determinant_matrixdeterminant_matrixDeterminantMatrixDeterminantMatrix (Operator)

Name

determinant_matrixdeterminant_matrixDeterminantMatrixDeterminantMatrix — Compute the determinant of a matrix.

Signature

Description

The operator determinant_matrixdeterminant_matrixDeterminantMatrixDeterminantMatrixDeterminantMatrix computes the determinant of the input MatrixMatrixMatrixMatrixmatrix given by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The type of the input MatrixMatrixMatrixMatrixmatrix can be selected via the parameter MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType. The following values are supported: 'general'"general""general""general""general" for general, 'symmetric'"symmetric""symmetric""symmetric""symmetric" for symmetric, 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite" for symmetric positive definite, 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal" for tridiagonal, 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular" for upper triangular, 'permuted_upper_triangular'"permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular" for permuted upper triangular, 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular" for lower triangular, and 'permuted_lower_triangular'"permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular" for permuted lower triangular matrices. The formula for the calculation of the result is:

  ValueValueValueValuevalue = det MatrixMatrixMatrixMatrixmatrix.

Example:

Attention

For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'symmetric'"symmetric""symmetric""symmetric""symmetric", 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite", or 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular" the upper triangular part of the input MatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly lower triangular part of the matrix is not referenced. For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular" the lower triangular part of the input MatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly upper triangular part of the matrix is not referenced. For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal", only the main diagonal, the superdiagonal, and the subdiagonal of the input MatrixMatrixMatrixMatrixmatrix are used. The other parts of the matrix are not referenced. If the referenced part of the input MatrixMatrixMatrixMatrixmatrix is not of the specified type, an exception is raised.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

If the parameters are valid, the operator determinant_matrixdeterminant_matrixDeterminantMatrixDeterminantMatrixDeterminantMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrix

References

David Poole: “Linear Algebra: A Modern Introduction”; Thomson; Belmont; 2006.
Gene H. Golub, Charles F. van Loan: “Matrix Computations”; The Johns Hopkins University Press; Baltimore and London; 1996.

Module

Foundation