NAG Library News, Mark 27
1
Introduction
At Mark 27, the NAG Library now consists of three main interface sets: the NAG FL Interface, the NAG CL Interface and the NAG AD Library Interfaces (see
Section 1.2). The NAG FL Interface now consists of 1908 user-callable routines while the NAG CL Interface now consists of 1619. All of these routines are fully documented and 62 are new since Mark 26. See
Section 2 for the full list of new routines which includes new routines introduced at Mark 26 point releases.
In collaboration with the group
Informatik 12: Software and Tools for Computational Engineering from RWTH Aachen University, the Library now includes the initial version of the NAG AD Library, introduced at Mark 26.2. Supplementary documentation is provided for the NAG AD Library, including: the
Introduction to the NAG AD Library and 58 user-callable routine documents listed in the
FL Interface Contents.
In addition to the new NAG AD Library, the following summarises additional content and changes to the NAG Library.
Chapter C05 (
Roots of One or More Transcendental Equations) has two new routines that find a solution of a system of nonlinear equations using Anderson acceleration.
Chapter C06 (
Summation of Series) has a new routine that calculates the fast Gauss transform approximation to the discrete Gauss transform.
Chapter E01 (
Interpolation) has two new routines to compute a monotone convex interpolation function and to evaluate this function at a set of points. Also, a new routine is provided for efficient interpolation of data supplied on a rectangular grid, in any number of dimensions; this routine should be used for gridded data in preference to older routines which are primarily designed for interpolation of scattered data sets.
Chapter E04 (
Minimizing or Maximizing a Function) has several significant additions to the NAG optimization modelling suite:
A new set of Derivative-free Optimization (DFO) solvers for general nonlinear objective with bound constraints and for least squares (data fitting, calibration) problems with bound constraints, available with both direct and reverse communication interfaces. These solvers should show an improved convergence rate compared to the existing DFO solutions in the NAG Library. They also have features designed to specifically handle noisy or expensive problems.
A new Second-order Cone Programming (SOCP) solver based on interior point method. This is particularly useful for many convex optimization problems, such as convex quadratically constrained quadratic programming (QCQP), which can be reformulated as SOCP.
A new First-order Active-set (FOAS) method for bound-constrained large-scale nonlinear programming problems. The new solver is based on nonlinear conjugate gradient method, it only requires first derivatives and has low memory requirements thus is suitable for very large scale problems. It is a modern replacement for the routine
e04dgf/e04dga and shows significant improvement over it. This modern solver has robust features to deal with missing objective values, to handle missing derivative entries, and to detect slow progress.
Chapter F01 (
Matrix Operations, Including Inversion) has two new routines for computing non-negative matrix factorizations and two new routines for computing the product of two (real and complex) triangular matrices.
Chapter F08 (
Least Squares and Eigenvalue Problems (LAPACK)) has: two (real and complex) new expert driver routines for computing the singular value decomposition (SVD) of general matrices; complex versions of the one-sided Jacobi SVD and its expert driver; and, an expert driver for the SVD of a real bidiagonal matrix.
Chapter F10 (
Randomized Numerical Linear Algebra) is a new chapter containing randomized linear algebra routines including a fast random projection and a randomized SVD algorithm. Randomized linear algebra routines are expected to outperform their deterministic counterparts in terms of computational efficiency particularly on rank-deficient problems. In many cases randomized linear algebra routines can achieve the same level of accuracy as deterministic algorithms.
Chapter G02 (
Correlation and Regression Analysis) has: two new nearest correlation matrix routines, one for calculating a rank-constrained nearest correlation matrix and one that allows arbitrary elements of the input matrix to be fixed; a new routine that combines communication arrays from calls to either
g02jcf or
g02jff allowing for the pre-processing of data in parallel; and a new suite of routines that offer an alternative method of specifying linear mixed effects regression models. The model is specified using the modelling language implemented in the
Chapter G22 chapter.
The implementation of the suite of routines for calculating the Pearson product-moment correlation coefficients and correlation-like coefficients has undergone some changes. The algorithm used has not changed and the results obtained from these routines should be comparable to the results obtained from previous releases of the NAG Library. Some of the routines in the suite have been threaded by NAG and details are given in Section 8 of the individual routine documents.
Chapter G04 (
Analysis of Variance) has a new routine for calculating the intraclass correlation (ICC) for a number of different rater reliability study designs.
