Difference between revisions of "Glossary of EM.Cube's Python Functions"
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| Line 164: | Line 164: | ||
| Ci(x) | | Ci(x) | ||
| Cosine integral function | | Cosine integral function | ||
| − | | See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric | + | | See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.] |
|- | |- | ||
| Si(x) | | Si(x) | ||
| Sine integral function | | Sine integral function | ||
| − | | See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric | + | | See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.] |
|- | |- | ||
| C(x) | | C(x) | ||
| Cosine Fresnel integral function | | Cosine Fresnel integral function | ||
| − | | See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel | + | | See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.] |
|- | |- | ||
| S(x) | | S(x) | ||
| Sine Fresnel integral function | | Sine Fresnel integral function | ||
| − | | See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel | + | | See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.] |
| - | | - | ||
|- | |- | ||
| Ellip_E(x) | | Ellip_E(x) | ||
| Elliptic function of the first kind | | Elliptic function of the first kind | ||
| − | | See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic | + | | See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.] |
|- | |- | ||
| Ellip_K(x) | | Ellip_K(x) | ||
| Elliptic function of the second kind | | Elliptic function of the second kind | ||
| − | | See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic | + | | See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.] |
| - | | - | ||
|- | |- | ||
| Ei(x) | | Ei(x) | ||
| Exponential integral function | | Exponential integral function | ||
| − | | See [https://en.wikipedia.org/wiki/Exponential_integral Exponential | + | | See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.] |
|- | |- | ||
| En(n,x) | | En(n,x) | ||
| Generalized exponential integral function of order n | | Generalized exponential integral function of order n | ||
| − | | See [https://en.wikipedia.org/wiki/Exponential_integral Exponential | + | | See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.] |
|- | |- | ||
| gauss(x) | | gauss(x) | ||
| Line 210: | Line 210: | ||
| Airy_A(x) | | Airy_A(x) | ||
| Airy function of the first kind | | Airy function of the first kind | ||
| − | | See [https://en.wikipedia.org/wiki/Airy_function Airy | + | | See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.] |
|- | |- | ||
| Airy_B(x) | | Airy_B(x) | ||
| Airy function of the second kind | | Airy function of the second kind | ||
| − | | See [https://en.wikipedia.org/wiki/Airy_function Airy | + | | See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.] |
|- | |- | ||
| Jn(n,x) | | Jn(n,x) | ||
| Bessel function of the first kind and order n | | Bessel function of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| Yn(n,x) | | Yn(n,x) | ||
| Bessel function of the second kind and order n | | Bessel function of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| In(n,x) | | In(n,x) | ||
| Modified Bessel function of the first kind and order n | | Modified Bessel function of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| Kn(n,x) | | Kn(n,x) | ||
| Modified Bessel function of the second kind and order n | | Modified Bessel function of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| SB_jn(n,x) | | SB_jn(n,x) | ||
| Spherical Bessel function of the first kind and order n | | Spherical Bessel function of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| SB_yn(n,x) | | SB_yn(n,x) | ||
| Spherical Bessel function of the second kind and order n | | Spherical Bessel function of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| SB_in(n,x) | | SB_in(n,x) | ||
| Modified spherical Bessel function of the first kind and order n | | Modified spherical Bessel function of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| SB_kn(n,x) | | SB_kn(n,x) | ||
| Modified spherical Bessel function of the second kind and order n | | Modified spherical Bessel function of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel | + | | See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.] |
|- | |- | ||
| Pn(n,x) | | Pn(n,x) | ||
| Legendre function of the first kind and order n | | Legendre function of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre | + | | See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.] |
