Files
file	Operators.h
	Operators on ScalarField's and ScalarFieldTilde's.

file	ScalarField.h
	Real and complex scalar fields in real and reciprocal space.

file	ScalarFieldIO.h
	I/O utilities for the data arrays.

file	VectorField.h
	Generic multiplet of data arrays (and specialized to triplets for vector fields in real/reciprocal space)

Classes
struct	FieldData
	Base class for ScalarFieldData and ScalarFieldTildeData. More...

struct	ScalarFieldData
	Real space real scalar field data Do not use this data structure directly or from a simple pointer ScalarFieldData*; work only with ScalarField's. The public functions of ScalarFieldData can be accessed with -> from the ScalarField. More...

struct	ScalarFieldTildeData
	Reciprocal space real scalar field data Do not use this data structure directly or from a simple pointer ScalarFieldTildeData*; work only with ScalarFieldTilde's. The public functions of ScalarFieldTildeData can be accessed with -> from the ScalarFieldTilde. More...

struct	complexScalarFieldData
	Real space complex scalar field data Do not use this data structure directly or from a simple pointer complexScalarFieldData*; work only with complexScalarField's. The public functions of complexScalarFieldData can be accessed with -> from the complexScalarField. More...

struct	complexScalarFieldTildeData
	Reciprocal space complex scalar field data Do not use this data structure directly or from a simple pointer complexScalarFieldTildeData*; work only with complexScalarFieldTilde's. The public functions of complexScalarFieldTildeData can be accessed with -> from the complexScalarFieldTilde. More...

struct	RealKernel
	Special class for storing real reciprocal-space kernels encountered ever so often for convolutions. More...

struct	ScalarFieldMultiplet< T, N >
	Generic multiplet object with overloaded arithmetic. More...

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

#define	DECLARE_DATA_PREF_ACCESS

#define	DECLARE_DATA_ACCESS

#define	Tptr std::shared_ptr<T>

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

#define	TptrMul ScalarFieldMultiplet<T,N>
	shorthand for the template operators/functions (undef'd at end of file)

#define	RptrMul ScalarFieldMultiplet<ScalarFieldData,N>
	shorthand for real-space-only template operators/functions (undef'd at end of file)

#define	GptrMul ScalarFieldMultiplet<ScalarFieldTildeData,N>
	shorthand for reciprocal-space-only template operators/functions (undef'd at end of file)

Typedefs
typedef std::shared_ptr< ScalarFieldData >	ScalarField
	A smart reference-counting pointer to ScalarFieldData.

typedef std::shared_ptr< ScalarFieldTildeData >	ScalarFieldTilde
	A smart reference-counting pointer to ScalarFieldTildeData.

typedef std::shared_ptr< complexScalarFieldData >	complexScalarField
	A smart reference-counting pointer to complexScalarFieldData.

typedef std::shared_ptr< complexScalarFieldTildeData >	complexScalarFieldTilde
	A smart reference-counting pointer to complexScalarFieldTildeData.

typedef ScalarFieldMultiplet< ScalarFieldData, 3 >	VectorField
	Real space vector field.

typedef ScalarFieldMultiplet< ScalarFieldTildeData, 3 >	VectorFieldTilde
	Reciprocal space vector field.

typedef ScalarFieldMultiplet< ScalarFieldData, 5 >	TensorField
	Symmetric traceless tensor: real space field.

typedef ScalarFieldMultiplet< ScalarFieldTildeData, 5 >	TensorFieldTilde
	Symmetric traceless tensor: reciprocal space field.

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 &, bool compat=false, int nThreads=0)
	Forward transform: PW basis -> real space (preserve input)

ScalarField	I (ScalarFieldTilde &&, bool compat=false, 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 &, bool compat=false, int nThreads=0)
	Inverse transform transpose: PW basis -> real space (preserve input)

ScalarField	Jdag (ScalarFieldTilde &&, bool compat=false, 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.

