NAG C Library News, Mark 23 (PDF version)
NAG C Library Manual

NAG Library

NAG C Library News, Mark 23

+ Contents

1  Introduction

This new release of the NAG C Library has been given the designation Mark 23 whereas the previous release was called Mark 9. This non-sequential numbering reflects the fact that, with the inclusion of this substantial update, the functionality provided in this release of the library is broadly comparable with that available in other NAG Libraries at that Mark.
At Mark 23 of the NAG C Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 1452 user-callable functions, all of which are documented, of which 345 are new at this mark.
Two new chapters have been introduced and there have been extensions in functionality included in the areas of statistics, nonlinear equations, wavelets, ordinary differential equations, interpolation, surface fitting, optimization, matrix operations, linear algebra, large scale linear systems, and special functions.
Chapter c05 (Roots of One or More Transcendental Equations) has a new function for solving sparse nonlinear systems and a new function for determining values of the complex Lambert–W function. Additionally, some functions have been added to provide more breadth to zero finding and solving dense nonlinear systems.
Chapter c06 (Fourier Transforms) has a function for summing a Chebyshev series at a vector of points.
Chapter c09 (Wavelet Transforms) has added one-dimensional continuous and two-dimensional discrete wavelet transform functions.
Chapter d01 (Quadrature) has additional functions for multidimensional integrals, which include integration over the n-hypersphere, a number theoretic method and Gaussian rules.
Chapter d02 (Ordinary Differential Equations) has a new suite of functions for solving boundary-value problems by an implementation of the Chebyshev pseudospectral method.
A new Chapter d04 chapter (Numerical Differentiation) provides functions to enable you to estimate derivatives of order up to 14.
Linear non-singular Fredholm integral equations of the second kind may now be solved using functions from the new Chapter d05 (Integral Equations). In addition the chapter contains functions for second kind, nonlinear Volterra convolution equations and both first and second kind, weakly singular, nonlinear convolution Volterra–Abel equations.
Chapter e01 (Interpolation) adds a modified Shepard's method for multivariate scattered data in four and five dimensions. It also includes the one-dimensional methods of Aitken and Everett.
Chapter e02 (Curve and Surface Fitting) has evaluation of the derivatives of spline surfaces.
Chapter e04 (Minimizing or Maximizing a Function) has a new function to minimize an arbitrary smooth function subject to constraints (which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints) using a sequential quadratic programming (SQP) method using reverse communication. A function to minimize a smooth function and several variables subject to upper and lower bounds on the variable, using methods of quadratic approximation based on BOBYQA has also been introduced.
Chapter e05 (Global Optimization of a Function) has new functions implementing Particle Swarm Optimization and multi-start Sequential Quadratic Programming. The existing function for multi-level coordinate search now allows equality bound constraints.
Chapter f01 (Matrix Operations, Including Inversion) has new routines for functions of real and complex matrices, including matrix log and exponentials, functions of symmetric/Hermitian matrices and functions of general matrices using user-supplied derivatives.
Chapter f07 (Linear Equations (LAPACK)) has LAPACK 3.2 simple and expert drivers for the solution systems of linear equations, where the system is general (full, banded or tridiagonal), symmetric/Hermitian positive definite (full with full or packed storage, banded or tridiagonal), and symmetric/Hermitian (full or packed storage). Additionally there are equilibration functions for various system types and support routines for tridiagonal systems.
Chapter f08 (Least Squares and Eigenvalue Problems (LAPACK)) has LAPACK functions for: solving under and over-determined systems of linear equations; obtaining minimum-norm solutions by SVD or divide-and-conquer algorithms; computing the QR, QL, RQ, RZ factorizations of real and complex matrices (and subsequently forming or applying Q or Z); find some or all eigenvalues/vectors of symmetric/Hermitian matrices (full, packed, banded or tridiagonal); computing the SVD of general matrices using the QR or divide-and-conquer algorithms; computing the Schur form for square matrices. Additionally, for matrix pairs, there are functions for computing the generalized eigenvalues, generalized SVD and Schur forms, and generalized QR and RQ factorizations.
Chapter f11 (Large Scale Eigenproblems) has new suites of reverse communication functions for the iterative solution of sparse symmetric/Hermitian and nonsymmetric/non-Hermitian systems of linear equations; black-box routines for solving sparse Hermitian/non-Hermitian complex systems employing a variety of methods and preconditioners; and some sparse matrix utility functions.
Chapter g01 (Simple Calculations on Statistical Data) has new functions for quantiles of streamed data, bivariate Student's t-distribution and two probability density functions.
Chapter g02 (Correlation and Regression Analysis) has new functions for nearest correlation matrices, hierarchical mixed effects regression, and quantile regression.
Chapter g05 (Random Number Generators) has a new function for skip-ahead by powers of 2 and weighted sampling without replacement. In addition, the suite of base generators has been extended to include the L'Ecuyer MRG32k3a generator. Skip-ahead for the Mersenne Twister base generator is also now available.
Chapter g07 (Univariate Estimation) has new functions for Pareto distribution parameter estimation and outlier detection by the method of Peirce.
Chapter g08 (Nonparametric Statistics) has routines for the Anderson–Darling goodness-of-fit test.
Chapter g12 (Survival Analysis) has a new function for computing rank statistics when comparing survival curves.
Chapter s (Approximations of Special Functions) has new beta and incomplete beta functions and the S30 sub-chapter has a new function for computing Greeks for Heston's model option pricing formula.
In addition there have been a number of enhancements included in Chapters g01 and s. These do not provide new functionality but instead focus on usability. Typically simple functions in these chapters return a single numeric value; a number of these have now been complemented by equivalent functions that conveniently return an array of such values via a single call.

