The request message for the operation nag_complex_abs(). The response message for the operation nag_complex_abs(). The request message for the operation nag_complex_add(). The response message for the operation nag_complex_add(). The request message for the operation nag_complex_arg(). The response message for the operation nag_complex_arg(). The request message for the operation nag_complex_c_power(). The response message for the operation nag_complex_c_power(). The request message for the operation nag_complex_conjg(). The response message for the operation nag_complex_conjg(). The request message for the operation nag_complex_cos(). The response message for the operation nag_complex_cos(). The request message for the operation nag_complex_divide(). The response message for the operation nag_complex_divide(). The request message for the operation nag_complex_equal(). The response message for the operation nag_complex_equal(). The request message for the operation nag_complex_exp(). The response message for the operation nag_complex_exp(). The request message for the operation nag_complex_i_power(). The response message for the operation nag_complex_i_power(). The request message for the operation nag_complex_log(). The response message for the operation nag_complex_log(). The request message for the operation nag_complex_multiply(). The response message for the operation nag_complex_multiply(). The request message for the operation nag_complex_negate(). The response message for the operation nag_complex_negate(). The request message for the operation nag_complex_not_equal(). The response message for the operation nag_complex_not_equal(). The request message for the operation nag_complex_r_power(). The response message for the operation nag_complex_r_power(). The request message for the operation nag_complex_sin(). The response message for the operation nag_complex_sin(). The request message for the operation nag_complex_sqrt(). The response message for the operation nag_complex_sqrt(). The request message for the operation nag_complex_subtract(). The response message for the operation nag_complex_subtract(). The request message for the operation nag_complex_tan(). The response message for the operation nag_complex_tan(). The request message for the operation nag_cubic_roots(). The response message for the operation nag_cubic_roots(). The request message for the operation nag_quartic_roots(). The response message for the operation nag_quartic_roots(). The request message for the operation nag_zeros_complex_poly(). The response message for the operation nag_zeros_complex_poly(). The request message for the operation nag_zeros_real_poly(). The response message for the operation nag_zeros_real_poly(). The request message for the operation nag_fft_real(). The response message for the operation nag_fft_real(). The request message for the operation nag_fft_hermitian(). The response message for the operation nag_fft_hermitian(). The request message for the operation nag_fft_complex(). The response message for the operation nag_fft_complex(). The request message for the operation nag_fft_multiple_real(). The response message for the operation nag_fft_multiple_real(). The request message for the operation nag_fft_init_trig(). The response message for the operation nag_fft_init_trig(). The request message for the operation nag_fft_multiple_hermitian(). The response message for the operation nag_fft_multiple_hermitian(). The request message for the operation nag_fft_multiple_complex(). The response message for the operation nag_fft_multiple_complex(). The request message for the operation nag_fft_2D_complex(). The response message for the operation nag_fft_2D_complex(). The request message for the operation nag_conjugate_hermitian(). The response message for the operation nag_conjugate_hermitian(). The request message for the operation nag_conjugate_complex(). The response message for the operation nag_conjugate_complex(). The request message for the operation nag_multiple_conjugate_hermitian(). The response message for the operation nag_multiple_conjugate_hermitian(). The request message for the operation nag_multiple_hermitian_to_complex(). The response message for the operation nag_multiple_hermitian_to_complex(). The request message for the operation nag_fft_multiple_sine(). The response message for the operation nag_fft_multiple_sine(). The request message for the operation nag_fft_multiple_cosine(). The response message for the operation nag_fft_multiple_cosine(). The