Interface NAG

Operations

xsd:double nag_complex_abs (nag:Complex z)
Modulus of a complex number z.

nag:Complex nag_complex_add (nag:Complex z1, nag:Complex z2)
Addition of two complex numbers z1 and z1.

xsd:double nag_complex_arg (nag:Complex z)
Argument of a complex number z.

nag:Complex nag_complex_c_power (nag:Complex z1, nag:Complex z2)
Complex number raised to complex power.

nag:Complex nag_complex_conjg (nag:Complex z)
Conjugate of a complex number z.

nag:Complex nag_complex_cos (nag:Complex z)
Complex cosine.

nag:Complex nag_complex_divide (nag:Complex z1, nag:Complex z2)
Quotient of two complex numbers z1 and z2.

xsd:boolean nag_complex_equal (nag:Complex z1, nag:Complex z2)
Equality of two complex numbers z1 and z2.

nag:Complex nag_complex_exp (nag:Complex z)
Complex exponential.

nag:Complex nag_complex_i_power (nag:Complex z, xsd:int i)
Complex number raised to integer power.

nag:Complex nag_complex_log (nag:Complex z)
Complex logarithm.

nag:Complex nag_complex_multiply (nag:Complex z1, nag:Complex z2)
Multiplication of two complex numbers z1 and z2.

nag:Complex nag_complex_negate (nag:Complex z)
Negation of a complex number z.

xsd:boolean nag_complex_not_equal (nag:Complex z1, nag:Complex z2)
Inequality of two complex numbers z1 and z2.

nag:Complex nag_complex_r_power (nag:Complex z, xsd:double r)
Complex number raised to real power.

nag:Complex nag_complex_sin (nag:Complex z)
Complex sine.

nag:Complex nag_complex_sqrt (nag:Complex z)
Square root of a complex number z.

nag:Complex nag_complex_subtract (nag:Complex z1, nag:Complex z2)
Subtraction of two complex numbers z1 and z2.

nag:Complex nag_complex_tan (nag:Complex z)
Complex tangent .

nag:ComplexArray nag_cubic_roots (xsd:double u, xsd:double r, xsd:double s, xsd:double t)
Zeros of a cubic polynomial with real coefficients.

nag:ComplexArray nag_quartic_roots (xsd:double e, xsd:double a, xsd:double b, xsd:double c, xsd:double d)
Zeros of a real quartic polynomial with real coefficients.

nag:ComplexArray nag_zeros_complex_poly (xsd:int n, nag:ComplexArray a, xsd:boolean scale)
Zeros of a polynomial with complex coefficients.

nag:ComplexArray nag_zeros_real_poly (xsd:int n, basic:DoubleArray a, xsd:boolean scale)
Zeros of a polynomial with real coefficients.

basic:DoubleArray nag_fft_real (xsd:int n, basic:DoubleArray x)
Single one-dimensional real discrete Fourier transform.

basic:DoubleArray nag_fft_hermitian (xsd:int n, basic:DoubleArray x)
Single one-dimensional Hermitian discrete Fourier transform.

nag:ComplexArray nag_fft_complex (xsd:int n, basic:DoubleArray x, basic:DoubleArray y)
Single one-dimensional complex discrete Fourier transform.

basic:DoubleArray nag_fft_multiple_real (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Multiple one-dimensional real discrete Fourier transforms.

basic:DoubleArray nag_fft_init_trig (xsd:int n, basic:DoubleArray trig)
Initialisation function for other c06 functions .

basic:DoubleArray nag_fft_multiple_hermitian (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Multiple one-dimensional Hermitian discrete Fourier transforms.

nag:ComplexArray nag_fft_multiple_complex (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray y, basic:DoubleArray trig)
Multiple one-dimensional complex discrete Fourier transforms.

nag:ComplexArray nag_fft_2D_complex (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray y, basic:DoubleArray trigm, basic:DoubleArray trign)
Two-dimensional complex discrete Fourier transform.