2  New Functions

The 345 new user-callable functions included in the NAG C Library at Mark 23 are as follows.
Function
Name

Purpose
c05aucZero of continuous function, Brent algorithm, from a given starting value, binary search for interval
c05awcZero of continuous function, continuation method, from a given starting value
c05aycZero of continuous function in a given interval, Brent algorithm
c05bbcValues of Lambert's W function, Wz
c05qbcSolution of a system of nonlinear equations using function values only (easy-to-use)
c05qccSolution of a system of nonlinear equations using function values only (comprehensive)
c05qdcSolution of a system of nonlinear equations using function values only (reverse communication)
c05qscSolution of a sparse system of nonlinear equations using function values only (easy-to-use)
c05rbcSolution of a system of nonlinear equations using first derivatives (easy-to-use)
c05rccSolution of a system of nonlinear equations using first derivatives (comprehensive)
c05rdcSolution of a system of nonlinear equations using first derivatives (reverse communication)
c05zdcCheck user's function for calculating first derivatives of a set of nonlinear functions of several variables
c06dccSum of a Chebyshev series at a set of points
c09abcTwo-dimensional wavelet filter initialization
c09bacOne-dimensional real continuous wavelet transform
c09eacTwo-dimensional discrete wavelet transform
c09ebcTwo-dimensional inverse discrete wavelet transform
c09eccTwo-dimensional multi-level discrete wavelet transform
c09edcTwo-dimensional inverse multi-level discrete wavelet transform
d01bdcOne-dimensional quadrature, non-adaptive, finite interval
d01dacTwo-dimensional quadrature, finite region
d01fbcMultidimensional Gaussian quadrature over hyper-rectangle
d01fdcMultidimensional quadrature, Sag–Szekeres method, general product region or n-sphere
d01gdcMultidimensional quadrature, general product region, number-theoretic method
d01gycKorobov optimal coefficients for use in nag_quad_md_numth_vec (d01gdc), when number of points is prime
d01gzcKorobov optimal coefficients for use in nag_quad_md_numth_vec (d01gdc), when number of points is product of two primes
d01pacMultidimensional quadrature over an n-simplex
d01tbcPre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
d01tccCalculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
d02uacCoefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
d02ubcFunction or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
d02uccChebyshev Gauss–Lobatto grid generation
d02udcDifferentiate a function by the FFT using function values on Chebyshev grid
d02uecSolve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
d02uwcInterpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
d02uycClenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
d02uzcChebyshev polynomial evaluation, Tkx
d04aacNumerical differentiation, derivatives up to order 14, function of one real variable
d04bacNumerical differentiation, user-supplied function values, derivatives up to order 14, derivatives with respect to one real variable
d04bbcGenerates sample points for function evaluations by nag_numdiff_1d_real_eval (d04bac)
d05aacLinear non-singular Fredholm integral equation, second kind, split kernel
d05abcLinear non-singular Fredholm integral equation, second kind, smooth kernel
d05bacNonlinear Volterra convolution equation, second kind
d05bdcNonlinear convolution Volterra–Abel equation, second kind, weakly singular
d05becNonlinear convolution Volterra–Abel equation, first kind, weakly singular
d05bwcGenerate weights for use in solving Volterra equations
d05bycGenerate weights for use in solving weakly singular Abel-type equations
e01aacInterpolated values, Aitken's technique, unequally spaced data, one variable
e01abcInterpolated values, Everett's formula, equally spaced data, one variable
e01tkcInterpolating functions, modified Shepard's method, four variables
e01tlcInterpolated values, evaluate interpolant computed by nag_4d_shep_interp (e01tkc), function and first derivatives, four variables
e01tmcInterpolating functions, modified Shepard's method, five variables
e01tncInterpolated values, evaluate interpolant computed by nag_5d_shep_interp (e01tmc), function and first derivatives, five variables
e02dhcEvaluation of spline surface at mesh of points with derivatives
e04jccMinimum by quadratic approximation, function of several variables, simple bounds, using function values only
e04udcSupply optional argument values for nag_opt_nlp (e04ucc) or nag_opt_nlp_revcomm (e04ufc) from external file
e04uecSupply optional argument values to nag_opt_nlp (e04ucc) or nag_opt_nlp_revcomm (e04ufc)
e04ufcMinimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive)
e04wbcInitialization function for nag_opt_nlp_revcomm (e04ufc)
e05sacGlobal optimization using particle swarm algorithm (PSO), bound constraints only
e05sbcGlobal optimization using particle swarm algorithm (PSO), comprehensive
e05uccGlobal optimization using multi-start, nonlinear constraints
e05zkcOption setting routine for nag_glopt_bnd_pso (e05sac), nag_glopt_nlp_pso (e05sbc) and nag_glopt_nlp_multistart_sqp (e05ucc)
e05zlcOption getting routine for nag_glopt_bnd_pso (e05sac), nag_glopt_nlp_pso (e05sbc) and nag_glopt_nlp_multistart_sqp (e05ucc)
f01efcFunction of a real symmetric matrix
f01ejcReal matrix logarithm
f01ekcExponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
f01emcFunction of a real matrix (using user-supplied derivatives)
f01fccComplex matrix exponential
f01fdcComplex Hermitian matrix exponential
f01ffcFunction of a complex Hermitian matrix
f01fjcComplex matrix logarithm
f01fkcExponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
f01fmcFunction of a complex matrix (using user-supplied derivatives)
f03bacLU factorization and determinant of real matrix
f03bfcLLT factorization and determinant of real symmetric positive definite matrix
f03bhcDeterminant of real symmetric positive definite banded matrix
f03bncDeterminant of complex matrix
f07aacComputes the solution to a real system of linear equations
