Operators.h File Reference

Operators on ScalarField's and ScalarFieldTilde's. More...

#include <core/ScalarField.h>
#include <core/BlasExtra.h>
#include <core/GridInfo.h>
#include <core/LoopMacros.h>
#include <core/RadialFunction.h>
#include <string.h>

Macros
#define	Tptr   std::shared_ptr<T>
	shorthand for writing the template operators (undef'd at end of header)

Functions
ScalarField	Real (const complexScalarField &)
	real part of a complex scalar field (real-space)
ScalarFieldTilde	Real (const complexScalarFieldTilde &)
	real part of a complex scalar field (reciprocal space)
ScalarField	Imag (const complexScalarField &)
	imaginary part of a complex scalar field (real-space)
ScalarFieldTilde	Imag (const complexScalarFieldTilde &)
	imaginary part of a complex scalar field (reciprocal space)
complexScalarField	Complex (const ScalarField &)
	convert real to complex scalar field with zero imaginary part (real-space)
complexScalarField	Complex (const ScalarField &re, const ScalarField &im)
	construct complex scalar field fromr eal and imaginary parts (real-space)
complexScalarFieldTilde	Complex (const ScalarFieldTilde &)
	convert real to complex scalar field with zero imaginary part (reciprocal-space)
ScalarFieldTilde	O (const ScalarFieldTilde &)
	Inner product operator (diagonal in PW basis)
ScalarFieldTilde	O (ScalarFieldTilde &&)
	Inner product operator (diagonal in PW basis)
complexScalarFieldTilde	O (const complexScalarFieldTilde &)
	Inner product operator (diagonal in PW basis)
complexScalarFieldTilde	O (complexScalarFieldTilde &&)
	Inner product operator (diagonal in PW basis)
ScalarField	I (const ScalarFieldTilde &, int nThreads=0)
	Forward transform: PW basis -> real space (preserve input)
ScalarField	I (ScalarFieldTilde &&, int nThreads=0)
	Forward transform: PW basis -> real space (destructible input)
complexScalarField	I (const complexScalarFieldTilde &, int nThreads=0)
	Forward transform: PW basis -> real space (preserve input)
complexScalarField	I (complexScalarFieldTilde &&, int nThreads=0)
	Forward transform: PW basis -> real space (destructible input)
ScalarFieldTilde	J (const ScalarField &, int nThreads=0)
	Inverse transform: Real space -> PW basis.
complexScalarFieldTilde	J (const complexScalarField &, int nThreads=0)
	Inverse transform: Real space -> PW basis (preserve input)
complexScalarFieldTilde	J (complexScalarField &&, int nThreads=0)
	Inverse transform: Real space -> PW basis (destructible input)
ScalarFieldTilde	Idag (const ScalarField &, int nThreads=0)
	Forward transform transpose: Real space -> PW basis.
complexScalarFieldTilde	Idag (const complexScalarField &, int nThreads=0)
	Forward transform transpose: Real space -> PW basis (preserve input)
complexScalarFieldTilde	Idag (complexScalarField &&, int nThreads=0)
	Forward transform transpose: Real space -> PW basis (destructible input)
ScalarField	Jdag (const ScalarFieldTilde &, int nThreads=0)
	Inverse transform transpose: PW basis -> real space (preserve input)
ScalarField	Jdag (ScalarFieldTilde &&, int nThreads=0)
	Inverse transform transpose: PW basis -> real space (destructible input)
complexScalarField	Jdag (const complexScalarFieldTilde &, int nThreads=0)
	Inverse transform transpose: PW basis -> real space (preserve input)
complexScalarField	Jdag (complexScalarFieldTilde &&, int nThreads=0)
	Inverse transform transpose: PW basis -> real space (destructible input)
ScalarField	JdagOJ (const ScalarField &)
	Evaluate Jdag(O(J())), which avoids 2 fourier transforms in PW basis (preserve input)
ScalarField	JdagOJ (ScalarField &&)
	Evaluate Jdag(O(J())), which avoids 2 fourier transforms in PW basis (destructible input)
complexScalarField	JdagOJ (const complexScalarField &)
	Evaluate Jdag(O(J())), which avoids 2 fourier transforms in PW basis (preserve input)
complexScalarField	JdagOJ (complexScalarField &&)
	Evaluate Jdag(O(J())), which avoids 2 fourier transforms in PW basis (destructible input)
ScalarFieldTilde	L (const ScalarFieldTilde &)
	Laplacian.
