Mark 7 Library Contents

a00 – Library Identification

Routine Name	Mark of Introduction	Purpose
a00aac	1	nag_implementation_details Library identification, details of implementation and mark

a02 – Complex Arithmetic

Routine Name	Mark of Introduction	Purpose
a02bac	2	nag_complex Complex number from real and imaginary parts
a02bbc	2	nag_complex_real Real part of a complex number
a02bcc	2	nag_complex_imag Imaginary part of a complex number
a02cac	2	nag_complex_add Addition of two complex numbers
a02cbc	2	nag_complex_subtract Subtraction of two complex numbers
a02ccc	2	nag_complex_multiply Multiplication of two complex numbers
a02cdc	2	nag_complex_divide Quotient of two complex numbers
a02cec	2	nag_complex_negate Negation of a complex number
a02cfc	2	nag_complex_conjg Conjugate of a complex number
a02cgc	2	nag_complex_equal Equality of two complex numbers
a02chc	2	nag_complex_not_equal Inequality of two complex numbers
a02dac	2	nag_complex_arg Argument of a complex number
a02dbc	2	nag_complex_abs Modulus of a complex number
a02dcc	2	nag_complex_sqrt Square root of a complex number
a02ddc	2	nag_complex_i_power Complex number raised to integer power
a02dec	2	nag_complex_r_power Complex number raised to real power
a02dfc	2	nag_complex_c_power Complex number raised to complex power
a02dgc	2	nag_complex_log Complex logarithm
a02dhc	2	nag_complex_exp Complex exponential
a02djc	2	nag_complex_sin Complex sine
a02dkc	2	nag_complex_cos Complex cosine
a02dlc	2	nag_complex_tan Complex tangent

c02 – Zeros of Polynomials

Routine Name	Mark of Introduction	Purpose
c02afc	2	nag_zeros_complex_poly Zeros of a polynomial with complex coefficients
c02agc	2	nag_zeros_real_poly Zeros of a polynomial with real coefficients
c02akc	6	nag_cubic_roots Zeros of a cubic polynomial with real coefficients
c02alc	6	nag_quartic_roots Zeros of a real quartic polynomial with real coefficients

c05 – Roots of One or More Transcendental Equations

Routine Name	Mark of Introduction	Purpose
c05adc	2	nag_zero_cont_func_bd Zero of a continuous function of one variable
c05nbc	2	nag_zero_nonlin_eqns Solution of a system of nonlinear equations (function values only)
c05pbc	2	nag_zero_nonlin_eqns_deriv Solution of a system of nonlinear equations (using first derivatives)
c05sdc	5	nag_zero_cont_func_bd_1 Zero of a continuous function of one variable, thread-safe
c05tbc	5	nag_zero_nonlin_eqns_1 Solution of a system of nonlinear equations (function values only), thread-safe
c05ubc	5	nag_zero_nonlin_eqns_deriv_1 Solution of a system of nonlinear equations (using first derivatives), thread-safe
c05zbc	2	nag_check_deriv Derivative checker for c05pbc
c05zcc	5	nag_check_deriv_1 Derivative checker for c05ubc, thread-safe

