mx::math Namespace Reference

Namespaces
namespace	fit
namespace	ft
namespace	func

Classes
struct	degradT
	Type holding constants related to angle calculations in degrees. More...
struct	degradT< degrees, _realT >
	Type holding constants related to angle calculations in degrees. More...
struct	degradT< radians, _realT >
	Type holding constants related to angle calculations in radians. More...
class	gnuPlot
	An interactive c++ interface to gnuplot. More...
struct	gpCurve
struct	gsl_interp_linear
	GSL Linear Interpolation. More...
struct	gsl_interp_steffen
	GSL Steffen Interpolation. More...
class	gslInterpolator
	Class to manage interpolation using the GSL interpolation library. More...
class	histogramUniform
	A histogram with uniform bin spacing. More...
class	laplace_distribution
	The Laplace (double exponential) continuous distribution for random numbers. More...
class	logInterpolator
	Interpolate a function in log space. More...
class	point2D
	A point in 2-dimensional space. More...
class	randomT
	A random number type, which functions like any other arithmetic type. More...
struct	syevrMem
	A struct to hold the working memory for eigenSYEVR and maintain it between calls if desired. More...

Typedefs
template<typename realT >
using	degreesT = degradT< degrees, realT >
template<typename realT >
using	radiansT = degradT< radians, realT >