f07abcUses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
f07accMixed precision real system solver
f07afcComputes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
f07ancComputes the solution to a complex system of linear equations
f07apcUses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
f07aqcMixed precision complex system solver
f07atcComputes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
f07bacComputes the solution to a real banded system of linear equations
f07bbcUses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
f07bfcComputes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
f07bncComputes the solution to a complex banded system of linear equations
f07bpcUses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
f07btcComputes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
f07cacComputes the solution to a real tridiagonal system of linear equations
f07cbcUses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
f07cdcLU factorization of real tridiagonal matrix
f07cecSolves a real tridiagonal system of linear equations using the LU factorization computed by nag_dgttrf (f07cdc)
f07cgcEstimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by nag_dgttrf (f07cdc)
f07chcRefined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
f07cncComputes the solution to a complex tridiagonal system of linear equations
f07cpcUses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
f07crcLU factorization of complex tridiagonal matrix
f07cscSolves a complex tridiagonal system of linear equations using the LU factorization computed by nag_dgttrf (f07cdc)
f07cucEstimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by nag_dgttrf (f07cdc)
f07cvcRefined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
f07facComputes the solution to a real symmetric positive definite system of linear equations
f07fbcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
f07ffcComputes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
f07fncComputes the solution to a complex Hermitian positive definite system of linear equations
f07fpcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
f07ftcComputes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
f07gacComputes the solution to a real symmetric positive definite system of linear equations, packed storage
f07gbcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
f07gfcComputes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
f07gncComputes the solution to a complex Hermitian positive definite system of linear equations, packed storage
f07gpcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
f07gtcComputes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
f07hacComputes the solution to a real symmetric positive definite banded system of linear equations
f07hbcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
f07hfcComputes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
f07hncComputes the solution to a complex Hermitian positive definite banded system of linear equations
f07hpcUses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
f07htcComputes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
f07jacComputes the solution to a real symmetric positive definite tridiagonal system of linear equations
f07jbcUses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
f07jdcComputes the modified Cholesky factorization of a real symmetric positive definite tridiagonal matrix
f07jecSolves a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by nag_dpttrf (f07jdc)
f07jgcComputes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by nag_dpttrf (f07jdc)
f07jhcRefined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
f07jncComputes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
f07jpcUses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
f07jrcComputes the modified Cholesky factorization of a complex Hermitian positive definite tridiagonal matrix
f07jscSolves a complex Hermitian positive definite tridiagonal system using the modified Cholesky factorization computed by nag_zpttrf (f07jrc)
f07jucComputes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the modified Cholesky factorization computed by nag_zpttrf (f07jrc)
f07jvcRefined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
f07macComputes the solution to a real symmetric system of linear equations
f07mbcUses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
f07mncComputes the solution to a complex Hermitian system of linear equations
f07mpcUses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
f07nncComputes the solution to a complex symmetric system of linear equations
f07npcUses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
f07pacComputes the solution to a real symmetric system of linear equations, packed storage
f07pbcUses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage
f07pncComputes the solution to a complex Hermitian system of linear equations, packed storage
f07ppcUses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage
f07qncComputes the solution to a complex symmetric system of linear equations, packed storage
f07qpcUses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage
f08aacSolves an overdetermined or underdetermined real linear system
f08ancSolves an overdetermined or underdetermined complex linear system
f08bacComputes the minimum-norm solution to a real linear least squares problem
f08bfcQR factorization of real general rectangular matrix with column pivoting, using BLAS-3
f08bhcReduces a real upper trapezoidal matrix to upper triangular form
f08bkcApply orthogonal transformation determined by nag_dtzrzf (f08bhc)
f08bncComputes the minimum-norm solution to a complex linear least squares problem
f08btcQR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
f08bvcReduces a complex upper trapezoidal matrix to upper triangular form
f08bxcApply unitary transformation determined by nag_ztzrzf (f08bvc)
f08cecQL factorization of real general rectangular matrix
f08cfcForm all or part of orthogonal Q from QL factorization determined by nag_dgeqlf (f08cec)
f08cgcApply orthogonal transformation determined by nag_dgeqlf (f08cec)
