NAG Library Contents Overview

Chapter Summaries

A00 – Library Identification

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A02 – Complex Arithmetic

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C02 – Zeros of Polynomials

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C05 – Roots of One or More Transcendental Equations

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C06 – Summation of Series

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C09 – Wavelet Transforms

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D01 – Quadrature

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D02 – Ordinary Differential Equations

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D03 – Partial Differential Equations

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D04 – Numerical Differentiation

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D05 – Integral Equations

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D06 – Mesh Generation

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E01 – Interpolation

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E02 – Curve and Surface Fitting

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E04 – Minimizing or Maximizing a Function

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E05 – Global Optimization of a Function

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F01 – Matrix Operations, Including Inversion

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F02 – Eigenvalues and Eigenvectors

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F03 – Determinants

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F04 – Simultaneous Linear Equations

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F05 – Orthogonalization

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F06 – Linear Algebra Support Routines

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F07 – Linear Equations (LAPACK)

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F08 – Least Squares and Eigenvalue Problems (LAPACK)

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F11 – Large Scale Linear Systems

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F12 – Large Scale Eigenproblems

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F16 – Further Linear Algebra Support Routines

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G01 – Simple Calculations on Statistical Data

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G02 – Correlation and Regression Analysis

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G03 – Multivariate Methods

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G04 – Analysis of Variance

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G05 – Random Number Generators

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G07 – Univariate Estimation

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G08 – Nonparametric Statistics

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G10 – Smoothing in Statistics

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G11 – Contingency Table Analysis

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G12 – Survival Analysis

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G13 – Time Series Analysis

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H – Operations Research

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M01 – Sorting and Searching

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S – Approximations of Special Functions

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X01 – Mathematical Constants

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X02 – Machine Constants

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X03 – Inner Products

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X04 – Input/Output Utilities

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X05 – Date and Time Utilities

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X06 – OpenMP Utilities

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X07 – IEEE Arithmetic

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Routine Summaries

A00 – Library Identification

Examples of routines and methods in this chapter.

A00AA nagf_info_impl_details
Library identification, details of implementation and mark
A00AC nagf_info_licence
Check availability of a valid licence key
A00AD nagf_info_impl_details_separate
Library identification, details of implementation, major and minor marks
Back to A00 Chapter Summary

A02 – Complex Arithmetic

Examples of routines and methods in this chapter.

A02AA nagf_complex_sqrt
Square root of complex number
A02AB nagf_complex_abs
Modulus of complex number
A02AC nagf_complex_divide
Quotient of two complex numbers
Back to A02 Chapter Summary

C02 – Zeros of Polynomials

Examples of routines and methods in this chapter.

C02AF nagf_zeros_poly_complex
All zeros of complex polynomial, modified Laguerre's method
C02AG nagf_zeros_poly_real
All zeros of real polynomial, modified Laguerre's method
C02AH nagf_zeros_quadratic_complex
All zeros of complex quadratic equation
C02AJ nagf_zeros_quadratic_real
All zeros of real quadratic equation
C02AK nagf_zeros_cubic_real
All zeros of real cubic equation
C02AL nagf_zeros_quartic_real
All zeros of real quartic equation
C02AM nagf_zeros_cubic_complex
All zeros of complex cubic equation
C02AN nagf_zeros_quartic_complex
All zeros of complex quartic equation
Back to C02 Chapter Summary

C05 – Roots of One or More Transcendental Equations

Examples of routines and methods in this chapter.

C05AU nagf_roots_contfn_brent_interval
Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
C05AV nagf_roots_contfn_interval_rcomm
Binary search for interval containing zero of continuous function (reverse communication)
C05AW nagf_roots_contfn_cntin
Zero of continuous function, continuation method, from a given starting value
C05AX nagf_roots_contfn_cntin_rcomm
Zero of continuous function, continuation method, from a given starting value (reverse communication)
C05AY nagf_roots_contfn_brent
Zero of continuous function in a given interval, Brent algorithm
C05AZ nagf_roots_contfn_brent_rcomm
Zero of continuous function in a given interval, Brent algorithm (reverse communication)
C05BA nagf_roots_lambertw_real
Real values of Lambert's W function, W(x)
C05BB nagf_roots_lambertw_complex
Values of Lambert's W function, W(z)
C05QB nagf_roots_sys_func_easy
Solution of a system of nonlinear equations using function values only (easy-to-use)
C05QC nagf_roots_sys_func_expert
Solution of a system of nonlinear equations using function values only (comprehensive)
C05QD nagf_roots_sys_func_rcomm
Solution of a system of nonlinear equations using function values only (reverse communication)
C05QS nagf_roots_sparsys_func_easy
Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
C05RB nagf_roots_sys_deriv_easy
Solution of a system of nonlinear equations using first derivatives (easy-to-use)
C05RC nagf_roots_sys_deriv_expert
Solution of a system of nonlinear equations using first derivatives (comprehensive)
C05RD nagf_roots_sys_deriv_rcomm
Solution of a system of nonlinear equations using first derivatives (reverse communication)
C05ZD nagf_roots_sys_deriv_check
Check user's routine for calculating first derivatives of a set of nonlinear functions of several variables
Back to C05 Chapter Summary

C06 – Summation of Series

Examples of routines and methods in this chapter.

C06BA nagf_sum_accelerate
Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
C06DC nagf_sum_chebyshev
Sum of a Chebyshev series at a set of points
C06FA nagf_sum_fft_real_1d_rfmt
Single one-dimensional real discrete Fourier transform, extra workspace for greater speed
C06FB nagf_sum_fft_hermitian_1d_rfmt
Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed
C06FC nagf_sum_fft_complex_1d_sep
Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed
C06FF nagf_sum_fft_complex_multid_1d_sep
One-dimensional complex discrete Fourier transform of multidimensional data
C06FJ nagf_sum_fft_complex_multid_sep
Multidimensional complex discrete Fourier transform of multidimensional data
C06FK nagf_sum_convcorr_real
Circular convolution or correlation of two real vectors, no restrictions on n
C06FX nagf_sum_fft_complex_3d_sep
Three-dimensional complex discrete Fourier transform
C06LA nagf_sum_invlaplace_crump
Inverse Laplace transform, Crump's method
C06LB nagf_sum_invlaplace_weeks
Inverse Laplace transform, modified Weeks' method
C06LC nagf_sum_invlaplace_weeks_eval
Evaluate inverse Laplace transform as computed by C06LB
C06PA nagf_sum_fft_realherm_1d
Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
C06PC nagf_sum_fft_complex_1d
Single one-dimensional complex discrete Fourier transform, complex data type
C06PF nagf_sum_fft_complex_multid_1d
One-dimensional complex discrete Fourier transform of multidimensional data (using complex data type)
C06PJ nagf_sum_fft_complex_multid
Multidimensional complex discrete Fourier transform of multidimensional data (using complex data type)
C06PK nagf_sum_convcorr_complex
Circular convolution or correlation of two complex vectors
C06PP nagf_sum_fft_realherm_1d_multi_row
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
C06PQ nagf_sum_fft_realherm_1d_multi_col
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
C06PR nagf_sum_fft_complex_1d_multi_row
Multiple one-dimensional complex discrete Fourier transforms using complex data type
C06PS nagf_sum_fft_complex_1d_multi_col
Multiple one-dimensional complex discrete Fourier transforms, complex data type
C06PU nagf_sum_fft_complex_2d
Two-dimensional complex discrete Fourier transform, complex data type
C06PV nagf_sum_fft_real_2d
Two-dimensional real-to-complex discrete Fourier transform
C06PW nagf_sum_fft_hermitian_2d
Two-dimensional complex-to-real discrete Fourier transform
C06PX nagf_sum_fft_complex_3d
Three-dimensional complex discrete Fourier transform, complex data type
C06PY nagf_sum_fft_real_3d
Three-dimensional real-to-complex discrete Fourier transform
C06PZ nagf_sum_fft_hermitian_3d
Three-dimensional complex-to-real discrete Fourier transform
C06RA nagf_sum_fft_real_sine_simple
Discrete sine transform (easy-to-use)
C06RB nagf_sum_fft_real_cosine_simple
Discrete cosine transform (easy-to-use)
C06RC nagf_sum_fft_real_qtrsine_simple
Discrete quarter-wave sine transform (easy-to-use)
C06RD nagf_sum_fft_real_qtrcosine_simple
Discrete quarter-wave cosine transform (easy-to-use)
C06RE nagf_sum_fft_sine
Multiple discrete sine transforms, simple
C06RF nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
C06RG nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
C06RH nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Back to C06 Chapter Summary

C09 – Wavelet Transforms

Examples of routines and methods in this chapter.

C09AA nagf_wav_1d_init
One-dimensional wavelet filter initialization
C09AB nagf_wav_2d_init
Two-dimensional wavelet filter initialization
C09AC nagf_wav_3d_init
Three-dimensional wavelet filter initialization
C09BA nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
C09CA nagf_wav_1d_sngl_fwd
One-dimensional discrete wavelet transform
C09CB nagf_wav_1d_sngl_inv
One-dimensional inverse discrete wavelet transform
C09CC nagf_wav_1d_multi_fwd
One-dimensional multi-level discrete wavelet transform
C09CD nagf_wav_1d_multi_inv
One-dimensional inverse multi-level discrete wavelet transform
C09DA nagf_wav_1d_mxolap_fwd
One-dimensional maximal overlap discrete wavelet transform (MODWT)
C09DB nagf_wav_1d_mxolap_inv
One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT)
C09DC nagf_wav_1d_mxolap_multi_fwd
One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT)
C09DD nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
C09EA nagf_wav_2d_sngl_fwd
Two-dimensional discrete wavelet transform
C09EB nagf_wav_2d_sngl_inv
Two-dimensional inverse discrete wavelet transform
C09EC nagf_wav_2d_multi_fwd
Two-dimensional multi-level discrete wavelet transform
C09ED nagf_wav_2d_multi_inv
Two-dimensional inverse multi-level discrete wavelet transform
C09EY nagf_wav_2d_coeff_ext
Two-dimensional discrete wavelet transform coefficient extraction
C09EZ nagf_wav_2d_coeff_ins
Two-dimensional discrete wavelet transform coefficient insertion
C09FA nagf_wav_3d_sngl_fwd
Three-dimensional discrete wavelet transform
C09FB nagf_wav_3d_sngl_inv
Three-dimensional inverse discrete wavelet transform
C09FC nagf_wav_3d_multi_fwd
Three-dimensional multi-level discrete wavelet transform
C09FD nagf_wav_3d_mxolap_multi_inv
Three-dimensional inverse multi-level discrete wavelet transform
C09FY nagf_wav_3d_coeff_ext
Three-dimensional discrete wavelet transform coefficient extraction
C09FZ nagf_wav_3d_coeff_ins
Three-dimensional discrete wavelet transform coefficient insertion
Back to C09 Chapter Summary

D01 – Quadrature

Examples of routines and methods in this chapter.

D01AH nagf_quad_1d_fin_well
One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
D01AJ nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
D01AK nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
D01AL nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
D01AM nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
D01AN nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos (ωx) or sin (ωx)
D01AP nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
D01AQ nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform)
D01AR nagf_quad_1d_indef
One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
D01AS nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos (ωx) or sin (ωx)
D01AT nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJ efficient on vector machines
D01AU nagf_quad_1d_fin_osc_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AK efficient on vector machines
D01BC nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
D01BD nagf_quad_1d_fin_smooth
One-dimensional quadrature, non-adaptive, finite interval
D01DA nagf_quad_2d_fin
Two-dimensional quadrature, finite region
D01EA nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
D01ES nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
D01FB nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
D01FC nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
D01FD nagf_quad_md_sphere
Multidimensional quadrature, Sag–Szekeres method, general product region or n-sphere
D01FD nagf_quad_md_sphere_dummy_region
dummy
D01GA nagf_quad_1d_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
D01GB nagf_quad_md_mcarlo
Multidimensional quadrature over hyper-rectangle, Monte–Carlo method
D01GC nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
D01GD nagf_quad_md_numth_vec
Multidimensional quadrature, general product region, number-theoretic method, variant of D01GC efficient on vector machines
D01GY nagf_quad_md_numth_coeff_prime
Korobov optimal coefficients for use in D01GC or D01GD, when number of points is prime
D01GZ nagf_quad_md_numth_coeff_2prime
Korobov optimal coefficients for use in D01GC or D01GD, when number of points is product of two primes
D01JA nagf_quad_md_sphere_bad
Multidimensional quadrature over an n-sphere, allowing for badly behaved integrands
D01PA nagf_quad_md_simplex
Multidimensional quadrature over an n-simplex
D01RA nagf_quad_1d_gen_vec_multi_rcomm
One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication
D01RB nagf_quad_d01rb_dummy
D01RC nagf_quad_1d_gen_vec_multi_dimreq
Determine required array dimensions for D01RA
D01RG nagf_quad_1d_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
D01TB nagf_quad_1d_gauss_wres
Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
D01TD nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
D01TE nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TD to calculate a Gaussian quadrature rule
D01UA nagf_quad_1d_gauss_vec
One-dimensional Gaussian quadrature, choice of weight functions (vectorized)
D01UB nagf_quad_1d_inf_exp_wt
Non-automatic routine to evaluate 0exp (-x2)f(x) dx
D01ZK nagf_quad_opt_set
Option setting routine
D01ZL nagf_quad_opt_get
Option getting routine
Back to D01 Chapter Summary

D02 D02M–N – Ordinary Differential Equations Integrators for Stiff Ordinary Differential Systems

Examples of routines and methods in this chapter.

D02AG nagf_ode_bvp_shoot_genpar_intern
Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
D02BG nagf_ode_ivp_rkm_val_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
D02BH nagf_ode_ivp_rkm_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
D02BJ nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
D02CJ nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
D02EJ nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
D02GA nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
D02GA nagf_ode_bvp_fd_nonlin_gen_dummy_jacobf
dummy
D02GA nagf_ode_bvp_fd_nonlin_gen_dummy_jacobg
dummy
D02GA nagf_ode_bvp_fd_nonlin_gen_dummy_jaceps
dummy
D02GA nagf_ode_bvp_fd_nonlin_gen_dummy_jacgep
dummy
D02GB nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
D02HA nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
D02HB nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
D02HB nagf_ode_bvp_shoot_genpar_algeq_dummy_prsol
dummy
D02HB nagf_ode_bvp_shoot_genpar_algeq_dummy_eqn
dummy
D02JA nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single nth-order linear equation
D02JB nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
D02KA nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
D02KA nagf_ode_sl2_reg_finite_dummy_monit
dummy
D02KD nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
D02KE nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
D02LA nagf_ode_ivp_2nd_rkn
Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
D02LX nagf_ode_ivp_2nd_rkn_setup
Second-order ordinary differential equations, initial value problem, setup for D02LA
D02LY nagf_ode_ivp_2nd_rkn_diag
Second-order ordinary differential equations, initial value problem, diagnostics for D02LA
D02LZ nagf_ode_ivp_2nd_rkn_interp
Second-order ordinary differential equations, initial value problem, interpolation for D02LA
D02MC nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NE
D02MV nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N routines
D02MW nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NE
D02MZ nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for D02M–N routines (all integration methods), natural interpolant
D02NB nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NB nagf_ode_ivp_stiff_exp_fulljac_dummy_monit
dummy
D02NB nagf_ode_ivp_stiff_exp_fulljac_dummy_jac
dummy
D02NC nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NC nagf_ode_ivp_stiff_exp_bandjac_dummy_jac
dummy
D02ND nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02ND nagf_ode_ivp_stiff_exp_sparjac_dummy_jac
dummy
D02NE nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
D02NE nagf_ode_dae_dassl_gen_dummy_jac
dummy
D02NG nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NG nagf_ode_ivp_stiff_imp_fulljac_dummy_jac
dummy
D02NH nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NH nagf_ode_ivp_stiff_imp_bandjac_dummy_jac
dummy
D02NJ nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NJ nagf_ode_ivp_stiff_imp_sparjac_dummy_jac
dummy
D02NM nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NN nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
D02NP nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NE
D02NR nagf_ode_ivp_stiff_sparjac_enq
Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, enquiry routine
D02NS nagf_ode_ivp_stiff_fulljac_setup
Ordinary differential equations, initial value problem, for use with D02M–N routines, full Jacobian, linear algebra set up
D02NT nagf_ode_ivp_stiff_bandjac_setup
Ordinary differential equations, initial value problem, for use with D02M–N routines, banded Jacobian, linear algebra set up
D02NU nagf_ode_ivp_stiff_sparjac_setup
Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, linear algebra set up
D02NV nagf_ode_ivp_stiff_bdf
Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for D02M–N routines
D02NW nagf_ode_ivp_stiff_blend
Ordinary differential equations, initial value problem, Blend method, setup for D02M–N routines
D02NX nagf_ode_ivp_stiff_sparjac_diag
Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines
D02NY nagf_ode_ivp_stiff_integ_diag
Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N routines
D02NZ nagf_ode_ivp_stiff_contin
Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N routines
D02PE nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
D02PF nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
D02PG nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
D02PH nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PG
D02PJ nagf_ode_ivp_rk_interp_eval
Evaluate interpolant, set up using D02PQ, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by D02PG
D02PQ nagf_ode_ivp_rkts_setup
Ordinary differential equations, initial value problem, setup for D02PE and D02PF
D02PR nagf_ode_ivp_rkts_reset_tend
Ordinary differential equations, initial value problem, resets end of range for D02PF
D02PS nagf_ode_ivp_rkts_interp
Ordinary differential equations, initial value problem, interpolation for D02PF
D02PT nagf_ode_ivp_rkts_diag
Ordinary differential equations, initial value problem, integration diagnostics for D02PE and D02PF
D02PU nagf_ode_ivp_rkts_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for D02PE and D02PF
D02QF nagf_ode_ivp_adams_roots
Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
D02QG nagf_ode_ivp_adams_roots_revcom
Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
D02QW nagf_ode_ivp_adams_setup
Ordinary differential equations, initial value problem, setup for D02QF and D02QG
D02QX nagf_ode_ivp_adams_diag
Ordinary differential equations, initial value problem, diagnostics for D02QF and D02QG
D02QY nagf_ode_ivp_adams_rootdiag
Ordinary differential equations, initial value problem, root-finding diagnostics for D02QF and D02QG
D02QZ nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for D02QF or D02QG
D02RA nagf_ode_bvp_fd_nonlin_gen
Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
D02SA nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
D02SA nagf_ode_bvp_shoot_genpar_algeq_dummy_monit
dummy
D02TG nagf_ode_bvp_coll_nth_comp
nth-order linear ordinary differential equations, boundary value problem, collocation and least squares
D02TL nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
D02TV nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for D02TL
D02TX nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TL
D02TY nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TL
D02TZ nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TL
D02UA nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
D02UB nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
D02UC nagf_ode_bvp_ps_lin_cgl_grid
Chebyshev Gauss–Lobatto grid generation
D02UD nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
D02UE nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
D02UW nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
D02UY nagf_ode_bvp_ps_lin_quad_weights
Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
D02UZ nagf_ode_bvp_ps_lin_cheb_eval
Chebyshev polynomial evaluation, Tk(x)
D02XJ nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for D02M–N routines (BLEND and BDF methods only), natural interpolant
D02XK nagf_ode_ivp_stiff_c1_interp
Ordinary differential equations, initial value problem, interpolation for D02M–N routines, C1 interpolant
D02ZA nagf_ode_ivp_stiff_errest
Ordinary differential equations, initial value problem, weighted norm of local error estimate for D02M–N routines
Back to D02 Chapter Summary