Functions
template<typename T >
constexpr T	pi ()
	Get the value of pi.
template<>
constexpr float	pi< float > ()
template<>
constexpr double	pi< double > ()
template<>
constexpr long double	pi< long double > ()
template<typename T >
constexpr T	two_pi ()
	Get the value of 2pi.
template<>
constexpr float	two_pi< float > ()
template<>
constexpr double	two_pi< double > ()
template<>
constexpr long double	two_pi< long double > ()
template<typename T >
constexpr T	half_pi ()
	Get the value of pi/2.
template<>
constexpr float	half_pi< float > ()
template<>
constexpr double	half_pi< double > ()
template<>
constexpr long double	half_pi< long double > ()
template<typename T >
constexpr T	rad2deg ()
	Get the value of 180/pi.
template<>
constexpr float	rad2deg< float > ()
template<>
constexpr double	rad2deg< double > ()
template<>
constexpr long double	rad2deg< long double > ()
template<typename T >
constexpr T	root_two ()
	Get the value of sqrt(2)
template<>
constexpr float	root_two< float > ()
template<>
constexpr double	root_two< double > ()
template<>
constexpr long double	root_two< long double > ()
template<typename T >
constexpr T	ln_two ()
	Get the value of ln(2)
template<>
constexpr float	ln_two< float > ()
template<>
constexpr double	ln_two< double > ()
template<>
constexpr long double	ln_two< long double > ()
template<typename T >
constexpr T	third ()
	Get the value of 1/3.
template<>
constexpr float	third< float > ()
template<>
constexpr double	third< double > ()
template<>
constexpr long double	third< long double > ()
template<typename floatT >
constexpr floatT	five_thirds ()
	Return 5/3 in the specified precision.
template<typename floatT >
constexpr floatT	five_sixths ()
	Return 5/6 in the specified precision.
template<typename floatT >
constexpr floatT	eleven_thirds ()
	Return 11/3 in the specified precision.
template<typename floatT >
constexpr floatT	eleven_sixths ()
	Return 11/6 in the specified precision.
template<typename floatT >
constexpr floatT	six_fifths ()
	Return 6/5 in the specified precision.
template<typename floatT >
constexpr floatT	three_fifths ()
	Return 3/5 in the specified precision.
template<typename floatT >
constexpr floatT	seventeen_thirds ()
	Return 17/3 in the specified precision.
template<typename eigenT1 , typename eigenT2 >
void	eigenSYRK (eigenT1 &cv, const eigenT2 &ims)
	Calculates the lower triangular part of the covariance matrix of ims.
template<typename arrT >
MXLAPACK_INT	eigenSYEVR (arrT &eigvec, arrT &eigval, arrT &X, int ev0=0, int ev1=-1, char UPLO='L', syevrMem< typename arrT::Scalar > *mem=0)
	Calculate select eigenvalues and eigenvectors of an Eigen Array.
template<typename _evCalcT = double, typename eigenT >
MXLAPACK_INT	calcEigenVecs (eigenT &evecs, eigenT &evals, eigenT &cv, int nVecs=0, bool normalize=false, bool check=false, syevrMem< _evCalcT > *mem=0, double *t_eigenv=nullptr)
	Calculate the eigenvectors and eigenvalues given a triangular matrix.
template<typename _evCalcT = double, typename eigenT , typename eigenT1 >
MXLAPACK_INT	calcKLModes (eigenT &klModes, eigenT &cv, const eigenT1 &Rims, int n_modes=0, syevrMem< _evCalcT > *mem=0, double *t_eigenv=nullptr, double *t_klim=nullptr)
	Calculate the K-L modes, or principle components, given a covariance matrix.
template<typename dataT >
MXLAPACK_INT	eigenGESDD (Eigen::Array< dataT, -1, -1 > &U, Eigen::Array< dataT, -1, -1 > &S, Eigen::Array< dataT, -1, -1 > &VT, Eigen::Array< dataT, -1, -1 > &A)
	Compute the SVD of an Eigen::Array using LAPACK's xgesdd.
template<typename dataT >
int	eigenPseudoInverse (Eigen::Array< dataT, -1, -1 > &PInv, dataT &condition, int &nRejected, Eigen::Array< dataT, -1, -1 > &U, Eigen::Array< dataT, -1, -1 > &S, Eigen::Array< dataT, -1, -1 > &VT, int minMN, dataT &maxCondition, dataT alpha=0, int interact=MX_PINV_NO_INTERACT)
	Calculate the pseudo-inverse of a patrix given its SVD.
template<typename dataT >
int	eigenPseudoInverse (Eigen::Array< dataT, -1, -1 > &PInv, dataT &condition, int &nRejected, Eigen::Array< dataT, -1, -1 > &U, Eigen::Array< dataT, -1, -1 > &S, Eigen::Array< dataT, -1, -1 > &VT, Eigen::Array< dataT, -1, -1 > &A, dataT &maxCondition, dataT alpha=0, int interact=MX_PINV_NO_INTERACT)
	Calculate the pseudo-inverse of a patrix using the SVD.
template<typename dataT >
int	eigenPseudoInverse (Eigen::Array< dataT, -1, -1 > &PInv, dataT &condition, int &nRejected, Eigen::Array< dataT, -1, -1 > &A, dataT &maxCondition, dataT alpha=0, int interact=MX_PINV_NO_INTERACT)
	Calculate the pseudo-inverse of a matrix using the SVD.
template<typename realT >
realT	dtor (realT q)
	Convert from degrees to radians.
template<typename realT >
realT	rtod (realT q)
	Convert from radians to degrees.
template<class angleT >
angleT::realT	angleMod (typename angleT::realT q)
	Calculate the angle modulo full-circle, normalizing to a positive value.
template<class angleT >
angleT::realT	angleDiff (typename angleT::realT q1, typename angleT::realT q2)
	Calculate the difference between two angles, correctly across 0/360.
template<class angleT >
angleT::realT	angleMean (const std::vector< typename angleT::realT > &q)
	Calculate the mean of a set of angles, correctly across 0/360.
template<int degrad = 0, typename realT >
int	continueAngles (std::vector< realT > &angles, realT threshold=0.75)
	Make a vector of angles continuous, fixing the 0/360 crossing.
template<typename realT >
void	rotatePoint (realT &x0, realT &y0, realT angle)
	Rotate a point about the origin.
template<typename realT >
int	gsl_interpolate (const gsl_interp_type *interpT, realT *xin, realT *yin, size_t Nin, realT *xout, realT *yout, size_t Nout)
	Interpolate a 1-D data X vs Y discrete function onto a new X axis.
template<typename realT >
int	gsl_interpolate (const gsl_interp_type *interpT, std::vector< realT > &xin, std::vector< realT > &yin, std::vector< realT > &xout, std::vector< realT > &yout)
	Interpolate a 1-D data X vs Y discrete function onto a new X axis (vector version)
template<typename interpT >
interpT::realT	logRadProfIntegrationF (typename interpT::realT x, void *params)
template<typename interpT >
interpT::realT	logRadProfIntegrator (const std::vector< typename interpT::realT > &x, const std::vector< typename interpT::realT > &y, typename interpT::realT x0, typename interpT::realT xf)
	Integrate a numerical radial profile using logarithmic interpolation.
template<typename interpT >
interpT::realT	logRadProfIntegrator (const std::vector< typename interpT::realT > &x, const std::vector< typename interpT::realT > &y)
	Integrate a numerical radial profile using logarithmic interpolation.
template<typename vectorScT , typename vectorT >
vectorT::value_type	radprofIntegral (vectorScT r, vectorT p, bool inczero=false)
	Calculate the 2D integral given a radial profile.
template<typename intT >
int	randomSeed (intT &seedval)
	Get a value to use as a random seed.
template<typename _RealType >
bool	operator== (const laplace_distribution< _RealType > &__d1, const laplace_distribution< _RealType > &__d2)
	Return true if two exponential distributions have the same parameters.
template<typename _RealType >
bool	operator!= (const laplace_distribution< _RealType > &__d1, const laplace_distribution< _RealType > &__d2)
	Return true if two exponential distributions have different parameters.
template<typename _RealType , typename _CharT , typename _Traits >
std::basic_ostream< _CharT, _Traits > &	operator<< (std::basic_ostream< _CharT, _Traits > &, const laplace_distribution< _RealType > &)
	Inserts a laplace_distribution random number distribution __x into the output stream __os.
template<typename _RealType , typename _CharT , typename _Traits >
std::basic_istream< _CharT, _Traits > &	operator>> (std::basic_istream< _CharT, _Traits > &, laplace_distribution< _RealType > &)
	Extracts a laplace_distribution random number distribution __x from the input stream __is.
template<typename realT >
realT	cubicDescriminant (const realT &a, const realT &b, const realT &c, const realT &d)
	Calculate the descriminant for the general cubic.
template<typename realT >
realT	cubicDescriminant (const realT &p, const realT &q)
	Calculate the descriminant for the depressed cubic.
template<typename realT >
void	cubicDepressed (realT &p, realT &q, const realT &a, const realT &b, const realT &c, const realT &d)
	Convert a general cubic equation to depressed form.
template<typename realT >
realT	cubicRealRoot (const realT &p, const realT &q)
	Calculate the real root for a depressed cubic with negative descriminant.
template<typename realT >
void	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.
template<typename dataT >
void	scal (const int N, const dataT &alpha, dataT *X, const int incX)
	Template wrapper for cblas xSCAL.
template<>
void	scal< float > (const int N, const float &alpha, float *X, const int incX)
template<>
void	scal< double > (const int N, const double &alpha, double *X, const int incX)
template<>
void	scal< std::complex< float > > (const int N, const std::complex< float > &alpha, std::complex< float > *X, const int incX)
template<>
void	scal< std::complex< double > > (const int N, const std::complex< double > &alpha, std::complex< double > *X, const int incX)
template<typename dataT >
void	hadp_impl (const int N, dataT *__restrict__ Y, dataT *__restrict__ X)
	Implementation of the Hadamard (element-wise) product of two vectors.
template<typename dataT >
void	hadp (const int N, dataT *Y, dataT *X)
	Template wrapper for cblas-extension xHADP.
template<typename dataT >
void	hadd_impl (const int N, const dataT alpha, const dataT *Y, const int incY, dataT *X, const int incX)
	Implementation of the Hadamard (element-wise) division of two vectors.
template<typename dataT >
void	hadd (const int N, const dataT alpha, const dataT *Y, const int incY, dataT *X, const int incX)
	Template wrapper for cblas-extension xHADD.
template<typename dataT >
void	gemm (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const dataT &alpha, const dataT *A, const int lda, const dataT *B, const int ldb, const dataT &beta, dataT *C, const int ldc)
	Template Wrapper for cblas xGEMM.
template<>
void	gemm< float > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const float &alpha, const float *A, const int lda, const float *B, const int ldb, const float &beta, float *C, const int ldc)
template<>
void	gemm< double > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const double &alpha, const double *A, const int lda, const double *B, const int ldb, const double &beta, double *C, const int ldc)
template<>
