General Mathematics

General mathematical utilities.

Classes
class	mx::math::histogramUniform< realT >
	A histogram with uniform bin spacing. More...

Topics
	Constants and units
	Geometry and Geodesy
	Special Functions
	Linear Algebra
	Integration
	Interpolation
	Data Fitting
	Plotting Data
	Random Numbers
	Vector Utilities
	Fourier Transforms
	Methods for calculating the Fourier Transform.
	NVIDIA Cuda Interface
	Mathematics Source Files

Functions
template<typename realT>
bool	mx::math::isNan (realT value)
	Test whether a floating-point value is NaN, including under finite-math-only optimization.
template<typename realT>
bool	mx::math::isFinite (realT value)
	Test whether a floating-point value is finite, including under finite-math-only optimization.
template<typename realT>
void	mx::math::quarticRoots (std::vector< std::complex< realT > > &x, realT a, realT b, realT c, realT d, realT e)
	Find the roots of the general quartic equation.

Function Documentation

isFinite()

template<typename realT>

bool mx::math::isFinite

(

realT

value

)

Test whether a floating-point value is finite, including under finite-math-only optimization.

Returns

true if value is neither infinite nor NaN, otherwise false.

Parameters

[in]

value

floating-point value to test

Definition at line 71 of file floatUtils.hpp.

References isFinite().

Referenced by mx::improc::azBoxKernel< _arrayT, _kernW, _verboseT >::azBoxKernel(), calcEigenVecs(), eigenSYEVR(), isFinite(), mx::improc::isInvalidPixel(), mx::AO::analysis::aoAtmosphere< _realT >::layer_Cn2(), mx::AO::analysis::aoAtmosphere< _realT >::loadConfig(), mx::AO::analysis::fourierTemporalPSD< _realT, aosysT >::makePSDGrid(), mx::AO::analysis::clGainOpt< _realT >::maxStableGain(), mx::improc::imageXCorrDiscrete< _ccImT >::operator()(), mx::AO::analysis::clGainOpt< _realT >::optGainOpenLoop(), mx::AO::analysis::clAOLinearPredictor< _realT >::regularizeCoefficients(), mx::improc::azBoxKernel< _arrayT, _kernW, _verboseT >::setKernel(), mx::improc::precalcKernel< kernelT >::setKernel(), mx::improc::azBoxKernel< _arrayT, _kernW, _verboseT >::setMaxWidth(), mx::AO::analysis::fourierTemporalPSD< _realT, aosysT >::singleLayerPSDImpl(), TEST_CASE(), TEST_CASE(), mx::improc::imageXCorrDiscrete< _ccImT >::tol(), mx::AO::analysis::aoAtmosphere< _realT >::validate(), mx::AO::analysis::fourierTemporalPSD< _realT, aosysT >::validateAtmosphere(), mx::improc::eigenCube< dataT >::validateMaskedCombination(), and mx::AO::analysis::fourierTemporalPSD< _realT, aosysT >::validatePsdInputs().

isNan()

template<typename realT>

bool mx::math::isNan

(

realT

value

)

Test whether a floating-point value is NaN, including under finite-math-only optimization.

Returns

true if value is a quiet or signaling NaN, otherwise false.

Parameters

[in]

value

floating-point value to test

Definition at line 39 of file floatUtils.hpp.

References isNan().

Referenced by isNan(), TEST_CASE(), TEST_CASE(), TEST_CASE(), TEST_CASE(), and unitTest::math_eigenLapack_test::TEST_CASE().

quarticRoots()

template<typename realT>

void mx::math::quarticRoots	(	std::vector< std::complex< realT > > &	x,
		realT	a,
		realT	b,
		realT	c,
		realT	d,
		realT	e )

Find the roots of the general quartic equation.

Finds the roots of

\[f(x) = a x^4 + b x^3 + c x^2 + d x + e \]

using the general formula for quartic roots. See https://en.wikipedia.org/wiki/Quartic_function.

Template Parameters

realT

is the floating point type used for calculations.

Parameters

[out]	x	On exit contains the 4 roots, is resized to length 4.
[in]	a	the coefficient of the \(x^4\) term.
[in]	b	the coefficient of the \(x^3\) term.
[in]	c	the coefficient of the \(x^2\) term.
[in]	d	the coefficient of the \(x^1\) term.
[in]	e	the coefficient of the \(x^0\) term.

Definition at line 126 of file roots.hpp.

Referenced by mx::AO::analysis::aoSystem< _realT, _inputSpectT, iosT >::optimumTauWFS().