ):fComplex; function MFb_det_sizeBuf( len:UIntSize ):UIntSize; function MFsym_det( MA:fMatrix; len:UIntSize ):Single;

Description

The determinant of MA is calculated. For large matrices, this is done via LU decomposition. For small matrices, individual formulae are applied. For the special case of symmetric matrices, MFsym_det provides a roughly two times faster way.

MF_det needs buffer memory. The "normal" versions (prefixes MF_, MCF_ etc.) allocate it themselves, whereas the version with the prefixes MFb_, MCFb_ etc. take a vector Buf as an additional argument. The required size of Buf can be obtained by calling MFb_det_sizeBuf() etc., whereby the size is given as the number of elements of Buf in the respective data type (rather than in bytes).

As noted above, the determinant of a symmetric matrix can potentially be obtained faster by MFsym_det. The syntax is the same as for MF_det. Internally, this function first attempts Cholesky decomposition. Only if that fails (i.e. the input matrix is not positive-definite), the way via LUD is used.

Return value

determinant of the matrix