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).
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 |
| f08mec | nag_dbdsqr SVD of real bidiagonal matrix reduced from real general matrix |
| f08msc | nag_zbdsqr SVD of real bidiagonal matrix reduced from complex general matrix |
| f08nec | nag_dgehrd Orthogonal reduction of real general matrix to upper Hessenberg form |
| f08nfc | nag_dorghr Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec |
| f08ngc | nag_dormhr Apply orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec |
| f08nhc | nag_dgebal Balance real general matrix |
| f08njc | nag_dgebak Transform eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc |
| f08nsc | nag_zgehrd Unitary reduction of complex general matrix to upper Hessenberg form |
| f08ntc | nag_zunghr Generate unitary transformation matrix from reduction to Hessenberg form determined by f08nsc |
| f08nuc | nag_zunmhr Apply unitary transformation matrix from reduction to Hessenberg form determined by f08nsc |
| f08nvc | nag_zgebal Balance complex general matrix |
| f08nwc | nag_zgebak Transform eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvc |
| f08pec | nag_dhseqr Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| f08pkc | nag_dhsein Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| f08psc | nag_zhseqr Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| f08pxc | nag_zhsein Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| f08qfc | nag_dtrexc Reorder Schur factorization of real matrix using orthogonal similarity transformation |
| f08qgc | nag_dtrsen Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| f08qhc | nag_dtrsyl Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes |
| f08qkc | nag_dtrevc Left and right eigenvectors of real upper quasi-triangular matrix |
| f08qlc | nag_dtrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| f08qtc | nag_ztrexc Reorder Schur factorization of complex matrix using unitary similarity transformation |
| f08quc | nag_ztrsen Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| f08qvc | nag_ztrsyl Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes |
| f08qxc | nag_ztrevc Left and right eigenvectors of complex upper triangular matrix |
| f08qyc | nag_ztrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| f08sec | nag_dsygst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07fdc |
| f08ssc | nag_zhegst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07frc |
| f08tec | nag_dspgst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07gdc |
| f08tsc | nag_zhpgst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07grc |
| f08uec | nag_dsbgst Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A |
| f08ufc | nag_dpbstf Computes a split Cholesky factorization of real symmetric positive-definite band matrix A |
| f08usc | nag_zhbgst Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A |
| f08utc | nag_zpbstf Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A |
| f08wec | nag_dgghrd Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08whc | nag_dggbal Balance a pair of real general matrices |
| f08wjc | nag_dggbak Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc |
| f08wsc | nag_zgghrd Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wvc | nag_zggbal Balance a pair of complex general matrices |
| f08wwc | nag_zggbak Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvc |
| f08xec | nag_dhgeqz Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
| f08xsc | nag_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices |
| f08ykc | nag_dtgevc Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| f08yxc | nag_ztgevc Left and right eigenvectors of a pair of complex upper triangular matrices |
| f16dbc | nag_iload Broadcast scalar into integer vector |
| f16ecc | nag_daxpby Multiply real vector by scalar, preserving input vector |
| f16fbc | nag_dload Broadcast scalar into real vector |
| f16hbc | nag_zload Broadcast scalar into complex vector |
| f16pjc | nag_dtrsv System of equations, real triangular matrix |
| f16qec | nag_dtr_copy Matrix copy, real triangular matrix |
| f16qfc | nag_dge_copy Matrix copy, real rectangular matrix |
| f16qgc | nag_dtr_load Matrix initialisation, real triangular matrix |
| f16qhc | nag_dge_load Matrix initialisation, real rectangular matrix |
| f16rac | nag_dge_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, real general matrix |
| f16rbc | nag_dgb_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, real band matrix |