void	gemm< std::complex< float > > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const std::complex< float > &alpha, const std::complex< float > *A, const int lda, const std::complex< float > *B, const int ldb, const std::complex< float > &beta, std::complex< float > *C, const int ldc)
template<>
void	gemm< std::complex< double > > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const std::complex< double > &alpha, const std::complex< double > *A, const int lda, const std::complex< double > *B, const int ldb, const std::complex< double > &beta, std::complex< double > *C, const int ldc)
template<typename dataT >
void	syrk (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const dataT &alpha, const dataT *A, const int lda, const dataT &beta, dataT *C, const int ldc)
	Template Wrapper for cblas xSYRK.
template<>
void	syrk< float > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const float &alpha, const float *A, const int lda, const float &beta, float *C, const int ldc)
template<>
void	syrk< double > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const double &alpha, const double *A, const int lda, const double &beta, double *C, const int ldc)
template<>
void	syrk< std::complex< float > > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const std::complex< float > &alpha, const std::complex< float > *A, const int lda, const std::complex< float > &beta, std::complex< float > *C, const int ldc)
template<>
void	syrk< std::complex< double > > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const std::complex< double > &alpha, const std::complex< double > *A, const int lda, const std::complex< double > &beta, std::complex< double > *C, const int ldc)
template<typename dataT >
dataT	lamch (char CMACH)
	Determine machine parameters.
template<>
float	lamch< float > (char CMACH)
template<>
double	lamch< double > (char CMACH)
template<typename dataT >
MXLAPACK_INT	potrf (char UPLO, MXLAPACK_INT N, dataT *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
	Compute the Cholesky factorization of a real symmetric positive definite matrix A.
template<>
MXLAPACK_INT	potrf< float > (char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< double > (char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< std::complex< float > > (char UPLO, MXLAPACK_INT N, std::complex< float > *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< std::complex< double > > (char UPLO, MXLAPACK_INT N, std::complex< double > *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<typename dataT >
MXLAPACK_INT	sytrd (char UPLO, MXLAPACK_INT N, dataT *A, MXLAPACK_INT LDA, dataT *D, dataT *E, dataT *TAU, dataT *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT INFO)
	Reduce a real symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.
template<>
MXLAPACK_INT	sytrd< float > (char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float *D, float *E, float *TAU, float *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT INFO)
template<>
MXLAPACK_INT	sytrd< double > (char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double *D, double *E, double *TAU, double *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT INFO)
template<typename dataT >
MXLAPACK_INT	syevr (char JOBZ, char RANGE, char UPLO, MXLAPACK_INT N, dataT *A, MXLAPACK_INT LDA, dataT VL, dataT VU, MXLAPACK_INT IL, MXLAPACK_INT IU, dataT ABSTOL, MXLAPACK_INT *M, dataT *W, dataT *Z, MXLAPACK_INT LDZ, MXLAPACK_INT *ISUPPZ, dataT *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT LIWORK)
	Compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix.
template<>
MXLAPACK_INT	syevr< float > (char JOBZ, char RANGE, char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float VL, float VU, MXLAPACK_INT IL, MXLAPACK_INT IU, float ABSTOL, MXLAPACK_INT *M, float *W, float *Z, MXLAPACK_INT LDZ, MXLAPACK_INT *ISUPPZ, float *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT LIWORK)
template<>
MXLAPACK_INT	syevr< double > (char JOBZ, char RANGE, char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double VL, double VU, MXLAPACK_INT IL, MXLAPACK_INT IU, double ABSTOL, MXLAPACK_INT *M, double *W, double *Z, MXLAPACK_INT LDZ, MXLAPACK_INT *ISUPPZ, double *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT LIWORK)
template<typename dataT >
MXLAPACK_INT	gesvd (char JOBU, char JOBVT, MXLAPACK_INT M, MXLAPACK_INT N, dataT *A, MXLAPACK_INT LDA, dataT *S, dataT *U, MXLAPACK_INT LDU, dataT *VT, MXLAPACK_INT LDVT, dataT *WORK, MXLAPACK_INT LWORK)
	Compute the singular value decomposition (SVD) of a real matrix.
template<>
MXLAPACK_INT	gesvd< float > (char JOBU, char JOBVT, MXLAPACK_INT M, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float *S, float *U, MXLAPACK_INT LDU, float *VT, MXLAPACK_INT LDVT, float *WORK, MXLAPACK_INT LWORK)
template<>
MXLAPACK_INT	gesvd< double > (char JOBU, char JOBVT, MXLAPACK_INT M, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double *S, double *U, MXLAPACK_INT LDU, double *VT, MXLAPACK_INT LDVT, double *WORK, MXLAPACK_INT LWORK)
template<typename dataT >
std::string	gpBinaryFormat ()
template<>
std::string	gpBinaryFormat< char > ()
template<>
std::string	gpBinaryFormat< unsigned char > ()
template<>
std::string	gpBinaryFormat< short > ()
template<>
std::string	gpBinaryFormat< unsigned short > ()
template<>
std::string	gpBinaryFormat< int > ()
template<>
std::string	gpBinaryFormat< unsigned int > ()
template<>
std::string	gpBinaryFormat< long > ()
template<>
std::string	gpBinaryFormat< unsigned long > ()
template<>
std::string	gpBinaryFormat< float > ()
template<>
std::string	gpBinaryFormat< double > ()
template<>
void	scal< float > (const int N, const float &alpha, float *X, const int incX)
template<>
void	scal< double > (const int N, const double &alpha, double *X, const int incX)
template<>
void	scal< std::complex< float > > (const int N, const std::complex< float > &alpha, std::complex< float > *X, const int incX)
template<>
void	scal< std::complex< double > > (const int N, const std::complex< double > &alpha, std::complex< double > *X, const int incX)
template<>
void	gemm< float > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const float &alpha, const float *A, const int lda, const float *B, const int ldb, const float &beta, float *C, const int ldc)
template<>
void	gemm< double > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const double &alpha, const double *A, const int lda, const double *B, const int ldb, const double &beta, double *C, const int ldc)
template<>
void	gemm< std::complex< float > > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const std::complex< float > &alpha, const std::complex< float > *A, const int lda, const std::complex< float > *B, const int ldb, const std::complex< float > &beta, std::complex< float > *C, const int ldc)
template<>
void	gemm< std::complex< double > > (const CBLAS_ORDER Order, const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const std::complex< double > &alpha, const std::complex< double > *A, const int lda, const std::complex< double > *B, const int ldb, const std::complex< double > &beta, std::complex< double > *C, const int ldc)
template<>
void	syrk< float > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const float &alpha, const float *A, const int lda, const float &beta, float *C, const int ldc)
template<>
void	syrk< double > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const double &alpha, const double *A, const int lda, const double &beta, double *C, const int ldc)
template<>
void	syrk< std::complex< float > > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const std::complex< float > &alpha, const std::complex< float > *A, const int lda, const std::complex< float > &beta, std::complex< float > *C, const int ldc)
template<>
void	syrk< std::complex< double > > (const CBLAS_ORDER Order, const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE Trans, const int N, const int K, const std::complex< double > &alpha, const std::complex< double > *A, const int lda, const std::complex< double > &beta, std::complex< double > *C, const int ldc)
template<>
float	lamch< float > (char CMACH)
template<>
double	lamch< double > (char CMACH)
template<>
MXLAPACK_INT	potrf< float > (char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< double > (char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< std::complex< float > > (char UPLO, MXLAPACK_INT N, std::complex< float > *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	potrf< std::complex< double > > (char UPLO, MXLAPACK_INT N, std::complex< double > *A, MXLAPACK_INT LDA, MXLAPACK_INT &INFO)
template<>
MXLAPACK_INT	sytrd< float > (char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float *D, float *E, float *TAU, float *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT INFO)
template<>
MXLAPACK_INT	sytrd< double > (char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double *D, double *E, double *TAU, double *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT INFO)
template<>
MXLAPACK_INT	syevr< float > (char JOBZ, char RANGE, char UPLO, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float VL, float VU, MXLAPACK_INT IL, MXLAPACK_INT IU, float ABSTOL, MXLAPACK_INT *M, float *W, float *Z, MXLAPACK_INT LDZ, MXLAPACK_INT *ISUPPZ, float *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT LIWORK)
template<>
MXLAPACK_INT	syevr< double > (char JOBZ, char RANGE, char UPLO, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double VL, double VU, MXLAPACK_INT IL, MXLAPACK_INT IU, double ABSTOL, MXLAPACK_INT *M, double *W, double *Z, MXLAPACK_INT LDZ, MXLAPACK_INT *ISUPPZ, double *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT LIWORK)
template<>
MXLAPACK_INT	gesvd< float > (char JOBU, char JOBVT, MXLAPACK_INT M, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float *S, float *U, MXLAPACK_INT LDU, float *VT, MXLAPACK_INT LDVT, float *WORK, MXLAPACK_INT LWORK)
template<>
MXLAPACK_INT	gesvd< double > (char JOBU, char JOBVT, MXLAPACK_INT M, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double *S, double *U, MXLAPACK_INT LDU, double *VT, MXLAPACK_INT LDVT, double *WORK, MXLAPACK_INT LWORK)
template<>
MXLAPACK_INT	gesdd< float > (char JOBZ, MXLAPACK_INT M, MXLAPACK_INT N, float *A, MXLAPACK_INT LDA, float *S, float *U, MXLAPACK_INT LDU, float *VT, MXLAPACK_INT LDVT, float *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT INFO)
template<>
MXLAPACK_INT	gesdd< double > (char JOBZ, MXLAPACK_INT M, MXLAPACK_INT N, double *A, MXLAPACK_INT LDA, double *S, double *U, MXLAPACK_INT LDU, double *VT, MXLAPACK_INT LDVT, double *WORK, MXLAPACK_INT LWORK, MXLAPACK_INT *IWORK, MXLAPACK_INT INFO)

