Polynomial3< T > Class Template Reference

The Polynomial3 class represents a cubic polynomial with real coefficients p(x) = c0 x^3 + c1 x^2 + c2 x + c3. More...

#include <gz/math/Polynomial3.hh>

Public Member Functions
	Polynomial3 ()=default
	Constructor. More...
	Polynomial3 (Vector4< T > _coeffs)
	Constructor. More...
const Vector4< T > &	Coeffs () const
	Get the polynomial coefficients. More...
T	Evaluate (const T &_x) const
	Evaluate the polynomial at _x For non-finite _x, this function computes p(z) as z tends to _x. More...
T	Minimum () const
	Compute polynomial minimum. More...
T	Minimum (const Interval< T > &_interval) const
	Compute polynomial minimum in an _interval More...
T	Minimum (const Interval< T > &_interval, T &_xMin) const
	Compute polynomial minimum in an _interval More...
T	Minimum (T &_xMin) const
	Compute polynomial minimum. More...
T	operator() (const T &_x) const
	Call operator overload. More...
void	Print (std::ostream &_out, const std::string &_x="x") const
	Prints polynomial as p(_x) to _out stream. More...

Static Public Member Functions
static Polynomial3	Constant (T _value)
	Make a constant polynomial. More...

Detailed Description

template<typename T>
class gz::math::Polynomial3< T >

The Polynomial3 class represents a cubic polynomial with real coefficients p(x) = c0 x^3 + c1 x^2 + c2 x + c3.

Example

#include <iostream>
#include <gz/math/Polynomial3.hh>
#include <gz/math/Vector4.hh>
 
int main(int argc, char **argv)
{
  // A default constructed polynomial should have zero coefficients.
  std::cout << "A default constructed polynomial is always: "
            << gz::math::Polynomial3d() << std::endl;
 
  // A constant polynomial only has an independent term.
  std::cout << "A constant polynomial only has an independent term: "
            << gz::math::Polynomial3d::Constant(-1.) << std::endl;
 
  // A cubic polynomial may be incomplete.
  const gz::math::Polynomial3d p(
      gz::math::Vector4d(1., 0., -1., 2.));
  std::cout << "A cubic polynomial may be incomplete: " << p << std::endl;
 
  // A polynomial can be evaluated.
  const double x = 0.5;
  std::cout << "Evaluating " << p << " at " << x
            << " yields " << p(x) << std::endl;
 
  // A polynomial can be queried for its minimum in a given interval,
  // as well as for its global minimum (which may not always be finite).
  const gz::math::Intervald interval =
      gz::math::Intervald::Closed(-1, 1.);
  std::cout << "The minimum of " << p << " in the " << interval
            << " interval is " << p.Minimum(interval) << std::endl;
  std::cout << "The global minimum of " << p
            << " is " << p.Minimum() << std::endl;
 
  const gz::math::Polynomial3d q(
      gz::math::Vector4d(0., 1., 2., 1.));
  std::cout << "The minimum of " << q << " in the " << interval
            << " interval is " << q.Minimum(interval) << std::endl;
  std::cout << "The global minimum of " << q
            << " is " << q.Minimum() << std::endl;
 
}

Constructor & Destructor Documentation

Polynomial3() [1/2]

Polynomial3 ( )

default

Constructor.

Referenced by Polynomial3< T >::Constant().

Polynomial3() [2/2]

Polynomial3 ( Vector4< T >  _coeffs )

inlineexplicit

Constructor.

Parameters

[in]

_coeffs

coefficients c0 through c3, left to right

Member Function Documentation

Coeffs()

const Vector4<T>& Coeffs ( ) const

inline

Get the polynomial coefficients.

Returns

this polynomial coefficients

Constant()

static Polynomial3 Constant ( T  _value )

inlinestatic

Make a constant polynomial.

Returns

a p(x) = _value polynomial

References Polynomial3< T >::Polynomial3().

Evaluate()

T Evaluate ( const T &  _x ) const

inline

Evaluate the polynomial at _x For non-finite _x, this function computes p(z) as z tends to _x.

Parameters

[in]

_x

polynomial argument

Returns

the result of evaluating p(_x)

References std::copysign(), numeric_limits::epsilon(), std::isfinite(), std::isnan(), and gz::math::isnan().

Referenced by Polynomial3< T >::Minimum(), and Polynomial3< T >::operator()().

Minimum() [1/4]

T Minimum ( ) const

inline

Compute polynomial minimum.

Returns

the polynomial minimum (may not be finite)

Referenced by Polynomial3< T >::Minimum().

Minimum() [2/4]

T Minimum ( const Interval< T > &  _interval ) const

inline

Compute polynomial minimum in an _interval

Parameters

[in]

_interval

polynomial argument interval to check

Returns

the polynomial minimum in the given interval (may not be finite), or NaN if the interval is empty

References Polynomial3< T >::Minimum().

Minimum() [3/4]

T Minimum ( const Interval< T > &  _interval, T &  _xMin  ) const

inline

Compute polynomial minimum in an _interval

Parameters

[in]	_interval	polynomial argument interval to check
[out]	_xMin	polynomial argument that yields minimum, or NaN if the interval is empty

Returns

the polynomial minimum in the given interval, or NaN if the interval is empty

References Interval< T >::Contains(), Interval< T >::Empty(), numeric_limits::epsilon(), Polynomial3< T >::Evaluate(), Interval< T >::LeftValue(), numeric_limits::quiet_NaN(), Interval< T >::RightValue(), and std::sqrt().

Minimum() [4/4]

T Minimum ( T &  _xMin ) const

inline

Compute polynomial minimum.

Parameters

[out]

_xMin

polynomial argument that yields minimum

Returns

the polynomial minimum (may not be finite)

References Polynomial3< T >::Minimum().

operator()()

T operator() ( const T &  _x ) const

inline

Call operator overload.

See also

Polynomial3::Evaluate()

References Polynomial3< T >::Evaluate().

Print()

void Print ( std::ostream &  _out, const std::string &  _x = "x"  ) const

inline

Prints polynomial as p(_x) to _out stream.

Parameters

[in]	_out	Output stream to print to
[in]	_x	Argument name to be used

References numeric_limits::epsilon().

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The documentation for this class was generated from the following file:

• gz/math/Polynomial3.hh