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Functions
Determinant
Base Module » Linear Algebra

Functions

double itpp::det (const mat &X)
 Determinant of real square matrix. More...
 
std::complex< double > itpp::det (const cmat &X)
 Determinant of complex square matrix. More...
 

Detailed Description

Function Documentation

◆ det() [1/2]

ITPP_EXPORT double itpp::det ( const mat &  X)

Determinant of real square matrix.

Calculate determinant of the real matrix $\mathbf{X}$

Uses LU-factorisation.

\[ \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) \]

and the determinant of the permuation matrix is $ \pm 1$ depending on the number of row permutations

Definition at line 43 of file det.cpp.

References it_assert_debug, and itpp::lu().

Referenced by itpp::MOG_generic::setup_covs().

◆ det() [2/2]

ITPP_EXPORT std::complex< double > itpp::det ( const cmat &  X)

Determinant of complex square matrix.

Calculate determinant of the complex matrix $\mathbf{X}$

Uses LU-factorisation.

\[ \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) \]

and the determinant of the permuation matrix is $ \pm 1$ depending on the number of row permutations

Definition at line 76 of file det.cpp.

References it_assert_debug, and itpp::lu().

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