basic:DoubleArray nag_conjugate_hermitian (xsd:int n, basic:DoubleArray x)
Complex conjugate of Hermitian sequence.

basic:DoubleArray nag_conjugate_complex (xsd:int n, basic:DoubleArray y)
Complex conjugate of complex sequence.

basic:DoubleArray nag_multiple_conjugate_hermitian (xsd:int m, xsd:int n, basic:DoubleArray y)
Complex conjugate of multiple Hermitian sequences.

nag:ComplexArray nag_multiple_hermitian_to_complex (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray u, basic:DoubleArray v)
Convert Hermitian sequences to general complex sequences.

basic:DoubleArray nag_fft_multiple_sine (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Discrete sine transform.

basic:DoubleArray nag_fft_multiple_cosine (xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Discrete cosine transform.

nag:Nag_convolution_real_result nag_convolution_real (nag:Nag_VectorOpType op, xsd:int n, basic:DoubleArray x, basic:DoubleArray y)
Circular convolution or correlation of two real vectors.

basic:DoubleArray nag_fft_multiple_qtr_sine (nag:Nag_TransformDirectionType direct, xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Discrete quarter-wave sine transform.

basic:DoubleArray nag_fft_multiple_qtr_cosine (nag:Nag_TransformDirectionType direct, xsd:int m, xsd:int n, basic:DoubleArray x, basic:DoubleArray trig)
Discrete quarter-wave cosine transform.

nag:ComplexArray nag_fft_multid_single (nag:Nag_TransformDirectionType direct, xsd:int ndim, xsd:int l, basic:IntArray nd, xsd:int n, nag:ComplexArray x)
One-dimensional complex discrete Fourier transform of multi-dimensional data - using complex data type.

nag:ComplexArray nag_fft_multid_full (nag:Nag_TransformDirectionType direct, xsd:int ndim, basic:IntArray nd, xsd:int n, nag:ComplexArray x)
Multi-dimensional complex discrete Fourier transform of multi-dimensional data - using complex data type.

nag:ComplexArray nag_fft_3D (nag:Nag_TransformDirectionType direct, xsd:int n1, xsd:int n2, xsd:int n3, nag:ComplexArray x)
Three-dimensional complex discrete Fourier transform, complex data format.

xsd:double nag_bessel_y0 (xsd:double x)
Bessel function Y0 (x).

xsd:double nag_shifted_log (xsd:double x)
ln (1+x).

xsd:double nag_tanh (xsd:double x)
Hyperbolic tangent, tanh x.

xsd:double nag_sinh (xsd:double x)
Hyperbolic sine, sinh x.

xsd:double nag_cosh (xsd:double x)
Hyperbolic cosine, cosh x.

xsd:double nag_arctanh (xsd:double x)
Inverse hyperbolic tangent, arctanh x.

xsd:double nag_arcsinh (xsd:double x)
Inverse hyperbolic sine, arcsinh x.

xsd:double nag_arccosh (xsd:double x)
Inverse hyperbolic cosine, arccosh x.

xsd:double nag_exp_integral (xsd:double x)
Exponential integral E1 (x).

xsd:double nag_cos_integral (xsd:double x)
Cosine integral Ci(x).

xsd:double nag_sin_integral (xsd:double x)
Sine integral Si(x).

xsd:double nag_gamma (xsd:double x)
Gamma function Γ (x).

xsd:double nag_log_gamma (xsd:double x)
Log Gamma function ln(Γ(x)).

xsd:double nag_polygamma_fun (xsd:double x)
ψ (x) - ln x.

basic:DoubleArray nag_polygamma_deriv (xsd:double x, xsd:int n, xsd:int m)
Scaled derivatives of ψ (x).

xsd:double nag_real_polygamma (xsd:double x, xsd:int k)
Derivative of the psi function ψ (x).