request message for the operation nag_convolution_real(). The response message for the operation nag_convolution_real(). The request message for the operation nag_fft_multiple_qtr_sine(). The response message for the operation nag_fft_multiple_qtr_sine(). The request message for the operation nag_fft_multiple_qtr_cosine(). The response message for the operation nag_fft_multiple_qtr_cosine(). The request message for the operation nag_fft_multid_single(). The response message for the operation nag_fft_multid_single(). The request message for the operation nag_fft_multid_full(). The response message for the operation nag_fft_multid_full(). The request message for the operation nag_fft_3D(). The response message for the operation nag_fft_3D(). The request message for the operation nag_bessel_y0(). The response message for the operation nag_bessel_y0(). The request message for the operation nag_shifted_log(). The response message for the operation nag_shifted_log(). The request message for the operation nag_tanh(). The response message for the operation nag_tanh(). The request message for the operation nag_sinh(). The response message for the operation nag_sinh(). The request message for the operation nag_cosh(). The response message for the operation nag_cosh(). The request message for the operation nag_arctanh(). The response message for the operation nag_arctanh(). The request message for the operation nag_arcsinh(). The response message for the operation nag_arcsinh(). The request message for the operation nag_arccosh(). The response message for the operation nag_arccosh(). The request message for the operation nag_exp_integral(). The response message for the operation nag_exp_integral(). The request message for the operation nag_cos_integral(). The response message for the operation nag_cos_integral(). The request message for the operation nag_sin_integral(). The response message for the operation nag_sin_integral(). The request message for the operation nag_gamma(). The response message for the operation nag_gamma(). The request message for the operation nag_log_gamma(). The response message for the operation nag_log_gamma(). The request message for the operation nag_polygamma_fun(). The response message for the operation nag_polygamma_fun(). The request message for the operation nag_polygamma_deriv(). The response message for the operation nag_polygamma_deriv(). The request message for the operation nag_real_polygamma(). The response message for the operation nag_real_polygamma(). The request message for the operation nag_complex_polygamma(). The response message for the operation nag_complex_polygamma(). The request message for the operation nag_complex_log_gamma(). The response message for the operation nag_complex_log_gamma(). The request message for the operation nag_incomplete_gamma(). The response message for the operation nag_incomplete_gamma(). The request message for the operation nag_cumul_normal(). The response message for the operation nag_cumul_normal(). The request message for the operation nag_cumul_normal_complem(). The response message for the operation nag_cumul_normal_complem(). The request message for the operation nag_erfc(). The response message for the operation nag_erfc(). The request message for the operation nag_erf(). The response message for the operation nag_erf(). The request message for the operation nag_dawson(). The response message for the operation nag_dawson(). The request message for the operation nag_complex_erfc(). The response message for the operation nag_complex_erfc(). The request message for the operation nag_bessel_y1(). The response message for the operation nag_bessel_y1(). The request message for the operation nag_bessel_j0(). The response message for the operation nag_bessel_j0(). The request message for the operation nag_bessel_j1(). The response message for the operation nag_bessel_j1(). The request message for the operation nag_airy_ai(). The response message for the operation nag_airy_ai(). The request message for the operation nag_airy_bi(). The response message for the operation nag_airy_bi(). The request message for the operation nag_airy_ai_deriv(). The response message for the operation nag_airy_ai_deriv(). The request message for the operation nag_airy_bi_deriv(). The response message for the operation nag_airy_bi_deriv(). The request message for the operation nag_bessel_zeros(). The response message for the operation nag_bessel_zeros(). The request message for the operation nag_complex_bessel_y(). The