Typedef Documentation

degreesT

template<typename realT >

using mx::math::degreesT = typedef degradT<degrees, realT>

Definition at line 106 of file geo.hpp.

radiansT

template<typename realT >

using mx::math::radiansT = typedef degradT<radians, realT>

Definition at line 124 of file geo.hpp.

Function Documentation

cubicDepressed()

template<typename realT >

void mx::math::cubicDepressed	(	realT &	p,
		realT &	q,
		const realT &	a,
		const realT &	b,
		const realT &	c,
		const realT &	d
	)

Convert a general cubic equation to depressed form.

The general cubic is

\[ ax^3 + bx^2 + cx + d = 0 \]

which can be converted to compressed form

\[ t^3 + pt + q = 0 \]

Parameters

[out]	p	the 1st order coefficient of the depressed cubic
[out]	q	the 0th order coefficient of the depressed cubic
[in]	a	the 3rd order coefficient of the general cubic
[in]	b	the 2nd order coefficient of the general cubic
[in]	c	the 1st order coefficient of the general cubic
[in]	d	the 0th order coefficient of the general cubic

Definition at line 77 of file roots.hpp.

References six_fifths().

Referenced by mx::AO::analysis::F_mod().

cubicDescriminant() [1/2]

template<typename realT >

realT mx::math::cubicDescriminant	(	const realT &	a,
		const realT &	b,
		const realT &	c,
		const realT &	d
	)

Calculate the descriminant for the general cubic.

Returns

the descriminant

Parameters

[in]	a	the 3rd order coefficient of the general cubic
[in]	b	the 2nd order coefficient of the general cubic
[in]	c	the 1st order coefficient of the general cubic
[in]	d	the 0th order coefficient of the general cubic

Definition at line 44 of file roots.hpp.

References six_fifths().

cubicDescriminant() [2/2]

template<typename realT >

realT mx::math::cubicDescriminant	(	const realT &	p,
		const realT &	q
	)

Calculate the descriminant for the depressed cubic.

Returns

the descriminant

Parameters

[in]	p	the 0th order coefficient of the depressed cubic
[in]	q	the 0th order coefficient of the depressed cubic

Definition at line 58 of file roots.hpp.

References six_fifths().

cubicRealRoot()

template<typename realT >

realT mx::math::cubicRealRoot	(	const realT &	p,
		const realT &	q
	)

Calculate the real root for a depressed cubic with negative descriminant.

Returns

the real root for a depressed cubic defined by p and q

Exceptions

std::runtime_error

if there are 3 real roots

Parameters

[in]	p	the 1st order coefficient of the depressed cubic
[in]	q	the 0th order coefficient of the depressed cubic

Definition at line 97 of file roots.hpp.

References six_fifths().

Referenced by mx::AO::analysis::F_mod().

gemm< double >() [1/2]

template<>

void mx::math::gemm< double >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const double &	alpha,
		const double *	A,
		const int	lda,
		const double *	B,
		const int	ldb,
		const double &	beta,
		double *	C,
		const int	ldc
	)

Definition at line 81 of file templateBLAS.cpp.

References six_fifths().

gemm< double >() [2/2]

template<>

void mx::math::gemm< double >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const double &	alpha,
		const double *	A,
		const int	lda,
		const double *	B,
		const int	ldb,
		const double &	beta,
		double *	C,
		const int	ldc
	)

Definition at line 81 of file templateBLAS.cpp.