nag:Complex nag_complex_polygamma (nag:Complex z, xsd:int k)
Derivative of the psi function ψ (z).

nag:Complex nag_complex_log_gamma (nag:Complex z)
Logarithm of the Gamma function ln Γ (z).

nag:Nag_incomplete_gamma_result nag_incomplete_gamma (xsd:double a, xsd:double x, xsd:double tol)
Incomplete Gamma functions P(a,x) and Q(a,x).

xsd:double nag_cumul_normal (xsd:double x)
Cumulative Normal distribution function P(x).

xsd:double nag_cumul_normal_complem (xsd:double x)
Complement of cumulative Normal distribution function Q(x).

xsd:double nag_erfc (xsd:double x)
Complement of error function erfc(x).

xsd:double nag_erf (xsd:double x)
Error function erf(x).

xsd:double nag_dawson (xsd:double x)
Dawson's integral.

nag:Complex nag_complex_erfc (nag:Complex z)
Scaled complex complement of error function, exp(-z2) erfc(-iz).

xsd:double nag_bessel_y1 (xsd:double x)
Bessel function Y1 (x).

xsd:double nag_bessel_j0 (xsd:double x)
Bessel function J0 (x).

xsd:double nag_bessel_j1 (xsd:double x)
Bessel function J1 (x).

xsd:double nag_airy_ai (xsd:double x)
Airy function Ai(x).

xsd:double nag_airy_bi (xsd:double x)
Airy function Bi(x).

xsd:double nag_airy_ai_deriv (xsd:double x)
Airy function Ai'(x).

xsd:double nag_airy_bi_deriv (xsd:double x)
Airy function Bi'(x).

basic:DoubleArray nag_bessel_zeros (xsd:double a, xsd:int n, xsd:int mode, xsd:double rel)
Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x).

nag:Nag_complex_bessel_y_result nag_complex_bessel_y (xsd:double fnu, nag:Complex z, xsd:int n, nag:Nag_ScaleResType scal)
Bessel functions Yν+a(z), real a >= 0, complex z, ν =0,1,2,... .

nag:Nag_complex_bessel_y_result nag_complex_bessel_j (xsd:double fnu, nag:Complex z, xsd:int n, nag:Nag_ScaleResType scal)
Bessel functions Jν+a(z), real a >= 0, complex z, ν =0,1,2,... .

nag:Nag_complex_airy_result nag_complex_airy_ai (nag:Nag_FunType deriv, nag:Complex z, nag:Nag_ScaleResType scal)
Airy functions Ai(z) and Ai'(z) , complex z.

nag:Complex nag_complex_airy_bi (nag:Nag_FunType deriv, nag:Complex z, nag:Nag_ScaleResType scal)
Airy functions Bi(z) and Bi'(z) , complex z.

nag:Nag_complex_bessel_y_result nag_complex_hankel (xsd:int m, xsd:double fnu, nag:Complex z, xsd:int n, nag:Nag_ScaleResType scal)
Hankel functions Hν+a(j)(z), j=1,2, real a >= 0, complex z, ν =0,1,2,... .

xsd:double nag_bessel_k0 (xsd:double x)
Modified Bessel function K0 (x).

xsd:double nag_bessel_k1 (xsd:double x)
Modified Bessel function K1 (x).

xsd:double nag_bessel_i0 (xsd:double x)
Modified Bessel function I0 (x).

xsd:double nag_bessel_i1 (xsd:double x)
Modified Bessel function I1 (x).

xsd:double nag_bessel_k0_scaled (xsd:double x)
Scaled modified Bessel function exK0(x).

xsd:double nag_bessel_k1_scaled (xsd:double x)
Scaled modified Bessel function exK1(x).

xsd:double nag_bessel_i0_scaled (xsd:double x)
Scaled modified Bessel function e-|x|I0(x).

xsd:double nag_bessel_i1_scaled (xsd:double x)
Scaled modified Bessel function e-|x|I1(x).