response message for the operation nag_complex_bessel_y(). The request message for the operation nag_complex_bessel_j(). The response message for the operation nag_complex_bessel_j(). The request message for the operation nag_complex_airy_ai(). The response message for the operation nag_complex_airy_ai(). The request message for the operation nag_complex_airy_bi(). The response message for the operation nag_complex_airy_bi(). The request message for the operation nag_complex_hankel(). The response message for the operation nag_complex_hankel(). The request message for the operation nag_bessel_k0(). The response message for the operation nag_bessel_k0(). The request message for the operation nag_bessel_k1(). The response message for the operation nag_bessel_k1(). The request message for the operation nag_bessel_i0(). The response message for the operation nag_bessel_i0(). The request message for the operation nag_bessel_i1(). The response message for the operation nag_bessel_i1(). The request message for the operation nag_bessel_k0_scaled(). The response message for the operation nag_bessel_k0_scaled(). The request message for the operation nag_bessel_k1_scaled(). The response message for the operation nag_bessel_k1_scaled(). The request message for the operation nag_bessel_i0_scaled(). The response message for the operation nag_bessel_i0_scaled(). The request message for the operation nag_bessel_i1_scaled(). The response message for the operation nag_bessel_i1_scaled(). The request message for the operation nag_complex_bessel_k(). The response message for the operation nag_complex_bessel_k(). The request message for the operation nag_complex_bessel_i(). The response message for the operation nag_complex_bessel_i(). The request message for the operation nag_bessel_i_nu_scaled(). The response message for the operation nag_bessel_i_nu_scaled(). The request message for the operation nag_bessel_k_nu_scaled(). The response message for the operation nag_bessel_k_nu_scaled(). The request message for the operation nag_bessel_i_nu(). The response message for the operation nag_bessel_i_nu(). The request message for the operation nag_bessel_k_nu(). The response message for the operation nag_bessel_k_nu(). The request message for the operation nag_bessel_k_alpha(). The response message for the operation nag_bessel_k_alpha(). The request message for the operation nag_bessel_k_alpha_scaled(). The response message for the operation nag_bessel_k_alpha_scaled(). The request message for the operation nag_bessel_i_alpha(). The response message for the operation nag_bessel_i_alpha(). The request message for the operation nag_bessel_j_alpha(). The response message for the operation nag_bessel_j_alpha(). The request message for the operation nag_complex_bessel_j_seq(). The response message for the operation nag_complex_bessel_j_seq(). The request message for the operation nag_kelvin_ber(). The response message for the operation nag_kelvin_ber(). The request message for the operation nag_kelvin_bei(). The response message for the operation nag_kelvin_bei(). The request message for the operation nag_kelvin_ker(). The response message for the operation nag_kelvin_ker(). The request message for the operation nag_kelvin_kei(). The response message for the operation nag_kelvin_kei(). The request message for the operation nag_fresnel_s(). The response message for the operation nag_fresnel_s(). The request message for the operation nag_fresnel_c(). The response message for the operation nag_fresnel_c(). The request message for the operation nag_elliptic_integral_rc(). The response message for the operation nag_elliptic_integral_rc(). The request message for the operation nag_elliptic_integral_rf(). The response message for the operation nag_elliptic_integral_rf(). The request message for the operation nag_elliptic_integral_rd(). The response message for the operation nag_elliptic_integral_rd(). The request message for the operation nag_elliptic_integral_rj(). The response message for the operation nag_elliptic_integral_rj(). The request message for the operation nag_real_jacobian_elliptic(). The response message for the operation nag_real_jacobian_elliptic(). The request message for the operation nag_jacobian_elliptic(). The response message for the operation nag_jacobian_elliptic(). The request message for the operation nag_jacobian_theta(). The response message for the operation nag_jacobian_theta(). The request message for the operation nag_elliptic_integral_f(). The response message for the