ScalarFieldTilde	Linv (const ScalarFieldTilde &)
	Inverse Laplacian.

ScalarFieldTilde	Linv (ScalarFieldTilde &&)
	Inverse Laplacian.

complexScalarFieldTilde	Linv (const complexScalarFieldTilde &)
	Inverse Laplacian.

complexScalarFieldTilde	Linv (complexScalarFieldTilde &&)
	Inverse Laplacian.

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

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	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)

template<typename T >
void	saveRawBinary (const Tptr &X, FILE *fp)
	Save the data in raw binary format to stream.

template<typename T >
void	saveRawBinary (const Tptr &X, const char *filename)
	Save the data in raw binary format to file.

template<typename T >
void	loadRawBinary (Tptr &X, FILE *fp)
	Load the data in raw binary format from stream.

template<typename T >
void	loadRawBinary (Tptr &X, const char *filename)
	Load the data in raw binary format from file.

void	saveDX (const ScalarField &, const char *filenamePrefix)

std::vector< std::vector< double > >	sphericalize (const ScalarField dataR, int nColumns, double drFac=1.0, vector3<> center=0)

void	saveSphericalized (const ScalarField dataR, int nColumns, const char filename, double drFac=1.0, vector3<> *center=0)

void	saveSphericalized (const ScalarFieldTilde dataG, int nColumns, const char filename, double dGFac=1.0)

template<class T , int N>
TptrMul	clone (const TptrMul &X)
	Clone (NOTE: operator= is by reference for ScalarField multiplets)

template<class T , int N>
void	initZero (TptrMul &X)
	Initialize data to 0 and scale factors to 1.

template<class T , int N>
void	nullToZero (TptrMul &X, const GridInfo &gInfo)
	Allocate and initialize each component of X to 0 if null.

template<int N>
void	initRandom (RptrMul &X, double cap=0.0)
	initialize element-wise with a unit-normal random number (with a cap if cap>0)

template<int N>
void	initRandomFlat (RptrMul &X)
	initialize element-wise with a unit-flat [0:1) random number

template<int N>
void	randomize (RptrMul &X)
	alternate interface required by Minimizable

template<class T , int N>
TptrMul &	operator*= (TptrMul &in, const TptrMul &other)
	Elementwise multiply each component.

template<class T , int N>
TptrMul	operator* (const TptrMul &in1, const TptrMul &in2)
	Elementwise multiply each component (preserve inputs)

template<class T , int N>
TptrMul	operator* (TptrMul &&in1, const TptrMul &in2)
	Elementwise multiply each component (destructible input)

template<class T , int N>
TptrMul	operator* (const TptrMul &in2, TptrMul &&in1)
	Elementwise multiply each component (destructible input)

template<class T , int N>
TptrMul	operator* (TptrMul &&in1, TptrMul &&in2)
	Elementwise multiply each component (destructible inputs)

template<class T , int N>
TptrMul &	operator*= (TptrMul &inM, const Tptr &inS)
	Elementwise multiply each component.

template<class T , int N>
TptrMul	operator* (const TptrMul &inM, const Tptr &inS)
	Elementwise multiply each component (preserve inputs)

template<class T , int N>
TptrMul	operator* (const Tptr &inS, const TptrMul &inM)
	Elementwise multiply each component (preserve inputs)

template<class T , int N>
TptrMul	operator* (TptrMul &&inM, const Tptr &inS)
	Elementwise multiply each component (destructible input)

template<class T , int N>
TptrMul	operator* (const Tptr &inS, TptrMul &&inM)
	Elementwise multiply each component (destructible input)

template<class T , int N>
TptrMul &	operator*= (TptrMul &in, double scaleFac)
	Scale.

