Mark 7 News (pdf version)
NAG C Library Manual

Mark 7 News

1  Introduction

At Mark 7 of the C Library new functionality has been introduced in addition to improvements in existing areas. The Library now contains 860 documented routines, of which 397 are new at this Mark.

This is a significant enhancement over Mark 6. New chapters have been introduced to cover LAPACK (Chapters f07 and f08), Partial Differential Equations (d03), Mesh Generation (d06) and Input/Output Utilities (x04). Significant new material capability has been added to Random Number Generators (g05). New functionality has also been added to Interpolation (e01), Curve and Surface Fitting (e02), Simple Calculations on Statistical Data (g01), Correlation and Regression Analysis (g02), Univariate Estimation (g07), Nonparametric Statistics (g08), Contingency Table Analysis (g11), Survival Analysis (g12) and Time Series Analysis (g13). The special function chapter (s) sees the addition of a number of special functions with particular appeal to theoretical physicists.

A major innovation at this mark is the introduction of the order parameter, which allows data to be specified either in row or column major order. This allows the C Library functions to be easily callable from other environments such as Visual Basic. For further details please refer to the Essential Introduction.

Finally, in environments where vendor supplied BLAS functions are available, these can now be called by the C Library to further enhance performance. This is achieved by the use of NAG's interface to BLAS, a proportion of which are documented in the new NAG C BLAS chapter (f16).

2  New Routines

The 397 new user-callable routines included in the C Library at Mark 7 are as follows.