Chapter G22 (
Linear Model Specification) contains utility routines for aiding in the construction of design matrices for use when fitting linear regression models.
Chapter M01 (
Sorting and Searching) has a new routine for searching a strictly ordered vector of real numbers for the elements of an unordered array of real numbers.
Chapter S (
Approximations of Special Functions) contains a new set of routines to evaluate Struve functions
,
,
and
. There is also a new routine for calculating a real-valued periodic angular Mathieu function and/or its derivative. There are also 12 vectorized versions of existing special functions which evaluate at multiple points.
1.1
Experimental Routines
At Mark 27 there are a number of routines which have been marked as ‘Experimental’. These routines have been flagged by a note at the top of the documentation.
Routines may be classified as experimental if:
-
(a)the interface and / or functionality of the routine may change between marks of the Library. The routine will have been designed in such a way as to minimize the number of such changes.
-
(b)the complexity of the routine, or suite of routines it is part of, are such that comprehensive testing is not practical. Routines classified as experimental have gone through the same testing and review processes as a normal Library routine, however it is recommended that additional care is taken when using the routine.
A routine classified as experimental may be reclassified as no longer being experimental, at which point the interface will become fixed as per a normal Library routine.
1.2
New Unified Library
At Mark 26 the NAG Fortran Library and the NAG C Library were considered as separate entities despite the fact that they shared, in large part, a common set of core algorithms.
At Mark 27 the NAG Library is a unification of these libraries, and additionally the NAG AD Library, into a single entity that can be called from many languages and environments, including C and Fortran. The NAG Library is now conceived and documented as having distinct interface sets: the NAG FL Interface, the NAG CL Interface and the NAG AD Library Interface.
1.3
Changes to NAG Documentation
At Mark 26 and at point release Mark 26.2 we made a number of changes to the documentation. This has been further developed to give you full access to a Library Manual which supports all the NAG interfaces available as part of the NAG Library.
The document "How to Use the NAG Library and its Documentation" has been replaced by two new documents,
How to Use the NAG Library and the
Guide to the NAG Library Documentation, providing general advice on how to use the Library and its documentation respectively. Interface specific information can be found in the
Introduction to the NAG Library FL Interface, the
Introduction to the NAG Library CL Interface and the
Introduction to the NAG AD Library.
On the left of each HTML page you will find navigational links to each NAG interface which will provide you with all the supporting documentation you need to use a particular interface in addition to the Keyword Search box. See
Section 7 in the Guide to the NAG Library Documentation.
On the left of each HTML page you will also find a Show Settings button which has been provided so that you can personalise your documentation to your preferred name style and specification language. See
Section 5 in the Guide to the NAG Library Documentation.
Please note that PDF is no longer provided, but most browsers provide a print-to-PDF feature. See
Section 10 in the Guide to the NAG Library Documentation
Finally, the specification of routines in routine documents (see for example
Section 2 in
d03pdf/d03pda) now includes the C++ Header interface which can be used to call a NAG Library routine from C or C++; the name used for this interface is the Fortran Interface short name appended by an underscore (e.g., d03faf_ corresponds to d03faf). For routines with 'a' and 'f' versions, the same approach also applies to the 'a' version (e.g., d03pda_ corresponds to d03pda). See
Section 5.2 in the Guide to the NAG Library Documentation.
2
New Routines since Mark 26
The lists in this section refer and link to the NAG FL Interface. In these lists there is a one-to-one correspondence between the NAG FL Interface and the NAG CL Interface; and, there is a direct hyperlink from the NAG FL Interface routine document to its corresponding NAG CL Interface routine document.
The new NAG AD Library routine documents currently available are listed in the
FL Interface Contents and there is a direct hyperlink from the NAG FL Interface routine document to its corresponding NAG AD Library routine document, and visa versa.