| f16rcc | nag_dsy_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix |
| f16rdc | nag_dsp_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage |
| f16rec | nag_dsb_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric band matrix |
| f16sjc | nag_ztrsv System of equations, complex triangular matrix |
| f16tec | nag_ztr_copy Matrix copy, complex triangular matrix |
| f16tfc | nag_zge_copy Matrix copy, complex rectangular matrix |
| f16tgc | nzg_ztr_load Matrix initialisation, complex triangular matrix |
| f16thc | nag_zge_load Matrix initialisation, complex rectangular matrix |
| f16uac | nag_zge_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex general matrix |
| f16ubc | nag_zgb_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex band matrix |
| f16ucc | nag_zhe_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix |
| f16udc | nag_zhp_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage |
| f16uec | nag_zhb_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian band matrix |
| f16ufc | nag_zsy_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix |
| f16ugc | nag_zsp_norm 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage |
| f16yjc | nag_dtrsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix |
| f16zjc | nag_ztrsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix |
| g01adc | nag_summary_stats_freq Mean, variance, skewness, kurtosis, etc., one variable, from frequency table |
| g01dac | nag_normal_scores_exact Normal scores, accurate values |
| g01dcc | nag_normal_scores_var Normal scores, approximate variance-covariance matrix |
| g01emc | nag_prob_studentized_range Computes probability for the Studentized range statistic |
| g01epc | nag_prob_durbin_watson Computes bounds for the significance of a Durbin–Watson statistic |
| g01erc | nag_prob_von_mises Computes probability for von Mises distribution |
| g01etc | nag_prob_landau Landau distribution function Φ (λ) |
| g01euc | nag_prob_vavilov Vavilov distribution function ΦV (λ;κ,β2) |
| g01eyc | nag_prob_1_sample_ks Computes probabilities for the one-sample Kolmogorov–Smirnov distribution |
| g01ezc | nag_prob_2_sample_ks Computes probabilities for the two-sample Kolmogorov–Smirnov distribution |
| g01fmc | nag_deviates_studentized_range Computes deviates for the Studentized range statistic |
| g01ftc | nag_deviates_landau Landau inverse function Ψ (x) |
| g01jcc | nag_prob_lin_non_central_chi_sq Computes probability for a positive linear combination of χ2 variables |
| g01jdc | nag_prob_lin_chi_sq Computes lower tail probability for a linear combination of (central) χ2 variables |
| g01mbc | nag_mills_ratio Computes reciprocal of Mills' Ratio |
| g01mtc | nag_prob_density_landau Landau density function φ (λ) |
| g01muc | nag_prob_density_vavilov Vavilov density function φV (λ;κ,β2) |
| g01nac | nag_moments_quad_form Cumulants and moments of quadratic forms in Normal variables |
| g01nbc | nag_moments_ratio_quad_forms Moments of ratios of quadratic forms in Normal variables, and related statistics |
| g01ptc | nag_moment_1_landau Landau first moment function Φ1 (x) |
| g01qtc | nag_moment_2_landau Landau second moment function Φ2 (x) |
| g01rtc | nag_prob_der_landau Landau derivative function φ ' (λ) |
| g01zuc | nag_init_vavilov Initialisation function for g01muc and g01euc |
| g02btc | nag_sum_sqs_update Update a weighted sum of squares matrix with a new observation |
| g02buc | nag_sum_sqs Computes a weighted sum of squares matrix |
| g02bwc | nag_cov_to_corr Computes a correlation matrix from a sum of squares matrix |
| g02eac | nag_all_regsn Computes residual sums of squares for all possible linear regressions for a set of independent variables |
| g02ecc | nag_cp_stat Calculates R2 and CP values from residual sums of squares |
| g02eec | nag_step_regsn Fits a linear regression model by forward selection |
| g02fcc | nag_durbin_watson_stat Computes Durbin–Watson test statistic |
| g02hbc | nag_robust_m_regsn_wts Robust regression, compute weights for use with g02hdc |
| g02hdc | nag_robust_m_regsn_user_fn Robust regression, compute regression with user-supplied functions and weights |
| g02hfc | nag_robust_m_regsn_param_var Robust regression, variance-covariance matrix following g02hdc |
| g02hlc | nag_robust_m_corr_user_fn Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives |
| g02hmc | nag_robust_m_corr_user_fn_no_derr Calculates a robust estimation of a correlation matrix, user-supplied weight function |