f08chcRQ factorization of real general rectangular matrix
f08cjcForm all or part of orthogonal Q from RQ factorization determined by nag_dgerqf (f08chc)
f08ckcApply orthogonal transformation determined by nag_dgerqf (f08chc)
f08cscQL factorization of complex general rectangular matrix
f08ctcForm all or part of orthogonal Q from QL factorization determined by nag_zgeqlf (f08csc)
f08cucApply unitary transformation determined by nag_zgeqlf (f08csc)
f08cvcRQ factorization of complex general rectangular matrix
f08cwcForm all or part of orthogonal Q from RQ factorization determined by nag_zgerqf (f08cvc)
f08cxcApply unitary transformation determined by nag_zgerqf (f08cvc)
f08facComputes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fdcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08flcComputes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
f08fncComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpcComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08frcComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08gacComputes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gncComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpcComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08hacComputes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hncComputes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpcComputes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08jacComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jdcComputes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jhcComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
f08jlcComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
f08jvcComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
f08jycComputes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
f08kacComputes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbcComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kccComputes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
f08kdcComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08khcComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kjcComputes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08kncComputes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpcComputes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqcComputes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
f08krcComputes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08mdcComputes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08nacComputes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbcComputes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
f08nncComputes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npcComputes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
f08pacComputes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
f08pbcComputes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
f08pncComputes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppcComputes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
f08sacComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbcComputes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sccComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sncComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spcComputes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqcComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08tacComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbcComputes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tccComputes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
f08tncComputes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpcComputes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqcComputes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08uacComputes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubcComputes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08uccComputes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uncComputes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upcComputes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqcComputes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08vecComputes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
f08vscComputes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
f08wacComputes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wbcComputes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
f08wncComputes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wpcComputes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
f08xacComputes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
f08xbcComputes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
f08xncComputes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
f08xpcComputes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
f08yecComputes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfcReorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygcReorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
f08yhcSolves the real-valued generalized Sylvester equation
f08ylcEstimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
f08yscComputes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytcReorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yucReorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
f08yvcSolves the complex generalized Sylvester equation
f08yycEstimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
f08zecComputes a generalized QR factorization of a real matrix pair
f08zfcComputes a generalized RQ factorization of a real matrix pair
f08zscComputes a generalized QR factorization of a complex matrix pair
f08ztcComputes a generalized RQ factorization of a complex matrix pair
f11bdcReal sparse nonsymmetric linear systems, setup for nag_sparse_nsym_basic_solver (f11bec)
f11becReal sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
f11bfcReal sparse nonsymmetric linear systems, diagnostic for nag_sparse_nsym_basic_solver (f11bec)
f11brcComplex sparse non-Hermitian linear systems, setup for nag_sparse_nherm_basic_solver (f11bsc)