c06 – Fourier Transforms

Routine Name	Mark of Introduction	Purpose
c06eac	1	nag_fft_real Single one-dimensional real discrete Fourier transform
c06ebc	1	nag_fft_hermitian Single one-dimensional Hermitian discrete Fourier transform
c06ecc	1	nag_fft_complex Single one-dimensional complex discrete Fourier transform
c06ekc	1	nag_convolution_real Circular convolution or correlation of two real vectors
c06fpc	1	nag_fft_multiple_real Multiple one-dimensional real discrete Fourier transforms
c06fqc	1	nag_fft_multiple_hermitian Multiple one-dimensional Hermitian discrete Fourier transforms
c06frc	1	nag_fft_multiple_complex Multiple one-dimensional complex discrete Fourier transforms
c06fuc	1	nag_fft_2d_complex two-dimensional complex discrete Fourier transform
c06gbc	1	nag_conjugate_hermitian Complex conjugate of Hermitian sequence
c06gcc	1	nag_conjugate_complex Complex conjugate of complex sequence
c06gqc	1	nag_multiple_conjugate_hermitian Complex conjugate of multiple Hermitian sequences
c06gsc	1	nag_multiple_hermitian_to_complex Convert Hermitian sequences to general complex sequences
c06gzc	1	nag_fft_init_trig Initialisation function for other c06 functions
c06hac	2	nag_fft_multiple_sine Discrete sine transform
c06hbc	2	nag_fft_multiple_cosine Discrete cosine transform
c06hcc	2	nag_fft_multiple_qtr_sine Discrete quarter-wave sine transform
c06hdc	2	nag_fft_multiple_qtr_cosine Discrete quarter-wave cosine transform
c06pfc	7	nag_fft_multid_single One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pjc	7	nag_fft_multid_full Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pxc	7	nag_fft_3d Three-dimensional complex discrete Fourier transform, complex data format

d01 – Quadrature

Routine Name	Mark of Introduction	Purpose
d01ajc	2	nag_1d_quad_gen One-dimensional adaptive quadrature, allowing for badly behaved integrands
d01akc	2	nag_1d_quad_osc One-dimensional adaptive quadrature, suitable for oscillating functions
d01alc	2	nag_1d_quad_brkpts One-dimensional adaptive quadrature, allowing for singularities at specified points
d01amc	2	nag_1d_quad_inf One-dimensional adaptive quadrature over infinite or semi-infinite interval
d01anc	2	nag_1d_quad_wt_trig One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions
d01apc	2	nag_1d_quad_wt_alglog One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type
d01aqc	2	nag_1d_quad_wt_cauchy One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value
d01asc	2	nag_1d_quad_inf_wt_trig One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function
d01bac	2	nag_1d_quad_guass One-dimensional Gaussian quadrature rule evaluation
d01fcc	2	nag_multid_quad_adapt Multi-dimensional adaptive quadrature
d01gac	2	nag_1d_quad_vals One-dimensional integration of a function defined by data values only
d01gbc	2	nag_multid_quad_monte_carlo Multi-dimensional quadrature, using Monte Carlo method
d01sjc	5	nag_1d_quad_gen_1 One-dimensional adaptive quadrature, allowing for badly behaved integrands, thread-safe
d01skc	5	nag_1d_quad_osc_1 One-dimensional adaptive quadrature, suitable for oscillating functions, thread-safe
d01slc	5	nag_1d_quad_brkpts_1 One-dimensional adaptive quadrature, allowing for singularities at specified points, thread-safe
d01smc	5	nag_1d_quad_inf_1 One-dimensional adaptive quadrature over infinite or semi-infinite interval, thread-safe
d01snc	5	nag_1d_quad_wt_trig_1 One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions, thread-safe
d01spc	5	nag_1d_quad_wt_alglog_1 One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type, thread-safe
d01sqc	5	nag_1d_quad_wt_cauchy_1 One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value, thread-safe
d01ssc	5	nag_1d_quad_inf_wt_trig_1 One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function, thread-safe
d01tac	5	nag_1d_quad_gauss_1 One-dimensional Gaussian quadrature rule evaluation, thread-safe
d01wcc	5	nag_multid_quad_adapt_1 Multi-dimensional adaptive quadrature, thread-safe
d01xbc	5	nag_multid_quad_monte_carlo_1 Multi-dimensional quadrature, using Monte Carlo method, thread-safe