|- | |- | ||
| Qn(n,x) | | Qn(n,x) | ||
| Legendre function of the second kind and order n | | Legendre function of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre | + | | See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.] |
|- | |- | ||
| Tn(n,x) | | Tn(n,x) | ||
| Chebyshev polynomial of the first kind and order n | | Chebyshev polynomial of the first kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev | + | | See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.] |
|- | |- | ||
| Un(n,x) | | Un(n,x) | ||
| Chebyshev polynomial of the second kind and order n | | Chebyshev polynomial of the second kind and order n | ||
| − | | See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev | + | | See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.] |
|- | |- | ||
| LGn(n,x) | | LGn(n,x) | ||
| Line 278: | Line 278: | ||
| Math_ce(n,r,x) | | Math_ce(n,r,x) | ||
| Even periodic (cosine) Mathieu function of order n | | Even periodic (cosine) Mathieu function of order n | ||
| − | | See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu | + | | See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.] |
|- | |- | ||
| Math_se(n,r,x) | | Math_se(n,r,x) | ||
| Odd periodic (sine) Mathieu function of order n | | Odd periodic (sine) Mathieu function of order n | ||
| − | | See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu | + | | See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.] |
|- | |- | ||
| Rect(x) | | Rect(x) | ||
Revision as of 13:39, 29 August 2016
The table below gives a list of all the currently available library functions in EM.Cube:
| Function Name / Syntax | Description | Notes | |
| sign(x) | Sign function | 1 if x>0, -1 if x<0 | |
| fac(x) | Factorial | For integer values of x: n! = n(n-1)(n-2)...3.2.1 | |
| fac2(x) | Double factorial | For even integer values of x: n!! = n(n-2)(n-4)...4.2, for odd integer values of x: n!! = n(n-2)(n-4)...5.3 | |
| ceiling(x) | Ceiling function | Nearest integer >= x | |
| floor(x) | Floor function | Nearest integer <= x | |
| power(x,y) | Power function | x^y | |
| sqrt(x) | Square root function | x^(1/2) | |
| exp(x) | Exponential function | e^x | |
| log10(x) | Base 10 logarithm function | ln(x)/ln(10) | |
| db(x) | Decibel function | 10*log10(x) | |
| ln(x) | Natural logarithm function | - | |
| log(x,a) | Base a logarithm function | ln(x)/ln(a) | |
| rms(x) | Root mean square function | - | |
| abs(x) | Absolute value function | x if x>0, -x if x<0 | |
| sin(x) | Sine function | - | |
| cos(x) | Cosine function | - | |
| tan(x) | Tangent function | - | |
| sec(x) | Secant function | - | |
| csc(x) | Cosecant function | - | |
| cot(x) | Cotangent function | - | |
| asin(x) | Inverse sine function | - | |
| acos(x) | Inverse cosine function | - | |
| atan(x) | Inverse tangent function | - | |
| atan2(x,y) | Inverse tangent function | - | |
| asec(x) | Inverse secant function | - | |
| acsc(x) | Inverse cosecant function | - | |
| acot(x) | Inverse cotangent function | - | |
| sinh(x) | Hyperbolic sine function | - | |
| cosh(x) | Hyperbolic cosine function | - | |
| tanh(x) | Hyperbolic tangent function | - | |
| sech(x) | Hyperbolic secant function | - | |
| csch(x) | Hyperbolic cosecant function | - | |
| coth(x) | Hyperbolic cotangent function | - | |
| asinh(x) | Inverse hyperbolic sine function | - | |
| acosh(x) | Inverse hyperbolic cosine function | - | |
| atanh(x) | Inverse hyperbolic tangent function | - | |
| asech(x) | Inverse hyperbolic secant function | - | |
| acsch(x) | Inverse hyperbolic cosecant function | - | |
| acoth(x) | Inverse hyperbolic cotangent function | - | |
| Ci(x) | Cosine integral function | See Trigonometric Integrals on Wikipedia. | |
| Si(x) | Sine integral function | See Trigonometric Integrals on Wikipedia. | |
| C(x) | Cosine Fresnel integral function | See Fresnel Integrals on Wikipedia. | |
| S(x) | Sine Fresnel integral function | See Fresnel Integrals on Wikipedia. | - |
| Ellip_E(x) | Elliptic function of the first kind | See Elliptic Integrals on Wikipedia. | |
| Ellip_K(x) | Elliptic function of the second kind | See Elliptic Integrals on Wikipedia. | - |
| Ei(x) | Exponential integral function | See Exponential Integrals on Wikipedia. | |
| En(n,x) | Generalized exponential integral function of order n | See Exponential Integrals on Wikipedia. | |
| gauss(x) | Gaussian function | - | |
| erf(x) | Error function | See Error Function on Wikipedia. | |