D03 – Partial Differential Equations

Examples of routines and methods in this chapter.

D03EA nagf_pde_2d_laplace
Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain
D03EB nagf_pde_2d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
D03EC nagf_pde_3d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
D03ED nagf_pde_2d_ellip_mgrid
Elliptic PDE, solution of finite difference equations by a multigrid technique
D03EE nagf_pde_2d_ellip_discret
Discretize a second-order elliptic PDE on a rectangle
D03FA nagf_pde_3d_ellip_helmholtz
Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates
D03MA nagf_pde_2d_triangulate
Triangulation of plane region
D03NC nagf_pde_1d_blackscholes_fd
Finite difference solution of the Black–Scholes equations
D03ND nagf_pde_1d_blackscholes_closed
Analytic solution of the Black–Scholes equations
D03NE nagf_pde_1d_blackscholes_means
Compute average values for D03ND
D03PC nagf_pde_1d_parab_fd_old
General system of parabolic PDEs, method of lines, finite differences, one space variable
D03PC nagf_pde_1d_parab_remesh_fd_dummy_odedef_old
dummy
D03PC nagf_pde_1d_parab_remesh_fd_dummy_monitf_old
dummy
D03PD nagf_pde_1d_parab_coll_old
General system of parabolic PDEs, method of lines, Chebyshev C0 collocation, one space variable
D03PE nagf_pde_1d_parab_keller
General system of first-order PDEs, method of lines, Keller box discretization, one space variable
D03PE nagf_pde_1d_parab_dae_keller_remesh_fd_dummy_odedef
dummy
D03PE nagf_pde_1d_parab_dae_keller_remesh_fd_dummy_monitf
dummy
D03PF nagf_pde_1d_parab_convdiff
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
D03PH nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
D03PJ nagf_pde_1d_parab_dae_coll_old
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C0 collocation, one space variable
D03PK nagf_pde_1d_parab_dae_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
D03PL nagf_pde_1d_parab_convdiff_dae
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
D03PP nagf_pde_1d_parab_remesh_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
D03PR nagf_pde_1d_parab_remesh_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
D03PS nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
D03PU nagf_pde_1d_parab_euler_roe
Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS
D03PV nagf_pde_1d_parab_euler_osher
Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS
D03PW nagf_pde_1d_parab_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS
D03PX nagf_pde_1d_parab_euler_exact
Exact Riemann solver for Euler equations in conservative form, for use with D03PF, D03PL and D03PS
D03PY nagf_pde_1d_parab_coll_interp
PDEs, spatial interpolation with D03PD or D03PJ
D03PZ nagf_pde_1d_parab_fd_interp
PDEs, spatial interpolation with D03PC, D03PE, D03PF, D03PH, D03PK, D03PL, D03PP, D03PR or D03PS
D03RA nagf_pde_2d_gen_order2_rectangle
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
D03RB nagf_pde_2d_gen_order2_rectilinear
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
D03RZ nagf_pde_2d_gen_order2_rectilinear_extractgrid
Extract grid data from D03RB
D03UA nagf_pde_2d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
D03UB nagf_pde_3d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration
Back to D03 Chapter Summary

D04 – Numerical Differentiation

Examples of routines and methods in this chapter.

D04AA nagf_numdiff
Numerical differentiation, derivatives up to order 14, function of one real variable
D04BA nagf_numdiff_rcomm
Numerical differentiation, user-supplied function values, derivatives up to order 14, derivatives with respect to one real variable
D04BB nagf_numdiff_sample
Generates sample points for function evaluations by D04BA
Back to D04 Chapter Summary

D05 – Integral Equations

Examples of routines and methods in this chapter.

D05AA nagf_inteq_fredholm2_split
Linear nonsingular Fredholm integral equation, second kind, split kernel
D05AB nagf_inteq_fredholm2_smooth
Linear nonsingular Fredholm integral equation, second kind, smooth kernel
D05BA nagf_inteq_volterra2
Nonlinear Volterra convolution equation, second kind
D05BD nagf_inteq_abel2_weak
Nonlinear convolution Volterra–Abel equation, second kind, weakly singular
D05BE nagf_inteq_abel1_weak
Nonlinear convolution Volterra–Abel equation, first kind, weakly singular
D05BW nagf_inteq_volterra_weights
Generate weights for use in solving Volterra equations
D05BY nagf_inteq_abel_weak_weights
Generate weights for use in solving weakly singular Abel-type equations
Back to D05 Chapter Summary

D06 – Mesh Generation

Examples of routines and methods in this chapter.

D06AA nagf_mesh_2d_gen_inc
Generates a two-dimensional mesh using a simple incremental method
D06AB nagf_mesh_2d_gen_delaunay
Generates a two-dimensional mesh using a Delaunay–Voronoi process
D06AC nagf_mesh_2d_gen_front
Generates a two-dimensional mesh using an Advancing-front method
D06BA nagf_mesh_2d_gen_boundary
Generates a boundary mesh
D06CA nagf_mesh_2d_smooth_bary
Uses a barycentering technique to smooth a given mesh
D06CB nagf_mesh_2d_sparsity
Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
D06CC nagf_mesh_2d_renumber
Renumbers a given mesh using Gibbs method
D06DA nagf_mesh_2d_transform_affine
Generates a mesh resulting from an affine transformation of a given mesh
D06DB nagf_mesh_2d_join
Joins together two given adjacent (possibly overlapping) meshes
Back to D06 Chapter Summary

E01 – Interpolation

Examples of routines and methods in this chapter.

E01AA nagf_interp_1d_aitken
Interpolated values, Aitken's technique, unequally spaced data, one variable
E01AB nagf_interp_1d_everett
Interpolated values, Everett's formula, equally spaced data, one variable
E01AE nagf_interp_1d_cheb
Interpolating functions, polynomial interpolant, data may include derivative values, one variable
E01BA nagf_interp_1d_spline
Interpolating functions, cubic spline interpolant, one variable
E01BE nagf_interp_1d_monotonic
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
E01BF nagf_interp_1d_monotonic_eval
Interpolated values, interpolant computed by E01BE, function only, one variable
E01BG nagf_interp_1d_monotonic_deriv
Interpolated values, interpolant computed by E01BE, function and first derivative, one variable
E01BH nagf_interp_1d_monotonic_intg
Interpolated values, interpolant computed by E01BE, definite integral, one variable
E01DA nagf_interp_2d_spline_grid
Interpolating functions, fitting bicubic spline, data on rectangular grid
E01EA nagf_interp_2d_triangulate
Triangulation of two-dimensional scattered grid, method of Renka and Cline
E01EB nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
E01RA nagf_interp_1d_ratnl
Interpolating functions, rational interpolant, one variable
E01RB nagf_interp_1d_ratnl_eval
Interpolated values, evaluate rational interpolant computed by E01RA, one variable
E01SA nagf_interp_2d_scat
Interpolating functions, method of Renka and Cline, two variables
E01SB nagf_interp_2d_scat_eval
Interpolated values, evaluate interpolant computed by E01SA, two variables
E01SG nagf_interp_2d_scat_shep
Interpolating functions, modified Shepard's method, two variables
E01SH nagf_interp_2d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01SG, function and first derivatives, two variables
E01TG nagf_interp_3d_scat_shep
Interpolating functions, modified Shepard's method, three variables
E01TH nagf_interp_3d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TG, function and first derivatives, three variables
E01TK nagf_interp_4d_scat_shep
Interpolating functions, modified Shepard's method, four variables
E01TL nagf_interp_4d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TK, function and first derivatives, four variables
E01TM nagf_interp_5d_scat_shep
Interpolating functions, modified Shepard's method, five variables
E01TN nagf_interp_5d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TM, function and first derivatives, five variables
E01ZM nagf_interp_nd_scat_shep
Interpolating function, modified Shepard's method, d dimensions
E01ZN nagf_interp_nd_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01ZM, function and first derivatives, d dimensions
Back to E01 Chapter Summary

E02 – Curve and Surface Fitting

Examples of routines and methods in this chapter.

E02AD nagf_fit_1dcheb_arb
Least squares curve fit, by polynomials, arbitrary data points
E02AE nagf_fit_1dcheb_eval
Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list)
E02AF nagf_fit_1dcheb_glp
Least squares polynomial fit, special data points (including interpolation)
E02AG nagf_fit_1dcheb_con
Least squares polynomial fit, values and derivatives may be constrained, arbitrary data points
E02AH nagf_fit_1dcheb_deriv
Derivative of fitted polynomial in Chebyshev series form
E02AJ nagf_fit_1dcheb_integ
Integral of fitted polynomial in Chebyshev series form
E02AK nagf_fit_1dcheb_eval2
Evaluation of fitted polynomial in one variable from Chebyshev series form
E02AL nagf_1d_minimax_polynomial
Minimax curve fit by polynomials
E02BA nagf_fit_1dspline_knots
Least squares curve cubic spline fit (including interpolation)
E02BB nagf_fit_1dspline_eval
Evaluation of fitted cubic spline, function only
E02BC nagf_fit_1dspline_deriv
Evaluation of fitted cubic spline, function and derivatives
E02BD nagf_fit_1dspline_integ
Evaluation of fitted cubic spline, definite integral
E02BE nagf_fit_1dspline_auto
Least squares cubic spline curve fit, automatic knot placement
E02BF nagf_fit_1dspline_deriv_vector
Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points
E02CA nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
E02CB nagf_fit_2dcheb_eval
Evaluation of fitted polynomial in two variables
E02DA nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
E02DC nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
E02DD nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
E02DE nagf_fit_2dspline_evalv
Evaluation of fitted bicubic spline at a vector of points
E02DF nagf_fit_2dspline_evalm
Evaluation of fitted bicubic spline at a mesh of points
E02DH nagf_fit_2dspline_derivm
Evaluation of spline surface at mesh of points with derivatives
E02GA nagf_fit_glin_l1sol
L1-approximation by general linear function
E02GB nagf_fit_glinc_l1sol
L1-approximation by general linear function subject to linear inequality constraints
E02GC nagf_fit_glin_linf
L-approximation by general linear function
E02JD nagf_fit_2dspline_ts_sctr
Spline approximation to a set of scattered data using a two-stage approximation method
E02JE nagf_fit_2dspline_ts_evalv
Evaluation at a vector of points of a spline computed by E02JD
E02JF nagf_fit_2dspline_ts_evalm
Evaluation at a mesh of points of a spline computed by E02JD
E02RA nagf_fit_pade_app
Padé approximants
E02RB nagf_fit_pade_eval
Evaluation of fitted rational function as computed by E02RA
E02ZA nagf_fit_2dspline_sort
Sort two-dimensional data into panels for fitting bicubic splines
E02ZK nagf_fit_opt_set
Option setting routine
E02ZL nagf_fit_opt_get
Option getting routine
Back to E02 Chapter Summary

E04 – Minimizing or Maximizing a Function

Examples of routines and methods in this chapter.