f11bscComplex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
f11btcComplex sparse non-Hermitian linear systems, diagnostic for nag_sparse_nherm_basic_solver (f11bsc)
f11dbcSolution of linear system involving incomplete LU preconditioning matrix generated by nag_sparse_nsym_fac (f11dac)
f11ddcSolution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
f11dkcReal sparse nonsymmetric linear systems, line Jacobi preconditioner
f11dncComplex sparse non-Hermitian linear systems, incomplete LU factorization
f11dpcSolution of complex linear system involving incomplete LU preconditioning matrix generated by nag_sparse_nherm_fac (f11dnc)
f11dqcSolution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by nag_sparse_nherm_fac (f11dnc) (Black Box)
f11drcSolution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
f11dscSolution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
f11dxcComplex sparse nonsymmetric linear systems, line Jacobi preconditioner
f11gdcReal sparse symmetric linear systems, setup for nag_sparse_sym_basic_solver (f11gec)
f11gecReal sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
f11gfcReal sparse symmetric linear systems, diagnostic for nag_sparse_sym_basic_solver (f11gec)
f11grcComplex sparse Hermitian linear systems, setup for nag_sparse_herm_basic_solver (f11gsc)
f11gscComplex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
f11gtcComplex sparse Hermitian linear systems, diagnostic for nag_sparse_herm_basic_solver (f11gsc)
f11jbcSolution of linear system involving incomplete Cholesky preconditioning matrix generated by nag_sparse_sym_chol_fac (f11jac)
f11jdcSolution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
f11jncComplex sparse Hermitian matrix, incomplete Cholesky factorization
f11jpcSolution of complex linear system involving incomplete Cholesky preconditioning matrix generated by nag_sparse_herm_chol_fac (f11jnc)
f11jqcSolution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by nag_sparse_herm_chol_fac (f11jnc) (Black Box)
f11jrcSolution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
f11jscSolution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
f11xacReal sparse nonsymmetric matrix vector multiply
f11xecReal sparse symmetric matrix vector multiply
f11xncComplex sparse non-Hermitian matrix vector multiply
f11xscComplex sparse Hermitian matrix vector multiply
f11zncComplex sparse non-Hermitian matrix reorder function
f11zpcComplex sparse Hermitian matrix reorder function
g01ancCalculates approximate quantiles from a data stream of known size
g01apcCalculates approximate quantiles from a data stream of unknown size
g01hccComputes probabilities for the bivariate Student's t-distribution
g01kkcCalculates a vector of values for the probability density function of the gamma distribution at chosen points
g01kqcCalculates a vector of values for the probability density function of the Normal distribution at chosen points
g01sacComputes a vector of probabilities for the standard Normal distribution
g01sbcComputes a vector of probabilities for Student's t-distribution
g01sccComputes a vector of probabilities for χ2 distribution
g01sdcComputes a vector of probabilities for F-distribution
g01secComputes a vector of probabilities for the beta distribution
g01sfcComputes a vector of probabilities for the gamma distribution
g01sjcComputes a vector of the binomial distribution
g01skcComputes a vector of the Poisson distribution
g01slcComputes a vector of the hypergeometeric distribution
g01tacComputes a vector of deviates for the standard Normal distribution
g01tbcComputes a vector of deviates for Student's t-distribution
g01tccComputes a vector of deviates for χ2 distribution
g01tdcComputes deviates for F-distribution
g01tecComputes a vector of deviates for the beta distribution
g01tfcComputes a vector of deviates for the gamma distribution
g02abcComputes the nearest correlation matrix to a real square matrix, augmented nag_nearest_correlation (g02aac) to incorporate weights and bounds
g02aecComputes the nearest correlation matrix with k-factor structure to a real square matrix
g02qfcQuantile linear regression, simple interface, independent, identically distributed (IID) errors
g02qgcQuantile linear regression, comprehensive interface
g02zkcOption setting function for nag_regsn_quant_linear (g02qgc)
g02zlcOption getting function for nag_regsn_quant_linear (g02qgc)
g05kkcPrimes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
g05necPseudorandom sample, without replacement, unequal weights
g07gacOutlier detection using method of Peirce, raw data or single variance supplied
g07gbcOutlier detection using method of Peirce, two variances supplied
g08chcCalculates the Anderson–Darling goodness-of-fit test statistic
g08cjcCalculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data
g08ckcCalculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
g08clcCalculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
g12abcComputes rank statistics for comparing survival curves
s14cbcLogarithm of the beta function lnB,a,b
s14cccIncomplete beta function Ixa,b and its complement 1-Ix
s17aqcBessel function vectorized Y0x
s17arcBessel function vectorized Y1x
s17ascBessel function vectorized J0x
s17atcBessel function vectorized J1x
s17aucAiry function vectorized Aix
s17avcAiry function vectorized Bix
s17awcAiry function vectorized Aix
s17axcAiry function vectorized Bix
s18aqcModified Bessel function vectorized K0x
s18arcModified Bessel function vectorized K1x
s18ascModified Bessel function vectorized I0x
s18atcModified Bessel function vectorized I1x
s18cqcScaled modified Bessel function vectorized exK0x
s18crcScaled modified Bessel function vectorized exK1x
s18cscScaled modified Bessel function vectorized e-xI0x
s18ctcScaled modified Bessel function vectorized e-xI1x
s19ancKelvin function vectorized berx
s19apcKelvin function vectorized beix
s19aqcKelvin function vectorized kerx
s19arcKelvin function vectorized keix
s20aqcFresnel integral vectorized Sx
s20arcFresnel integral vectorized Cx
s30nbcHeston's model option pricing formula with Greeks