| g05kac | nag_rngs_basic Pseudo-random real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly |
| g05kbc | nag_rngs_init_repeatable Initialise seeds of a given generator for random number generating functions (that pass seeds explicitly) to give a repeatable sequence |
| g05kcc | nag_rngs_init_nonrepeatable Initialise seeds of a given generator for random number generating functions (that pass seeds expicitly) to give non-repeatable sequence |
| g05kec | nag_rngs_logical Pseudo-random logical (boolean) value, seeds and generator number passed explicitly |
| g05lac | nag_rngs_normal Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly |
| g05lbc | nag_rngs_students_t Generates a vector of random numbers from a Student's t-distribution, seeds and generator number passed explicitly |
| g05lcc | nag_rngs_chi_sq Generates a vector of random numbers from a χ2 distribution, seeds and generator number passed explicitly |
| g05ldc | nag_rngs_f Generates a vector of random numbers from an F-distribution, seeds and generator number passed explicitly |
| g05lec | nag_rngs_beta Generates a vector of random numbers from a β distribution, seeds and generator number passed explicitly |
| g05lfc | nag_rngs_gamma Generates a vector of random numbers from a γ distribution, seeds and generator number passed explicitly |
| g05lgc | nag_rngs_uniform Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly |
| g05lhc | nag_rngs_triangular Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly |
| g05ljc | nag_rngs_exp Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly |
| g05lkc | nag_rngs_lognormal Generates a vector of random numbers from a lognormal distribution, seeds and generator number passed explicitly |
| g05llc | nag_rngs_cauchy Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly |
| g05lmc | nag_rngs_weibull Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly |
| g05lnc | nag_rngs_logistic Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly |
| g05lpc | nag_rngs_von_mises Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly |
| g05lqc | nag_rngs_exp_mix Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly |
| g05lzc | nag_rngs_multi_normal Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly |
| g05mac | nag_rngs_discrete_uniform Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly |
| g05mbc | nag_rngs_geom Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly |
| g05mcc | nag_rngs_neg_bin Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly |
| g05mdc | nag_rngs_logarithmic Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly |
| g05mec | nag_rngs_compd_poisson Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly |
| g05mjc | nag_rngs_binomial Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly |
| g05mkc | nag_rngs_poisson Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly |
| g05mlc | nag_rngs_hypergeometric Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly |
| g05mrc | nag_rngs_gen_multinomial Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly |
| g05mzc | nag_rngs_gen_discrete Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly |
| g05nac | nag_rngs_permute Pseudo-random permutation of an integer vector |
| g05nbc | nag_rngs_sample Pseudo-random sample from an integer vector |
| g05pac | nag_rngs_arma_time_series Generates a realisation of a time series from an ARMA model |
| g05pcc | nag_rngs_varma_time_series Generates a realisation of a multivariate time series from a VARMA model |
| g05qac | nag_rngs_orthog_matrix Computes a random orthogonal matrix |
| g05qbc | nag_rngs_corr_matrix Computes a random correlation matrix |
| g05qdc | nag_rngs_2_way_table Generates a random table matrix |
| g05yac | nag_quasi_random_uniform Multi-dimensional quasi-random number generator with a uniform probability distribution |
| g05ybc | nag_quasi_random_normal Multi-dimensional quasi-random number generator with a Gaussian or log-normal probability distribution |
| g07aac | nag_binomial_ci Computes confidence interval for the parameter of a binomial distribution |
| g07abc | nag_poisson_ci Computes confidence interval for the parameter of a Poisson distribution |
| g07bbc | nag_censored_normal Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data |
| g07bec | nag_estim_weibull Computes maximum likelihood estimates for parameters of the Weibull distribution |
| g07dcc | nag_robust_m_estim_1var_usr Robust estimation, M-estimates for location and scale parameters, user-defined weight functions |
