numeric::xyzMatrix Class Reference

Detailed Description

xyzMatrix is a fast 3x3 matrix template class. Functions are inlined and loop-free for optimal speed. The destructor is declared non-virtual for speed so xyzMatrix is not set up for use as a base class. As a template class, xyzMatrix can hold various value types.

Forward declarations and typedefs for common value types are provided in the file xyzMatrix.fwd.hh. This header should be included in files that only use the names of the xyzMatrix types (e.g., function declarations and functions that just pass the types through to other functions by pointer or reference).

Common operations that are normally coded in loops are provided and include:

right_multiply_by() - Multiply on the right by an xyzMatrix

right_multiply_by_transpose() - Multiply on the right by the transpose of an xyzMatrix

left_multiply_by() - Multiply on the left by an xyzMatrix

left_multiply_by_transpose() - Multiply on the left by the transpose of an xyzMatrix

det() - Determinant

trace() - Trace

transpose() - Transpose

transposed() - Transposed copy

Note that tranpose() and transposed() follow the library convention that the 'ed' version does not modify the xyzMatrix, but generates an xyzMatrix.

xyzMatrix offers a number of construction methods including several column or row oriented methods: from nine elements, from pointer(s) to contiguous values, or from three xyzVectors.

Additionally, the header xyz_functions.hh contains common functions that interact with xyzMatrix such as:

product() - xyzMatrix * xyzVector product

inplace_product() - xyzMatrix * xyzVector product, input xyzVector is modified

outer_product() - xyzVector * xyzVector outer product

projection_matrix() - projection matrix onto the line through an xyzVector

rotation_matrix() - rotation matrix about a helical axis through the origin through an angle

rotation_axis() - transformation from rotation matrix to helical axis of rotation

eigenvalue_jacobi() - classic Jacobi algorithm for the eigenvalues of a real symmetric matrix

eigenvector_jacobi() - classic Jacobi algorithm for the eigenvalues and eigenvectors of a real symmetric matrix