E04AB nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
E04BB nagf_opt_one_var_deriv_old
Minimum, function of one variable, using first derivative
E04CB nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
E04CB nagf_opt_uncon_simplex_dummy_monit
E04DG nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
E04DJ nagf_opt_uncon_conjgrd_option_file_old
Supply optional parameter values for E04DG from external file
E04DK nagf_opt_uncon_conjgrd_option_string_old
Supply optional parameter values to E04DG from a character string
E04FC nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
E04FD nagf_opt_lsq_dummy_lsqmon
dummy
E04FY nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
E04GB nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
E04GD nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
E04GY nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
E04GZ nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
E04HC nagf_opt_check_deriv
Check user's routine for calculating first derivatives of function
E04HD nagf_opt_check_deriv2
Check user's routine for calculating second derivatives of function
E04HE nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
E04HY nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
E04JC nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
E04JY nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
E04KD nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
E04KY nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
E04KZ nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
E04LB nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
E04LY nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
E04MF nagf_opt_lp_solve_old
Linear programming (LP), dense, active-set method
E04MG nagf_opt_lp_option_file_old
Supply optional parameter values for E04MF from external file
E04MH nagf_opt_lp_option_string_old
Supply optional parameter values to E04MF from a character string
E04MW nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
E04MX nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
E04MZ nagf_opt_qpconvex1_sparse_mps
Read MPS data file defining LP or QP problem, deprecated
E04NC nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
E04ND nagf_opt_lsq_lincon_option_file_old
Supply optional parameter values for E04NC from external file
E04NE nagf_opt_lsq_lincon_option_string_old
Supply optional parameter values to E04NC from a character string
E04NF nagf_opt_qp_dense_solve_old
General (possibly non-convex) quadratic programming (QP) , dense, active-set method
E04NG nagf_opt_qp_dense_option_file_old
Supply optional parameter values for E04NF from external file
E04NH nagf_opt_qp_dense_option_string_old
Supply optional parameter values to E04NF from a character string
E04NK nagf_opt_qpconvex1_sparse_solve_old
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method
E04NK nagf_opt_qpconvex1_sparse_dummy_qphx_old
dummy
E04NL nagf_opt_qpconvex1_sparse_option_file_old
Supply optional parameter values for E04NK from external file
E04NM nagf_opt_qpconvex1_sparse_option_string_old
Supply optional parameter values to E04NK from a character string
E04NP nagf_opt_qpconvex2_sparse_init
Initialization routine for E04NQ
E04NQ nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
E04NR nagf_opt_qpconvex2_sparse_option_file
Supply optional parameter values for E04NQ from external file
E04NS nagf_opt_qpconvex2_sparse_option_string
Set a single option for E04NQ from a character string
E04NS nagf_opt_qpconvex2_sparse_dummy_qphx
dummy
E04NT nagf_opt_qpconvex2_sparse_option_integer_set
Set a single option for E04NQ from an integer argument
E04NU nagf_opt_qpconvex2_sparse_option_double_set
Set a single option for E04NQ from a real argument
E04NX nagf_opt_qpconvex2_sparse_option_integer_get
Get the setting of an integer valued option of E04NQ
E04NY nagf_opt_qpconvex2_sparse_option_double_get
Get the setting of a real valued option of E04NQ
E04PC nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
E04RA nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, quadratic programming (QP), nonlinear programming (NLP), linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
E04RD nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
E04RE nagf_opt_handle_set_linobj
Define a linear objective function to a problem initialized by E04RA
E04RF nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RA
E04RG nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RA
E04RH nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RA
E04RJ nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RA
E04RK nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RA
E04RL nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RA
E04RN nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RA
E04RP nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RA
E04RY nagf_opt_handle_print
Print information about a problem handle initialized by E04RA
E04RZ nagf_opt_handle_free
Destroy the problem handle initialized by E04RA and deallocate all the memory used
E04ST nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RA and defined by other routines from the suite
E04ST nagf_opt_ipopt_dummy_mon
dummy
E04ST nagf_opt_ipopt_dummy_objfun
dummy
E04ST nagf_opt_ipopt_dummy_objgrd
dummy
E04ST nagf_opt_ipopt_dummy_confun
dummy
E04ST nagf_opt_ipopt_dummy_congrd
dummy
E04ST nagf_opt_ipopt_dummy_hess
dummy
E04SV nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RA and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
E04UC nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
E04UD nagf_opt_nlp1_option_file_old
Supply optional parameter values for E04UC or E04UF from external file
E04UD nagf_opt_nlp1_dummy_confun
dummy
E04UE nagf_opt_nlp1_option_string_old
Supply optional parameter values to E04UC or E04UF from a character string
E04UF nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
E04UG nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
E04UG nagf_opt_nlp1_sparse_dummy_confun
dummy
E04UG nagf_opt_nlp1_sparse_dummy_objfun
dummy
E04UH nagf_opt_nlp1_sparse_option_file_old
Supply optional parameter values for E04UG from external file
E04UJ nagf_opt_nlp1_sparse_option_string_old
Supply optional parameter values to E04UG from a character string
E04UQ nagf_opt_lsq_gencon_deriv_option_file_old
Supply optional parameter values for E04US from external file
E04UR nagf_opt_lsq_gencon_deriv_option_string_old
Supply optional parameter values to E04US from a character string
E04US nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
E04VG nagf_opt_nlp2_sparse_init
Initialization routine for E04VH
E04VH nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
E04VJ nagf_opt_nlp2_sparse_jacobian
Determine the pattern of nonzeros in the Jacobian matrix for E04VH
E04VK nagf_opt_nlp2_sparse_option_file
Supply optional parameter values for E04VH from external file
E04VL nagf_opt_nlp2_sparse_option_string
Set a single option for E04VH from a character string
E04VM nagf_opt_nlp2_sparse_option_integer_set
Set a single option for E04VH from an integer argument
E04VN nagf_opt_nlp2_sparse_option_double_set
Set a single option for E04VH from a real argument
E04VR nagf_opt_nlp2_sparse_option_integer_get
Get the setting of an integer valued option of E04VH
E04VS nagf_opt_nlp2_sparse_option_double_get
Get the setting of a real valued option of E04VH
E04WB nagf_opt_init
Initialization routine for E04DG, E04MF, E04NC, E04NF, E04NK, E04UC, E04UF, E04UG and E04US
E04WC nagf_opt_nlp2_init
Initialization routine for E04WD
E04WD nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
E04WD nagf_opt_nlp2_dummy_confun
dummy
E04WE nagf_opt_nlp2_option_file
Supply optional parameter values for E04WD from external file
E04WF nagf_opt_nlp2_option_string
Set a single option for E04WD from a character string
E04WG nagf_opt_nlp2_option_integer_set
Set a single option for E04WD from an integer argument
E04WH nagf_opt_nlp2_option_double_set
Set a single option for E04WD from a real argument
E04WK nagf_opt_nlp2_option_integer_get
Get the setting of an integer valued option of E04WD
E04WL nagf_opt_nlp2_option_double_get
Get the setting of a real valued option of E04WD
E04XA nagf_opt_estimate_deriv_old
Estimate (using numerical differentiation) gradient and/or Hessian of a function
E04YA nagf_opt_lsq_check_deriv
Check user's routine for calculating Jacobian of first derivatives
E04YB nagf_opt_lsq_check_hessian
Check user's routine for calculating Hessian of a sum of squares
E04YC nagf_opt_lsq_uncon_covariance
Covariance matrix for nonlinear least squares problem (unconstrained)
E04ZM nagf_opt_handle_opt_set
Option setting routine for the solvers from the NAG optimization modelling suite
E04ZN nagf_opt_handle_opt_get
Option getting routine for the solvers from the NAG optimization modelling suite
E04ZP nagf_opt_handle_opt_set_file
Option setting routine for the solvers from the NAG optimization modelling suite from external file
Back to E04 Chapter Summary

E05 – Global Optimization of a Function

Examples of routines and methods in this chapter.

E05JA nagf_glopt_bnd_mcs_init
Initialization routine for E05JB
E05JB nagf_glopt_bnd_mcs_solve
Global optimization by multi-level coordinate search, simple bounds, using function values only
E05JC nagf_glopt_bnd_mcs_optset_file
Supply optional parameter values for E05JB from external file
E05JD nagf_glopt_bnd_mcs_optset_string
Set a single optional parameter for E05JB from a character string
E05JE nagf_glopt_bnd_mcs_optset_char
Set a single optional parameter for E05JB from an 'ON'/'OFF'-valued character argument
E05JF nagf_glopt_bnd_mcs_optset_int
Set a single optional parameter for E05JB from an integer argument
E05JG nagf_glopt_bnd_mcs_optset_real
Set a single optional parameter for E05JB from a real argument
E05JH nagf_glopt_bnd_mcs_option_check
Determine whether an optional parameter for E05JB has been set by you or not
E05JJ nagf_glopt_bnd_mcs_optget_char
Get the setting of an 'ON'/'OFF'-valued character optional parameter of E05JB
E05JK nagf_glopt_bnd_mcs_optget_int
Get the setting of an integer valued optional parameter of E05JB
E05JL nagf_glopt_bnd_mcs_optget_real
Get the setting of a real valued optional parameter of E05JB
E05SA nagf_glopt_bnd_pso
Global optimization using particle swarm algorithm (PSO), bound constraints only
E05SB nagf_glopt_nlp_pso
Global optimization using particle swarm algorithm (PSO), comprehensive
E05SX nagf_glopt_bnd_pso_dummy_monmod
dummy
E05SY nagf_glopt_nlp_pso_dummy_monmod
dummy
E05UC nagf_glopt_nlp_multistart_sqp
Global optimization using multi-start, nonlinear constraints
E05UD nagf_glopt_nlp_multistart_dcf
dummy
E05US nagf_glopt_nlp_multistart_sqp_lsq
Global optimization of a sum of squares problem using multi-start, nonlinear constraints
E05ZK nagf_glopt_optset
Option setting routine for E05SA, E05SB, E05UC and E05US
E05ZL nagf_glopt_optget
Option getting routine for E05SA, E05SB, E05UC and E05US
Back to E05 Chapter Summary

F01 – Matrix Operations, Including Inversion

Examples of routines and methods in this chapter.

F01AB nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
F01AD nagf_matop_real_symm_posdef_inv_noref
Inverse of real symmetric positive definite matrix
F01BL nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real m by n matrix (mn)
F01BR nagf_matop_real_gen_sparse_lu
LU factorization of real sparse matrix
F01BS nagf_matop_real_gen_sparse_lu_reuse
LU factorization of real sparse matrix with known sparsity pattern
F01BU nagf_matop_real_symm_posdef_fac
ULDLTUT factorization of real symmetric positive definite band matrix
F01BV nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
F01CK nagf_matop_real_gen_matmul
Multiplication of real matrices
F01CR nagf_matop_real_gen_trans_inplace
Transposition of a real matrix
F01CT nagf_matop_real_addsub
Sum or difference of two real matrices, optional scaling and transposition
F01CW nagf_matop_complex_addsub
Sum or difference of two complex matrices, optional scaling and transposition
F01EC nagf_matop_real_gen_matrix_exp
Real matrix exponential
F01ED nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
F01EF nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
F01EJ nagf_matop_real_gen_matrix_log
Real matrix logarithm
F01EK nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
F01EL nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
F01EM nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
F01EN nagf_matop_real_gen_matrix_sqrt
Real matrix square root
F01EP nagf_matop_real_tri_matrix_sqrt
Real upper quasi-triangular matrix square root
F01EQ nagf_matop_real_gen_matrix_pow
General power of a real matrix
F01FC nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
F01FD nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
F01FF nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
F01FJ nagf_matop_complex_gen_matrix_log
Complex matrix logarithm
F01FK nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
F01FL nagf_matop_complex_gen_matrix_fun_num
Function of a complex matrix (using numerical differentiation)
F01FM nagf_matop_complex_gen_matrix_fun_usd
Function of a complex matrix (using user-supplied derivatives)
F01FN nagf_matop_complex_gen_matrix_sqrt
Complex matrix square root
F01FP nagf_matop_complex_tri_matrix_sqrt
Complex upper triangular matrix square root
F01FQ nagf_matop_complex_gen_matrix_pow
General power of a complex matrix
F01GA nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
F01GB nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
F01HA nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
F01HB nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
F01JA nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
F01JB nagf_matop_real_gen_matrix_cond_num
Condition number for a function of a real matrix (using numerical differentiation)
F01JC nagf_matop_real_gen_matrix_cond_usd
Condition number for a function of a real matrix (using user-supplied derivatives)
F01JD nagf_matop_real_gen_matrix_cond_sqrt
Condition number for square root of real matrix
F01JE nagf_matop_real_gen_matrix_cond_pow
Condition number for real matrix power
F01JF nagf_matop_real_gen_matrix_frcht_pow
Fréchet derivative of real matrix power
F01JG nagf_matop_real_gen_matrix_cond_exp
Condition number for real matrix exponential
F01JH nagf_matop_real_gen_matrix_frcht_exp
Fréchet derivative of real matrix exponential
F01JJ nagf_matop_real_gen_matrix_cond_log
Condition number for real matrix logarithm
F01JK nagf_matop_real_gen_matrix_frcht_log
Fréchet derivative of real matrix logarithm
F01KA nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
F01KB nagf_matop_complex_gen_matrix_cond_num
Condition number for a function of a complex matrix (using numerical differentiation)
F01KC nagf_matop_complex_gen_matrix_cond_usd
Condition number for a function of a complex matrix (using user-supplied derivatives)
F01KD nagf_matop_complex_gen_matrix_cond_sqrt
Condition number for square root of complex matrix
F01KE nagf_matop_complex_gen_matrix_cond_pow
Condition number for complex matrix power
F01KF nagf_matop_complex_gen_matrix_frcht_pow
Fréchet derivative of complex matrix power
F01KG nagf_matop_complex_gen_matrix_cond_exp
Condition number for complex matrix exponential
F01KH nagf_matop_complex_gen_matrix_frcht_exp
Fréchet derivative of complex matrix exponential
F01KJ nagf_matop_complex_gen_matrix_cond_log
Condition number for complex matrix logarithm
F01KK nagf_matop_complex_gen_matrix_frcht_log
Fréchet derivative of complex matrix logarithm
F01LE nagf_matop_real_gen_tridiag_lu
LU factorization of real tridiagonal matrix
F01LH nagf_matop_real_gen_blkdiag_lu
LU factorization of real almost block diagonal matrix
F01MC nagf_matop_real_vband_posdef_fac
LDLT factorization of real symmetric positive definite variable-bandwidth matrix
F01QG nagf_matop_real_trapez_rq
RQ factorization of real m by n upper trapezoidal matrix (mn)
F01QJ nagf_matop_real_gen_rq
RQ factorization of real m by n matrix (mn)
F01QK nagf_matop_real_gen_rq_formq
Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJ
F01RG nagf_matop_complex_trapez_rq
RQ factorization of complex m by n upper trapezoidal matrix (mn)
F01RJ nagf_matop_complex_gen_rq
RQ factorization of complex m by n matrix (mn)
F01RK nagf_matop_complex_gen_rq_formq
Operations with unitary matrices, form rows of Q, after RQ factorization by F01RJ
F01VA nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
F01VB nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
F01VC nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
F01VD nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
F01VE nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
F01VF nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
F01VG nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
F01VH nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
F01VJ nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
F01VK nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
F01VL nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
F01VM nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
F01ZA nagf_matop_real_tri_pack
Convert real matrix between packed triangular and square storage formats
F01ZB nagf_matop_complex_tri_pack
Convert complex matrix between packed triangular and square storage formats
F01ZC nagf_matop_real_band_pack
Convert real matrix between packed banded and rectangular storage formats
F01ZD nagf_matop_complex_band_pack
Convert complex matrix between packed banded and rectangular storage formats
Back to F01 Chapter Summary

F02 – Eigenvalues and Eigenvectors

Examples of routines and methods in this chapter.

F02EC nagf_eigen_real_gen_eigsys
Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
F02EK nagf_eigen_real_gen_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real sparse general matrix
F02EK nagf_eigen_arnoldi_option
dummy
F02EK nagf_eigen_arnoldi_monit_gen
dummy
F02FJ nagf_eigen_real_symm_sparse_eigsys
Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
F02FJ nagf_eigen_monit
dummy
F02FK nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
F02FK nagf_eigen_arnoldi_monit_symm
dummy
F02GC nagf_eigen_complex_gen_eigsys
Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
F02JC nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
F02JQ nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
F02WG nagf_eigen_real_gen_partialsvd
Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
F02WU nagf_eigen_real_triang_svd
SVD of real upper triangular matrix (Black Box)
F02XU nagf_eigen_complex_triang_svd
SVD of complex upper triangular matrix (Black Box)
Back to F02 Chapter Summary

F03 – Determinants

Examples of routines and methods in this chapter.

F03BA nagf_det_real_gen
Determinant of real matrix, matrix already factorized by F07AD
F03BF nagf_det_real_sym
Determinant of real symmetric positive definite matrix
F03BH nagf_det_real_band_sym
Determinant of real symmetric positive definite banded matrix previously factorized by F07HD
F03BN nagf_det_complex_gen
Determinant of complex matrix previously LU factorized
Back to F03 Chapter Summary

F04 – Simultaneous Linear Equations

Examples of routines and methods in this chapter.

F04AM nagf_linsys_real_gen_lsqsol
Least squares solution of m real equations in n unknowns, rank =n, mn using iterative refinement (Black Box)
F04AX nagf_linsys_real_sparse_fac_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F04BA nagf_linsys_real_square_solve
Computes the solution, estimated condition number and error-bound to a real system of linear equations
F04BB nagf_linsys_real_band_solve
Computes the solution, estimated condition number and error-bound to a real banded system of linear equations
F04BC nagf_linsys_real_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations
F04BD nagf_linsys_real_posdef_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations
F04BE nagf_linsys_real_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations, packed storage
F04BF nagf_linsys_real_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite banded system of linear equations
F04BG nagf_linsys_real_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite tridiagonal system of linear equations
F04BH nagf_linsys_real_symm_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations
F04BJ nagf_linsys_real_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations, packed storage
F04CA nagf_linsys_complex_square_solve
Computes the solution, estimated condition number and error-bound to a complex system of linear equations
F04CB nagf_linsys_complex_band_solve
Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations
F04CC nagf_linsys_complex_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations
F04CD nagf_linsys_complex_posdef_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations
F04CE nagf_linsys_complex_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations, packed storage
F04CF nagf_linsys_complex_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite banded system of linear equations
F04CG nagf_linsys_complex_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite tridiagonal system of linear equations
F04CH nagf_linsys_complex_herm_solve
Computes the solution and error-bound to a complex Hermitian system of linear equations
F04CJ nagf_linsys_complex_herm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian system of linear equations, packed storage
F04DH nagf_linsys_complex_symm_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations
F04DJ nagf_linsys_complex_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations, packed storage
F04FE nagf_linsys_real_toeplitz_yule
Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side
F04FF nagf_linsys_real_toeplitz_solve
Solution of real symmetric positive definite Toeplitz system, one right-hand side
F04JG nagf_linsys_real_gen_solve
Least squares (if rank =n) or minimal least squares (if rank <n) solution of m real equations in n unknowns, mn
F04LE nagf_linsys_real_tridiag_fac_solve
Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LE)
F04LH nagf_linsys_real_blkdiag_fac_solve
Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LH)
F04MC nagf_linsys_real_posdef_vband_solve
Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MC)
F04ME nagf_linsys_real_toeplitz_yule_update
Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix
F04MF nagf_linsys_real_toeplitz_update
Update solution of real symmetric positive definite Toeplitz system
F04QA nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
F04YA nagf_linsys_real_gen_lsq_covmat
Covariance matrix for linear least squares problems, m real equations in n unknowns
F04YD nagf_linsys_real_gen_norm_rcomm
Norm estimation (for use in condition estimation), real rectangular matrix
F04ZD nagf_linsys_complex_gen_norm_rcomm
Norm estimation (for use in condition estimation), complex rectangular matrix
Back to F04 Chapter Summary

F05 – Orthogonalization

Examples of routines and methods in this chapter.

F05AA nagf_orthog_real_gram_schmidt
Gram–Schmidt orthogonalization of n vectors of order m
Back to F05 Chapter Summary

F06 – Linear Algebra Support Routines

Examples of routines and methods in this chapter.

