What's New in the NAG Library Mark 27.3
Nearest Correlation Matrix Solver Update 70x Faster and 2500x More Efficient

Using the highly anticipated new NAG® Library symbolic adjoint NCM solver can dramatically reduce the runtime and memory footprint required to compute derivatives of the NCM

Mark 27.3 of the NAG® AD Library contains functionality for computing the symbolic adjoint of the nearest correlation matrix (NCM). The symbolic adjoint is accessed via a new mode for the solver g02aa. Computing derivatives of the NCM allows sensitivities to the input data to be found. Previously this could be done in the NAG AD Library by computing the algorithmic adjoint, which differentiates the code line by line. The symbolic adjoint computes the derivative mathematically, resulting in a routine that is 70 times faster and uses 2500 times less memory than the algorithmic adjoint. This new solver is available in Mark 27.3 of the NAG LibraryFull product trials are available.

New FEAST Eigensolver – For Large, Sparse Eigenproblems

The NAG® Library, Mark 27.3 now features a new suite of routines implementing the FEAST algorithm. FEAST is a general-purpose eigensolver for standard, generalized and polynomial eigenvalue problems. It is suitable for both sparse and dense matrices, and routines are available for real, complex, symmetric, Hermitian and non-Hermitian eigenproblems. What sets FEAST apart from other NAG Library eigensolvers is that it allows users to specify a particular region in the complex plane within which eigenvalues will be found. This is particularly useful when applied to large, sparse eigenproblems when a subset of the spectrum is required. Solvers such as ARPACK are typically only able to find the largest/smallest magnitude eigenvalues or a specified number of eigenvalues close to a given complex value. Only the FEAST eigensolver can search within a specific contour within which the number of eigenvalues might be unknown. We are aware of several areas in which such functionality is useful, including modelling the oscillations of railway tracks, simulation of fluid flows and electronic structure computations. FEAST is a highly versatile algorithm, available in Mark 27.3 of the NAG Library. Full product trials are available. 

More Second-order Automatic Differentiation Variants Available in the NAG AD Library

The C++ interfaces to the NAG AD Library have been updated to make it easier for dco/c++ users to access NAG Library functionality.  Users can now also pass lambdas and functors in addition to function pointers, greatly easing the integration of the NAG AD Library into modern C++ code bases. Adding to the functionality previously available, we've increased the number of second-order tangent and adjoint routines available, and some NAG AD Library routines now benefit from symbolic Level 3 BLAS functions making them significantly faster and more memory efficient. This new solver is available in Mark 27.3 of the NAG Library. Full product trials are available.

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Support for Fitting Problems with Incomplete Data

The NAG® Library nonlinear least squares solver (BXNL) e04gg now also supports underdetermined problems where the number of parameters to fit is greater than the number of observations available. These kinds of problems are a major obstacle for the majority of existing solvers. This new feature makes it possible to tackle problems where obtaining observations is costly and time-consuming, for example, the fit can be computed early on as the observations are made available. 

In addition, the solver also provides statistics on the quality of fit, such as the estimated variance vector or covariance matrix. These provide the user with insight into the quality of the solution.