nag:Nag_complex_bessel_y_result nag_complex_bessel_k (xsd:double fnu, nag:Complex z, xsd:int n, nag:Nag_ScaleResType scal)
Modified Bessel functions Kν+a(z), real a >= 0, complex z, ν =0,1,2,... .

nag:Nag_complex_bessel_y_result nag_complex_bessel_i (xsd:double fnu, nag:Complex z, xsd:int n, nag:Nag_ScaleResType scal)
Modified Bessel functions Iν+a(z), real a >= 0, complex z, ν =0,1,2,... .

xsd:double nag_bessel_i_nu_scaled (xsd:double x, xsd:int nu)
Scaled modified Bessel function e-x Iν/4 (x).

xsd:double nag_bessel_k_nu_scaled (xsd:double x, xsd:int nu)
Scaled modified Bessel function ex Kν/4 (x).

xsd:double nag_bessel_i_nu (xsd:double x, xsd:int nu)
Modified Bessel function Iν/4 (x).

xsd:double nag_bessel_k_nu (xsd:double x, xsd:int nu)
Modified Bessel function Kν/4 (x).

basic:DoubleArray nag_bessel_k_alpha (xsd:double x, xsd:int ia, xsd:int ja, xsd:int nl)
Modified Bessel functions Kα+n (x) for real x > 0, selected values of α>=0 and n = 0,1,...,N .

basic:DoubleArray nag_bessel_k_alpha_scaled (xsd:double x, xsd:int ia, xsd:int ja, xsd:int nl)
Scaled modified Bessel functions Kα+n (x) for real x > 0, selected values of α>=0 and n = 0,1,...,N .

nag:Complex nag_bessel_i_alpha (xsd:double x, xsd:double a, xsd:int nl)
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 .

nag:ComplexArray nag_bessel_j_alpha (xsd:double x, xsd:double a, xsd:int nl)
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 .

nag:ComplexArray nag_complex_bessel_j_seq (nag:Complex z, xsd:double a, xsd:int nl)
Bessel function of the 1st kind Jα ± n(z).

xsd:double nag_kelvin_ber (xsd:double x)
Kelvin function ber x.

xsd:double nag_kelvin_bei (xsd:double x)
Kelvin function bei x.

xsd:double nag_kelvin_ker (xsd:double x)
Kelvin function ker x.

xsd:double nag_kelvin_kei (xsd:double x)
Kelvin function kei x.

xsd:double nag_fresnel_s (xsd:double x)
Fresnel integral S(x).

xsd:double nag_fresnel_c (xsd:double x)
Fresnel integral C(x).

xsd:double nag_elliptic_integral_rc (xsd:double x, xsd:double y)
Degenerate symmetrised elliptic integral of 1st kind RC(x,y).

xsd:double nag_elliptic_integral_rf (xsd:double x, xsd:double y, xsd:double z)
Symmetrised elliptic integral of 1st kind RF(x,y,z).

xsd:double nag_elliptic_integral_rd (xsd:double x, xsd:double y, xsd:double z)
Symmetrised elliptic integral of 2nd kind RD(x,y,z).

xsd:double nag_elliptic_integral_rj (xsd:double x, xsd:double y, xsd:double z, xsd:double r)
Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r).

nag:Nag_real_jacobian_elliptic_result nag_real_jacobian_elliptic (xsd:double u, xsd:double m)
Jacobian elliptic functions sn, cn and dn of real argument.

nag:Nag_jacobian_elliptic_result nag_jacobian_elliptic (nag:Complex z, xsd:double ak2)
Jacobian elliptic functions sn, cn and dn of complex argument.

xsd:double nag_jacobian_theta (xsd:int k, xsd:double x, xsd:double q)
Jacobian theta functions with real arguments.

nag:Complex nag_elliptic_integral_f (nag:Complex z, xsd:double akp, xsd:double a, xsd:double b)
Elliptic integrals of the second kind with complex arguments.