F06AA nagf_blas_drotg
Generate real plane rotation
F06BA nagf_blas_drotgc
Generate real plane rotation, storing tangent
F06BC nagf_blas_dcsg
Recover cosine and sine from given real tangent
F06BE nagf_blas_drotj
Generate real Jacobi plane rotation
F06BH nagf_blas_drot2
Apply real similarity rotation to 2 by 2 symmetric matrix
F06BL nagf_blas_ddiv
Compute quotient of two real scalars, with overflow flag
F06BM nagf_blas_dnorm
Compute Euclidean norm from scaled form
F06BN nagf_blas_dpyth
Compute square root of (a2+b2), real a and b
F06BP nagf_blas_deig2
Compute eigenvalue of 2 by 2 real symmetric matrix
F06CA nagf_blas_zrotgc
Generate complex plane rotation, storing tangent, real cosine
F06CB nagf_blas_zrotgs
Generate complex plane rotation, storing tangent, real sine
F06CC nagf_blas_zcsg
Recover cosine and sine from given complex tangent, real cosine
F06CD nagf_blas_zcsgs
Recover cosine and sine from given complex tangent, real sine
F06CH nagf_blas_zrot2
Apply complex similarity rotation to 2 by 2 Hermitian matrix
F06CL nagf_blas_zdiv
Compute quotient of two complex scalars, with overflow flag
F06DB nagf_blas_iload
Broadcast scalar into integer vector
F06DF nagf_blas_icopy
Copy integer vector
F06EA nagf_blas_ddot
Dot product of two real vectors
F06EC nagf_blas_daxpy
Add scalar times real vector to real vector
F06ED nagf_blas_dscal
Multiply real vector by scalar
F06EF nagf_blas_dcopy
Copy real vector
F06EG nagf_blas_dswap
Swap two real vectors
F06EJ nagf_blas_dnrm2
Compute Euclidean norm of real vector
F06EK nagf_blas_dasum
Sum absolute values of real vector elements
F06EP nagf_blas_drot
Apply real plane rotation
F06ER nagf_blas_ddoti
Dot product of a real sparse and a full vector
F06ET nagf_blas_daxpyi
Add scalar times real sparse vector to a full vector
F06EU nagf_blas_dgthr
Gather real sparse vector
F06EV nagf_blas_dgthrz
Gather and set to zero real sparse vector
F06EW nagf_blas_dsctr
Scatter real sparse vector
F06EX nagf_blas_droti
Apply plane rotation to a real sparse and a full vector
F06FA nagf_blas_dvcos
Compute cosine of angle between two real vectors
F06FB nagf_blas_dload
Broadcast scalar into real vector
F06FC nagf_blas_ddscl
Multiply real vector by diagonal matrix
F06FD nagf_blas_axpzy
Multiply real vector by scalar, preserving input vector
F06FE nagf_blas_drscl
Multiply real vector by reciprocal of scalar
F06FG nagf_blas_dnegv
Negate real vector
F06FJ nagf_blas_dssq
Update Euclidean norm of real vector in scaled form
F06FK nagf_blas_dnrm2w
Compute weighted Euclidean norm of real vector
F06FL nagf_blas_darang
Elements of real vector with largest and smallest absolute value
F06FP nagf_blas_drots
Apply real symmetric plane rotation to two vectors
F06FQ nagf_blas_dsrotg
Generate sequence of real plane rotations
F06FR nagf_blas_dnhousg
Generate real elementary reflection, NAG style
F06FS nagf_blas_dlhousg
Generate real elementary reflection, LINPACK style
F06FT nagf_blas_dnhous
Apply real elementary reflection, NAG style
F06FU nagf_blas_dlhous
Apply real elementary reflection, LINPACK style
F06GA nagf_blas_zdotu
Dot product of two complex vectors, unconjugated
F06GB nagf_blas_zdotc
Dot product of two complex vectors, conjugated
F06GC nagf_blas_zaxpy
Add scalar times complex vector to complex vector
F06GD nagf_blas_zscal
Multiply complex vector by complex scalar
F06GF nagf_blas_zcopy
Copy complex vector
F06GG nagf_blas_zswap
Swap two complex vectors
F06GR nagf_blas_zdotui
Dot product of a complex sparse and a full vector, unconjugated
F06GS nagf_blas_zdotci
Dot product of a complex sparse and a full vector, conjugated
F06GT nagf_blas_zaxpyi
Add scalar times complex sparse vector to a full vector
F06GU nagf_blas_zgthr
Gather complex sparse vector
F06GV nagf_blas_zgthrz
Gather and set to zero complex sparse vector
F06GW nagf_blas_zsctr
Scatter complex sparse vector
F06HB nagf_blas_zload
Broadcast scalar into complex vector
F06HC nagf_blas_zdscl
Multiply complex vector by complex diagonal matrix
F06HD nagf_blas_zaxpzy
Multiply complex vector by complex scalar, preserving input vector
F06HG nagf_blas_znegv
Negate complex vector
F06HM nagf_blas_zrot
Apply plane rotation with real cosine and complex sine
F06HP nagf_blas_zcrot
Apply complex plane rotation
F06HQ nagf_blas_zsrotg
Generate sequence of complex plane rotations
F06HR nagf_blas_zhousg
Generate complex elementary reflection
F06HT nagf_blas_zhous
Apply complex elementary reflection
F06JD nagf_blas_zdscal
Multiply complex vector by real scalar
F06JJ nagf_blas_dznrm2
Compute Euclidean norm of complex vector
F06JK nagf_blas_dzasum
Sum absolute values of complex vector elements
F06JL nagf_blas_idamax
Index, real vector element with largest absolute value
F06JM nagf_blas_izamax
Index, complex vector element with largest absolute value
F06KC nagf_blas_zddscl
Multiply complex vector by real diagonal matrix
F06KD nagf_blas_zdaxpzy
Multiply complex vector by real scalar, preserving input vector
F06KE nagf_blas_zdrscl
Multiply complex vector by reciprocal of real scalar
F06KF nagf_blas_zdcopy
Copy real vector to complex vector
F06KJ nagf_blas_dzssq
Update Euclidean norm of complex vector in scaled form
F06KL nagf_blas_idrank
Last non-negligible element of real vector
F06KP nagf_blas_zdrot
Apply real plane rotation to two complex vectors
F06PA nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
F06PB nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
F06PC nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
F06PD nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
F06PE nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
F06PF nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
F06PG nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
F06PH nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
F06PJ nagf_blas_dtrsv
System of equations, real triangular matrix
F06PK nagf_blas_dtbsv
System of equations, real triangular band matrix
F06PL nagf_blas_dtpsv
System of equations, real triangular packed matrix
F06PM nagf_blas_dger
Rank-1 update, real rectangular matrix
F06PP nagf_blas_dsyr
Rank-1 update, real symmetric matrix
F06PQ nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
F06PR nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
F06PS nagf_blas_dspr2
Rank-2 update, real symmetric packed matrix
F06QF nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
F06QH nagf_blas_dmload
Matrix initialization, real rectangular matrix
F06QJ nagf_blas_dgeap
Permute rows or columns, real rectangular matrix, permutations represented by an integer array
F06QK nagf_blas_dgeapr
Permute rows or columns, real rectangular matrix, permutations represented by a real array
F06QM nagf_blas_dsysrc
Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
F06QP nagf_blas_dutr1
QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
F06QQ nagf_blas_dutupd
QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
F06QR nagf_blas_duhqr
QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix
F06QS nagf_blas_dusqr
QR or RQ factorization by sequence of plane rotations, real upper spiked matrix
F06QT nagf_blas_dutsqr
QR factorization of UP or RQ factorization of PU, U real upper triangular, P a sequence of plane rotations
F06QV nagf_blas_dutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
F06QW nagf_blas_dutsrs
Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
F06QX nagf_blas_dgesrc
Apply sequence of plane rotations, real rectangular matrix
F06RA nagf_blas_dlange
1-norm, -norm, Frobenius norm, largest absolute element, real general matrix
F06RB nagf_blas_dlangb
1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
F06RC nagf_blas_dlansy
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
F06RD nagf_blas_dlansp
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
F06RE nagf_blas_dlansb
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
F06RJ nagf_blas_dlantr
1-norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
F06RK nagf_blas_dlantp
1-norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
F06RL nagf_blas_dlantb
1-norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
F06RM nagf_blas_dlanhs
1-norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
F06RN nagf_blas_dlangt
1-norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
F06RP nagf_blas_dlanst
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
F06SA nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
F06SB nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
F06SC nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
F06SD nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
F06SE nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
F06SF nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
F06SG nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
F06SH nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
F06SJ nagf_blas_ztrsv
System of equations, complex triangular matrix
F06SK nagf_blas_ztbsv
System of equations, complex triangular band matrix
F06SL nagf_blas_ztpsv
System of equations, complex triangular packed matrix
F06SM nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
F06SN nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
F06SP nagf_blas_zher
Rank-1 update, complex Hermitian matrix
F06SQ nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
F06SR nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
F06SS nagf_blas_zhpr2
Rank-2 update, complex Hermitian packed matrix
F06TA nagf_blas_zsymv
Matrix-vector product, complex symmetric matrix
F06TB nagf_blas_zsyr
Rank-1 update, complex symmetric matrix
F06TC nagf_blas_zspmv
Matrix-vector product, complex symmetric packed matrix
F06TD nagf_blas_zspr
Rank-1 update, complex symmetric packed matrix
F06TF nagf_blas_zmcopy
Matrix copy, complex rectangular or trapezoidal matrix
F06TH nagf_blas_zmload
Matrix initialization, complex rectangular matrix
F06TM nagf_blas_zhesrc
Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
F06TP nagf_blas_zutr1
QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
F06TQ nagf_blas_zutupd
QR factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
F06TR nagf_blas_zuhqr
QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix
F06TS nagf_blas_zusqr
QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix
F06TT nagf_blas_zutsqr
QR factorization of UP or RQ factorization of PU, U complex upper triangular, P a sequence of plane rotations
F06TV nagf_blas_zutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
F06TW nagf_blas_zutsrs
Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
F06TX nagf_blas_zgesrc
Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
F06TY nagf_blas_zgesrs
Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
F06UA nagf_blas_zlange
1-norm, -norm, Frobenius norm, largest absolute element, complex general matrix
F06UB nagf_blas_zlangb
1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
F06UC nagf_blas_zlanhe
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
F06UD nagf_blas_zlanhp
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
F06UE nagf_blas_zlanhb
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
F06UF nagf_blas_zlansy
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
F06UG nagf_blas_zlansp
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
F06UH nagf_blas_zlansb
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
F06UJ nagf_blas_zlantr
1-norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
F06UK nagf_blas_zlantp
1-norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
F06UL nagf_blas_zlantb
1-norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
F06UM nagf_blas_zlanhs
1-norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
F06UN nagf_blas_zlangt
1-norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
F06UP nagf_blas_zlanht
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
F06VJ nagf_blas_zgeap
Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
F06VK nagf_blas_zgeapr
Permute rows or columns, complex rectangular matrix, permutations represented by a real array
F06VX nagf_blas_zsgesr
Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
F06WA nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
F06WB nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
F06WC nagf_blas_dsfrk
Rank-k update of a real symmetric matrix, Rectangular Full Packed format
F06WN nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
F06WP nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
F06WQ nagf_blas_zhfrk
Rank-k update of a complex Hermitian matrix, Rectangular Full Packed format
F06YA nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
F06YC nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
F06YF nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
F06YJ nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
F06YP nagf_blas_dsyrk
Rank-k update of a real symmetric matrix
F06YR nagf_blas_dsyr2k
Rank-2k update of a real symmetric matrix
F06ZA nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
F06ZC nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
F06ZF nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
F06ZJ nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
F06ZP nagf_blas_zherk
Rank-k update of a complex Hermitian matrix
F06ZR nagf_blas_zher2k
Rank-2k update of a complex Hermitian matrix
F06ZT nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
F06ZU nagf_blas_zsyrk
Rank-k update of a complex symmetric matrix
F06ZW nagf_blas_zsyr2k
Rank-2k update of a complex symmetric matrix
Back to F06 Chapter Summary

F07 – Linear Equations (LAPACK)

Examples of routines and methods in this chapter.

F07AA nagf_lapack_dgesv
Computes the solution to a real system of linear equations
F07AB nagf_lapack_dgesvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
F07AC nagf_lapack_dsgesv
Computes the solution to a real system of linear equations using mixed precision arithmetic
F07AD nagf_lapack_dgetrf
LU factorization of real m by n matrix
F07AE nagf_lapack_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07AD
F07AF nagf_lapack_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
F07AG nagf_lapack_dgecon
Estimate condition number of real matrix, matrix already factorized by F07AD
F07AH nagf_lapack_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07AJ nagf_lapack_dgetri
Inverse of real matrix, matrix already factorized by F07AD
F07AN nagf_lapack_zgesv
Computes the solution to a complex system of linear equations
F07AP nagf_lapack_zgesvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
F07AQ nagf_lapack_zcgesv
Computes the solution to a complex system of linear equations using mixed precision arithmetic
F07AR nagf_lapack_zgetrf
LU factorization of complex m by n matrix
F07AS nagf_lapack_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07AR
F07AT nagf_lapack_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
F07AU nagf_lapack_zgecon
Estimate condition number of complex matrix, matrix already factorized by F07AR
F07AV nagf_lapack_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07AW nagf_lapack_zgetri
Inverse of complex matrix, matrix already factorized by F07AR
F07BA nagf_lapack_dgbsv
Computes the solution to a real banded system of linear equations
F07BB nagf_lapack_dgbsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
F07BD nagf_lapack_dgbtrf
LU factorization of real m by n band matrix
F07BE nagf_lapack_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BD
F07BF nagf_lapack_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
F07BG nagf_lapack_dgbcon
Estimate condition number of real band matrix, matrix already factorized by F07BD
F07BH nagf_lapack_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BN nagf_lapack_zgbsv
Computes the solution to a complex banded system of linear equations
F07BP nagf_lapack_zgbsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
F07BR nagf_lapack_zgbtrf
LU factorization of complex m by n band matrix
F07BS nagf_lapack_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BR
F07BT nagf_lapack_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
F07BU nagf_lapack_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by F07BR
F07BV nagf_lapack_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07CA nagf_lapack_dgtsv
Computes the solution to a real tridiagonal system of linear equations
F07CB nagf_lapack_dgtsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
F07CD nagf_lapack_dgttrf
LU factorization of real tridiagonal matrix
F07CE nagf_lapack_dgttrs
Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CD
F07CG nagf_lapack_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CD
F07CH nagf_lapack_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
F07CN nagf_lapack_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
F07CP nagf_lapack_zgtsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
F07CR nagf_lapack_zgttrf
LU factorization of complex tridiagonal matrix
F07CS nagf_lapack_zgttrs
Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CD
F07CU nagf_lapack_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CD
F07CV nagf_lapack_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
F07FA nagf_lapack_dposv
Computes the solution to a real symmetric positive definite system of linear equations
F07FB nagf_lapack_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
F07FC nagf_lapack_dsposv
Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic
F07FD nagf_lapack_dpotrf
Cholesky factorization of real symmetric positive definite matrix
F07FE nagf_lapack_dpotrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FD
F07FF nagf_lapack_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
F07FG nagf_lapack_dpocon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FD
F07FH nagf_lapack_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
F07FJ nagf_lapack_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FD
F07FN nagf_lapack_zposv
Computes the solution to a complex Hermitian positive definite system of linear equations
F07FP nagf_lapack_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
F07FQ nagf_lapack_zcposv
Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic
F07FR nagf_lapack_zpotrf
Cholesky factorization of complex Hermitian positive definite matrix
F07FS nagf_lapack_zpotrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FR
F07FT nagf_lapack_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
F07FU nagf_lapack_zpocon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FR
F07FV nagf_lapack_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
F07FW nagf_lapack_zpotri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07FR
F07GA nagf_lapack_dppsv
Computes the solution to a real symmetric positive definite system of linear equations, packed storage
F07GB nagf_lapack_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
F07GD nagf_lapack_dpptrf
Cholesky factorization of real symmetric positive definite matrix, packed storage
F07GE nagf_lapack_dpptrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GD, packed storage
F07GF nagf_lapack_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
F07GG nagf_lapack_dppcon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GD, packed storage
F07GH nagf_lapack_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
F07GJ nagf_lapack_dpptri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07GD, packed storage
F07GN nagf_lapack_zppsv
Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage
F07GP nagf_lapack_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
F07GR nagf_lapack_zpptrf
Cholesky factorization of complex Hermitian positive definite matrix, packed storage
F07GS nagf_lapack_zpptrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GR, packed storage
F07GT nagf_lapack_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
F07GU nagf_lapack_zppcon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07GR, packed storage
F07GV nagf_lapack_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
F07GW nagf_lapack_zpptri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GR, packed storage
F07HA nagf_lapack_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
F07HB nagf_lapack_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
F07HD nagf_lapack_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
F07HE nagf_lapack_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HD
F07HF nagf_lapack_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
F07HG nagf_lapack_dpbcon
Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HD
F07HH nagf_lapack_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
F07HN nagf_lapack_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
F07HP nagf_lapack_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
F07HR nagf_lapack_zpbtrf
Cholesky factorization of complex Hermitian positive definite band matrix
F07HS nagf_lapack_zpbtrs
Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HR
F07HT nagf_lapack_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
F07HU nagf_lapack_zpbcon
Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HR
F07HV nagf_lapack_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
F07JA nagf_lapack_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
F07JB nagf_lapack_dptsvx
Uses the LDLT factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
F07JD nagf_lapack_dpttrf
Computes the LDLT factorization of a real symmetric positive definite tridiagonal matrix
F07JE nagf_lapack_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDLT factorization computed by F07JD
F07JG nagf_lapack_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDLT factorization computed by F07JD
F07JH nagf_lapack_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
F07JN nagf_lapack_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
F07JP nagf_lapack_zptsvx
Uses the LDLT factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
F07JR nagf_lapack_zpttrf
Computes the LDLH factorization of a complex Hermitian positive definite tridiagonal matrix
F07JS nagf_lapack_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDLH factorization computed by F07JR
F07JU nagf_lapack_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDLH factorization computed by F07JR
F07JV nagf_lapack_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
F07KD nagf_lapack_dpstrf
Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix
F07KR nagf_lapack_zpstrf
Cholesky factorization of complex Hermitian positive semidefinite matrix
F07MA nagf_lapack_dsysv
Computes the solution to a real symmetric system of linear equations
F07MB nagf_lapack_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
F07MD nagf_lapack_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
F07ME nagf_lapack_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MD
F07MG nagf_lapack_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MD
F07MH nagf_lapack_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MJ nagf_lapack_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MD
F07MN nagf_lapack_zhesv
Computes the solution to a complex Hermitian system of linear equations
F07MP nagf_lapack_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
F07MR nagf_lapack_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
F07MS nagf_lapack_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MR
F07MU nagf_lapack_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MR
F07MV nagf_lapack_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07MW nagf_lapack_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MR
F07NN nagf_lapack_zsysv
Computes the solution to a complex symmetric system of linear equations
F07NP nagf_lapack_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
F07NR nagf_lapack_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
F07NS nagf_lapack_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NR
F07NU nagf_lapack_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NR
F07NV nagf_lapack_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07NW nagf_lapack_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NR
F07PA nagf_lapack_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
F07PB nagf_lapack_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
F07PD nagf_lapack_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
F07PE nagf_lapack_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PD, packed storage
F07PG nagf_lapack_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PD, packed storage
F07PH nagf_lapack_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PJ nagf_lapack_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PD, packed storage
F07PN nagf_lapack_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
F07PP nagf_lapack_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
F07PR nagf_lapack_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
F07PS nagf_lapack_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PR, packed storage
F07PU nagf_lapack_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PR, packed storage
F07PV nagf_lapack_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07PW nagf_lapack_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PR, packed storage
F07QN nagf_lapack_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
F07QP nagf_lapack_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
F07QR nagf_lapack_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
F07QS nagf_lapack_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QR, packed storage
F07QU nagf_lapack_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QR, packed storage
F07QV nagf_lapack_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07QW nagf_lapack_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QR, packed storage
F07TE nagf_lapack_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
F07TG nagf_lapack_dtrcon
Estimate condition number of real triangular matrix
F07TH nagf_lapack_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TJ nagf_lapack_dtrtri
Inverse of real triangular matrix
F07TS nagf_lapack_ztrtrs
Solution of complex triangular system of linear equations, multiple right-hand sides
F07TU nagf_lapack_ztrcon
Estimate condition number of complex triangular matrix
F07TV nagf_lapack_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07TW nagf_lapack_ztrtri
Inverse of complex triangular matrix
F07UE nagf_lapack_dtptrs
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UG nagf_lapack_dtpcon
Estimate condition number of real triangular matrix, packed storage
F07UH nagf_lapack_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UJ nagf_lapack_dtptri
Inverse of real triangular matrix, packed storage
F07US nagf_lapack_ztptrs
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UU nagf_lapack_ztpcon
Estimate condition number of complex triangular matrix, packed storage
F07UV nagf_lapack_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UW nagf_lapack_ztptri
Inverse of complex triangular matrix, packed storage
F07VE nagf_lapack_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
F07VG nagf_lapack_dtbcon
Estimate condition number of real band triangular matrix
F07VH nagf_lapack_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VS nagf_lapack_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
F07VU nagf_lapack_ztbcon
Estimate condition number of complex band triangular matrix
F07VV nagf_lapack_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
F07WD nagf_lapack_dpftrf
Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
F07WE nagf_lapack_dpftrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WD, Rectangular Full Packed format
F07WJ nagf_lapack_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07WD, Rectangular Full Packed format
F07WK nagf_lapack_dtftri
Inverse of real triangular matrix, Rectangular Full Packed format
F07WR nagf_lapack_zpftrf
Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
F07WS nagf_lapack_zpftrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WR, Rectangular Full Packed format
F07WW nagf_lapack_zpftri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WR, Rectangular Full Packed format
F07WX nagf_lapack_ztftri
Inverse of complex triangular matrix, Rectangular Full Packed format
Back to F07 Chapter Summary