ScalarFieldTilde	L (ScalarFieldTilde &&)
	Laplacian.
complexScalarFieldTilde	L (const complexScalarFieldTilde &)
	Laplacian.
complexScalarFieldTilde	L (complexScalarFieldTilde &&)
	Laplacian.
matrix3	Lstress (const ScalarFieldTilde &X, const ScalarFieldTilde &Y)
	Lattice vector derivative of dot(X,L(Y))
ScalarFieldTilde	Linv (const ScalarFieldTilde &)
	Inverse Laplacian.
ScalarFieldTilde	Linv (ScalarFieldTilde &&)
	Inverse Laplacian.
complexScalarFieldTilde	Linv (const complexScalarFieldTilde &, vector3<> *k=0)
	Inverse Laplacian.
complexScalarFieldTilde	Linv (complexScalarFieldTilde &&, vector3<> *k=0)
	Inverse Laplacian.
complexScalarFieldTilde	Linv (const ScalarFieldTilde &in, vector3<> *k)
matrix3	LinvStress (const ScalarFieldTilde &X, const ScalarFieldTilde &Y)
	Lattice vector derivative of dot(X,Linv(Y))
ScalarFieldTilde	D (const ScalarFieldTilde &, int iDir)
	compute the gradient in the iDir'th cartesian direction
ScalarFieldTilde	D (const ScalarFieldTilde &in, const vector3<> &dir)
	directional derivative of scalar field along (cartesian direction) dir
ScalarFieldTilde	DD (const ScalarFieldTilde &, int iDir, int jDir)
	second derivative along iDir'th and jDir'th cartesian directions
void	zeroNyquist (RealKernel &Gdata)
	zeros out all the nyquist components of a real G-kernel
void	zeroNyquist (ScalarFieldTilde &Gptr)
	zeros out all the nyquist components of a G-space data array
void	zeroNyquist (ScalarField &Rptr)
	zeros out all the nyquist components of an R-space data array
void	removePhase (size_t N, complex *data, double &meanPhase, double &sigmaPhase, double &rmsImagErr)
void	translate (ScalarFieldTilde &, const vector3<> &r)
	Translate by vector r in Cartesian coordinates.
void	translate (complexScalarFieldTilde &, const vector3<> &r)
	Translate by vector r in Cartesian coordinates.
void	multiplyBlochPhase (complexScalarField &, const vector3<> &k)
	Multiply by Block phase for wave-vector k (in reciprocal lattice coordinates)
ScalarField	radialFunction (const GridInfo &gInfo, const RadialFunctionG &f, vector3<> r0)
	Create spherically-symmetric scalar field from radial form f, centered at lattice coordinates r0.
void	radialFunctionG (const RadialFunctionG &f, RealKernel &Kernel)
	Create a spherically-symmetric RealKernel from its radial form f.
ScalarFieldTilde	radialFunctionG (const GridInfo &gInfo, const RadialFunctionG &f, vector3<> r0)
	Create spherically-symmetric scalar field from radial form f, centered at lattice coordinates r0.
ScalarFieldTilde	operator* (const RadialFunctionG &, const ScalarFieldTilde &)
	Convolve a scalar field by a radial function (preserve input)
ScalarFieldTilde	operator* (const RadialFunctionG &, ScalarFieldTilde &&)
	Convolve a scalar field by a radial function (destructible input)
matrix3	convolveStress (const RadialFunctionG &w, const ScalarFieldTilde &X, const ScalarFieldTilde &Y)
	stress due to dot(X,O(w*Y))
ScalarField	exp (const ScalarField &)
	Elementwise exponential (preserve input)
ScalarField	exp (ScalarField &&)
	Elementwise exponential (destructible input)
ScalarField	log (const ScalarField &)
	Elementwise logarithm (preserve input)
ScalarField	log (ScalarField &&)
	Elementwise logarithm (destructible input)
ScalarField	sqrt (const ScalarField &)
	Elementwise square root (preserve input)
ScalarField	sqrt (ScalarField &&)
	Elementwise square root (destructible input)
ScalarField	inv (const ScalarField &)
	Elementwise reciprocal (preserve input)
ScalarField	inv (ScalarField &&)
	Elementwise reciprocal (destructible input)
ScalarField	pow (const ScalarField &, double alpha)
	Elementwise power (preserve input)
ScalarField	pow (ScalarField &&, double alpha)
	Elementwise power (destructible input)
template<class T >
Tptr	clone (const Tptr &X)
	Clone (NOTE: operator= is by reference for the ScalarField classes)
template<class T >
Tptr &	operator*= (Tptr &in, double scaleFac)
	Scale.