2.1
New Routines at Mark 27
| Routine |
Purpose |
| c05mbf |
Solution of a system of nonlinear equations using Anderson acceleration |
| e01cef |
Interpolating variables, monotone convex Hagan–West procedure, one variable |
| e01cff |
Interpolated values, variables computed by e01cef, monotone convex Hagan–West procedure, one variable |
| e01zaf |
Interpolates an -dimensional point on grid data using either linear, cubic or modified Shepard's method |
| e04fgf |
Reverse communication derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables |
| e04jdf |
Direct communication derivative-free (DFO) solver for a nonlinear objective function with bounded variables |
| e04jef |
Reverse communication derivative-free (DFO) solver for a nonlinear objective function with bounded variables |
| e04kff |
First-order active-set method for box constrained nonlinear optimization with low memory requirements |
| e04ptf |
Solve second-order cone programming (SOCP) and other convex related
problems, such as, quadratically constrained quadratic programming (QCQP), quadratic programming (QP), sparse, interior point method (IPM) |
| e04rbf |
Define a set of variables which form a second-order cone to a problem initialized by e04raf |
| e04saf |
Load a problem from a file to a new handle for the NAG optimization
modelling suite; supported formats: extended MPS, SDPA |
| f01dgf |
Matrix-matrix product, two real lower or upper triangular matrices |
| f01duf |
Matrix-matrix product, two complex lower or upper triangular matrices |
| f01saf |
Non-negative matrix factorization of real non-negative matrix |
| f01sbf |
Non-negative matrix factorization of real non-negative matrix (reverse communication) |
| f08kmf |
Computes all or selected singular values of the singular value decomposition of a real general matrix, optionally computing the corresponding left and right singular vectors |
| f08kvf |
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |
| f08kwf |
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |
| f08kzf |
Computes all or selected singular values of the singular value decomposition of a complex general matrix, optionally computing the corresponding left and right singular vectors |
| f08mbf |
Computes all or selected singular values of the singular value decomposition of a real square bidiagonal matrix, optionally computing the corresponding left and right singular vectors |
| f10caf |
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |
| f10daf |
Computes a fast random projection of a real matrix using a discrete cosine transform |
| f11zcf |
Sorts and merges elements of a real sparse rectangular matrix, represented in coordinate storage format, and provides the compressed column storage format of the result |
| g02akf |
Computes the rank-constrained nearest correlation matrix to a real square matrix, using the method of Qi and Sun |
| g02asf |
Computes the nearest correlation matrix to a real square matrix, with fixed elements |
| g02jff |
Linear mixed effects regression, initialization routine for g02jhf |
| g02jgf |
Linear mixed effects regression, initialization routine for g02jgf and g02jhf |
| g02jhf |
Linear mixed effects regression using either Restricted Maximum Likelihood (REML) or Maximum Likelihood (ML) |
| m01ndf |
Searches an ordered set of real numbers using an method |
| s14anf |
Gamma function, vectorized |
| s14apf |
Log gamma function, vectorized |
| s14bnf |
Incomplete gamma functions, vectorized and |
| s14cpf |
Logarithm of the beta function, vectorized |
| s14cqf |
Regularized incomplete beta function, vectorized and its complement |
| s15apf |
Cumulative Normal distribution function, vectorized |
| s15aqf |
Complement of cumulative Normal distribution function, vectorized |
| s15arf |
Complement of error function, vectorized |
| s15asf |
Error function, vectorized |
| s15atf |
Dawson's integral, vectorized |
| s15auf |
Scaled complement of error function, vectorized |
| s15drf |
Scaled complex complement of error function, vectorized |
| s22caf |
Calculates values of real periodic angular Mathieu functions |
2.2
New Routines at Mark 26.2
The NAG Library at Mark 26.2 included the first release of the NAG AD Library. See the
NAG AD Library Contents.
2.3
New Routines at Mark 26.1
| Routine |
Purpose |
| c05mdf |
Solution of a system of nonlinear equations using Anderson acceleration (reverse communication) |
| c06saf |
Multidimensional fast Gauss transform |
| e04fff |
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables |
| e04mtf |
Linear programming (LP), sparse, interior point method (IPM) |
| e04rmf |
Define a nonlinear least squares objective function for a problem initialized by e04raf |
| e04rxf |
Insert or extract data relating to a problem initialized by e04raf |
| g04gaf |
Intraclass correlation (ICC) for assessing rater reliability |
| g22yaf |
Specify a linear model via a formula string |
| g22ybf |
Describe a dataset |
| g22ycf |
Construct a design matrix from a linear model specified using g22yaf |
| g22ydf |
Construct a vector indicating which columns of a design matrix to include in a submodel specified using g22yaf |
| g22zaf |
Destroy a G22 handle and deallocate all the memory used |
| g22zmf |
Option setting routine for Chapter G22 |
| g22znf |
Option getting routine for Chapter G22 |
| s17gaf |
Struve function of order , |
| s17gbf |
Struve function of order , |
| s18gaf |
Modified Struve function of order , |
| s18gbf |
Modified Struve function of order , |
| s18gcf |
The function , where is a modified Bessel function and is a Struve function |
| s18gdf |
The function , where is a modified Bessel function and is a Struve function |
3
Internal Changes Affecting the User and Other Known Issues
The argument names of some routines have changed to be more consistent, particularly with regard to the names of user-supplied routine arguments. This will only affect those program units that use the FL Interface and also use the Fortran argument keyword facility to call routines which have new argument names. For example,
Call d01fcf(... , functn=myfun, ...)