F08 – Least Squares and Eigenvalue Problems (LAPACK)

Examples of routines and methods in this chapter.

F08AA nagf_lapack_dgels
Solves a real linear least squares problem of full rank
F08AB nagf_lapack_dgeqrt
Performs a QR factorization of real general rectangular matrix, with explicit blocking
F08AC nagf_lapack_dgemqrt
Applies the orthogonal transformation determined by F08AB
F08AE nagf_lapack_dgeqrf
Performs a QR factorization of real general rectangular matrix
F08AF nagf_lapack_dorgqr
Forms all or part of orthogonal Q from QR factorization determined by F08AE, F08BE and F08BF
F08AG nagf_lapack_dormqr
Applies an orthogonal transformation determined by F08AE, F08BE and F08BF
F08AH nagf_lapack_dgelqf
Performs a LQ factorization of real general rectangular matrix
F08AJ nagf_lapack_dorglq
Forms all or part of orthogonal Q from LQ factorization determined by F08AH
F08AK nagf_lapack_dormlq
Applies the orthogonal transformation determined by F08AH
F08AN nagf_lapack_zgels
Solves a complex linear least problem of full rank
F08AP nagf_lapack_zgeqrt
Performs a QR factorization of complex general rectangular matrix using recursive algorithm
F08AQ nagf_lapack_zgemqrt
Applies the unitary transformation determined by F08AP
F08AS nagf_lapack_zgeqrf
Performs a QR factorization of complex general rectangular matrix
F08AT nagf_lapack_zungqr
Forms all or part of unitary Q from QR factorization determined by F08AS, F08BS and F08BT
F08AU nagf_lapack_zunmqr
Applies a unitary transformation determined by F08AS, F08BS and F08BT
F08AV nagf_lapack_zgelqf
Performs a LQ factorization of complex general rectangular matrix
F08AW nagf_lapack_zunglq
Forms all or part of unitary Q from LQ factorization determined by F08AV
F08AX nagf_lapack_zunmlq
Applies the unitary transformation determined by F08AV
F08BA nagf_lapack_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
F08BB nagf_lapack_dtpqrt
QR factorization of real general triangular-pentagonal matrix
F08BC nagf_lapack_dtpmqrt
Applies the orthogonal transformation determined by F08BB
F08BE nagf_lapack_dgeqpf
QR factorization, with column pivoting, of real general rectangular matrix
F08BF nagf_lapack_dgeqp3
QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
F08BH nagf_lapack_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
F08BK nagf_lapack_dormrz
Applies the orthogonal transformation determined by F08BH
F08BN nagf_lapack_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
F08BP nagf_lapack_ztpqrt
QR factorization of complex triangular-pentagonal matrix
F08BQ nagf_lapack_ztpmqrt
Applies the unitary transformation determined by F08BP
F08BS nagf_lapack_zgeqpf
QR factorization, with column pivoting, of complex general rectangular matrix
F08BT nagf_lapack_zgeqp3
QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
F08BV nagf_lapack_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
F08BX nagf_lapack_zunmrz
Applies the unitary transformation determined by F08BV
F08CE nagf_lapack_dgeqlf
QL factorization of real general rectangular matrix
F08CF nagf_lapack_dorgql
Form all or part of orthogonal Q from QL factorization determined by F08CE
F08CG nagf_lapack_dormql
Applies the orthogonal transformation determined by F08CE
F08CH nagf_lapack_dgerqf
RQ factorization of real general rectangular matrix
F08CJ nagf_lapack_dorgrq
Form all or part of orthogonal Q from RQ factorization determined by F08CH
F08CK nagf_lapack_dormrq
Applies the orthogonal transformation determined by F08CH
F08CS nagf_lapack_zgeqlf
QL factorization of complex general rectangular matrix
F08CT nagf_lapack_zungql
Form all or part of unitary Q from QL factorization determined by F08CS
F08CU nagf_lapack_zunmql
Applies the unitary transformation determined by F08CS
F08CV nagf_lapack_zgerqf
RQ factorization of complex general rectangular matrix
F08CW nagf_lapack_zungrq
Form all or part of unitary Q from RQ factorization determined by F08CV
F08CX nagf_lapack_zunmrq
Applies the unitary transformation determined by F08CV
F08FA nagf_lapack_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FB nagf_lapack_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FC nagf_lapack_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FD nagf_lapack_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FE nagf_lapack_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FF nagf_lapack_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FE
F08FG nagf_lapack_dormtr
Applies the orthogonal transformation determined by F08FE
F08FL nagf_lapack_ddisna
Computes 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
F08FN nagf_lapack_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FP nagf_lapack_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQ nagf_lapack_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FR nagf_lapack_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FS nagf_lapack_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FT nagf_lapack_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FS
F08FU nagf_lapack_zunmtr
Applies the unitary transformation matrix determined by F08FS
F08GA nagf_lapack_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GB nagf_lapack_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GC nagf_lapack_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08GE nagf_lapack_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GF nagf_lapack_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GE
F08GG nagf_lapack_dopmtr
Applies the orthogonal transformation determined by F08GE
F08GN nagf_lapack_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GP nagf_lapack_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQ nagf_lapack_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08GS nagf_lapack_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GT nagf_lapack_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GS
F08GU nagf_lapack_zupmtr
Applies the unitary transformation matrix determined by F08GS
F08HA nagf_lapack_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HB nagf_lapack_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HC nagf_lapack_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08HE nagf_lapack_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HN nagf_lapack_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HP nagf_lapack_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQ nagf_lapack_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08HS nagf_lapack_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JA nagf_lapack_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JB nagf_lapack_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JC nagf_lapack_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JD nagf_lapack_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JE nagf_lapack_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
F08JF nagf_lapack_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
F08JG nagf_lapack_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
F08JH nagf_lapack_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JJ nagf_lapack_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JK nagf_lapack_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JL nagf_lapack_dstegr
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JS nagf_lapack_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JU nagf_lapack_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
F08JV nagf_lapack_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JX nagf_lapack_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JY nagf_lapack_zstegr
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KA nagf_lapack_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
F08KB nagf_lapack_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KC nagf_lapack_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
F08KD nagf_lapack_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KE nagf_lapack_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KF nagf_lapack_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KE
F08KG nagf_lapack_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KE
F08KH nagf_lapack_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
F08KJ nagf_lapack_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
F08KN nagf_lapack_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
F08KP nagf_lapack_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQ nagf_lapack_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
F08KR nagf_lapack_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KS nagf_lapack_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
F08KT nagf_lapack_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KS
F08KU nagf_lapack_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by F08KS
F08LE nagf_lapack_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
F08LS nagf_lapack_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
F08MD nagf_lapack_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08ME nagf_lapack_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
F08MS nagf_lapack_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
F08NA nagf_lapack_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NB nagf_lapack_dgeevx
Computes 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
F08NE nagf_lapack_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
F08NF nagf_lapack_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NE
F08NG nagf_lapack_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NE
F08NH nagf_lapack_dgebal
Balances a real general matrix
F08NJ nagf_lapack_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NH
F08NN nagf_lapack_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NP nagf_lapack_zgeevx
Computes 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
F08NS nagf_lapack_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
F08NT nagf_lapack_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NS
F08NU nagf_lapack_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NS
F08NV nagf_lapack_zgebal
Balances a complex general matrix
F08NW nagf_lapack_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NV
F08PA nagf_lapack_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PB nagf_lapack_dgeesx
Computes 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
F08PE nagf_lapack_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PK nagf_lapack_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PN nagf_lapack_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PP nagf_lapack_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
F08PS nagf_lapack_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PX nagf_lapack_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QF nagf_lapack_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
F08QG nagf_lapack_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QH nagf_lapack_dtrsyl
Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
F08QK nagf_lapack_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
F08QL nagf_lapack_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QT nagf_lapack_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
F08QU nagf_lapack_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QV nagf_lapack_ztrsyl
Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
F08QX nagf_lapack_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
F08QY nagf_lapack_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08RA nagf_lapack_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
F08RN nagf_lapack_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
F08SA nagf_lapack_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SB nagf_lapack_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SC nagf_lapack_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SE nagf_lapack_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FD
F08SN nagf_lapack_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SP nagf_lapack_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQ nagf_lapack_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08SS nagf_lapack_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FR
F08TA nagf_lapack_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TB nagf_lapack_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TC nagf_lapack_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TE nagf_lapack_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GD
F08TN nagf_lapack_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TP nagf_lapack_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQ nagf_lapack_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
F08TS nagf_lapack_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GR
F08UA nagf_lapack_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UB nagf_lapack_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UC nagf_lapack_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UE nagf_lapack_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
F08UF nagf_lapack_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
F08UN nagf_lapack_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UP nagf_lapack_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQ nagf_lapack_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08US nagf_lapack_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
F08UT nagf_lapack_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
F08VA nagf_lapack_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
F08VC nagf_lapack_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
F08VE nagf_lapack_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
F08VG nagf_lapack_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
F08VN nagf_lapack_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
F08VQ nagf_lapack_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
F08VS nagf_lapack_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form
F08VU nagf_lapack_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form
F08WA nagf_lapack_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WB nagf_lapack_dggevx
Computes, 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
F08WC nagf_lapack_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WE nagf_lapack_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WF nagf_lapack_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WH nagf_lapack_dggbal
Balances a pair of real, square, matrices
F08WJ nagf_lapack_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WH
F08WN nagf_lapack_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WP nagf_lapack_zggevx
Computes, 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
F08WQ nagf_lapack_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WS nagf_lapack_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WT nagf_lapack_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WV nagf_lapack_zggbal
Balances a pair of complex, square, matrices
F08WW nagf_lapack_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WV
F08XA nagf_lapack_dgges
Computes, 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
F08XB nagf_lapack_dggesx
Computes, 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
F08XC nagf_lapack_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XE nagf_lapack_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XN nagf_lapack_zgges
Computes, 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
F08XP nagf_lapack_zggesx
Computes, 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
F08XQ nagf_lapack_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XS nagf_lapack_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
F08YE nagf_lapack_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
F08YF nagf_lapack_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
F08YG nagf_lapack_dtgsen
Reorders 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
F08YH nagf_lapack_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
F08YK nagf_lapack_dtgevc
Computes right and left generalized eigenvectors of the matrix pair (A,B) which is assumed to be in generalized upper Schur form
F08YL nagf_lapack_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
F08YS nagf_lapack_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
F08YT nagf_lapack_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
F08YU nagf_lapack_ztgsen
Reorders 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
F08YV nagf_lapack_ztgsyl
Solves the complex generalized Sylvester equation
F08YX nagf_lapack_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
F08YY nagf_lapack_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
F08ZA nagf_lapack_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
F08ZB nagf_lapack_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
F08ZE nagf_lapack_dggqrf
Computes a generalized QR factorization of a real matrix pair
F08ZF nagf_lapack_dggrqf
Computes a generalized RQ factorization of a real matrix pair
F08ZN nagf_lapack_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
F08ZP nagf_lapack_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZS nagf_lapack_zggqrf
Computes a generalized QR factorization of a complex matrix pair
F08ZT nagf_lapack_zggrqf
Computes a generalized RQ factorization of a complex matrix pair
Back to F08 Chapter Summary

F11 – Large Scale Linear Systems

Examples of routines and methods in this chapter.

