osc::analytic Namespace Reference

Classes
class	_OscCalc
struct	cmplx
	std::complex takes a lot of care with inf/nan which we don't want More...
struct	Eigenvalues
struct	Hermitian
class	ProbCache
class	Probs

Functions
template<class T , class U >
cmplx< T, U >	make_cmplx (const T &re, const U &im)
template<class A , class B , class C , class D >
	__attribute__ ((always_inline)) auto operator*(const cmplx<A
template<class A , class B , class C >
	__attribute__ ((always_inline)) auto operator*(const A &x
template<class T , class U >
	__attribute__ ((always_inline)) auto operator/(const cmplx< T > &x
template<class T >
	__attribute__ ((always_inline)) cmplx< T > operator-(const cmplx< T > &x)
template<class T >
T	sqr (T x)
template<class T >
T	cube (T x)
template<class T >
std::array< T, 3 >	SolveCubic (T b, T c, T d)
	Solve x^3 + b*x^2 + c*x + d = 0. More...

Variables
B &	x
B const cmplx< C, D > &	y
const double	sqrt3 = sqrt(3)

Function Documentation

template<class A , class B , class C , class D >

osc::analytic::__attribute__ ( (always_inline)  ) const

inline

Referenced by make_cmplx().

template<class A , class B , class C >

osc::analytic::__attribute__ ( (always_inline)  ) const

inline

template<class T , class U >

osc::analytic::__attribute__ ( (always_inline)  ) const

inline

template<class T >

osc::analytic::__attribute__ ( (always_inline)  ) const

inline

Definition at line 93 of file OscCalcAnalytic.cxx.

References make_cmplx().

  {
    return make_cmplx(-x.re, -x.im);
  }

template<class T >

T osc::analytic::cube

(

T

x

)

Definition at line 212 of file OscCalcAnalytic.cxx.

References x.

Referenced by SolveCubic().

{return x*x*x;}

template<class T , class U >

cmplx<T, U> osc::analytic::make_cmplx	(	const T &	re,
		const U &	im
	)

Definition at line 31 of file OscCalcAnalytic.cxx.

References __attribute__().

Referenced by __attribute__().

{return cmplx<T, U>(re, im);}

template<class T >

std::array<T, 3> osc::analytic::SolveCubic	(	T	b,
		T	c,
		T	d
	)

Solve x^3 + b*x^2 + c*x + d = 0.

Definition at line 218 of file OscCalcAnalytic.cxx.

References osc::analytic::_OscCalc< T >::_P(), std::acos(), b, plot_validation_datamc::c, osc::analytic::_OscCalc< T >::c12, osc::analytic::_OscCalc< T >::c13, osc::analytic::_OscCalc< T >::c23, osc::analytic::_OscCalc< T >::cCP, osc::analytic::_OscCalc< T >::ClearProbCaches(), osc::analytic::cmplx< T, U >::conj(), cube(), d, osc::_IOscCalcAdjustable< T >::fDmsq21, osc::_IOscCalcAdjustable< T >::fDmsq32, osc::analytic::_OscCalc< T >::Hee, osc::analytic::_OscCalc< T >::Hem, osc::analytic::_OscCalc< T >::Het, osc::analytic::_OscCalc< T >::Hmm, osc::analytic::_OscCalc< T >::Hmt, osc::analytic::_OscCalc< T >::Htt, P, r(), osc::analytic::_OscCalc< T >::s12, osc::analytic::_OscCalc< T >::s13, osc::analytic::_OscCalc< T >::s23, osc::analytic::_OscCalc< T >::sCP, sincos(), sqr(), std::sqrt(), T, getGoodRuns4SAM::t0, getGoodRuns4SAM::t1, t2, osc::analytic::_OscCalc< T >::Ue2, osc::analytic::_OscCalc< T >::Ue3, osc::analytic::_OscCalc< T >::Um2, osc::analytic::_OscCalc< T >::Um3, osc::analytic::_OscCalc< T >::Ut2, and osc::analytic::_OscCalc< T >::Ut3.

  {
    b /= 3;
    // Now solving x^3 + 3*b*x^2 + c*x + d = 0

    // https://en.wikipedia.org/wiki/Cubic_equation#Depressed_cubic
    const T p = c/3 - sqr(b);
    const T q = 2*cube(b) - b*c + d;
    // Now solving t^3 + 3*p*t + q = 0

    // https://en.wikipedia.org/wiki/Cubic_equation#Trigonometric_solution_for_three_real_roots
    //
    // Cardano's formula looks simpler, but you still have to involve trig
    // operations anyway for the cube root, and it's harder to keep everything
    // explicitly real.

    const T s = sqrt(-p);

    const T r = acos(q/(2*p*s)) / 3;

    // t_k = 2*s * cos(r/3 + 2pi*k/3)

    // Use cos(a+b) = cosa*cosb - sina*sinb to save one trig operation
    T sinr, cosr;
    sincos(r, &sinr, &cosr);

    const T t0 = 2*s*cosr;
    const T t1 = s*(sqrt3*sinr - cosr);
    const T t2 = -t0-t1;

    return {t0 - b, t1 - b, t2 - b};
  }

template<class T >

T osc::analytic::sqr

(

T

x

)

Definition at line 211 of file OscCalcAnalytic.cxx.

References x.

Referenced by SolveCubic().

{return x*x;}

Variable Documentation

const double osc::analytic::sqrt3 = sqrt(3)

Definition at line 214 of file OscCalcAnalytic.cxx.

B & osc::analytic::x

Definition at line 34 of file OscCalcAnalytic.cxx.

Referenced by cube(), and sqr().

const cmplx< B, C > & osc::analytic::y

Initial value:

{
    return make_cmplx(x.re*y.re - x.im*y.im, x.re*y.im + x.im*y.re)

Definition at line 35 of file OscCalcAnalytic.cxx.