| gamma(x) | Gamma function | See Gamma Function on Wikipedia. | |
| Airy_A(x) | Airy function of the first kind | See Airy Functions on Wikipedia. | |
| Airy_B(x) | Airy function of the second kind | See Airy Functions on Wikipedia. | |
| Jn(n,x) | Bessel function of the first kind and order n | See Bessel Functions on Wikipedia. | |
| Yn(n,x) | Bessel function of the second kind and order n | See Bessel Functions on Wikipedia. | |
| In(n,x) | Modified Bessel function of the first kind and order n | See Bessel Functions on Wikipedia. | |
| Kn(n,x) | Modified Bessel function of the second kind and order n | See Bessel Functions on Wikipedia. | |
| SB_jn(n,x) | Spherical Bessel function of the first kind and order n | See Bessel Functions on Wikipedia. | |
| SB_yn(n,x) | Spherical Bessel function of the second kind and order n | See Bessel Functions on Wikipedia. | |
| SB_in(n,x) | Modified spherical Bessel function of the first kind and order n | See Bessel Functions on Wikipedia. | |
| SB_kn(n,x) | Modified spherical Bessel function of the second kind and order n | See Bessel Functions on Wikipedia. | |
| Pn(n,x) | Legendre function of the first kind and order n | See Legendre Polynomials on Wikipedia. | |
| Qn(n,x) | Legendre function of the second kind and order n | See Legendre Polynomials on Wikipedia. | |
| Tn(n,x) | Chebyshev polynomial of the first kind and order n | See Chebyshev Polynomials on Wikipedia. | |
| Un(n,x) | Chebyshev polynomial of the second kind and order n | See Chebyshev Polynomials on Wikipedia. | |
| LGn(n,x) | Laguerre polynomial of order n | See Laguerre Polynomials on Wikipedia. | |
| Hn(n,x) | Hermite polynomial of order n | See Hermite Polynomials on Wikipedia. | |
| Un(n,x) | Hermite-Gauss function of order n | - | |
| Math_ce(n,r,x) | Even periodic (cosine) Mathieu function of order n | See Mathieu Functions on Wikipedia. | |
| Math_se(n,r,x) | Odd periodic (sine) Mathieu function of order n | See Mathieu Functions on Wikipedia. | |
| Rect(x) | Rectangle function | x|≤0.5, 0 elsewhere | |
| Tri(x) | Triangle function | 1-x|≤1, 0 elsewhere | |
| Spln2(x) | Quadratic spline function | - | |
| Spln3(x) | Cubic spline function | - | |
| Step(x) | Step function | 1 if x>0, 0 if x<0 | |
| Haar(x) | Haar function | x|<0.5, 0 elsewhere | |
| Ramp(x) | Ramp function | - | |
| Trapz(a,x) | Trapezoidal function | - | |
| Sqwv(x) | Square wave function | - | |
| Stwv(x) | Sawtooth wave function | - | |
| Trwv(x) | Triangle wave function | - | |
| Plstr(d,x) | Pulse train function with duty cycle d | - | |
| Sinc(d,x) | Sinc function | sin(pi*x)/(pi*x) | |
| Fejer(n,x) | Fejer function of order n | - | |
| Rand(x) | Random function | - | |
| Fltr_B(n,x) | Butterworth filter function of order n | - | |
| Fltr_CH1(n,e,x) | Chebyshev filter function of the first kind, order n | e: ripple factor e | |
| Fltr_CH2(n,e,x) | Chebyshev filter function of the second kind, order n | e: ripple factor e | |
| Fltr_E(n,s,e,x) | Elliptic filter function of order n | s: selectivity factor s, ripple factor e, n = 0, 1, 2, 3, 4, 6, 8, 9, 12 | |
| Z0_MS(e,x) | Characteristic impedance of a microstrip transmission line | x: width-to-height ratio, e: substrate permittivity | |
| w_MS(z,e,t) | Width of a microstrip transmission line | z: characteristic impedance, e: substrate permittivity, t: substrate thickness | |
| eeff_MS(e,x) | Effective permittivity of a microstrip transmission line | x: width-to-height ratio, e: substrate permittivity | |
| woh_MS(e,z) | Width-to-height ratio of a microstrip transmission line | z: characteristic impedance z, e: substrate permittivity | |
| Z0_CPW(e,x,y) | Characteristic impedance of a coplanar waveguide transmission line | x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity | |
| eeff_CPW(e,x,y) | Effective permittivity of a coplanar waveguide transmission line | x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity | |
| horn_a(d,x,y) | Wavelength-normalized a-dimension of an optimal pyramidal horn antenna | d: directivity d, x and y: wavelength-normalized waveguide dimensions | |
| horn_b(d,x,y) | Wavelength-normalized b-dimension of an optimal pyramidal horn antenna | d: directivity d, x and y: wavelength-normalized waveguide dimensions | |
| horn_l(d,x,y) | Wavelength-normalized length of an optimal pyramidal horn antenna | d: directivity d, x and y: wavelength-normalized waveguide dimensions |