F11BD nagf_sparse_real_gen_basic_setup
Real sparse nonsymmetric linear systems, setup for F11BE
F11BE nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BF nagf_sparse_real_gen_basic_diag
Real sparse nonsymmetric linear systems, diagnostic for F11BE
F11BR nagf_sparse_complex_gen_basic_setup
Complex sparse non-Hermitian linear systems, setup for F11BS
F11BS nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
F11BT nagf_sparse_complex_gen_basic_diag
Complex sparse non-Hermitian linear systems, diagnostic for F11BS
F11DA nagf_sparse_real_gen_precon_ilu
Real sparse nonsymmetric linear systems, incomplete LU factorization
F11DB nagf_sparse_real_gen_precon_ilu_solve
Solution of linear system involving incomplete LU preconditioning matrix generated by F11DA
F11DC nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DA
F11DD nagf_sparse_real_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
F11DE nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
F11DF nagf_sparse_real_gen_precon_bdilu
Real sparse nonsymmetric linear system, incomplete LU factorization of local or overlapping diagonal blocks
F11DG nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete LU block diagonal preconditioner computed by F11DF
F11DK nagf_sparse_real_gen_precon_jacobi
Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner
F11DN nagf_sparse_complex_gen_precon_ilu
Complex sparse non-Hermitian linear systems, incomplete LU factorization
F11DP nagf_sparse_complex_gen_precon_ilu_solve
Solution of complex linear system involving incomplete LU preconditioning matrix generated by F11DN
F11DQ nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DN (Black Box)
F11DR nagf_sparse_complex_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
F11DS nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
F11DT nagf_sparse_complex_gen_precon_bdilu
Complex, sparse, non-Hermitian linear system, incomplete LU factorization of local or overlapping diagonal blocks
F11DU nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete LU block diagonal preconditioner computed by F11DT
F11DX nagf_sparse_complex_gen_precon_jacobi
Complex, sparse, Hermitian or non-Hermitian, linear systems, line Jacobi preconditioner
F11GD nagf_sparse_real_symm_basic_setup
Real sparse symmetric linear systems, setup for F11GE
F11GE nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
F11GF nagf_sparse_real_symm_basic_diag
Real sparse symmetric linear systems, diagnostic for F11GE
F11GR nagf_sparse_complex_herm_basic_setup
Complex sparse Hermitian linear systems, setup for F11GS
F11GS nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
F11GT nagf_sparse_complex_herm_basic_diag
Complex sparse Hermitian linear systems, diagnostic for F11GS
F11JA nagf_sparse_real_symm_precon_ichol
Real sparse symmetric matrix, incomplete Cholesky factorization
F11JB nagf_sparse_real_symm_precon_ichol_solve
Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JA
F11JC nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JA (Black Box)
F11JD nagf_sparse_real_symm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
F11JE nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11JN nagf_sparse_complex_herm_precon_ilu
Complex sparse Hermitian matrix, incomplete Cholesky factorization
F11JP nagf_sparse_complex_herm_precon_ilu_solve
Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JN
F11JQ nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JN (Black Box)
F11JR nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
F11JS nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
F11MD nagf_sparse_direct_real_gen_setup
Real sparse nonsymmetric linear systems, setup for F11ME
F11ME nagf_sparse_direct_real_gen_lu
LU factorization of real sparse matrix
F11MF nagf_sparse_direct_real_gen_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
F11MG nagf_sparse_direct_real_gen_cond
Estimate condition number of real matrix, matrix already factorized by F11ME
F11MH nagf_sparse_direct_real_gen_refine
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F11MK nagf_sparse_direct_real_gen_matmul
Real sparse nonsymmetric matrix-matrix multiply, compressed column storage
F11ML nagf_sparse_direct_real_gen_norm
1-norm, -norm, largest absolute element, real, square, sparse matrix
F11MM nagf_sparse_direct_real_gen_diag
Real sparse nonsymmetric linear systems, diagnostic for F11ME
F11XA nagf_sparse_real_gen_matvec
Real, sparse, nonsymmetric matrix-vector multiply
F11XE nagf_sparse_real_symm_matvec
Real sparse symmetric matrix-vector multiply
F11XN nagf_sparse_complex_gen_matvec
Complex sparse non-Hermitian matrix-vector multiply
F11XS nagf_sparse_complex_herm_matvec
Complex sparse Hermitian matrix-vector multiply
F11YE nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
F11ZA nagf_sparse_real_gen_sort
Real sparse nonsymmetric matrix reorder routine
F11ZB nagf_sparse_real_symm_sort
Real sparse symmetric matrix reorder routine
F11ZN nagf_sparse_complex_gen_sort
Complex sparse non-Hermitian matrix reorder routine
F11ZP nagf_sparse_complex_herm_sort
Complex sparse Hermitian matrix reorder routine
Back to F11 Chapter Summary

F12 – Large Scale Eigenproblems

Examples of routines and methods in this chapter.

F12AA nagf_sparseig_real_init
Initialization routine for (F12AB) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
F12AB nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
F12AC nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12AB
F12AD nagf_sparseig_real_option
Set a single option from a string (F12AB/F12AC/F12AG)
F12AE nagf_sparseig_real_monit
Provides monitoring information for F12AB
F12AF nagf_sparseig_real_band_init
Initialization routine for (F12AG) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
F12AG nagf_sparseig_real_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
F12AN nagf_sparseig_complex_init
Initialization routine for (F12AP) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem
F12AP nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
F12AQ nagf_sparseig_complex_proc
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, postprocessing for F12AP
F12AR nagf_sparseig_complex_option
Set a single option from a string (F12AP/F12AQ)
F12AS nagf_sparseig_complex_monit
Provides monitoring information for F12AP
F12AT nagf_sparseig_complex_band_init
Initialization routine for F12AU computing selected eigenvalues and, optionally, eigenvectors of a complex banded (standard or generalized) eigenproblem
F12AU nagf_sparseig_complex_band_solve
Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver
F12FA nagf_sparseig_real_symm_init
Initialization routine for (F12FB) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
F12FB nagf_sparseig_real_symm_iter
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
F12FC nagf_sparseig_real_symm_proc
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FB
F12FD nagf_sparseig_real_symm_option
Set a single option from a string (F12FB/F12FC/F12FG)
F12FE nagf_sparseig_real_symm_monit
Provides monitoring information for F12FB
F12FF nagf_sparseig_real_symm_band_init
Initialization routine for (F12FG) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
F12FG nagf_sparseig_real_symm_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Back to F12 Chapter Summary

F16 – Further Linear Algebra Support Routines

Examples of routines and methods in this chapter.

F16DL nagf_blast_isum
Sum elements of integer vector
F16DN nagf_blast_imax_val
Maximum value and location, integer vector
F16DP nagf_blast_imin_val
Minimum value and location, integer vector
F16DQ nagf_blast_iamax_val
Maximum absolute value and location, integer vector
F16DR nagf_blast_iamin_val
Minimum absolute value and location, integer vector
F16EA nagf_blast_ddot
Dot product of two vectors, allows scaling and accumulation
F16EC nagf_blast_daxpby
Real weighted vector addition
F16EH nagf_blast_dwaxpby
Real weighted vector addition preserving input
F16EL nagf_blast_dsum
Sum elements of real vector
F16GC nagf_blast_zaxpby
Complex weighted vector addition
F16GH nagf_blast_zwaxpby
Complex weighted vector addition preserving input
F16GL nagf_blast_zsum
Sum elements of complex vector
F16JN nagf_blast_dmax_val
Maximum value and location, real vector
F16JP nagf_blast_dmin_val
Minimum value and location, real vector
F16JQ nagf_blast_damax_val
Maximum absolute value and location, real vector
F16JR nagf_blast_damin_val
Minimum absolute value and location, real vector
F16JS nagf_blast_zamax_val
Maximum absolute value and location, complex vector
F16JT nagf_blast_zamin_val
Minimum absolute value and location, complex vector
F16RB nagf_blast_dgb_norm
1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
F16UB nagf_blast_zgb_norm
1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Back to F16 Chapter Summary

G01 – Simple Calculations on Statistical Data

Examples of routines and methods in this chapter.

G01AB nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
G01AD nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
G01AE nagf_stat_frequency_table
Frequency table from raw data
G01AF nagf_stat_contingency_table
Two-way contingency table analysis, with χ2/Fisher's exact test
G01AL nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
G01AM nagf_stat_quantiles
Find quantiles of an unordered vector, real numbers
G01AN nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
G01AP nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
G01AR nagf_stat_plot_stem_leaf
Constructs a stem and leaf plot
G01AS nagf_stat_plot_box_whisker
Constructs a box and whisker plot
G01AT nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
G01AU nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01AT
G01BJ nagf_stat_prob_binomial
Binomial distribution function
G01BK nagf_stat_prob_poisson
Poisson distribution function
G01BL nagf_stat_prob_hypergeom
Hypergeometric distribution function
G01DA nagf_stat_normal_scores_exact
Normal scores, accurate values
G01DB nagf_stat_normal_scores_approx
Normal scores, approximate values
G01DC nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
G01DD nagf_stat_test_shapiro_wilk
Shapiro and Wilk's W test for Normality
G01DH nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
G01EA nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
G01EB nagf_stat_prob_students_t
Computes probabilities for Student's t-distribution
G01EC nagf_stat_prob_chisq
Computes probabilities for χ2 distribution
G01ED nagf_stat_prob_f
Computes probabilities for F-distribution
G01EE nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
G01EF nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
G01EM nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
G01EP nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
G01ER nagf_stat_prob_vonmises
Computes probability for von Mises distribution
G01ET nagf_stat_prob_landau
Landau distribution function
G01EU nagf_stat_prob_vavilov
Vavilov distribution function
G01EW nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
G01EY nagf_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
G01EZ nagf_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
G01FA nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
G01FB nagf_stat_inv_cdf_students_t
Computes deviates for Student's t-distribution
G01FC nagf_stat_inv_cdf_chisq
Computes deviates for the χ2 distribution
G01FD nagf_stat_inv_cdf_f
Computes deviates for the F-distribution
G01FE nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
G01FF nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
G01FM nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
G01FT nagf_stat_inv_cdf_landau
Landau inverse function Ψ(x)
G01GB nagf_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's t-distribution
G01GC nagf_stat_prob_chisq_noncentral
Computes probabilities for the non-central χ2 distribution
G01GD nagf_stat_prob_f_noncentral
Computes probabilities for the non-central F-distribution
G01GE nagf_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
G01HA nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
G01HB nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
G01HC nagf_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's t-distribution
G01HD nagf_stat_prob_multi_students_t
Computes the probability for the multivariate Student's t-distribution
G01JC nagf_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of χ2 variables
G01JD nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ2 variables
G01KA nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
G01KF nagf_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
G01KK nagf_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
G01KQ nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
G01LB nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
G01MB nagf_stat_mills_ratio
Computes reciprocal of Mills' Ratio
G01MT nagf_stat_pdf_landau
Landau density function ϕ(λ)
G01MU nagf_stat_pdf_vavilov
Vavilov density function ϕV(λ;κ,β2)
G01NA nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
G01NB nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
G01PT nagf_stat_pdf_landau_moment1
Landau first moment function Φ1(x)
G01QT nagf_stat_pdf_landau_moment2
Landau second moment function Φ2(x)
G01RT nagf_stat_pdf_landau_deriv
Landau derivative function ϕ(λ)
G01SA nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
G01SB nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t-distribution
G01SC nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ2 distribution
G01SD nagf_stat_prob_f_vector
Computes a vector of probabilities for F-distribution
G01SE nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
G01SF nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
G01SJ nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
G01SK nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
G01SL nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
G01TA nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
G01TB nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t-distribution
G01TC nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ2 distribution
G01TD nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F-distribution
G01TE nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
G01TF nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
G01WA nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
G01ZU nagf_stat_init_vavilov
Initialization routine for G01MU and G01EU
Back to G01 Chapter Summary

G02 – Correlation and Regression Analysis

Examples of routines and methods in this chapter.

G02AA nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
G02AB nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmented G02AA to incorporate weights and bounds
G02AE nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k-factor structure to a real square matrix
G02AJ nagf_nearest_correlation_h_weight
Computes the nearest correlation matrix to a real square matrix, using element-wise weighting
G02AN nagf_nearest_correlation_shrinking
Computes a correlation matrix from an approximate matrix with fixed submatrix
G02AP nagf_nearest_correlation_target
Computes a correlation matrix from an approximate one using a specified target matrix
G02BA nagf_correg_coeffs_pearson
Pearson product-moment correlation coefficients, all variables, no missing values
G02BB nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
G02BC nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
G02BD nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
G02BE nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
G02BF nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
G02BG nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
G02BH nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
G02BJ nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
G02BK nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
G02BL nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
G02BM nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
G02BN nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
G02BP nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
G02BQ nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
G02BR nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
G02BS nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
G02BT nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
G02BU nagf_correg_ssqmat
Computes a weighted sum of squares matrix
G02BW nagf_correg_ssqmat_to_corrmat
Computes a correlation matrix from a sum of squares matrix
G02BX nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
G02BY nagf_correg_corrmat_partial
Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BX
G02BZ nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BU
G02CA nagf_correg_linregs_const
Simple linear regression with constant term, no missing values
G02CB nagf_correg_linregs_noconst
Simple linear regression without constant term, no missing values
G02CC nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
G02CD nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
G02CE nagf_correg_linregm_service_select
Service routine for multiple linear regression, select elements from vectors and matrices
G02CF nagf_correg_linregm_service_reorder
Service routine for multiple linear regression, reorder elements of vectors and matrices
G02CG nagf_correg_linregm_coeffs_const
Multiple linear regression, from correlation coefficients, with constant term
G02CH nagf_correg_linregm_coeffs_noconst
Multiple linear regression, from correlation-like coefficients, without constant term
G02DA nagf_correg_linregm_fit
Fits a general (multiple) linear regression model
G02DC nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
G02DD nagf_correg_linregm_update
Estimates of linear parameters and general linear regression model from updated model
G02DE nagf_correg_linregm_var_add
Add a new independent variable to a general linear regression model
G02DF nagf_correg_linregm_var_del
Delete an independent variable from a general linear regression model
G02DG nagf_correg_linregm_fit_newvar
Fits a general linear regression model to new dependent variable
G02DK nagf_correg_linregm_constrain
Estimates and standard errors of parameters of a general linear regression model for given constraints
G02DN nagf_correg_linregm_estfunc
Computes estimable function of a general linear regression model and its standard error
G02EA nagf_correg_linregm_rssq
Computes residual sums of squares for all possible linear regressions for a set of independent variables
G02EC nagf_correg_linregm_rssq_stat
Calculates R2 and CP values from residual sums of squares
G02EE nagf_correg_linregm_fit_onestep
Fits a linear regression model by forward selection
G02EF nagf_correg_linregm_fit_stepwise
Stepwise linear regression
G02FA nagf_correg_linregm_stat_resinf
Calculates standardized residuals and influence statistics
G02FC nagf_correg_linregm_stat_durbwat
Computes Durbin–Watson test statistic
G02GA nagf_correg_glm_normal
Fits a generalized linear model with Normal errors
G02GB nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
G02GC nagf_correg_glm_poisson
Fits a generalized linear model with Poisson errors
G02GD nagf_correg_glm_gamma
Fits a generalized linear model with gamma errors
G02GK nagf_correg_glm_constrain
Estimates and standard errors of parameters of a general linear model for given constraints
G02GN nagf_correg_glm_estfunc
Computes estimable function of a generalized linear model and its standard error
G02GP nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
G02HA nagf_correg_robustm
Robust regression, standard M-estimates
G02HB nagf_correg_robustm_wts
Robust regression, compute weights for use with G02HD
G02HD nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
G02HF nagf_correg_robustm_user_varmat
Robust regression, variance-covariance matrix following G02HD
G02HK nagf_correg_robustm_corr_huber
Calculates a robust estimation of a covariance matrix, Huber's weight function
G02HL nagf_correg_robustm_corr_user_deriv
Calculates a robust estimation of a covariance matrix, user-supplied weight function plus derivatives
G02HM nagf_correg_robustm_corr_user
Calculates a robust estimation of a covariance matrix, user-supplied weight function
G02JA nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
G02JB nagf_correg_mixeff_ml
Linear mixed effects regression using Maximum Likelihood (ML)
G02JC nagf_correg_mixeff_hier_init
Hierarchical mixed effects regression, initialization routine for G02JD and G02JE
G02JD nagf_correg_mixeff_hier_reml
Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
G02JE nagf_correg_mixeff_hier_ml
Hierarchical mixed effects regression using Maximum Likelihood (ML)
G02KA nagf_correg_ridge_opt
Ridge regression, optimizing a ridge regression parameter
G02KB nagf_correg_ridge
Ridge regression using a number of supplied ridge regression parameters
G02LA nagf_correg_pls_svd
Partial least squares (PLS) regression using singular value decomposition
G02LB nagf_correg_pls_wold
Partial least squares (PLS) regression using Wold's iterative method
G02LC nagf_correg_pls_fit
PLS parameter estimates following partial least squares regression by G02LA and G02LB
G02LD nagf_correg_pls_pred
PLS predictions based on parameter estimates from G02LC
G02MA nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
G02MB nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
G02MC nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
G02QF nagf_correg_quantile_linreg_easy
Linear quantile regression, simple interface, independent, identically distributed (IID) errors
G02QG nagf_correg_quantile_linreg
Linear quantile regression, comprehensive interface
G02ZK nagf_correg_optset
Option setting routine for G02QG
G02ZL nagf_correg_optget
Option getting routine for G02QG
Back to G02 Chapter Summary

G03 – Multivariate Methods

Examples of routines and methods in this chapter.