3  Withdrawn Functions

The following functions have been withdrawn from the NAG C Library at Mark 23. Warning of their withdrawal was included in the NAG C Library Manual at Mark 9, together with advice on which functions to use instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Functions’ for more detailed guidance.
Withdrawn
Function

Replacement Function(s)
e01sacnag_2d_shep_interp (e01sgc) or nag_2d_triang_interp (e01sjc)
e01sbcnag_2d_shep_eval (e01shc) or nag_2d_triang_eval (e01skc)
e01szcNo longer required.
f06pacnag_dgemv (f16pac)
f06pbcnag_dgbmv (f16pbc)
f06pccnag_dsymv (f16pcc)
f06pdcnag_dsbmv (f16pdc)
f06pecnag_dspmv (f16pec)
f06pfcnag_dtrmv (f16pfc)
f06pgcnag_dtbmv (f16pgc)
f06phcnag_dtpmv (f16phc)
f06pjcnag_dtrsv (f16pjc)
f06pkcnag_dtbsv (f16pkc)
f06plcnag_dtpsv (f16plc)
f06pmcnag_dger (f16pmc)
f06ppcnag_dsyr (f16ppc)
f06pqcnag_dspr (f16pqc)
f06prcnag_dsyr2 (f16prc)
f06pscnag_dspr2 (f16psc)
f06sacnag_zgemv (f16sac)
f06sbcnag_zgbmv (f16sbc)
f06sccnag_zhemv (f16scc)
f06sdcnag_zhbmv (f16sdc)
f06secnag_zhpmv (f16sec)
f06sfcnag_ztrmv (f16sfc)
f06sgcnag_ztbmv (f16sgc)
f06shcnag_ztpmv (f16shc)
f06sjcnag_ztrsv (f16sjc)
f06skcnag_ztbsv (f16skc)
f06slcnag_ztpsv (f16slc)
f06smcnag_zger (f16smc)
f06sncnag_zger (f16smc)
f06spcnag_zher (f16spc)
f06sqcnag_zhpr (f16sqc)
f06srcnag_zher2 (f16src)
f06sscnag_zhpr2 (f16ssc)
f06yacnag_dgemm (f16yac)
f06yccnag_dsymm (f16ycc)
f06yfcnag_dtrmm (f16yfc)
f06yjcnag_dtrsm (f16yjc)
f06ypcnag_dsyrk (f16ypc)
f06yrcnag_dsyr2k (f16yrc)
f06zacnag_zgemm (f16zac)
f06zccnag_zhemm (f16zcc)
f06zfcnag_ztrmm (f16zfc)
f06zjcnag_ztrsm (f16zjc)
f06zpcnag_zherk (f16zpc)
f06zrcnag_zher2k (f16zrc)
f06ztcnag_zsymm (f16ztc)
f06zucnag_zsyrk (f16zuc)
f06zwcnag_zsyr2k (f16zwc)

4  Functions Scheduled for Withdrawal

The functions listed below are scheduled for withdrawal from the NAG C Library, because improved functions have now been included in the Library. You are advised to stop using functions which are scheduled for withdrawal and to use recommended replacement functions instead. See the document ‘Advice on Replacement Calls for Withdrawn/Superseded Functions’ for more detailed guidance, including advice on how to change a call to the old function into a call to its recommended replacement.
The following functions will be withdrawn at Mark 24.
Functions Scheduled
for Withdrawal