template<class T , int N>
TptrMul	operator* (const TptrMul &in, double scaleFac)
	Scalar multiply (preserve input)

template<class T , int N>
TptrMul	operator* (double scaleFac, const TptrMul &in)
	Scalar multiply (preserve input)

template<class T , int N>
TptrMul	operator* (TptrMul &&in, double scaleFac)
	Scalar multiply (destructible input)

template<class T , int N>
TptrMul	operator* (double scaleFac, TptrMul &&in)
	Scalar multiply (destructible input)

template<class T >
ScalarFieldMultiplet< T, 3 >	operator* (vector3<> v, const Tptr &in)
	3-vector multiply

template<class T >
Tptr	dot (vector3<> v, const ScalarFieldMultiplet< T, 3 > &in)
	3-vector multiply

template<class T , int N>
void	axpy (double alpha, const TptrMul &X, TptrMul &Y)
	Linear combine Y += alpha * X.

template<class T , int N>
TptrMul &	operator+= (TptrMul &in, const TptrMul &other)
	Increment.

template<class T , int N>
TptrMul &	operator-= (TptrMul &in, const TptrMul &other)
	Decrement.

template<class T , int N>
TptrMul	operator+ (const TptrMul &in1, const TptrMul &in2)
	Add (preserve inputs)

template<class T , int N>
TptrMul	operator+ (const TptrMul &in1, TptrMul &&in2)
	Add (destructible input)

template<class T , int N>
TptrMul	operator+ (TptrMul &&in1, const TptrMul &in2)
	Add (destructible input)

template<class T , int N>
TptrMul	operator+ (TptrMul &&in1, TptrMul &&in2)
	Add (destructible inputs)

template<class T , int N>
TptrMul	operator- (const TptrMul &in1, const TptrMul &in2)
	Subtract (preserve input)

template<class T , int N>
TptrMul	operator- (const TptrMul &in1, TptrMul &&in2)
	Subtract (destructible input)

template<class T , int N>
TptrMul	operator- (TptrMul &&in1, const TptrMul &in2)
	Subtract (destructible input)

template<class T , int N>
TptrMul	operator- (TptrMul &&in1, TptrMul &&in2)
	Subtract (destructible inputs)

template<class T , int N>
TptrMul	operator- (const TptrMul &in)
	Negate.

template<class T , int N>
TptrMul	operator- (TptrMul &&in)
	Negate.

template<class T , int N>
void	axpy (double alpha, const Tptr &X, TptrMul &Y)
	Linear combine Y += alpha * X.

template<class T , int N>
TptrMul &	operator+= (TptrMul &in, const Tptr &other)
	Increment.

template<class T , int N>
TptrMul &	operator-= (TptrMul &in, const Tptr &other)
	Decrement.

template<class T , int N>
TptrMul	operator+ (const TptrMul &in1, const Tptr &in2)
	Add (preserve inputs)

template<class T , int N>
TptrMul	operator+ (const Tptr &in1, const TptrMul &in2)
	Add (preserve inputs)

template<class T , int N>
TptrMul	operator+ (const Tptr &in1, TptrMul &&in2)
	Add (destructible input)

template<class T , int N>
TptrMul	operator+ (TptrMul &&in1, const Tptr &in2)
	Add (destructible input)

template<class T , int N>
TptrMul	operator- (const TptrMul &in1, const Tptr &in2)
	Subtract (preserve input)

template<class T , int N>
TptrMul	operator- (const Tptr &in1, const TptrMul &in2)
	Subtract (preserve input)

template<class T , int N>
TptrMul	operator- (TptrMul &&in1, const Tptr &in2)
	Subtract (destructible input)

template<class T , int N>
TptrMul	operator- (const Tptr &in1, TptrMul &&in2)
	Subtract (destructible input)

template<class T , int N>
double	dot (const TptrMul &X, const TptrMul &Y)
	Inner product.

template<class T , int N>
double	nrm2 (const TptrMul &X)
	2-norm

template<class T , int N>
double	sum (const TptrMul &X)
	Sum of elements.

vector3	getGzero (const VectorFieldTilde &X)
	return G=0 components

void	setGzero (const VectorFieldTilde &X, vector3<> v)
	set G=0 components

vector3	sumComponents (const VectorField &X)
	Sum of elements (component-wise)

ScalarField	lengthSquared (const VectorField &X)
	Elementwise length squared.