template<class T >
Tptr	operator* (const Tptr &in, double scaleFac)
	Scalar multiply (preserve input)
template<class T >
Tptr	operator* (double scaleFac, const Tptr &in)
	Scalar multiply (preserve input)
template<class T >
Tptr	operator* (Tptr &&in, double scaleFac)
	Scalar multiply (destructible input)
template<class T >
Tptr	operator* (double scaleFac, Tptr &&in)
	Scalar multiply (destructible input)
template<class T >
Tptr	conj (Tptr &&in)
	Generic elementwise conjugate for complex data:
template<class T >
Tptr	conj (const Tptr &in)
template<class T >
Tptr &	operator*= (Tptr &in, const Tptr &other)
	Generic elementwise multiply for complex data:
ScalarField &	operator*= (ScalarField &in, const ScalarField &other)
	Elementwise multiply for real data.
template<class T >
Tptr	operator* (const Tptr &in1, const Tptr &in2)
	Elementwise multiply (preserve inputs)
template<class T >
Tptr	operator* (const Tptr &in1, Tptr &&in2)
	Elementwise multiply (destructible input)
template<class T >
Tptr	operator* (Tptr &&in1, const Tptr &in2)
	Elementwise multiply (destructible input)
template<class T >
Tptr	operator* (Tptr &&in1, Tptr &&in2)
	Elementwise multiply (destructible inputs)
complexScalarField &	operator*= (complexScalarField &, const ScalarField &)
	elementwise multiply
complexScalarField	operator* (const complexScalarField &, const ScalarField &)
	elementwise multiply (preserve inputs)
complexScalarField	operator* (const ScalarField &, const complexScalarField &)
	elementwise multiply (preserve inputs)
complexScalarField	operator* (complexScalarField &&, const ScalarField &)
	elementwise multiply (destructible inputs)
complexScalarField	operator* (const ScalarField &, complexScalarField &&)
	elementwise multiply (destructible inputs)
ScalarFieldTilde &	operator*= (ScalarFieldTilde &, const RealKernel &)
	Elementwise multiply.
ScalarFieldTilde	operator* (const RealKernel &, const ScalarFieldTilde &)
	Elementwise multiply (preserve inputs)
ScalarFieldTilde	operator* (const ScalarFieldTilde &, const RealKernel &)
	Elementwise multiply (preserve inputs)
ScalarFieldTilde	operator* (const RealKernel &, ScalarFieldTilde &&)
	Elementwise multiply (destructible input)
ScalarFieldTilde	operator* (ScalarFieldTilde &&, const RealKernel &)
	Elementwise multiply (destructible input)
template<typename T >
void	axpy (double alpha, const Tptr &X, Tptr &Y)
	Generic axpy for complex data types (Note: null pointers are treated as zero)
void	axpy (double alpha, const ScalarField &X, ScalarField &Y)
	Real data Linear combine: Y += alpha * X (Note: null pointers are treated as zero)
template<class T >
Tptr &	operator+= (Tptr &in, const Tptr &other)
	Increment.
template<class T >
Tptr &	operator-= (Tptr &in, const Tptr &other)
	Decrement.
template<class T >
Tptr	operator+ (const Tptr &in1, const Tptr &in2)
	Add (preserve inputs)
template<class T >
Tptr	operator+ (const Tptr &in1, Tptr &&in2)
	Add (destructible input)
template<class T >
Tptr	operator+ (Tptr &&in1, const Tptr &in2)
	Add (destructible input)
template<class T >
Tptr	operator+ (Tptr &&in1, Tptr &&in2)
	Add (destructible inputs)
template<class T >
Tptr	operator- (const Tptr &in1, const Tptr &in2)
	Subtract (preserve inputs)
template<class T >
Tptr	operator- (const Tptr &in1, Tptr &&in2)
	Subtract (destructible input)
template<class T >
Tptr	operator- (Tptr &&in1, const Tptr &in2)
	Subtract (destructible input)
template<class T >
Tptr	operator- (Tptr &&in1, Tptr &&in2)
	Subtract (destructible inputs)
template<class T >
Tptr	operator- (const Tptr &in)
	Negate.
template<class T >
Tptr	operator- (Tptr &&in)
	Negate.