G03AA nagf_mv_prin_comp
Performs principal component analysis
G03AC nagf_mv_canon_var
Performs canonical variate analysis
G03AD nagf_mv_canon_corr
Performs canonical correlation analysis
G03BA nagf_mv_rot_orthomax
Computes orthogonal rotations for loading matrix, generalized orthomax criterion
G03BC nagf_mv_rot_procrustes
Computes Procrustes rotations
G03BD nagf_mv_rot_promax
ProMax rotations
G03CA nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
G03CC nagf_mv_factor_score
Computes factor score coefficients (for use after G03CA)
G03DA nagf_mv_discrim
Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
G03DB nagf_mv_discrim_mahal
Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DA)
G03DC nagf_mv_discrim_group
Allocates observations to groups according to selected rules (for use after G03DA)
G03EA nagf_mv_distance_mat
Computes distance matrix
G03EC nagf_mv_cluster_hier
Hierarchical cluster analysis
G03EF nagf_mv_cluster_kmeans
K-means cluster analysis
G03EH nagf_mv_cluster_hier_dendrogram
Constructs dendrogram (for use after G03EC)
G03EJ nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03EC)
G03FA nagf_mv_multidimscal_metric
Performs principal coordinate analysis, classical metric scaling
G03FC nagf_mv_multidimscal_ordinal
Performs non-metric (ordinal) multidimensional scaling
G03GA nagf_mv_gaussian_mixture
Fits a Gaussian mixture model
G03ZA nagf_mv_z_scores
Produces standardized values (z-scores) for a data matrix
Back to G03 Chapter Summary

G04 – Analysis of Variance

Examples of routines and methods in this chapter.

G04AG nagf_anova_hier2
Two-way analysis of variance, hierarchical classification, subgroups of unequal size
G04BB nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
G04BC nagf_anova_rowcol
Analysis of variance, general row and column design, treatment means and standard errors
G04CA nagf_anova_factorial
Analysis of variance, complete factorial design, treatment means and standard errors
G04DA nagf_anova_contrasts
Computes sum of squares for contrast between means
G04DB nagf_anova_confidence
Computes confidence intervals for differences between means computed by G04BB or G04BC
G04EA nagf_anova_dummyvars
Computes orthogonal polynomials or dummy variables for factor/classification variable
Back to G04 Chapter Summary

G05 – Random Number Generators

Examples of routines and methods in this chapter.

G05KF nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
G05KG nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
G05KH nagf_rand_init_leapfrog
Primes a pseudorandom number generator for generating multiple streams using leap-frog
G05KJ nagf_rand_init_skipahead
Primes a pseudorandom number generator for generating multiple streams using skip-ahead
G05KK nagf_rand_init_skipahead_power2
Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
G05NC nagf_rand_permute
Pseudorandom permutation of an integer vector
G05ND nagf_rand_sample
Pseudorandom sample from an integer vector
G05NE nagf_rand_sample_wgt
Pseudorandom sample, without replacement, unequal weights
G05PD nagf_rand_times_garch_asym1
Generates a realization of a time series from a GARCH process with asymmetry of the form (εt-1+γ)2
G05PE nagf_rand_times_garch_asym2
Generates a realization of a time series from a GARCH process with asymmetry of the form (|εt-1|+γεt-1)2
G05PF nagf_rand_times_garch_GJR
Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G05PG nagf_rand_times_garch_exp
Generates a realization of a time series from an exponential GARCH (EGARCH) process
G05PH nagf_rand_times_arma
Generates a realization of a time series from an ARMA model
G05PJ nagf_rand_times_mv_varma
Generates a realization of a multivariate time series from a VARMA model
G05PM nagf_rand_times_smooth_exp
Generates a realization of a time series from an exponential smoothing model
G05PV nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K-fold cross validation
G05PW nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
G05PX nagf_rand_matrix_orthog
Generates a random orthogonal matrix
G05PY nagf_rand_matrix_corr
Generates a random correlation matrix
G05PZ nagf_rand_matrix_2waytable
Generates a random two-way table
G05RC nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's t-copula
G05RD nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
G05RE nagf_rand_copula_clayton_bivar
Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
G05RF nagf_rand_copula_frank_bivar
Generates a matrix of pseudorandom numbers from a bivariate Frank copula
G05RG nagf_rand_copula_plackett_bivar
Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
G05RH nagf_rand_copula_clayton
Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
G05RJ nagf_rand_copula_frank
Generates a matrix of pseudorandom numbers from a multivariate Frank copula
G05RK nagf_rand_copula_gumbel
Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
G05RY nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's t-distribution
G05RZ nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
G05SA nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over (0,1]
G05SB nagf_rand_dist_beta
Generates a vector of pseudorandom numbers from a beta distribution
G05SC nagf_rand_dist_cauchy
Generates a vector of pseudorandom numbers from a Cauchy distribution
G05SD nagf_rand_dist_chisq
Generates a vector of pseudorandom numbers from a χ2 distribution
G05SE nagf_rand_dist_dirichlet
Generates a vector of pseudorandom numbers from a Dirichlet distribution
G05SF nagf_rand_dist_exp
Generates a vector of pseudorandom numbers from an exponential distribution
G05SG nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
G05SH nagf_rand_dist_f
Generates a vector of pseudorandom numbers from an F-distribution
G05SJ nagf_rand_dist_gamma
Generates a vector of pseudorandom numbers from a gamma distribution
G05SK nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
G05SL nagf_rand_dist_logistic
Generates a vector of pseudorandom numbers from a logistic distribution
G05SM nagf_rand_dist_lognormal
Generates a vector of pseudorandom numbers from a log-normal distribution
G05SN nagf_rand_dist_students_t
Generates a vector of pseudorandom numbers from a Student's t-distribution
G05SP nagf_rand_dist_triangular
Generates a vector of pseudorandom numbers from a triangular distribution
G05SQ nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over [a,b]
G05SR nagf_rand_dist_vonmises
Generates a vector of pseudorandom numbers from a von Mises distribution
G05SS nagf_rand_dist_weibull
Generates a vector of pseudorandom numbers from a Weibull distribution
G05TA nagf_rand_int_binomial
Generates a vector of pseudorandom integers from a binomial distribution
G05TB nagf_rand_logical
Generates a vector of pseudorandom logical values
G05TC nagf_rand_int_geom
Generates a vector of pseudorandom integers from a geometric distribution
G05TD nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
G05TE nagf_rand_int_hypergeom
Generates a vector of pseudorandom integers from a hypergeometric distribution
G05TF nagf_rand_int_log
Generates a vector of pseudorandom integers from a logarithmic distribution
G05TG nagf_rand_int_multinomial
Generates a vector of pseudorandom integers from a multinomial distribution
G05TH nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
G05TJ nagf_rand_int_poisson
Generates a vector of pseudorandom integers from a Poisson distribution
G05TK nagf_rand_int_poisson_varmean
Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
G05TL nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
G05XA nagf_rand_bb_init
Initializes the Brownian bridge generator
G05XB nagf_rand_bb
Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm
G05XC nagf_rand_bb_inc_init
Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm
G05XD nagf_rand_bb_inc
Backs out the increments from sample paths generated by a Brownian bridge algorithm
G05XE nagf_rand_bb_make_bridge_order
Creates a Brownian bridge construction order out of a set of input times
G05YJ nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
G05YK nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
G05YL nagf_rand_quasi_init
Initializes a quasi-random number generator
G05YM nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
G05YN nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
G05ZM nagf_rand_field_1d_user_setup
Setup for simulating one-dimensional random fields, user-defined variogram
G05ZN nagf_rand_field_1d_predef_setup
Setup for simulating one-dimensional random fields
G05ZP nagf_rand_field_1d_generate
Generates realizations of a one-dimensional random field
G05ZQ nagf_rand_field_2d_user_setup
Setup for simulating two-dimensional random fields, user-defined variogram
G05ZR nagf_rand_field_2d_predef_setup
Setup for simulating two-dimensional random fields, preset variogram
G05ZS nagf_rand_field_2d_generate
Generates realizations of a two-dimensional random field
G05ZT nagf_rand_field_fracbm_generate
Generates realizations of fractional Brownian motion
Back to G05 Chapter Summary

G07 – Univariate Estimation

Examples of routines and methods in this chapter.

G07AA nagf_univar_ci_binomial
Computes confidence interval for the parameter of a binomial distribution
G07AB nagf_univar_ci_poisson
Computes confidence interval for the parameter of a Poisson distribution
G07BB nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
G07BE nagf_univar_estim_weibull
Computes maximum likelihood estimates for parameters of the Weibull distribution
G07BF nagf_univar_estim_genpareto
Estimates parameter values of the generalized Pareto distribution
G07CA nagf_univar_ttest_2normal
Computes t-test statistic for a difference in means between two Normal populations, confidence interval
G07DA nagf_univar_robust_1var_median
Robust estimation, median, median absolute deviation, robust standard deviation
G07DB nagf_univar_robust_1var_mestim
Robust estimation, M-estimates for location and scale parameters, standard weight functions
G07DC nagf_univar_robust_1var_mestim_wgt
Robust estimation, M-estimates for location and scale parameters, user-defined weight functions
G07DD nagf_univar_robust_1var_trimmed
Computes a trimmed and winsorized mean of a single sample with estimates of their variance
G07EA nagf_univar_robust_1var_ci
Robust confidence intervals, one-sample
G07EB nagf_univar_robust_2var_ci
Robust confidence intervals, two-sample
G07GA nagf_univar_outlier_peirce_1var
Outlier detection using method of Peirce, raw data or single variance supplied
G07GB nagf_univar_outlier_peirce_2var
Outlier detection using method of Peirce, two variances supplied
Back to G07 Chapter Summary

G08 – Nonparametric Statistics

Examples of routines and methods in this chapter.

G08AA nagf_nonpar_test_sign
Sign test on two paired samples
G08AC nagf_nonpar_test_median
Median test on two samples of unequal size
G08AE nagf_nonpar_test_friedman
Friedman two-way analysis of variance on k matched samples
G08AF nagf_nonpar_test_kruskal
Kruskal–Wallis one-way analysis of variance on k samples of unequal size
G08AG nagf_nonpar_test_wilcoxon
Performs the Wilcoxon one-sample (matched pairs) signed rank test
G08AH nagf_nonpar_test_mwu
Performs the Mann–Whitney U test on two independent samples
G08AJ nagf_nonpar_prob_mwu_noties
Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample
G08AK nagf_nonpar_prob_mwu_ties
Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
G08AL nagf_nonpar_test_cochranq
Performs the Cochran Q test on cross-classified binary data
G08BA nagf_nonpar_test_mooddavid
Mood's and David's tests on two samples of unequal size
G08CB nagf_nonpar_test_ks_1sample
Performs the one-sample Kolmogorov–Smirnov test for standard distributions
G08CC nagf_nonpar_test_ks_1sample_user
Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
G08CD nagf_nonpar_test_ks_2sample
Performs the two-sample Kolmogorov–Smirnov test
G08CG nagf_nonpar_test_chisq
Performs the χ2 goodness-of-fit test, for standard continuous distributions
G08CH nagf_nonpar_gofstat_anddar
Calculates the Anderson–Darling goodness-of-fit test statistic
G08CJ nagf_nonpar_gofstat_anddar_unif
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data
G08CK nagf_nonpar_gofstat_anddar_normal
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
G08CL nagf_nonpar_gofstat_anddar_exp
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
G08DA nagf_nonpar_concordance_kendall
Kendall's coefficient of concordance
G08EA nagf_nonpar_randtest_runs
Performs the runs up or runs down test for randomness
G08EB nagf_nonpar_randtest_pairs
Performs the pairs (serial) test for randomness
G08EC nagf_nonpar_randtest_triplets
Performs the triplets test for randomness
G08ED nagf_nonpar_randtest_gaps
Performs the gaps test for randomness
G08RA nagf_nonpar_rank_regsn
Regression using ranks, uncensored data
G08RB nagf_nonpar_rank_regsn_censored
Regression using ranks, right-censored data
Back to G08 Chapter Summary

G10 – Smoothing in Statistics

Examples of routines and methods in this chapter.

G10AB nagf_smooth_fit_spline
Fit cubic smoothing spline, smoothing parameter given
G10AC nagf_smooth_fit_spline_parest
Fit cubic smoothing spline, smoothing parameter estimated
G10BB nagf_smooth_kerndens_gauss
Kernel density estimate using Gaussian kernel (thread safe)
G10CA nagf_smooth_data_runningmedian
Compute smoothed data sequence using running median smoothers
G10ZA nagf_smooth_data_order
Reorder data to give ordered distinct observations
Back to G10 Chapter Summary

G11 – Contingency Table Analysis

Examples of routines and methods in this chapter.

G11AA nagf_contab_chisq
χ2 statistics for two-way contingency table
G11BA nagf_contab_tabulate_stat
Computes multiway table from set of classification factors using selected statistic
G11BB nagf_contab_tabulate_percentile
Computes multiway table from set of classification factors using given percentile/quantile
G11BC nagf_contab_tabulate_margin
Computes marginal tables for multiway table computed by G11BA or G11BB
G11CA nagf_contab_condl_logistic
Returns parameter estimates for the conditional analysis of stratified data
G11SA nagf_contab_binary
Contingency table, latent variable model for binary data
G11SB nagf_contab_binary_service
Frequency count for G11SA
Back to G11 Chapter Summary

G12 – Survival Analysis

Examples of routines and methods in this chapter.

G12AA nagf_surviv_kaplanmeier
Computes Kaplan–Meier (product-limit) estimates of survival probabilities
G12AB nagf_surviv_logrank
Computes rank statistics for comparing survival curves
G12BA nagf_surviv_coxmodel
Fits Cox's proportional hazard model
G12ZA nagf_surviv_coxmodel_risksets
Creates the risk sets associated with the Cox proportional hazards model for fixed covariates
Back to G12 Chapter Summary

G13 – Time Series Analysis

Examples of routines and methods in this chapter.

G13AA nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
G13AB nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
G13AC nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
G13AD nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model
G13AE nagf_tsa_uni_arima_estim
Univariate time series, estimation, seasonal ARIMA model (comprehensive)
G13AF nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
G13AG nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting
G13AH nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set
G13AJ nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
G13AM nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
G13AS nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AE or G13AF
G13AU nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
G13AW nagf_tsa_uni_dickey_fuller_unit
Computes (augmented) Dickey–Fuller unit root test statistic
G13BA nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
G13BB nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
G13BC nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations
G13BD nagf_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model
G13BE nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
G13BG nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
G13BH nagf_tsa_multi_inputmod_forecast_state
Multivariate time series, forecasting from state set of multi-input model
G13BJ nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model
G13CA nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CB nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CC nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
G13CD nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
G13CE nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
G13CF nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
G13CG nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
G13DB nagf_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations
G13DD nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
G13DJ nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
G13DK nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
G13DL nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms
G13DM nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
G13DN nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ2 statistics and significance levels
G13DP nagf_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices
G13DS nagf_tsa_multi_varma_diag
Multivariate time series, diagnostic checking of residuals, following G13DD
G13DX nagf_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator
G13EA nagf_tsa_multi_kalman_sqrt_var
Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
G13EB nagf_tsa_multi_kalman_sqrt_invar
Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
G13EJ nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
G13EK nagf_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
G13FA nagf_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (εt-1+γ)2
G13FB nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (εt-1+γ)2
G13FC nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|εt-1|+γεt-1)2
G13FD nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form (|εt-1|+γεt-1)2
G13FE nagf_tsa_uni_garch_GJR_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FF nagf_tsa_uni_garch_GJR_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
G13FG nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
G13FH nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
G13ME nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
G13MF nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
G13MG nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
G13NA nagf_tsa_cp_pelt
Change point detection, using the PELT algorithm
G13NB nagf_tsa_cp_pelt_user
Change points detection using the PELT algorithm, user supplied cost function
G13ND nagf_tsa_cp_binary
Change point detection, using binary segmentation
G13NE nagf_tsa_cp_binary_user
Change point detection, using binary segmentation, user supplied cost function
Back to G13 Chapter Summary

G22 – Linear Model Specification

Examples of routines and methods in this chapter.

Back to G22 Chapter Summary

H – Operations Research

Examples of routines and methods in this chapter.

H02BB nagf_mip_ilp_dense
Integer LP problem (dense)
H02BF nagf_mip_ilp_mpsx
Interpret MPSX data file defining IP or LP problem, optimize and print solution
H02BU nagf_mip_ilp_mpsx_convert
Convert MPSX data file defining IP or LP problem to format required by H02BB or E04MF
H02BV nagf_mip_ilp_print
Print IP or LP solutions with user-specified names for rows and columns
H02BZ nagf_mip_ilp_info
Integer programming solution, supplies further information on solution obtained by H02BB
H02CB nagf_mip_iqp_dense
Integer QP problem (dense)
H02CB nagf_mip_iqp_dense_dummy_monit
dummy
H02CC nagf_mip_iqp_dense_optfile
Read optional parameter values for H02CB from external file
H02CD nagf_mip_iqp_dense_optstr
Supply optional parameter values to H02CB
H02CE nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NK
H02CE nagf_mip_iqp_sparse_dummy_monit
dummy
H02CF nagf_mip_iqp_sparse_optfile
Read optional parameter values for H02CE from external file
H02CG nagf_mip_iqp_sparse_optstr
Supply optional parameter values to H02CE
H02DA nagf_mip_sqp
Mixed integer nonlinear programming
H02ZK nagf_mip_optset
Option setting routine for H02DA
H02ZL nagf_mip_optget
Option getting routine for H02DA
H03AB nagf_mip_transportation
Transportation problem, modified 'stepping stone' method
H03AD nagf_mip_shortestpath
Shortest path problem, Dijkstra's algorithm
H03BB nagf_mip_tsp_simann
Travelling Salesman Problem, simulated annealing
H05AA nagf_best_subset_given_size_revcomm
Best n subsets of size p (reverse communication)
H05AB nagf_best_subset_given_size
Best n subsets of size p (direct communication)
Back to H Chapter Summary

J10 –

Examples of routines and methods in this chapter.