References six_fifths().

gemm< float >() [1/2]

template<>

void mx::math::gemm< float >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const float &	alpha,
		const float *	A,
		const int	lda,
		const float *	B,
		const int	ldb,
		const float &	beta,
		float *	C,
		const int	ldc
	)

Definition at line 62 of file templateBLAS.cpp.

References six_fifths().

gemm< float >() [2/2]

template<>

void mx::math::gemm< float >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const float &	alpha,
		const float *	A,
		const int	lda,
		const float *	B,
		const int	ldb,
		const float &	beta,
		float *	C,
		const int	ldc
	)

Definition at line 62 of file templateBLAS.cpp.

References six_fifths().

gemm< std::complex< double > >() [1/2]

template<>

void mx::math::gemm< std::complex< double > >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const std::complex< double > &	alpha,
		const std::complex< double > *	A,
		const int	lda,
		const std::complex< double > *	B,
		const int	ldb,
		const std::complex< double > &	beta,
		std::complex< double > *	C,
		const int	ldc
	)

Definition at line 119 of file templateBLAS.cpp.

References six_fifths().

gemm< std::complex< double > >() [2/2]

template<>

void mx::math::gemm< std::complex< double > >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const std::complex< double > &	alpha,
		const std::complex< double > *	A,
		const int	lda,
		const std::complex< double > *	B,
		const int	ldb,
		const std::complex< double > &	beta,
		std::complex< double > *	C,
		const int	ldc
	)

Definition at line 119 of file templateBLAS.cpp.

References six_fifths().

gemm< std::complex< float > >() [1/2]

template<>

void mx::math::gemm< std::complex< float > >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const std::complex< float > &	alpha,
		const std::complex< float > *	A,
		const int	lda,
		const std::complex< float > *	B,
		const int	ldb,
		const std::complex< float > &	beta,
		std::complex< float > *	C,
		const int	ldc
	)

Definition at line 100 of file templateBLAS.cpp.

References six_fifths().

gemm< std::complex< float > >() [2/2]

template<>

void mx::math::gemm< std::complex< float > >	(	const CBLAS_ORDER	Order,
		const CBLAS_TRANSPOSE	TransA,
		const CBLAS_TRANSPOSE	TransB,
		const int	M,
		const int	N,
		const int	K,
		const std::complex< float > &	alpha,
		const std::complex< float > *	A,
		const int	lda,
		const std::complex< float > *	B,
		const int	ldb,
		const std::complex< float > &	beta,
		std::complex< float > *	C,
		const int	ldc
	)

Definition at line 100 of file templateBLAS.cpp.

References six_fifths().

gesdd< double >()

template<>

MXLAPACK_INT mx::math::gesdd< double >	(	char	JOBZ,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double *	S,
		double *	U,
		MXLAPACK_INT	LDU,
		double *	VT,
		MXLAPACK_INT	LDVT,
		double *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 433 of file templateLapack.cpp.

References six_fifths().

gesdd< float >()

template<>

MXLAPACK_INT mx::math::gesdd< float >	(	char	JOBZ,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float *	S,
		float *	U,
		MXLAPACK_INT	LDU,
		float *	VT,
		MXLAPACK_INT	LDVT,
		float *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 393 of file templateLapack.cpp.

References six_fifths().

gesvd< double >() [1/2]

template<>

MXLAPACK_INT mx::math::gesvd< double >	(	char	JOBU,
		char	JOBVT,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double *	S,
		double *	U,
		MXLAPACK_INT	LDU,
		double *	VT,
		MXLAPACK_INT	LDVT,
		double *	WORK,
		MXLAPACK_INT	LWORK
	)

Definition at line 351 of file templateLapack.cpp.

References six_fifths().

gesvd< double >() [2/2]

template<>

MXLAPACK_INT mx::math::gesvd< double >	(	char	JOBU,
		char	JOBVT,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double *	S,
		double *	U,
		MXLAPACK_INT	LDU,
		double *	VT,
		MXLAPACK_INT	LDVT,
		double *	WORK,
		MXLAPACK_INT	LWORK
	)

Definition at line 351 of file templateLapack.cpp.

References six_fifths().

gesvd< float >() [1/2]

template<>

MXLAPACK_INT mx::math::gesvd< float >	(	char	JOBU,
		char	JOBVT,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float *	S,
		float *	U,
		MXLAPACK_INT	LDU,
		float *	VT,
		MXLAPACK_INT	LDVT,
		float *	WORK,
		MXLAPACK_INT	LWORK
	)

Definition at line 309 of file templateLapack.cpp.

References six_fifths().

gesvd< float >() [2/2]

template<>

MXLAPACK_INT mx::math::gesvd< float >	(	char	JOBU,
		char	JOBVT,
		MXLAPACK_INT	M,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float *	S,
		float *	U,
		MXLAPACK_INT	LDU,
		float *	VT,
		MXLAPACK_INT	LDVT,
		float *	WORK,
		MXLAPACK_INT	LWORK
	)

Definition at line 309 of file templateLapack.cpp.

References six_fifths().

gpBinaryFormat()

template<typename dataT >

std::string mx::math::gpBinaryFormat

(

)

Definition at line 91 of file gnuPlot.hpp.

gpBinaryFormat< char >()

template<>

std::string mx::math::gpBinaryFormat< char >

(

)

gpBinaryFormat< double >()

template<>

std::string mx::math::gpBinaryFormat< double >

(

)

gpBinaryFormat< float >()

template<>

std::string mx::math::gpBinaryFormat< float >

(

)

gpBinaryFormat< int >()

template<>

std::string mx::math::gpBinaryFormat< int >

(

)

gpBinaryFormat< long >()

template<>

std::string mx::math::gpBinaryFormat< long >

(

)

gpBinaryFormat< short >()

template<>

std::string mx::math::gpBinaryFormat< short >

(

)

gpBinaryFormat< unsigned char >()

template<>

std::string mx::math::gpBinaryFormat< unsigned char >

(

)

gpBinaryFormat< unsigned int >()

template<>

std::string mx::math::gpBinaryFormat< unsigned int >

(

)

gpBinaryFormat< unsigned long >()

template<>

std::string mx::math::gpBinaryFormat< unsigned long >

(

)

gpBinaryFormat< unsigned short >()

template<>

std::string mx::math::gpBinaryFormat< unsigned short >

(

)

half_pi< double >()

template<>

constexpr double mx::math::half_pi< double > ( )

constexpr

Definition at line 164 of file constants.hpp.

