NAG AD Library f01ej_a1w_f (real_gen_matrix_log_a1w)
Note:a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype.
Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document.
Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types.
The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
The routine may be called by the names f01ej_a1w_f or nagf_matop_real_gen_matrix_log_a1w. The corresponding t1w and p0w variants of this routine are also available.
is the adjoint version of the primal routine
f01ejf computes the principal matrix logarithm, , of a real matrix , with no eigenvalues on the closed negative real line.
For further information see Section 3 in the documentation for f01ejf.
Al–Mohy A H and Higham N J (2011) Improved inverse scaling and squaring algorithms for the matrix logarithm SIAM J. Sci. Comput.34(4) C152–C169
Al–Mohy A H, Higham N J and Relton S D (2012) Computing the Fréchet derivative of the matrix logarithm and estimating the condition number SIAM J. Sci. Comput.35(4) C394–C410
Higham N J (2008) Functions of Matrices: Theory and Computation SIAM, Philadelphia, PA, USA
In addition to the arguments present in the interface of the primal routine,
f01ej_a1w_f includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine.
A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.