Back to J10 Chapter Summary

M01 – Sorting and Searching

Examples of routines and methods in this chapter.

M01CA nagf_sort_realvec_sort
Sort a vector, real numbers
M01CB nagf_sort_intvec_sort
Sort a vector, integer numbers
M01CC nagf_sort_charvec_sort
Sort a vector, character data
M01DA nagf_sort_realvec_rank
Rank a vector, real numbers
M01DB nagf_sort_intvec_rank
Rank a vector, integer numbers
M01DC nagf_sort_charvec_rank
Rank a vector, character data
M01DE nagf_sort_realmat_rank_rows
Rank rows of a matrix, real numbers
M01DF nagf_sort_intmat_rank_rows
Rank rows of a matrix, integer numbers
M01DJ nagf_sort_realmat_rank_columns
Rank columns of a matrix, real numbers
M01DK nagf_sort_intmat_rank_columns
Rank columns of a matrix, integer numbers
M01DZ nagf_sort_arbitrary_rank
Rank arbitrary data
M01EA nagf_sort_realvec_rank_rearrange
Rearrange a vector according to given ranks, real numbers
M01EB nagf_sort_intvec_rank_rearrange
Rearrange a vector according to given ranks, integer numbers
M01EC nagf_sort_charvec_rank_rearrange
Rearrange a vector according to given ranks, character data
M01ED nagf_sort_cmplxvec_rank_rearrange
Rearrange a vector according to given ranks, complex numbers
M01NA nagf_sort_realvec_search
Binary search in set of real numbers
M01NB nagf_sort_intvec_search
Binary search in set of integer numbers
M01NC nagf_sort_charvec_search
Binary search in set of character data
M01ZA nagf_sort_permute_invert
Invert a permutation
M01ZB nagf_sort_permute_check
Check validity of a permutation
M01ZC nagf_sort_permute_decompose
Decompose a permutation into cycles
Back to M01 Chapter Summary

P01 – Error Trapping

Examples of routines and methods in this chapter.

Back to P01 Chapter Summary

S – Approximations of Special Functions

Examples of routines and methods in this chapter.

S01BA nagf_specfun_log_shifted
ln (1+x)
S01EA nagf_specfun_exp_complex
Complex exponential, ez
S07AA nagf_specfun_tan
tan x
S09AA nagf_specfun_arcsin
arcsin x
S09AB nagf_specfun_arccos
arccos x
S10AA nagf_specfun_tanh
tanh x
S10AB nagf_specfun_sinh
sinh x
S10AC nagf_specfun_cosh
cosh x
S11AA nagf_specfun_arctanh
arctanh x
S11AB nagf_specfun_arcsinh
arcsinh x
S11AC nagf_specfun_arccosh
arccosh x
S13AA nagf_specfun_integral_exp
Exponential integral E1(x)
S13AC nagf_specfun_integral_cos
Cosine integral Ci (x)
S13AD nagf_specfun_integral_sin
Sine integral Si (x)
S14AA nagf_specfun_gamma
Gamma function
S14AB nagf_specfun_gamma_log_real
Log gamma function, real argument
S14AC nagf_specfun_polygamma
ψ(x)-ln x
S14AD nagf_specfun_polygamma_deriv
Scaled derivatives of ψ(x)
S14AE nagf_specfun_psi_deriv_real
Polygamma function ψ(n)(x) for real x
S14AF nagf_specfun_psi_deriv_complex
Polygamma function ψ(n)(z) for complex z
S14AG nagf_specfun_gamma_log_complex
Logarithm of the gamma function ln Γ(z), complex argument
S14AH nagf_specfun_gamma_log_scaled_real
Scaled log gamma function
S14BA nagf_specfun_gamma_incomplete
Incomplete gamma functions P(a,x) and Q(a,x)
S14CB nagf_specfun_beta_log_real
Logarithm of the beta function ln B(a,b)
S14CC nagf_specfun_beta_incomplete
Incomplete beta function Ix(a,b) and its complement 1-Ix
S15AB nagf_specfun_cdf_normal
Cumulative Normal distribution function P(x)
S15AC nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q(x)
S15AD nagf_specfun_erfc_real
Complement of error function erfc (x)
S15AE nagf_specfun_erf_real
Error function erf (x)
S15AF nagf_specfun_dawson
Dawson's integral
S15AG nagf_specfun_erfcx_real
Scaled complement of error function, erfcx (x)
S15DD nagf_specfun_erfc_complex
Scaled complex complement of error function, exp (-z2)erfc (-iz)
S17AC nagf_specfun_bessel_y0_real
Bessel function Y0(x)
S17AD nagf_specfun_bessel_y1_real
Bessel function Y1(x)
S17AE nagf_specfun_bessel_j0_real
Bessel function J0(x)
S17AF nagf_specfun_bessel_j1_real
Bessel function J1(x)
S17AG nagf_specfun_airy_ai_real
Airy function Ai (x)
S17AH nagf_specfun_airy_bi_real
Airy function Bi (x)
S17AJ nagf_specfun_airy_ai_deriv
Airy function Ai (x)
S17AK nagf_specfun_airy_bi_deriv
Airy function Bi (x)
S17AL nagf_specfun_bessel_zeros
Zeros of Bessel functions Jα(x), Jα(x), Yα(x) or Yα(x)
S17AQ nagf_specfun_bessel_y0_real_vector
Bessel function vectorized Y0(x)
S17AR nagf_specfun_bessel_y1_real_vector
Bessel function vectorized Y1(x)
S17AS nagf_specfun_bessel_j0_real_vector
Bessel function vectorized J0(x)
S17AT nagf_specfun_bessel_j1_real_vector
Bessel function vectorized J1(x)
S17AU nagf_specfun_airy_ai_real_vector
Airy function vectorized Ai (x)
S17AV nagf_specfun_airy_bi_real_vector
Airy function vectorized Bi (x)
S17AW nagf_specfun_airy_ai_deriv_vector
Derivatives of the Airy function, vectorized Ai (x)
S17AX nagf_specfun_airy_bi_deriv_vector
Derivatives of the Airy function, vectorized Bi (x)
S17DC nagf_specfun_bessel_y_complex
Bessel functions Yν+a(z), real a0, complex z, ν=0,1,2,
S17DE nagf_specfun_bessel_j_complex
Bessel functions Jν+a(z), real a0, complex z, ν=0,1,2,
S17DG nagf_specfun_airy_ai_complex
Airy functions Ai (z) and Ai (z), complex z
S17DH nagf_specfun_airy_bi_complex
Airy functions Bi (z) and Bi (z), complex z
S17DL nagf_specfun_hankel_complex
Hankel functions Hν+a(j)(z), j=1,2, real a0, complex z, ν=0,1,2,
S18AC nagf_specfun_bessel_k0_real
Modified Bessel function K0(x)
S18AD nagf_specfun_bessel_k1_real
Modified Bessel function K1(x)
S18AE nagf_specfun_bessel_i0_real
Modified Bessel function I0(x)
S18AF nagf_specfun_bessel_i1_real
Modified Bessel function I1(x)
S18AQ nagf_specfun_bessel_k0_real_vector
Modified Bessel function vectorized K0(x)
S18AR nagf_specfun_bessel_k1_real_vector
Modified Bessel function vectorized K1(x)
S18AS nagf_specfun_bessel_i0_real_vector
Modified Bessel function vectorized I0(x)
S18AT nagf_specfun_bessel_i1_real_vector
Modified Bessel function vectorized I1(x)
S18CC nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function exK0(x)
S18CD nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function exK1(x)
S18CE nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e-|x|I0(x)
S18CF nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e-|x|I1(x)
S18CQ nagf_specfun_bessel_k0_scaled_vector
Scaled modified Bessel function vectorized exK0(x)
S18CR nagf_specfun_bessel_k1_scaled_vector
Scaled modified Bessel function vectorized exK1(x)
S18CS nagf_specfun_bessel_i0_scaled_vector
Scaled modified Bessel function vectorized e-|x|I0(x)
S18CT nagf_specfun_bessel_i1_scaled_vector
Scaled modified Bessel function vectorized e-|x|I1(x)
S18DC nagf_specfun_bessel_k_complex
Modified Bessel functions Kν+a(z), real a0, complex z, ν=0,1,2,
S18DE nagf_specfun_bessel_i_complex
Modified Bessel functions Iν+a(z), real a0, complex z, ν=0,1,2,
S18GK nagf_specfun_bessel_j_seq_complex
Bessel function of the 1st kind Jα±n(z)
S19AA nagf_specfun_kelvin_ber
Kelvin function ber x
S19AB nagf_specfun_kelvin_bei
Kelvin function bei x
S19AC nagf_specfun_kelvin_ker
Kelvin function ker x
S19AD nagf_specfun_kelvin_kei
Kelvin function kei x
S19AN nagf_specfun_kelvin_ber_vector
Kelvin function vectorized ber x
S19AP nagf_specfun_kelvin_bei_vector
Kelvin function vectorized bei x
S19AQ nagf_specfun_kelvin_ker_vector
Kelvin function vectorized ker x
S19AR nagf_specfun_kelvin_kei_vector
Kelvin function vectorized kei x
S20AC nagf_specfun_fresnel_s
Fresnel integral S(x)
S20AD nagf_specfun_fresnel_c
Fresnel integral C(x)
S20AQ nagf_specfun_fresnel_s_vector
Fresnel integral vectorized S(x)
S20AR nagf_specfun_fresnel_c_vector
Fresnel integral vectorized C(x)
S21BA nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
S21BB nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind RF(x,y,z)
S21BC nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind RD(x,y,z)
S21BD nagf_specfun_ellipint_symm_3
Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
S21BE nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, F(ϕm)
S21BF nagf_specfun_ellipint_legendre_2
Elliptic integral of 2nd kind, Legendre form, E(ϕm)
S21BG nagf_specfun_ellipint_legendre_3
Elliptic integral of 3rd kind, Legendre form, Π(n;ϕm)
S21BH nagf_specfun_ellipint_complete_1
Complete elliptic integral of 1st kind, Legendre form, K(m)
S21BJ nagf_specfun_ellipint_complete_2
Complete elliptic integral of 2nd kind, Legendre form, E(m)
S21CA nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
S21CB nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
S21CC nagf_specfun_jactheta_real
Jacobian theta functions θk(x,q) of real argument
S21DA nagf_specfun_ellipint_general_2
General elliptic integral of 2nd kind F(z,k,a,b) of complex argument
S22AA nagf_specfun_legendre_p
Legendre functions of 1st kind Pnm(x) or Pnm-(x)
S22BA nagf_specfun_1f1_real
Real confluent hypergeometric function 1F1(a;b;x)
S22BB nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function 1F1(a;b;x) in scaled form
S22BE nagf_specfun_2f1_real
Real Gauss hypergeometric function 2F1(a,b;c;x)
S22BF nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function 2F1(a,b;c;x) in scaled form
S30AA nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
S30AB nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
S30BA nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
S30BB nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
S30CA nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
S30CB nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
S30CC nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
S30CD nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
S30FA nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
S30JA nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
S30JB nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NA nagf_specfun_opt_heston_price
Heston's model option pricing formula
S30NB nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
S30NC nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
S30QC nagf_specfun_opt_amer_bs_price
American option, Bjerksund and Stensland pricing formula
S30SA nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
S30SB nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Back to S Chapter Summary

X01 – Mathematical Constants

Examples of routines and methods in this chapter.

X01AA nagf_math_pi
Provides the mathematical constant π
X01AB nagf_math_euler
Provides the mathematical constant γ (Euler's constant)
Back to X01 Chapter Summary

X02 – Machine Constants

Examples of routines and methods in this chapter.

X02AH nagf_machine_sinarg_max
The largest permissible argument for sin and cos
X02AJ nagf_machine_precision
The machine precision
X02AK nagf_machine_real_smallest
The smallest positive model number
X02AL nagf_machine_real_largest
The largest positive model number
X02AM nagf_machine_real_safe
The safe range parameter
X02AN nagf_machine_complex_safe
The safe range parameter for complex floating-point arithmetic
X02BB nagf_machine_integer_max
The largest representable integer
X02BE nagf_machine_decimal_digits
The maximum number of decimal digits that can be represented
X02BH nagf_machine_model_base
The floating-point model parameter, b
X02BJ nagf_machine_model_digits
The floating-point model parameter, p
X02BK nagf_machine_model_minexp
The floating-point model parameter emin
X02BL nagf_machine_model_maxexp
The floating-point model parameter emax
Back to X02 Chapter Summary

X03 – Inner Products

Examples of routines and methods in this chapter.

X03AA nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
X03AB nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Back to X03 Chapter Summary

X04 – Input/Output Utilities

Examples of routines and methods in this chapter.

X04AA nagf_file_set_unit_error
Return or set unit number for error messages
X04AB nagf_file_set_unit_advisory
Return or set unit number for advisory messages
X04AC nagf_file_open
Open unit number for reading, writing or appending, and associate unit with named file
X04AD nagf_file_close
Close file associated with given unit number
X04BA nagf_file_line_write
Write formatted record to external file
X04BB nagf_file_line_read
Read formatted record from external file
X04CA nagf_file_print_matrix_real_gen
Print real general matrix (easy-to-use)
X04CB nagf_file_print_matrix_real_gen_comp
Print real general matrix (comprehensive)
X04CC nagf_file_print_matrix_real_packed
Print real packed triangular matrix (easy-to-use)
X04CD nagf_file_print_matrix_real_packed_comp
Print real packed triangular matrix (comprehensive)
X04CE nagf_file_print_matrix_real_band
Print real packed banded matrix (easy-to-use)
X04CF nagf_file_print_matrix_real_band_comp
Print real packed banded matrix (comprehensive)
X04DA nagf_file_print_matrix_complex_gen
Print complex general matrix (easy-to-use)
X04DB nagf_file_print_matrix_complex_gen_comp
Print complex general matrix (comprehensive)
X04DC nagf_file_print_matrix_complex_packed
Print complex packed triangular matrix (easy-to-use)
X04DD nagf_file_print_matrix_complex_packed_comp
Print complex packed triangular matrix (comprehensive)
X04DE nagf_file_print_matrix_complex_band
Print complex packed banded matrix (easy-to-use)
X04DF nagf_file_print_matrix_complex_band_comp
Print complex packed banded matrix (comprehensive)
X04EA nagf_file_print_matrix_integer
Print integer matrix (easy-to-use)
X04EB nagf_file_print_matrix_integer_comp
Print integer matrix (comprehensive)
Back to X04 Chapter Summary

X05 – Date and Time Utilities

Examples of routines and methods in this chapter.

X05AA nagf_time_date_array
Return date and time as an array of integers
X05AB nagf_time_date_array_string
Convert array of integers representing date and time to character string
X05AC nagf_time_date_string_compare
Compare two character strings representing date and time
X05BA nagf_time_cpu
Return the CPU time
Back to X05 Chapter Summary

X06 – OpenMP Utilities

Examples of routines and methods in this chapter.

X06AA nagf_omp_set_num_threads
Sets the number of threads for OpenMP parallel regions
X06AB nagf_omp_get_num_threads
The number of OpenMP threads in the current team
X06AC nagf_omp_get_max_threads
An upper bound on the number of threads in the next parallel region
X06AD nagf_omp_get_thread_num
The OpenMP thread number of the calling thread
X06AF nagf_omp_in_parallel
Tests for an active OpenMP parallel region
X06AG nagf_omp_set_nested
Enables or disables nested OpenMP parallelism
X06AH nagf_omp_get_nested
Tests the status of nested OpenMP parallelism
X06XA nagf_omp_using_threaded_impl
Tests whether a threaded NAG Library is being used
Back to X06 Chapter Summary

X07 – IEEE Arithmetic

Examples of routines and methods in this chapter.

X07AA nagf_is_finite
Determines whether its argument has a finite value
X07AB nagf_is_nan
Determines whether its argument is a NaN (Not A Number)
X07BA nagf_create_infinity
Creates a signed infinite value
X07BB nagf_create_nan
Creates a NaN (Not A Number)
X07CA nagf_get_ieee_exception_mode
Gets current behaviour of floating-point exceptions
X07CB nagf_set_ieee_exception_mode
Sets behaviour of floating-point exceptions
Back to X07 Chapter Summary

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016