becomes, at Mark 27,
Call d01fcf(..., f=myfun, ...)
where
myfun is the user-supplied function argument.
The following routines have been significantly updated or enhanced since Mark 26 and details are available in each routine document.
| Routine |
Summary of the changes |
|
e01sgf
|
The algorithm used by this routine has been changed to produce more reliable results and work better on certain data sets.
|
|
e01shf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01tgf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01thf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01tkf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01tlf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01tmf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01tnf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01zmf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e01znf
|
The algorithm used by this routine
has been changed to produce more reliable results and work
better on certain data sets.
|
|
e04ffc
|
The underlying algorithm has been improved, improving performance, and new options have been provided.
|
|
e04fff
|
The underlying algorithm has been improved, improving performance, and new options have been provided.
|
|
e04rhc
|
Some limitations on specifying model fixed variables have been lifted.
|
|
e04rhf
|
Some limitations on specifying model fixed variables have been lifted.
|
|
e04stc
|
The name of the monitoring argument has been changed to
monit, and there have been changes to the optional parameters.
|
|
e04stf
|
The name of the monitoring argument has been changed to
monit, and there have been changes to the optional parameters.
|
|
e04svc
|
Additional error check for unsupported models.
|
|
e04svf
|
Additional error check for unsupported models.
|
|
f11zaf
|
The example for this routine has been extended to show how the routine can be used to add sparse matrices, and to demonstrate conversion of sparse matrices between Coordinate Storage and Compressed Column Storage formats.
|
|
g01fbc
|
The algorithm underlying this routine has been altered to improve the accuracy in cases where .
|
|
g01fbf
|
The algorithm underlying this routine has been altered to improve the accuracy in cases where .
|
|
g02baf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bbf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bcf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bdf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bef
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bff
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bgf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bhf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bjf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02bkf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02blf
|
The algorithm underlying this routine has been altered to improve efficiency for large problem sizes on a multi-threaded system.
|
|
g02dac
|
Corrections made to the documented array sizes and improvements made to the example program.
|
|
g02dgc
|
Corrections made to the documented array sizes and improvements made to the example program.
|
|
g02jdc
|
The algorithm underlying this routine has been altered to improve efficiency.
|
|
g02jdf
|
The algorithm underlying this routine has been altered to improve efficiency.
|
|
g02jec
|
The algorithm underlying this routine has been altered to improve efficiency.
|
|
g02jef
|
The algorithm underlying this routine has been altered to improve efficiency.
|
|
g22ybc
|
Functionality has been expanded, an additional argument has been added to the interface and some of the error exits have been renumbered.
|
|
g22ybf
|
Functionality has been expanded, an additional argument has been added to the interface and some of the error exits have been renumbered.
|
For details of all known issues which have been reported for the NAG Library please refer to the Known Issues lists for the Library
FL Interface and
CL Interface.
4
Withdrawn or Deprecated Routines
The following routines have been withdrawn or deprecated from the NAG FL Interface since Mark 26. Warning of their withdrawal has been included in the NAG Library Manual since Mark 25, together with advice on which routines to use instead.
Please note that unless a Mark of Withdrawal is shown below, the routine will continue to form part of the Library but you are advised to stop using the deprecated routines and to use the recommended replacement routines instead.
Please see the chapter introduction documents and the ‘
FL Interface Replacement Calls Advice’ (or the CL version ‘
CL Interface Replacement Calls Advice’) for more detailed guidance, including advice on how to change a call to the deprecated routine into a call to its recommended replacement, or use the links provided in the following table.