d02 – Ordinary Differential Equations

Routine Name	Mark of Introduction	Purpose
d02cjc	2	nag_ode_ivp_adams_gen Ordinary differential equation solver using a variable-order variable-step Adams method (Black Box)
d02ejc	3	nag_ode_ivp_bdf_gen Ordinary differential equations solver, stiff, initial value problems using the Backward Differentiation Formulae
d02gac	3	nag_ode_bvp_fd_nonlin_fixedbc Ordinary differential equations solver, for simple nonlinear two-point boundary value problems, using a finite difference technique with deferred correction
d02gbc	3	nag_ode_bvp_fd_lin_gen Ordinary differential equations solver, for general linear two-point boundary value problems, using a finite difference technique with deferred correction
d02pcc	3	nag_ode_ivp_rk_range Ordinary differential equations solver, initial value problems over a range using Runge–Kutta methods
d02pdc	3	nag_ode_ivp_rk_onestep Ordinary differential equations solver, initial value problems, one time step using Runge–Kutta methods
d02ppc	3	nag_ode_ivp_rk_free Freeing function for use with the Runge–Kutta suite (d02p functions)
d02pvc	3	nag_ode_ivp_rk_setup Setup function for use with d02pcc and/or d02pdc
d02pwc	3	nag_ode_ivp_rk_reset_tend A function to re-set the end point following a call to d02pdc
d02pxc	3	nag_ode_ivp_rk_interp Ordinary differential equations solver, computes the solution by interpolation anywhere on an integration step taken by d02pdc
d02pzc	3	nag_ode_ivp_rk_errass A function to provide global error assessment during an integration with either d02pcc or d02pdc
d02qfc	2	nag_ode_ivp_adams_roots Ordinary differential equation solver using Adams method (sophisticated use)
d02qwc	2	nag_ode_ivp_adams_setup Setup function for d02qfc
d02qyc	2	nag_ode_ivp_adams_free Freeing function for use with d02qfc
d02qzc	2	nag_ode_ivp_adams_interp Interpolation function for use with d02qfc
d02rac	3	nag_ode_bvp_fd_nonlin_gen Ordinary differential equations solver, for general nonlinear two-point boundary value problems, using a finite difference technique with deferred correction

d03 – Partial Differential Equations

Routine Name	Mark of Introduction	Purpose
d03ncc	7	nag_pde_bs_1d Finite difference solution of the Black–Scholes equations
d03ndc	7	nag_pde_bs_1d_analytic Analytic solution of the Black–Scholes equations
d03nec	7	nag_pde_bs_1d_means Compute average values for d03ndc
d03pcc	7	nag_pde_parab_1d_fd General system of parabolic PDEs, method of lines, finite differences, one space variable
d03pdc	7	nag_pde_parab_1d_coll General system of parabolic PDEs, method of lines, Chebyshev C⁰ collocation, one space variable
d03pec	7	nag_pde_parab_1d_keller General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
d03pfc	7	nag_pde_parab_1d_cd General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03phc	7	nag_pde_parab_1d_fd_ode General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
d03pjc	7	nag_pde_parab_1d_coll_ode General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C⁰ collocation, one space variable
d03pkc	7	nag_pde_parab_1d_keller_ode General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
d03plc	7	nag_pde_parab_1d_cd_ode General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03ppc	7	nag_pde_parab_1d_fd_ode_remesh General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
d03prc	7	nag_pde_parab_1d_keller_ode_remesh General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
d03psc	7	nag_pde_parab_1d_cd_ode_remesh General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, remeshing, one space variable
d03puc	7	nag_pde_parab_1d_euler_roe Roe's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pvc	7	nag_pde_parab_1d_euler_osher Osher's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pwc	7	nag_pde_parab_1d_euler_hll Modified HLL Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pxc	7	nag_pde_parab_1d_euler_exact Exact Riemann Solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pyc	7	nag_pde_interp_1d_coll PDEs, spatial interpolation with d03pdc or d03pjc
d03pzc	7	nag_pde_interp_1d_fd PDEs, spatial interpolation with d03pcc, d03pec, d03pfc, d03phc, d03pkc, d03plc,