operation nag_elliptic_integral_f(). The request message for the operation nag_legendre_p(). The response message for the operation nag_legendre_p(). The request message for the operation nag_complex_lin_eqn_mult_rhs(). The response message for the operation nag_complex_lin_eqn_mult_rhs(). The request message for the operation nag_real_cholesky_solve_mult_rhs(). The response message for the operation nag_real_cholesky_solve_mult_rhs(). The request message for the operation nag_real_lin_eqn(). The response message for the operation nag_real_lin_eqn(). The request message for the operation nag_zero_cont_func_bd(). The response message for the operation nag_zero_cont_func_bd(). The request message for the operation nag_zero_nonlin_eqns(). The response message for the operation nag_zero_nonlin_eqns(). The request message for the operation nag_1D_quad_gen(). The response message for the operation nag_1D_quad_gen(). The request message for the operation nag_1D_quad_osc(). The response message for the operation nag_1D_quad_osc(). The request message for the operation nag_1D_quad_brkpts(). The response message for the operation nag_1D_quad_brkpts(). The request message for the operation nag_1D_quad_inf(). The response message for the operation nag_1D_quad_inf(). The request message for the operation nag_1D_quad_wt_trig(). The response message for the operation nag_1D_quad_wt_trig(). The request message for the operation nag_1D_quad_wt_alglog(). The response message for the operation nag_1D_quad_wt_alglog(). The request message for the operation nag_1D_quad_wt_cauchy(). The response message for the operation nag_1D_quad_wt_cauchy(). The request message for the operation nag_1D_quad_inf_wt_trig(). The response message for the operation nag_1D_quad_inf_wt_trig(). The request message for the operation nag_1D_quad_gauss(). The response message for the operation nag_1D_quad_gauss(). The request message for the operation nag_multid_quad_adapt(). The response message for the operation nag_multid_quad_adapt(). The request message for the operation nag_1D_quad_vals(). The response message for the operation nag_1D_quad_vals(). The request message for the operation nag_dgetrf(). The response message for the operation nag_dgetrf(). Modulus of a complex number z. Addition of two complex numbers z1 and z1. Argument of a complex number z. Complex number raised to complex power. Conjugate of a complex number z. Complex cosine. Quotient of two complex numbers z1 and z2. Equality of two complex numbers z1 and z2. Complex exponential. Complex number raised to integer power. Complex logarithm. Multiplication of two complex numbers z1 and z2. Negation of a complex number z. Inequality of two complex numbers z1 and z2. Complex number raised to real power. Complex sine. Square root of a complex number z. Subtraction of two complex numbers z1 and z2. Complex tangent . Zeros of a cubic polynomial with real coefficients. Zeros of a real quartic polynomial with real coefficients. Zeros of a polynomial with complex coefficients. Zeros of a polynomial with real coefficients. Single one-dimensional real discrete Fourier transform. Single one-dimensional Hermitian discrete Fourier transform. Single one-dimensional complex discrete Fourier transform. Multiple one-dimensional real discrete Fourier transforms. Initialisation function for other c06 functions . Multiple one-dimensional Hermitian discrete Fourier transforms. Multiple one-dimensional complex discrete Fourier transforms. Two-dimensional complex discrete Fourier transform. Complex conjugate of Hermitian sequence. Complex conjugate of complex sequence. Complex conjugate of multiple Hermitian sequences. Convert Hermitian sequences to general complex sequences. Discrete sine transform. Discrete cosine transform. Circular convolution or correlation of two real vectors. Discrete quarter-wave sine transform. Discrete quarter-wave cosine transform. One-dimensional complex discrete Fourier transform of multi-dimensional data - using complex data type. Multi-dimensional complex discrete Fourier transform of multi-dimensional data - using complex data type. Three-dimensional complex discrete Fourier transform, complex data format. Bessel function Y0 (x). ln (1+x). Hyperbolic tangent, tanh x. Hyperbolic sine, sinh x. Hyperbolic cosine, cosh x. Inverse hyperbolic tangent, arctanh x. Inverse hyperbolic sine, arcsinh x. Inverse hyperbolic cosine, arccosh x. Exponential integral E1 (x). Cosine integral Ci(x). Sine integral Si(x). Gamma function Γ (x). Log Gamma function ln(Γ(x)). ψ (x) - ln x. Scaled derivatives of ψ (x). Derivative of the psi function ψ (x). Derivative of the psi function ψ (z). Logarithm of the Gamma function ln Γ (z). Incomplete Gamma functions P(a,x) and Q(a,x). Cumulative Normal distribution function P(x). Complement of cumulative Normal distribution function Q(x). Complement of error function erfc(x). Error function erf(x). Dawson's integral. Scaled complex complement of error function, exp(-z2) erfc(-iz). Bessel function Y1 (x). Bessel function J0 (x). Bessel function J1 (x). Airy function Ai(x). Airy function Bi(x). Airy function Ai'(x). Airy function Bi'(x). Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x). Bessel functions Yν+a(z), real a >= 0, complex z, ν =0,1,2,... . Bessel functions Jν+a(z), real a >= 0, complex z, ν =0,1,2,... . Airy functions Ai(z) and Ai'(z) , complex z. Airy functions Bi(z) and Bi'(z) , complex z. Hankel functions Hν+a(j)(z), j=1,2, real a >= 0, complex z, ν =0,1,2,... . Modified Bessel function K0 (x). Modified Bessel function K1 (x). Modified Bessel function I0 (x). Modified Bessel function I1 (x). Scaled modified Bessel function exK0(x). Scaled modified Bessel function exK1(x). Scaled modified Bessel function e-|x|I0(x). Scaled modified Bessel function e-|x|I1(x). Modified Bessel functions Kν+a(z), real a >= 0, complex z, ν =0,1,2,... . Modified Bessel functions Iν+a(z), real a >= 0, complex z, ν =0,1,2,... . Scaled modified Bessel function e-x Iν/4 (x). Scaled modified Bessel function ex Kν/4 (x). Modified Bessel function Iν/4 (x). Modified Bessel function Kν/4 (x). Modified Bessel functions Kα+n (x) for real x > 0, selected values of α>=0 and n = 0,1,...,N . Scaled modified Bessel functions Kα+n (x) for real x > 0, selected values of α>=0 and n = 0,1,...,N . Modified Bessel functions Iα +n-1 (x) or Iα -n+1 (x) for real x ≠ 0, non-negative α < 1 and n = 1,2,...,|N|+1 . Modified Bessel functions Jα +n-1 (x) or Jα -n+1 (x) for real x ≠ 0, non-negative α < 1 and n = 1,2,...,|N|+1 . Bessel function of the 1st kind Jα ± n(z). Kelvin function ber x. Kelvin function bei x. Kelvin function ker x. Kelvin function kei x. Fresnel integral S(x). Fresnel integral C(x). Degenerate symmetrised elliptic integral of 1st kind RC(x,y). Symmetrised elliptic integral of 1st kind RF(x,y,z). Symmetrised elliptic integral of 2nd kind RD(x,y,z). Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r). Jacobian elliptic functions sn, cn and dn of real argument. Jacobian elliptic functions sn, cn and dn of complex argument. Jacobian theta functions with real arguments. Elliptic integrals of the second kind with complex arguments. Legendre and associated Legendre functions of the first kind with real arguments. Approximate solution of complex simultaneous linear equations with multiple right-hand sides. Approximate solution of real symmetric positive-definite simultaneous linear equations - coefficient matrix already factorized by f03aec. Approximate solution of real simultaneous linear equations, one right-hand side. Zero of a continuous function of one variable. Solution of a system of nonlinear equations - function values only. A general purpose integrator which calculates an approximation to the integral of a function f(x) over a finite interval [a;b] . One-dimensional adaptive quadrature, suitable for oscillating functions. One-dimensional adaptive quadrature, allowing for singularities at specified points. One-dimensional adaptive quadrature over infinite or semi-infinite interval. One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions. One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type. One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value. One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function. One-dimensional Gaussian quadrature rule evaluation. Multi-dimensional adaptive quadrature. One-dimensional integration of a function defined by data values only. Multi-dimensional quadrature, using Monte Carlo method. operation nag:Nag_multid_quad_result nag_multid_quad_monte_carlo(xsd:int ndim, xsd:string code, xsd:string f, //nag:Nag_MCMethodType method, nag:Nag_StartType cont, basic:DoubleArray a, basic:DoubleArray b, basic:IntArray mincls, xsd:int //maxcls, xsd:double eps); One-dimensional adaptive quadrature, allowing for badly behaved integrands, thread-safe. operation nag:Complex nag_1D_quad_gen_1(xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double epsabs, xsd:double //epsrel, xsd:int max_num_subint); LU factorization of real m by n matrix.