| g07eac | nag_rank_ci_1var Robust confidence intervals, one-sample |
| g07ebc | nag_rank_ci_2var Robust confidence intervals, two-sample |
| g08rac | nag_rank_regsn Regression using ranks, uncensored data |
| g08rbc | nag_rank_regsn_censored Regression using ranks, right-censored data |
| g11bcc | nag_tabulate_margin Computes marginal tables for multiway table computed by g11bac or g11bbc |
| g11cac | nag_condl_logistic Returns parameter estimates for the conditional analysis of stratified data |
| g11sac | nag_binary_factor Contingency table, latent variable model for binary data |
| g11sbc | nag_binary_factor_service Frequency count for g11sac |
| g12zac | nag_surviv_risk_sets Creates the risk sets associated with the Cox proportional hazards model for fixed covariates |
| g13aac | nag_tsa_diff Univariate time series, seasonal and non-seasonal differencing |
| g13auc | nag_tsa_mean_range Computes quantities needed for range-mean or standard deviation-mean plot |
| g13bac | nag_tsa_arma_filter Multivariate time series, filtering (pre-whitening) by an ARIMA model |
| g13bbc | nag_tsa_transf_filter Multivariate time series, filtering by a transfer function model |
| g13bcc | nag_tsa_cross_corr Multivariate time series, cross-correlations |
| g13bdc | nag_tsa_transf_prelim_fit Multivariate time series, preliminary estimation of transfer function model |
| g13cac | nag_tsa_spectrum_univar_cov Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window |
| g13ccc | nag_tsa_spectrum_bivar_cov Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window |
| g13dbc | nag_tsa_multi_auto_corr_part Multivariate time series, multiple squared partial autocorrelations |
| g13dlc | nag_tsa_multi_diff Multivariate time series, differences and/or transforms |
| g13dmc | nag_tsa_multi_cross_corr Multivariate time series, sample cross-correlation or cross-covariance matrices |
| g13dnc | nag_tsa_multi_part_lag_corr Multivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels |
| g13dpc | nag_tsa_multi_part_regsn Multivariate time series, partial autoregression matrices |
| g13dxc | nag_tsa_arma_roots Calculates the zeros of a vector autoregressive (or moving average) operator |
| s01bac | nag_shifted_log ln (1+x) |
| s14acc | nag_polygamma_fun ψ (x) - ln x |
| s14adc | nag_polygamma_deriv Scaled derivatives of ψ (x) |
| s14agc | nag_complex_log_gamma Logarithm of the Gamma function ln Γ (z) |
| s15afc | nag_dawson Dawson's integral |
| s15ddc | nag_complex_erfc Scaled complex complement of error function, exp(-z2) erfc(-iz) |
| s17dcc | nag_complex_bessel_y Bessel functions Yν+a(z), real a ≥ 0, complex z, ν =0,1, 2,... |
| s17dec | nag_complex_bessel_j Bessel functions Jν+a(z), real a ≥ 0, complex z, ν =0,1, 2,... |
| s17dgc | nag_complex_airy_ai Airy functions Ai(z) and Ai'(z), complex z |
| s17dhc | nag_complex_airy_bi Airy functions Bi(z) and Bi'(z), complex z |
| s17dlc | nag_complex_hankel Hankel functions Hν+a(j)(z), j=1,2, real a ≥ 0, complex z, ν =0,1,2,... |
| s18dcc | nag_complex_bessel_k Modified Bessel functions Kν+a(z), real a ≥ 0, complex z, ν =0,1,2,... |
| s18dec | nag_complex_bessel_i Modified Bessel functions Iν+a(z), real a ≥ 0, complex z, ν =0,1,2,... |
| s18gkc | nag_complex_bessel_j_seq Bessel function of the 1st kind Jα ± n(z) |
| s21cac | nag_real_jacobian_elliptic Jacobian elliptic functions sn, cn and dn of real argument |
| x04cac | nag_gen_real_mat_print Print real general matrix (easy-to-use) |
| x04cbc | nag_gen_real_mat_print_comp Print real general matrix (comprehensive) |
| x04ccc | nag_pack_real_mat_print Print real packed triangular matrix (easy-to-use) |
| x04cdc | nag_pack_real_mat_print_comp Print real packed triangular matrix (comprehensive) |
| x04cec | nag_band_real_mat_print Print real packed banded matrix (easy-to-use) |
| x04cfc | nag_band_real_mat_print_comp Print real packed banded matrix (comprehensive) |
| x04dac | nag_gen_complx_mat_print Print complex general matrix (easy-to-use) |
| x04dbc | nag_gen_complx_mat_print_comp Print complex general matrix (comprehensive) |
| x04dcc | nag_pack_complx_mat_print Print complex packed triangular matrix (easy-to-use) |
| x04ddc | nag_pack_complx_mat_print_comp Print complex packed triangular matrix (comprehensive) |
| x04dec | nag_band_complx_mat_print Print complex packed banded matrix (easy-to-use) |
| x04dfc | nag_band_complx_mat_print_comp Print complex packed banded matrix (comprehensive) |