Module russell_lab::math

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This module implements mathematical (specialized) functions and constants

Constants§

Functions§

  • bessel_i0
    Evaluates the modified Bessel function I0(x) for any real x
  • bessel_i1
    Evaluates the modified Bessel function I1(x) for any real x
  • bessel_in
    Evaluates the modified Bessel function In(x) for any real x and n ≥ 0
  • bessel_j0
    Evaluates the Bessel function J0(x) for any real x
  • bessel_j1
    Evaluates the Bessel function J1(x) for any real x
  • bessel_jn
    Evaluates the Bessel function Jn(x) for any real x
  • bessel_k0
    Evaluates the modified Bessel function K0(x) for positive real x
  • bessel_k1
    Evaluates the modified Bessel function K1(x) for positive real x
  • bessel_kn
    Evaluates the modified Bessel function Kn(x) for positive x and n ≥ 0
  • bessel_y0
    Evaluates the Bessel function Y0(x) for positive real x
  • bessel_y1
    Evaluates the Bessel function Y1(x) for positive real x
  • bessel_yn
    Evaluates the Bessel function Yn(x) for positive real x
  • beta
    Evaluates the Euler beta function B(a, b)
  • boxcar
    Evaluates the boxcar function
  • chebyshev_gauss_points
    Computes Chebyshev-Gauss points
  • chebyshev_lobatto_points
    Computes Chebyshev-Gauss-Lobatto points
  • chebyshev_tn
    Evaluates the Chebyshev polynomial of first kind Tn(x) using the trigonometric functions
  • chebyshev_tn_deriv1
    Computes the first derivative of the Chebyshev T(n, x) function
  • chebyshev_tn_deriv2
    Computes the second derivative of the Chebyshev Tn(x) function
  • elliptic_e
    Computes the elliptic integral of the second kind E(φ, m)
  • elliptic_f
    Computes the elliptic integral of the first kind F(φ, m)
  • elliptic_pi
    Computes the elliptic integral of the third kind Π(n, φ, m)
  • erf
    Evaluates the error function
  • erf_inv
    Evaluates the inverse error function of x
  • erfc
    Evaluates the complementary error function
  • erfc_inv
    Evaluates the inverse of the complementary error function
  • factorial_lookup_22
    Returns the factorial of n smaller than or equal to 22 by table lookup
  • float_compose
    (ldexp) Composes a floating-point number from a mantissa and exponent
  • float_decompose
    (frexp) Decomposes a floating-point number into a mantissa and exponent parts
  • float_is_integer
    Reports if a floating-point number corresponds to an integer
  • float_is_neg_integer
    Reports if a floating-point number corresponds to a negative integer
  • float_split
    (modf) Splits a floating-point number into an integer and a fractional part
  • gamma
    Evaluates the Gamma function Γ(x)
  • heaviside
    Evaluates the Heaviside step function (derivative of ramp(x))
  • i_pow_n
    Calculates the imaginary unit (i) raised to power of n
  • ln_beta
    Evaluates the natural logarithm of the Beta function B(a, b)
  • ln_gamma
    Evaluates the natural logarithm and sign of Γ(x)
  • logistic
    Evaluates the standard logistic (sigmoid) function
  • logistic_deriv1
    Returns the first derivative of the standard logistic function
  • modulo
    (fmod) Returns the floating-point remainder of x/y
  • neg_one_pow_n
    Calculates negative one raised to the power of n
  • ramp
    Evaluates the ramp function (Macaulay brackets)
  • sign
    Evaluates the sign function
  • smooth_ramp
    Evaluates the smooth ramp function
  • smooth_ramp_deriv1
    Returns the first derivative of smooth_ramp
  • smooth_ramp_deriv2
    Returns the second derivative of smooth_ramp
  • suq_cos
    Evaluates the superquadric function involving cos(x)
  • suq_sin
    Evaluates the superquadric function involving sin(x)
  • x_times_i_pow_n
    Calculates a real number x times the imaginary unit (i) raised to the power of n