ScalarField	dotElemwise (const VectorField &X, const VectorField &Y)
	Elementwise dot.

template<int N>
RptrMul &	operator+= (RptrMul &in, double scalar)
	Increment by scalar.

template<int N>
RptrMul	operator+ (double scalar, const RptrMul &in)
	Add scalar (preserve input)

template<int N>
RptrMul	operator+ (const RptrMul &in, double scalar)
	Add scalar (preserve input)

template<int N>
RptrMul	operator+ (double scalar, RptrMul &&in)
	Add scalar (destructible input)

template<int N>
RptrMul	operator+ (RptrMul &&in, double scalar)
	Add scalar (destructible input)

template<int N>
GptrMul &	operator*= (GptrMul &in, const RealKernel &kernel)
	Multiply by kernel.

template<int N>
GptrMul	operator* (const RealKernel &kernel, const GptrMul &in)
	Multiply by kernel (preserve input)

template<int N>
GptrMul	operator* (const GptrMul &in, const RealKernel &kernel)
	Multiply by kernel (preserve input)

template<int N>
GptrMul	operator* (const RealKernel &kernel, GptrMul &&in)
	Multiply by kernel (destructible input)

template<int N>
GptrMul	operator* (GptrMul &&in, const RealKernel &kernel)
	Multiply by kernel (destructible input)

template<int N>
GptrMul	O (GptrMul &&X)
	Inner product operator (diagonal in PW basis)

template<int N>
GptrMul	O (const GptrMul &X)
	Inner product operator (diagonal in PW basis)

template<int N>
RptrMul	I (GptrMul &&X, bool compat=false)
	Forward transform: PW basis -> real space (destructible input)

template<int N>
GptrMul	J (const RptrMul &X)
	Inverse transform: Real space -> PW basis.

template<int N>
GptrMul	Idag (const RptrMul &X)
	Forward transform transpose: Real space -> PW basis.

template<int N>
RptrMul	Jdag (GptrMul &&X, bool compat=false)
	Inverse transform transpose: PW basis -> real space (destructible input)

template<int N>
RptrMul	Jdag (const GptrMul &X, bool compat=false)
	Inverse transform transpose: PW basis -> real space (preserve input)

template<int N>
RptrMul	I (const GptrMul &X, bool compat=false)
	Forward transform: PW basis -> real space (preserve input)

VectorFieldTilde	gradient (const ScalarFieldTilde &)
	compute the gradient of a complex field, returns cartesian components

VectorField	gradient (const ScalarField &)
	compute the gradient of a complex field, returns cartesian components

ScalarFieldTilde	divergence (const VectorFieldTilde &)
	compute the divergence of a vector field specified in cartesian components

ScalarField	divergence (const VectorField &)
	compute the divergence of a vector field specified in cartesian components

TensorFieldTilde	tensorGradient (const ScalarFieldTilde &)
	symmetric traceless tensor second derivative of a scalar field

ScalarFieldTilde	tensorDivergence (const TensorFieldTilde &)
	second derivative contraction of a symmetric traceless tensor field

template<int N>
void	printStats (const RptrMul &, const char name, FILE fpLog=stdout)
	Print mean and standard deviation of each component array with specified name (debug utility)

Detailed Description

Macro Definition Documentation

#define DECLARE_DATA_ACCESS

Value:

DataType* data(bool shouldAbsorbScale=true) { return (DataType*)FieldData::data(shouldAbsorbScale); } \
                const DataType* data(bool shouldAbsorbScale=true) const { return (const DataType*)FieldData::data(shouldAbsorbScale); } \
                DataType* dataGpu(bool shouldAbsorbScale=true) { return (DataType*)FieldData::dataGpu(shouldAbsorbScale); } \
                const DataType* dataGpu(bool shouldAbsorbScale=true) const { return (const DataType*)FieldData::dataGpu(shouldAbsorbScale); }