Replacement Function(s)
c05adcnag_zero_cont_func_brent (c05ayc)
c05nbcnag_zero_nonlin_eqns_easy (c05qbc)
c05pbcnag_zero_nonlin_eqns_deriv_easy (c05rbc)
c05tbcnag_zero_nonlin_eqns_easy (c05qbc)
c05zbcnag_check_derivs (c05zdc)
c05zccnag_check_derivs (c05zdc)
d01ajcnag_1d_quad_gen_1 (d01sjc)
d01akcnag_1d_quad_osc_1 (d01skc)
d01alcnag_1d_quad_brkpts_1 (d01slc)
d01amcnag_1d_quad_inf_1 (d01smc)
d01ancnag_1d_quad_wt_trig_1 (d01snc)
d01apcnag_1d_quad_wt_alglog_1 (d01spc)
d01aqcnag_1d_quad_wt_cauchy_1 (d01sqc)
d01ascnag_1d_quad_inf_wt_trig_1 (d01ssc)
d01bacnag_1d_quad_gauss_1 (d01tac)
d01fccnag_multid_quad_adapt_1 (d01wcc)
d01gbcnag_multid_quad_monte_carlo_1 (d01xbc)
e04cccnag_opt_simplex_easy (e04cbc)
g01cecnag_deviates_normal (g01fac)
g05cacnag_rand_basic (g05sac)
g05cbcnag_rand_init_repeatable (g05kfc)
g05cccnag_rand_init_nonrepeatable (g05kgc)
g05cfcNo longer required.
g05cgcNo longer required.
g05dacnag_rand_uniform (g05sqc)
g05dbcnag_rand_exp (g05sfc)
g05ddcnag_rand_normal (g05skc)
g05dycnag_rand_discrete_uniform (g05tlc)
g05eacnag_rand_matrix_multi_normal (g05rzc)
g05eccnag_rand_poisson (g05tjc)
g05edcnag_rand_binomial (g05tac)
g05ehcnag_rand_permute (g05ncc)
g05ejcnag_rand_sample (g05ndc)
g05excnag_rand_gen_discrete (g05tdc)
g05eycnag_rand_gen_discrete (g05tdc)
g05ezcnag_rand_matrix_multi_normal (g05rzc)
g05fecnag_rand_beta (g05sbc)
g05ffcnag_rand_gamma (g05sjc)
g05hacnag_rand_arma (g05phc)
g05hkcnag_rand_agarchI (g05pdc)
g05hlcnag_rand_agarchII (g05pec)
g05hmcnag_rand_garchGJR (g05pfc)
g05kacnag_rand_basic (g05sac)
g05kbcnag_rand_init_repeatable (g05kfc)
g05kccnag_rand_init_nonrepeatable (g05kgc)
g05kecnag_rand_logical (g05tbc)
g05lacnag_rand_normal (g05skc)
g05lbcnag_rand_students_t (g05snc)
g05lccnag_rand_chi_sq (g05sdc)
g05ldcnag_rand_f (g05shc)
g05lecnag_rand_beta (g05sbc)
g05lfcnag_rand_gamma (g05sjc)
g05lgcnag_rand_uniform (g05sqc)
g05lhcnag_rand_triangular (g05spc)
g05ljcnag_rand_exp (g05sfc)
g05lkcnag_rand_lognormal (g05smc)
g05llcnag_rand_cauchy (g05scc)
g05lmcnag_rand_weibull (g05ssc)