References MX_INTERNAL_PI_100.

half_pi< float >()

template<>

constexpr float mx::math::half_pi< float > ( )

constexpr

Definition at line 158 of file constants.hpp.

References MX_INTERNAL_PI_100.

half_pi< long double >()

template<>

constexpr long double mx::math::half_pi< long double > ( )

constexpr

Definition at line 170 of file constants.hpp.

References MX_INTERNAL_PI_100.

lamch< double >() [1/2]

template<>

double mx::math::lamch< double >

(

char

CMACH

)

Definition at line 47 of file templateLapack.cpp.

References six_fifths().

Referenced by SCENARIO().

lamch< double >() [2/2]

template<>

double mx::math::lamch< double >

(

char

CMACH

)

Definition at line 47 of file templateLapack.cpp.

References six_fifths().

Referenced by SCENARIO().

lamch< float >() [1/2]

template<>

float mx::math::lamch< float >

(

char

CMACH

)

Definition at line 35 of file templateLapack.cpp.

References six_fifths().

Referenced by SCENARIO().

lamch< float >() [2/2]

template<>

float mx::math::lamch< float >

(

char

CMACH

)

Definition at line 35 of file templateLapack.cpp.

References six_fifths().

Referenced by SCENARIO().

ln_two< double >()

template<>

constexpr double mx::math::ln_two< double > ( )

constexpr

Definition at line 300 of file constants.hpp.

References MX_INTERNAL_LN2_100.

ln_two< float >()

template<>

constexpr float mx::math::ln_two< float > ( )

constexpr

Definition at line 294 of file constants.hpp.

References MX_INTERNAL_LN2_100.

ln_two< long double >()

template<>

constexpr long double mx::math::ln_two< long double > ( )

constexpr

Definition at line 306 of file constants.hpp.

References MX_INTERNAL_LN2_100.

logRadProfIntegrationF()

template<typename interpT >

interpT::realT mx::math::logRadProfIntegrationF	(	typename interpT::realT	x,
		void *	params
	)

Definition at line 14 of file logRadProfIntegrator.hpp.

References six_fifths().

logRadProfIntegrator() [1/2]

template<typename interpT >

interpT::realT mx::math::logRadProfIntegrator	(	const std::vector< typename interpT::realT > &	x,
		const std::vector< typename interpT::realT > &	y
	)

Integrate a numerical radial profile using logarithmic interpolation.

Useful for steep power-law like functions like power-spectra

Returns

the value of the integral over the entire domain given by x

Parameters

[in]	x	the x values of the function. Must be positive definite (can not contain 0).
[in]	y	the y values of the function. Must be positive definite (can not contain 0).

Definition at line 68 of file logRadProfIntegrator.hpp.

References six_fifths().

logRadProfIntegrator() [2/2]

template<typename interpT >

interpT::realT mx::math::logRadProfIntegrator	(	const std::vector< typename interpT::realT > &	x,
		const std::vector< typename interpT::realT > &	y,
		typename interpT::realT	x0,
		typename interpT::realT	xf
	)

Integrate a numerical radial profile using logarithmic interpolation.

Useful for steep power-law like functions like power-spectra

Returns

the value of the integral over the limits

Parameters

[in]	x	the x values of the function. Must be positive definite (can not contain 0).
[in]	y	the y values of the function. Must be positive definite (can not contain 0).
[in]	x0	[optional] the lower limit of integration
[in]	xf	[optional] the uper limit of integration

Definition at line 28 of file logRadProfIntegrator.hpp.

References mx::math::logInterpolator< interpT >::setup(), and six_fifths().

operator!=()

template<typename _RealType >

bool mx::math::operator!=	(	const laplace_distribution< _RealType > &	__d1,
		const laplace_distribution< _RealType > &	__d2
	)

Return true if two exponential distributions have different parameters.

Definition at line 281 of file randomT.hpp.

References six_fifths().

operator<<()

template<typename _RealType , typename _CharT , typename _Traits >

std::basic_ostream< _CharT, _Traits > & mx::math::operator<<	(	std::basic_ostream< _CharT, _Traits > &	,
		const laplace_distribution< _RealType > &
	)

Inserts a laplace_distribution random number distribution __x into the output stream __os.

Parameters

__os	An output stream.
__x	A laplace_distribution random number distribution.

Returns

The output stream with the state of __x inserted or in an error state.

operator==()

template<typename _RealType >

bool mx::math::operator==	(	const laplace_distribution< _RealType > &	__d1,
		const laplace_distribution< _RealType > &	__d2
	)

Return true if two exponential distributions have the same parameters.

Definition at line 271 of file randomT.hpp.

References six_fifths().

operator>>()

template<typename _RealType , typename _CharT , typename _Traits >

std::basic_istream< _CharT, _Traits > & mx::math::operator>>	(	std::basic_istream< _CharT, _Traits > &	,
		laplace_distribution< _RealType > &
	)

Extracts a laplace_distribution random number distribution __x from the input stream __is.

Parameters

__is	An input stream.
__x	A laplace_distribution random number generator engine.

Returns

The input stream with __x extracted or in an error state.

pi< double >()

template<>

constexpr double mx::math::pi< double > ( )

constexpr

Definition at line 74 of file constants.hpp.

References MX_INTERNAL_PI_100.

Referenced by mx::sigproc::makeFourierModeFreqs_Circ().

pi< float >()

template<>

constexpr float mx::math::pi< float > ( )

constexpr

Definition at line 68 of file constants.hpp.

References MX_INTERNAL_PI_100.

pi< long double >()

template<>

constexpr long double mx::math::pi< long double > ( )

constexpr

Definition at line 80 of file constants.hpp.

References MX_INTERNAL_PI_100.

potrf()

template<typename dataT >

MXLAPACK_INT mx::math::potrf	(	char	UPLO,
		MXLAPACK_INT	N,
		dataT *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Compute the Cholesky factorization of a real symmetric positive definite matrix A.

The factorization has the form A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular.

Parameters

[in]	UPLO	'U' if upper triangle of A is stored, 'L' if lower triangle of A is stored.
[in]	N	The order of the matrix A, >= 0.
	A	[in.out] Symmetric matrix of dimension (LDA,N), stored as specified in UPLO. Note that the opposite half is not referenced.
[in]	LDA	The leading dimension of A.
[out]	INFO	0 on success, < 0 -INFO means the i-th argument had an illegal value, >0 the leading minor of order INFO is not positive definite, and the factorization could not be completed.

potrf< double >() [1/2]

template<>

MXLAPACK_INT mx::math::potrf< double >	(	char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 75 of file templateLapack.cpp.