#define DECLARE_DATA_PREF_ACCESS

Value:

DataType* dataPref(bool shouldAbsorbScale=true) { return dataGpu(shouldAbsorbScale); } \

const DataType* dataPref(bool shouldAbsorbScale=true) const { return dataGpu(shouldAbsorbScale); }

dataPref

std::vector< typename T::DataType * > dataPref(TptrCollection &x)

Extract a std::vector of data pointers from a ScalarFieldArray.

Definition: ScalarFieldArray.h:37

Function Documentation

template<typename Callable , typename Vec >

void checkSymmetry	(	Callable *	func,
		const Vec &	v1,
		const Vec &	v2,
		const char *	funcName
	)

Check the symmetry of a linear operator

Template Parameters

Callable	An operator with function call signature Vec Callable(const Vec&)
Vec	Any operand type representing an element of a vector space

template<typename T >

complex dot	(	const Tptr &	X,
		const Tptr &	Y
	)

Parameters

Y	Generic inner product for complex types

template<typename T >

double nrm2 ( const Tptr & X )

Parameters

X	Generic 2-norm for complex types

void saveDX	(	const ScalarField &	,
		const char *	filenamePrefix
	)

Save data to a raw binary along with a DataExplorer header

Parameters

filenamePrefix Binary data is saved to filenamePrefix.bin with DataExplorer header filenamePrefix.dx

void saveSphericalized	(	const ScalarField *	dataR,
		int	nColumns,
		const char *	filename,
		double	drFac = `1.0`,
		vector3<> *	center = `0`
	)

Saves an array of real space data pointers to a multicolumn 1D 'sphericalized' file (for gnuplot)

Parameters

dataR	The data to sphericalize and save
nColumns	Number of ScalarField's in dataR[]
filename	Output file in which column 1 will be the radius, column 2 to nColumns+1 would be the sphericalized versions of dataR[0 to nColumns-1]
drFac	is the spacing in radius as a fraction of the diameter of the sample box (R ./ S) (drFac << 1 is likely to give noisy results, particularly close to r=0)
center	The origin for spherical coordinates [default = center of box (if null pointer is passed)]

void saveSphericalized	(	const ScalarFieldTilde *	dataG,
		int	nColumns,
		const char *	filename,
		double	dGFac = `1.0`
	)

Saves an array of reciprocal space data pointers to a multicolumn 1D 'sphericalized' file (for gnuplot)

Parameters

dataG	The data to sphericalize (about G=0) and save
nColumns	Number of ScalarFieldTilde's in dataG[]
filename	Output file in which column 1 will be the radius, column 2 to nColumns+1 would be the sphericalized versions of dataG[0 to nColumns-1]
dGFac	is the spacing in radius as a fraction of the diameter of the Brillouin zone (dGFac << 1 is likely to give noisy results, particularly close to G=0)

std::vector< std::vector<double> > sphericalize	(	const ScalarField *	dataR,
		int	nColumns,
		double	drFac = `1.0`,
		vector3<> *	center = `0`
	)

Spherically average scalar fields about an arbitrary center (with Wigner-Seitz wrapping)

Parameters

dataR	The data to sphericalize and save
nColumns	Number of ScalarField's in dataR[]
drFac	is the spacing in radius as a fraction of the diameter of the sample box (R ./ S) (drFac << 1 is likely to give noisy results, particularly close to r=0)
center	The origin for spherical coordinates [default = center of box (if null pointer is passed)]

Returns: The first array contains the radial grid, and the subsequent ones the spherically-averaged results, one for each dataR, and the last column contains the weight of the radial grid point

template<typename T >

complex sum ( const Tptr & X )

Parameters

X	Generic sum for complex types

Files

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

Function Documentation