c06pfc nag_fft_multid_single
One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pjc nag_fft_multid_full
Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pxc nag_fft_3d
Three-dimensional complex discrete Fourier transform, complex data format
d03ncc nag_pde_bs_1d
Finite difference solution of the Black–Scholes equations
d03ndc nag_pde_bs_1d_analytic
Analytic solution of the Black–Scholes equations
d03nec nag_pde_bs_1d_means
Compute average values for d03ndc
d03pcc nag_pde_parab_1d_fd
General system of parabolic PDEs, method of lines, finite differences, one space variable
d03pdc nag_pde_parab_1d_coll
General system of parabolic PDEs, method of lines, Chebyshev C0 collocation, one space variable
d03pec nag_pde_parab_1d_keller
General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
d03pfc nag_pde_parab_1d_cd
General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03phc nag_pde_parab_1d_fd_ode
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
d03pjc nag_pde_parab_1d_coll_ode
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0 collocation, one space variable
d03pkc nag_pde_parab_1d_keller_ode
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
d03plc nag_pde_parab_1d_cd_ode
General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03ppc nag_pde_parab_1d_fd_ode_remesh
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
d03prc nag_pde_parab_1d_keller_ode_remesh
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
d03psc nag_pde_parab_1d_cd_ode_remesh
General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, remeshing, one space variable
d03puc nag_pde_parab_1d_euler_roe
Roe's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pvc nag_pde_parab_1d_euler_osher
Osher's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pwc nag_pde_parab_1d_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pxc nag_pde_parab_1d_euler_exact
Exact Riemann Solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pyc nag_pde_interp_1d_coll
PDEs, spatial interpolation with d03pdc or d03pjc
d03pzc nag_pde_interp_1d_fd
PDEs, spatial interpolation with d03pcc, d03pec, d03pfc, d03phc, d03pkc, d03plc, d03ppc, d03prc or d03psc
d06aac nag_mesh2d_inc
Generates a two-dimensional mesh using a simple incremental method
d06abc nag_mesh2d_delaunay
Generates a two-dimensional mesh using a Delaunay–Voronoi process
d06acc nag_mesh2d_front
Generates a two-dimensional mesh using an Advancing-front method
d06bac nag_mesh2d_bound
Generates a boundary mesh
d06cac nag_mesh2d_smooth
Uses a barycentering technique to smooth a given mesh
d06cbc nag_mesh2d_sparse
Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
d06ccc nag_mesh2d_renum
Renumbers a given mesh using Gibbs method
d06dac nag_mesh2d_trans
Generates a mesh resulting from an affine transformation of a given mesh
d06dbc nag_mesh2d_join
Joins together two given adjacent (possibly overlapping) meshes
e01aec nag_1d_cheb_interp
Interpolating functions, polynomial interpolant, data may include derivative values, one variable
e01rac nag_1d_ratnl_interp
Interpolating functions, rational interpolant, one variable
e01rbc nag_1d_ratnl_eval
Interpolated values, evaluate rational interpolant computed by e01rac, one variable
e01tgc nag_3d_shep_interp
Interpolating functions, modified Shepard's method, three variables
e01thc nag_3d_shep_eval
Interpolated values, evaluate interpolant computed by e01tgc, function and first derivatives, three variables
e02agc nag_1d_cheb_fit_constr
Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points
e02ahc nag_1d_cheb_deriv
Derivative of fitted polynomial in Chebyshev series form
e02ajc nag_1d_cheb_intg
Integral of fitted polynomial in Chebyshev series form
e02akc nag_1d_cheb_eval2
Evaluation of fitted polynomial in one variable from Chebyshev series form
e02cac nag_2d_cheb_fit_lines
Least-squares surface fit by polynomials, data on lines
e02cbc nag_2d_cheb_eval
Evaluation of fitted polynomial in two variables
e02gac nag_lone_fit
L1-approximation by general linear function
e02gcc nag_linf_fit
L-approximation by general linear function
e02rac nag_1d_pade
Padé-approximants
e02rbc nag_1d_pade_eval
Evaluation of fitted rational function as computed by e02rac
f07adc nag_dgetrf
LU factorization of real m by n matrix
f07aec nag_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by f07adc
f07agc nag_dgecon
Estimate condition number of real matrix, matrix already factorized by f07adc
f07ahc nag_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
f07ajc nag_dgetri
Inverse of real matrix, matrix already factorized by f07adc
f07arc nag_zgetrf
LU factorization of complex m by n matrix
f07asc nag_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by f07arc
f07auc nag_zgecon
Estimate condition number of complex matrix, matrix already factorized by f07arc
f07avc nag_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
f07awc nag_zgetri
Inverse of complex matrix, matrix already factorized by f07arc
f07bdc nag_dgbtrf
LU factorization of real m by n band matrix
f07bec nag_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by f07bdc
f07bgc nag_dgbcon
Estimate condition number of real band matrix, matrix already factorized by f07bdc
f07bhc nag_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
f07brc nag_zgbtrf
LU factorization of complex m by n band matrix
f07bsc nag_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by f07brc
f07buc nag_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by f07brc
f07bvc nag_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
f07fdc nag_dpotrf
Cholesky factorization of real symmetric positive-definite matrix
f07fec nag_dpotrs
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07fdc
f07fgc nag_dpocon
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07fdc
f07fhc nag_dporfs
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
f07fjc nag_dpotri
Inverse of real symmetric positive-definite matrix, matrix already factorized by f07fdc
f07frc nag_zpotrf
Cholesky factorization of complex Hermitian positive-definite matrix
f07fsc nag_zpotrs
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07frc
f07fuc nag_zpocon
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by f07frc
f07fvc nag_zporfs
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
f07fwc nag_zpotri
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by f07frc
f07gdc nag_dpptrf
Cholesky factorization of real symmetric positive-definite matrix, packed storage
f07gec nag_dpptrs
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07gdc, packed storage
f07ggc nag_dppcon
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07gdc, packed storage
f07ghc nag_dpprfs
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gjc nag_dpptri
Inverse of real symmetric positive-definite matrix, matrix already factorized by f07gdc, packed storage
f07grc nag_zpptrf
Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
f07gsc nag_zpptrs
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07grc, packed storage
f07guc nag_zppcon
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by f07grc, packed storage
f07gvc nag_zpprfs
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gwc nag_zpptri
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by f07grc, packed storage
f07hdc nag_dpbtrf
Cholesky factorization of real symmetric positive-definite band matrix
f07hec nag_dpbtrs
Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hdc
f07hgc nag_dpbcon
Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by f07hdc
f07hhc nag_dpbrfs
Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
f07hrc nag_zpbtrf
Cholesky factorization of complex Hermitian positive-definite band matrix
f07hsc nag_zpbtrs
Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hrc
f07huc nag_zpbcon
Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by f07hrc
f07hvc nag_zpbrfs
Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
f07mdc nag_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
f07mec nag_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mdc
f07mgc nag_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07mdc
f07mhc nag_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
f07mjc nag_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by f07mdc
f07mrc nag_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
f07msc nag_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mrc
f07muc nag_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07mrc
f07mvc nag_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
f07mwc nag_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07mrc
f07nrc nag_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
f07nsc nag_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07nrc
f07nuc nag_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by f07nrc
f07nvc nag_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
f07nwc nag_zsytri
Inverse of complex symmetric matrix, matrix already factorized by f07nrc
f07pdc nag_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
f07pec nag_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07pdc, packed storage
f07pgc nag_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07pdc, packed storage
f07phc nag_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
f07pjc nag_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by f07pdc, packed storage
f07prc nag_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
f07psc nag_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07prc, packed storage
f07puc nag_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07prc, packed storage
f07pvc nag_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
f07pwc nag_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07prc, packed storage
f07qrc nag_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
f07qsc nag_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07qrc, packed storage
f07quc nag_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by f07qrc, packed storage
f07qvc nag_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
f07qwc nag_zsptri
Inverse of complex symmetric matrix, matrix already factorized by f07qrc, packed storage
f07tec nag_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
f07tgc nag_dtrcon
Estimate condition number of real triangular matrix
f07thc nag_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
f07tjc nag_dtrtri
Inverse of real triangular matrix
f07tsc nag_ztrtrs
Solution of complex triangular system of linear equations, multiple right-hand sides
f07tuc nag_ztrcon
Estimate condition number of complex triangular matrix
f07tvc nag_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
f07twc nag_ztrtri
Inverse of complex triangular matrix
f07uec nag_dtptrs
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ugc nag_dtpcon
Estimate condition number of real triangular matrix, packed storage
f07uhc nag_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ujc nag_dtptri
Inverse of real triangular matrix, packed storage
f07usc nag_ztptrs
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uuc nag_ztpcon
Estimate condition number of complex triangular matrix, packed storage
f07uvc nag_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uwc nag_ztptri
Inverse of complex triangular matrix, packed storage
f07vec nag_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
f07vgc nag_dtbcon
Estimate condition number of real band triangular matrix
f07vhc nag_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
f07vsc nag_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
f07vuc nag_ztbcon
Estimate condition number of complex band triangular matrix
f07vvc nag_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
f08aec nag_dgeqrf
QR factorization of real general rectangular matrix
f08afc nag_dorgqr
Form all or part of orthogonal Q from QR factorization determined by f08aec or f08bec
f08agc nag_dormqr
Apply orthogonal transformation determined by f08aec or f08bec
f08ahc nag_dgelqf
LQ factorization of real general rectangular matrix
f08ajc nag_dorglq
Form all or part of orthogonal Q from LQ factorization determined by f08ahc
f08akc nag_dormlq
Apply orthogonal transformation determined by f08ahc
f08asc nag_zgeqrf
QR factorization of complex general rectangular matrix
f08atc nag_zungqr
Form all or part of unitary Q from QR factorization determined by f08asc or f08bsc
f08auc nag_zunmqr
Apply unitary transformation determined by f08asc or f08bsc
f08avc nag_zgelqf
LQ factorization of complex general rectangular matrix
f08awc nag_zunglq
Form all or part of unitary Q from LQ factorization determined by f08avc
f08axc nag_zunmlq
Apply unitary transformation determined by f08avc
f08bec nag_dgeqpf
QR factorization of real general rectangular matrix with column pivoting
f08bsc nag_zgeqpf
QR factorization of complex general rectangular matrix with column pivoting
f08fcc nag_dsyevd
All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
f08fec nag_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc nag_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec
f08fgc nag_dormtr
Apply orthogonal transformation determined by f08fec
f08fqc nag_zheevd
All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
f08fsc nag_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc nag_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc
f08fuc nag_zunmtr
Apply unitary transformation matrix determined by f08fsc
f08gcc nag_dspevd
All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
f08gec nag_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc nag_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec
f08ggc nag_dopmtr
Apply orthogonal transformation determined by f08gec
f08gqc nag_zhpevd
All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
f08gsc nag_zhptrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc nag_zupgtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08gsc
f08guc nag_zupmtr
Apply unitary transformation matrix determined by f08gsc
f08hcc nag_dsbevd
All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
f08hec nag_dsbtrd
Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hqc nag_zhbevd
All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
f08hsc nag_zhbtrd
Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jcc nag_dstevd
All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
f08jec nag_dsteqr
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
f08jfc nag_dsterf
All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
f08jgc nag_dpteqr
All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
f08jjc nag_dstebz
Selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc nag_dstein
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jsc nag_zsteqr
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
f08juc nag_zpteqr
All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
f08jxc nag_zstein
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08kec nag_dgebrd
Orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc nag_dorgbr
Generate orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec
f08kgc nag_dormbr
Apply orthogonal transformations from reduction to bidiagonal form determined by f08kec
f08ksc nag_zgebrd
Unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc nag_zungbr
Generate unitary transformation matrices from reduction to bidiagonal form determined by f08ksc
f08kuc nag_zunmbr
Apply unitary transformations from reduction to bidiagonal form determined by f08ksc
f08lec nag_dgbbrd
Reduction of real rectangular band matrix to upper bidiagonal form
f08lsc nag_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form