basic:DoubleArray nag_legendre_p (xsd:int mode, xsd:double x, xsd:int m, xsd:int nl)
Legendre and associated Legendre functions of the first kind with real arguments.

nag:ComplexArray nag_complex_lin_eqn_mult_rhs (xsd:int n, xsd:int nrhs, nag:ComplexArray a, xsd:int tda, nag:ComplexArray b, xsd:int tdb, xsd:int tdx)
Approximate solution of complex simultaneous linear equations with multiple right-hand sides.

basic:DoubleArray nag_real_cholesky_solve_mult_rhs (xsd:int n, xsd:int nrhs, basic:DoubleArray a, xsd:int tda, basic:DoubleArray p, basic:DoubleArray b, xsd:int tdb, xsd:int tdx)
Approximate solution of real symmetric positive-definite simultaneous linear equations - coefficient matrix already factorized by f03aec.

basic:DoubleArray nag_real_lin_eqn (xsd:int n, basic:DoubleArray a, xsd:int tda, basic:DoubleArray b)
Approximate solution of real simultaneous linear equations, one right-hand side.

basic:DoubleArray nag_zero_cont_func_bd (xsd:double a, xsd:double b, xsd:string code, xsd:string f, xsd:double xtol, xsd:double ftol)
Zero of a continuous function of one variable.

basic:DoubleArray nag_zero_nonlin_eqns (xsd:int n, basic:DoubleArray x, xsd:string code, xsd:string f, xsd:double xtol)
Solution of a system of nonlinear equations - function values only.

nag:Complex nag_1D_quad_gen (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
A general purpose integrator which calculates an approximation to the integral of a function f(x) over a finite interval [a;b] .

nag:Complex nag_1D_quad_osc (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature, suitable for oscillating functions.

nag:Complex nag_1D_quad_brkpts (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:int nbrkpts, basic:DoubleArray brkpts, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature, allowing for singularities at specified points.

nag:Complex nag_1D_quad_inf (xsd:string code, xsd:string f, nag:Nag_BoundIntervalType bounds, xsd:double bound, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature over infinite or semi-infinite interval.

nag:Complex nag_1D_quad_wt_trig (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double omega, nag:Nag_TrigTransformType wt_func, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions.

nag:Complex nag_1D_quad_wt_alglog (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double alfa, xsd:double beta, nag:Nag_QuadWeightType wt_func, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type.

nag:Complex nag_1D_quad_wt_cauchy (xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:double c, xsd:double epsabs, xsd:double epsrel, xsd:int max_num_subint)
One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value.

nag:Complex nag_1D_quad_inf_wt_trig (xsd:string code, xsd:string f, xsd:double a, xsd:double omega, nag:Nag_TrigTransformType wt_func, xsd:int maxintervals, xsd:int maxsubints_per_interval, xsd:double epsabs)
One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function.

xsd:double nag_1D_quad_gauss (nag:Nag_GaussFormulaeType quadrule, xsd:string code, xsd:string f, xsd:double a, xsd:double b, xsd:int npts)
One-dimensional Gaussian quadrature rule evaluation.

nag:Nag_multid_quad_result nag_multid_quad_adapt (xsd:int ndim, xsd:string code, xsd:string f, basic:DoubleArray a, basic:DoubleArray b, basic:IntArray minpts, xsd:int maxpts, xsd:double eps)
Multi-dimensional adaptive quadrature.

nag:Complex nag_1D_quad_vals (xsd:int n, basic:DoubleArray x, basic:DoubleArray y)
One-dimensional integration of a function defined by data values only.

nag:Nag_dgetrf_result nag_dgetrf (nag:Nag_OrderType order, xsd:int m, xsd:int n, basic:DoubleArray a, xsd:int pda)
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.

Interface NAG

XML Namespace

XSD Data Types

Operations