g05lncnag_rand_logistic (g05slc)
g05lpcnag_rand_von_mises (g05src)
g05lqcnag_rand_exp_mix (g05sgc)
g05lxcnag_rand_matrix_multi_students_t (g05ryc)
g05lycnag_rand_matrix_multi_normal (g05rzc)
g05lzcnag_rand_matrix_multi_normal (g05rzc)
g05macnag_rand_discrete_uniform (g05tlc)
g05mbcnag_rand_geom (g05tcc)
g05mccnag_rand_neg_bin (g05thc)
g05mdcnag_rand_logarithmic (g05tfc)
g05mecnag_rand_compd_poisson (g05tkc)
g05mjcnag_rand_binomial (g05tac)
g05mkcnag_rand_poisson (g05tjc)
g05mlcnag_rand_hypergeometric (g05tec)
g05mrcnag_rand_gen_multinomial (g05tgc)
g05mzcnag_rand_gen_discrete (g05tdc)
g05nacnag_rand_permute (g05ncc)
g05nbcnag_rand_sample (g05ndc)
g05pacnag_rand_arma (g05phc)
g05pccnag_rand_varma (g05pjc)
g05qacnag_rand_orthog_matrix (g05pxc)
g05qbcnag_rand_corr_matrix (g05pyc)
g05qdcnag_rand_2_way_table (g05pzc)
g05racnag_rand_copula_normal (g05rdc)
g05rbcnag_rand_copula_students_t (g05rcc)
g05yacnag_quasi_init (g05ylc) and nag_quasi_rand_uniform (g05ymc)
g05ybcnag_quasi_rand_normal (g05yjc) and nag_quasi_init (g05ylc)
x02dacNo longer required.
x02djcNo longer required.
The following functions have been superseded, but will not be withdrawn from the Library until Mark 25 at the earliest.
Superseded
Function

Replacement Function(s)
c05agcnag_zero_cont_func_brent_binsrch (c05auc)
c05sdcnag_zero_cont_func_brent (c05ayc)
c05ubcnag_zero_nonlin_eqns_deriv_easy (c05rbc)
f01bncnag_zpotrf (f07frc)
f01qccnag_dgeqrf (f08aec)
f01qdcnag_dormqr (f08agc)
f01qecnag_dorgqr (f08afc)
f01rccnag_zgeqrf (f08asc)
f01rdcnag_zunmqr (f08auc)
f01recnag_zungqr (f08atc)
f03aecnag_dpotrf (f07fdc) and nag_det_real_sym (f03bfc)
f03afcnag_dgetrf (f07adc) and nag_det_real_gen (f03bac)
f03ahcnag_zgetrf (f07arc) and nag_det_complex_gen (f03bnc)
f04adcnag_complex_gen_lin_solve (f04cac)
f04agcnag_dpotrs (f07fec)
f04ajcnag_dgetrs (f07aec)
f04akcnag_zgetrs (f07asc)
f04arcnag_real_gen_lin_solve (f04bac)
f04awcnag_zpotrs (f07fsc)
x04aecNo replacement required.

NAG C Library News, Mark 23 (PDF version)
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012