ScalarField &	operator+= (ScalarField &, double)
	Increment by scalar.
ScalarField	operator+ (double, const ScalarField &)
	Add scalar (preserve inputs)
ScalarField	operator+ (const ScalarField &, double)
	Add scalar (preserve inputs)
ScalarField	operator+ (double, ScalarField &&)
	Add scalar (destructible input)
ScalarField	operator+ (ScalarField &&, double)
	Add scalar (destructible input)
ScalarField &	operator-= (ScalarField &, double)
	Decrement by scalar.
ScalarField	operator- (double, const ScalarField &)
	Subtract from scalar (preserve inputs)
ScalarField	operator- (const ScalarField &, double)
	Subtract scalar (preserve inputs)
ScalarField	operator- (double, ScalarField &&)
	Subtract from scalar (destructible input)
ScalarField	operator- (ScalarField &&, double)
	Subtract scalar (destructible input)
template<typename T >
complex	dot (const Tptr &X, const Tptr &Y)
template<typename T >
double	nrm2 (const Tptr &X)
template<typename T >
complex	sum (const Tptr &X)
double	dot (const ScalarField &, const ScalarField &)
	Inner product.
double	dot (const ScalarFieldTilde &, const ScalarFieldTilde &)
	Inner product.
double	nrm2 (const ScalarField &)
	2-norm
double	nrm2 (const ScalarFieldTilde &)
	2-norm
double	sum (const ScalarField &)
	Sum of elements.
double	sum (const ScalarFieldTilde &)
	Equivalent to dot() with a ScalarFieldTilde of all 1s (NOTE: sum(X) != sum(I(X)))
double	integral (const ScalarField &)
	Integral in the unit cell (dV times sum())
double	integral (const ScalarFieldTilde &)
	Integral in the unit cell (just fetches the G=0 component with correct prefactor)
complex	integral (const complexScalarField &)
	Integral in the unit cell (dV times sum())
complex	integral (const complexScalarFieldTilde &)
	Integral in the unit cell (just fetches the G=0 component with correct prefactor)
ScalarFieldTilde	changeGrid (const ScalarFieldTilde &, const GridInfo &gInfoNew)
ScalarField	changeGrid (const ScalarField &, const GridInfo &gInfoNew)
complexScalarFieldTilde	changeGrid (const complexScalarFieldTilde &, const GridInfo &gInfoNew)
complexScalarField	changeGrid (const complexScalarField &, const GridInfo &gInfoNew)
template<typename T >
void	initZero (Tptr &X)
template<typename T >
void	initZero (Tptr &X, const GridInfo &gInfo)
template<typename T >
void	nullToZero (Tptr &X, const GridInfo &gInfo)
	If X is null, allocate and initialize to 0.
void	initRandom (ScalarField &, double cap=0.0)
	initialize element-wise with a unit-normal random number (with a cap if cap>0)
void	initRandomFlat (ScalarField &)
	initialize element-wise with a unit-flat [0:1) random number
void	randomize (ScalarFieldTilde &)
	alternate interface needed for Mnimize
void	initGaussianKernel (RealKernel &, double x0)
	initialize to gaussian kernel exp(-(G x0/2)^2)
void	initTranslation (ScalarFieldTilde &, const vector3<> &r)
	initialize to translation operator exp(-i G.r)
ScalarFieldTilde	gaussConvolve (const ScalarFieldTilde &, double sigma)
	convolve with a gaussian
ScalarFieldTilde	gaussConvolve (ScalarFieldTilde &&, double sigma)
	convolve with a gaussian (destructible input)
template<typename Func , typename... Args>
void	applyFuncGsq (const GridInfo &gInfo, const Func &f, Args... args)
	Evaluate a function f(i, Gsq, args...) at each point in reciprocal space indexed by i.
template<typename Func , typename... Args>
void	applyFunc_r (const GridInfo &gInfo, const Func &f, Args... args)
	Evaluate a function f(i, r, args...) at each point in real space index by i.
void	printStats (const ScalarField &X, const char *name, FILE *fp=stdout)
	Print mean and standard deviation of array with specified name (debug utility)
template<typename Callable , typename Vec >
void	checkSymmetry (Callable *func, const Vec &v1, const Vec &v2, const char *funcName)

Detailed Description

Operators on ScalarField's and ScalarFieldTilde's.