References six_fifths().

potrf< double >() [2/2]

template<>

MXLAPACK_INT mx::math::potrf< double >	(	char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 75 of file templateLapack.cpp.

References six_fifths().

potrf< float >() [1/2]

template<>

MXLAPACK_INT mx::math::potrf< float >	(	char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 58 of file templateLapack.cpp.

References six_fifths().

potrf< float >() [2/2]

template<>

MXLAPACK_INT mx::math::potrf< float >	(	char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 58 of file templateLapack.cpp.

References six_fifths().

potrf< std::complex< double > >() [1/2]

template<>

MXLAPACK_INT mx::math::potrf< std::complex< double > >	(	char	UPLO,
		MXLAPACK_INT	N,
		std::complex< double > *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 110 of file templateLapack.cpp.

References six_fifths().

potrf< std::complex< double > >() [2/2]

template<>

MXLAPACK_INT mx::math::potrf< std::complex< double > >	(	char	UPLO,
		MXLAPACK_INT	N,
		std::complex< double > *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 110 of file templateLapack.cpp.

References six_fifths().

potrf< std::complex< float > >() [1/2]

template<>

MXLAPACK_INT mx::math::potrf< std::complex< float > >	(	char	UPLO,
		MXLAPACK_INT	N,
		std::complex< float > *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 92 of file templateLapack.cpp.

References six_fifths().

potrf< std::complex< float > >() [2/2]

template<>

MXLAPACK_INT mx::math::potrf< std::complex< float > >	(	char	UPLO,
		MXLAPACK_INT	N,
		std::complex< float > *	A,
		MXLAPACK_INT	LDA,
		MXLAPACK_INT &	INFO
	)

Definition at line 92 of file templateLapack.cpp.

References six_fifths().

rad2deg< double >()

template<>

constexpr double mx::math::rad2deg< double > ( )

constexpr

Definition at line 210 of file constants.hpp.

References MX_INTERNAL_PI_100.

rad2deg< float >()

template<>

constexpr float mx::math::rad2deg< float > ( )

constexpr

Definition at line 204 of file constants.hpp.

References MX_INTERNAL_PI_100.

rad2deg< long double >()

template<>

constexpr long double mx::math::rad2deg< long double > ( )

constexpr

Definition at line 216 of file constants.hpp.

References MX_INTERNAL_PI_100.

root_two< double >()

template<>

constexpr double mx::math::root_two< double > ( )

constexpr

Definition at line 255 of file constants.hpp.

References MX_INTERNAL_ROOT2_100.

root_two< float >()

template<>

constexpr float mx::math::root_two< float > ( )

constexpr

Definition at line 249 of file constants.hpp.

References MX_INTERNAL_ROOT2_100.

root_two< long double >()

template<>

constexpr long double mx::math::root_two< long double > ( )

constexpr

Definition at line 261 of file constants.hpp.

References MX_INTERNAL_ROOT2_100.

scal< double >() [1/2]

template<>

void mx::math::scal< double >	(	const int	N,
		const double &	alpha,
		double *	X,
		const int	incX
	)

Definition at line 41 of file templateBLAS.cpp.

References six_fifths().

scal< double >() [2/2]

template<>

void mx::math::scal< double >	(	const int	N,
		const double &	alpha,
		double *	X,
		const int	incX
	)

Definition at line 41 of file templateBLAS.cpp.

References six_fifths().

scal< float >() [1/2]

template<>

void mx::math::scal< float >	(	const int	N,
		const float &	alpha,
		float *	X,
		const int	incX
	)

Definition at line 35 of file templateBLAS.cpp.

References six_fifths().

scal< float >() [2/2]

template<>

void mx::math::scal< float >	(	const int	N,
		const float &	alpha,
		float *	X,
		const int	incX
	)

Definition at line 35 of file templateBLAS.cpp.

References six_fifths().

scal< std::complex< double > >() [1/2]

template<>

void mx::math::scal< std::complex< double > >	(	const int	N,
		const std::complex< double > &	alpha,
		std::complex< double > *	X,
		const int	incX
	)

Definition at line 53 of file templateBLAS.cpp.

References six_fifths().

scal< std::complex< double > >() [2/2]

template<>

void mx::math::scal< std::complex< double > >	(	const int	N,
		const std::complex< double > &	alpha,
		std::complex< double > *	X,
		const int	incX
	)

Definition at line 53 of file templateBLAS.cpp.

References six_fifths().

scal< std::complex< float > >() [1/2]

template<>

void mx::math::scal< std::complex< float > >	(	const int	N,
		const std::complex< float > &	alpha,
		std::complex< float > *	X,
		const int	incX
	)

Definition at line 47 of file templateBLAS.cpp.

References six_fifths().

scal< std::complex< float > >() [2/2]

template<>

void mx::math::scal< std::complex< float > >	(	const int	N,
		const std::complex< float > &	alpha,
		std::complex< float > *	X,
		const int	incX
	)

Definition at line 47 of file templateBLAS.cpp.

References six_fifths().

syevr< double >() [1/2]

template<>

MXLAPACK_INT mx::math::syevr< double >	(	char	JOBZ,
		char	RANGE,
		char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double	VL,
		double	VU,
		MXLAPACK_INT	IL,
		MXLAPACK_INT	IU,
		double	ABSTOL,
		MXLAPACK_INT *	M,
		double *	W,
		double *	Z,
		MXLAPACK_INT	LDZ,
		MXLAPACK_INT *	ISUPPZ,
		double *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	LIWORK
	)

Definition at line 251 of file templateLapack.cpp.

References six_fifths().

syevr< double >() [2/2]

template<>

MXLAPACK_INT mx::math::syevr< double >	(	char	JOBZ,
		char	RANGE,
		char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double	VL,
		double	VU,
		MXLAPACK_INT	IL,
		MXLAPACK_INT	IU,
		double	ABSTOL,
		MXLAPACK_INT *	M,
		double *	W,
		double *	Z,
		MXLAPACK_INT	LDZ,
		MXLAPACK_INT *	ISUPPZ,
		double *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	LIWORK
	)

Definition at line 251 of file templateLapack.cpp.

References six_fifths().

syevr< float >() [1/2]

template<>

MXLAPACK_INT mx::math::syevr< float >	(	char	JOBZ,
		char	RANGE,
		char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float	VL,
		float	VU,
		MXLAPACK_INT	IL,
		MXLAPACK_INT	IU,
		float	ABSTOL,
		MXLAPACK_INT *	M,
		float *	W,
		float *	Z,
		MXLAPACK_INT	LDZ,
		MXLAPACK_INT *	ISUPPZ,
		float *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	LIWORK
	)

Definition at line 193 of file templateLapack.cpp.

References six_fifths().

syevr< float >() [2/2]

template<>

MXLAPACK_INT mx::math::syevr< float >	(	char	JOBZ,
		char	RANGE,
		char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float	VL,
		float	VU,
		MXLAPACK_INT	IL,
		MXLAPACK_INT	IU,
		float	ABSTOL,
		MXLAPACK_INT *	M,
		float *	W,
		float *	Z,
		MXLAPACK_INT	LDZ,
		MXLAPACK_INT *	ISUPPZ,
		float *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT *	IWORK,
		MXLAPACK_INT	LIWORK
	)

Definition at line 193 of file templateLapack.cpp.

References six_fifths().

syrk< double >() [1/2]

template<>

void mx::math::syrk< double >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const double &	alpha,
		const double *	A,
		const int	lda,
		const double &	beta,
		double *	C,
		const int	ldc
	)

Definition at line 154 of file templateBLAS.cpp.

References six_fifths().

syrk< double >() [2/2]

template<>

void mx::math::syrk< double >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const double &	alpha,
		const double *	A,
		const int	lda,
		const double &	beta,
		double *	C,
		const int	ldc
	)

Definition at line 154 of file templateBLAS.cpp.

References six_fifths().

syrk< float >() [1/2]

template<>

void mx::math::syrk< float >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const float &	alpha,
		const float *	A,
		const int	lda,
		const float &	beta,
		float *	C,
		const int	ldc
	)

Definition at line 138 of file templateBLAS.cpp.

References six_fifths().

syrk< float >() [2/2]

template<>

void mx::math::syrk< float >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const float &	alpha,
		const float *	A,
		const int	lda,
		const float &	beta,
		float *	C,
		const int	ldc
	)

Definition at line 138 of file templateBLAS.cpp.

References six_fifths().

syrk< std::complex< double > >() [1/2]

template<>

void mx::math::syrk< std::complex< double > >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const std::complex< double > &	alpha,
		const std::complex< double > *	A,
		const int	lda,
		const std::complex< double > &	beta,
		std::complex< double > *	C,
		const int	ldc
	)

Definition at line 186 of file templateBLAS.cpp.

References six_fifths().

syrk< std::complex< double > >() [2/2]

template<>

void mx::math::syrk< std::complex< double > >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const std::complex< double > &	alpha,
		const std::complex< double > *	A,
		const int	lda,
		const std::complex< double > &	beta,
		std::complex< double > *	C,
		const int	ldc
	)

Definition at line 186 of file templateBLAS.cpp.

References six_fifths().

syrk< std::complex< float > >() [1/2]

template<>

void mx::math::syrk< std::complex< float > >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const std::complex< float > &	alpha,
		const std::complex< float > *	A,
		const int	lda,
		const std::complex< float > &	beta,
		std::complex< float > *	C,
		const int	ldc
	)

Definition at line 170 of file templateBLAS.cpp.

References six_fifths().

syrk< std::complex< float > >() [2/2]

template<>

void mx::math::syrk< std::complex< float > >	(	const CBLAS_ORDER	Order,
		const CBLAS_UPLO	Uplo,
		const CBLAS_TRANSPOSE	Trans,
		const int	N,
		const int	K,
		const std::complex< float > &	alpha,
		const std::complex< float > *	A,
		const int	lda,
		const std::complex< float > &	beta,
		std::complex< float > *	C,
		const int	ldc
	)

Definition at line 170 of file templateBLAS.cpp.

References six_fifths().

sytrd< double >() [1/2]

template<>

MXLAPACK_INT mx::math::sytrd< double >	(	char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double *	D,
		double *	E,
		double *	TAU,
		double *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 160 of file templateLapack.cpp.

References six_fifths().

sytrd< double >() [2/2]

template<>

MXLAPACK_INT mx::math::sytrd< double >	(	char	UPLO,
		MXLAPACK_INT	N,
		double *	A,
		MXLAPACK_INT	LDA,
		double *	D,
		double *	E,
		double *	TAU,
		double *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 160 of file templateLapack.cpp.

References six_fifths().

sytrd< float >() [1/2]

template<>

MXLAPACK_INT mx::math::sytrd< float >	(	char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float *	D,
		float *	E,
		float *	TAU,
		float *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 128 of file templateLapack.cpp.

References six_fifths().

sytrd< float >() [2/2]

template<>

MXLAPACK_INT mx::math::sytrd< float >	(	char	UPLO,
		MXLAPACK_INT	N,
		float *	A,
		MXLAPACK_INT	LDA,
		float *	D,
		float *	E,
		float *	TAU,
		float *	WORK,
		MXLAPACK_INT	LWORK,
		MXLAPACK_INT	INFO
	)

Definition at line 128 of file templateLapack.cpp.

References six_fifths().

third< double >()

template<>

constexpr double mx::math::third< double > ( )

constexpr

Definition at line 344 of file constants.hpp.

third< float >()

template<>

constexpr float mx::math::third< float > ( )

constexpr

Definition at line 338 of file constants.hpp.

third< long double >()

template<>

constexpr long double mx::math::third< long double > ( )

constexpr

Definition at line 350 of file constants.hpp.

two_pi< double >()

template<>

constexpr double mx::math::two_pi< double > ( )

constexpr

Definition at line 119 of file constants.hpp.

References MX_INTERNAL_PI_100.

Referenced by mx::sigproc::comp_fourierModeDef(), mx::AO::analysis::kInt(), and mx::AO::analysis::zernikeCovariance< realT, aosysT >::kInt().

two_pi< float >()

template<>

constexpr float mx::math::two_pi< float > ( )

constexpr

Definition at line 113 of file constants.hpp.

References MX_INTERNAL_PI_100.

two_pi< long double >()

template<>

constexpr long double mx::math::two_pi< long double > ( )

constexpr

Definition at line 125 of file constants.hpp.

References MX_INTERNAL_PI_100.