Operator implementations

Files
file	BlasExtra.h
	Commonly used BLAS-like routines.
file	Operators.h
	Operators on ScalarField's and ScalarFieldTilde's.
file	TranslationOperator.h

Classes
class	ColumnBundleTransform
	Handle transformation of ColumnBundles upon symmetry operations. More...
class	TranslationOperator
	Abstract base class for translation operators. More...
class	TranslationOperatorSpline
	Translation operator which works in real space using interpolating splines. More...
class	TranslationOperatorFourier
	The exact translation operator in PW basis, although much slower and with potential ringing issues. More...

Macros
#define	callPref(functionName)   functionName##_gpu
	Select between functionName and functionName_gpu for the CPU and GPU executables respectively.
#define	Tptr   std::shared_ptr<T>
	shorthand for writing the template operators (undef'd at end of header)

Functions
template<typename Ty , typename Tx >
void	eblas_mul (const int N, const Tx *X, const int incX, Ty *Y, const int incY)
	Templated elementwise multiply Y *= X for arrays X, Y. More...
void	eblas_dmul (const int N, const double *X, const int incX, double *Y, const int incY)
	Specialization of eblas_mul() for double[] *= double[].
void	eblas_zmul (const int N, const complex *X, const int incX, complex *Y, const int incY)
	Specialization of eblas_mul() for complex[] *= complex[].
void	eblas_zmuld (const int N, const double *X, const int incX, complex *Y, const int incY)
	Specialization of eblas_mul() for complex[] *= double[].
void	eblas_dmul_gpu (const int N, const double *X, const int incX, double *Y, const int incY)
	Equivalent of eblas_dmul() for GPU data pointers.
void	eblas_zmul_gpu (const int N, const complex *X, const int incX, complex *Y, const int incY)
	Equivalent of eblas_zmul() for GPU data pointers.
void	eblas_zmuld_gpu (const int N, const double *X, const int incX, complex *Y, const int incY)
	Equivalent of eblas_zmuld() for GPU data pointers.
template<typename Ty , typename Tx >
void	eblas_div (const int N, const Tx *X, const int incX, Ty *Y, const int incY)
	Templated elementwise divide Y /= X for arrays X, Y. More...
void	eblas_ddiv (const int N, const double *X, const int incX, double *Y, const int incY)
	Specialization of eblas_div() for double[] /= double[].
void	eblas_zdiv (const int N, const complex *X, const int incX, complex *Y, const int incY)
	Specialization of eblas_div() for complex[] /= complex[].
void	eblas_zdivd (const int N, const double *X, const int incX, complex *Y, const int incY)
	Specialization of eblas_div() for complex[] /= double[].
void	eblas_ddiv_gpu (const int N, const double *X, const int incX, double *Y, const int incY)
	Equivalent of eblas_ddiv() for GPU data pointers.
void	eblas_zdiv_gpu (const int N, const complex *X, const int incX, complex *Y, const int incY)
	Equivalent of eblas_zdiv() for GPU data pointers.
void	eblas_zdivd_gpu (const int N, const double *X, const int incX, complex *Y, const int incY)
	Equivalent of eblas_zdivd() for GPU data pointers.
void	eblas_sumStrided (const int N, const int stride, const double *X, double *result)
	Return sum over array of doubles with specified stride.
void	eblas_sumStrided_gpu (const int N, const int stride, const double *X, double *result)
	Equivalent of eblas_sumStrided() for X on GPU; result is on CPU.
template<typename T >
T	eblas_sum (const int N, const T *X)
	Return sum over array of generic type T composed only of a certain number of double members.
template<typename T >
T	eblas_sum_gpu (const int N, const T *X)
	Equivalent of eblas_sum() for GPU data pointers.
void	eblas_lincomb (const int N, const complex &sX, const complex *X, const int incX, const complex &sY, const complex *Y, const int incY, complex *Z, const int incZ)
	Elementwise linear combination Z = sX * X + sY * Y. More...
void	eblas_lincomb_gpu (const int N, const complex &sX, const complex *X, const int incX, const complex &sY, const complex *Y, const int incY, complex *Z, const int incZ)
	Equivalent of eblas_lincomb() for GPU data pointers.
void	eblas_zgemm (CBLAS_TRANSPOSE TransA, CBLAS_TRANSPOSE TransB, int M, int N, int K, const complex &alpha, const complex *A, const int lda, const complex *B, const int ldb, const complex &beta, complex *C, const int ldc)
	Threaded complex matrix multiply (threaded wrapper around zgemm) All the parameters have the same meaning as in cblas_zgemm, except element order is always Column Major (FORTRAN order!)
void	eblas_zgemm_gpu (CBLAS_TRANSPOSE TransA, CBLAS_TRANSPOSE TransB, int M, int N, int K, const complex &alpha, const complex *A, const int lda, const complex *B, const int ldb, const complex &beta, complex *C, const int ldc)
	Wrap cublasZgemm to provide the same interface as eblas_zgemm()
void	eblas_scatter_zdaxpy (const int Nindex, double a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Scatter y(index) += a * x. More...
void	eblas_scatter_zaxpy (const int Nindex, complex a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_scatter_zdaxpy() with a complex scale factor.
void	eblas_scatter_daxpy (const int Nindex, double a, const int *index, const double *x, double *y, const double *w=0)
	Equivalent of eblas_scatter_zdaxpy() for real data arrays.
void	eblas_gather_zdaxpy (const int Nindex, double a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Gather y += a * x(index) More...
void	eblas_gather_zaxpy (const int Nindex, complex a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_gather_zdaxpy() with a complex scale factor.
void	eblas_gather_daxpy (const int Nindex, double a, const int *index, const double *x, double *y, const double *w=0)
	Equivalent of eblas_scatter_zdaxpy() for real data arrays.
void	eblas_scatter_zdaxpy_gpu (const int Nindex, double a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_scatter_zdaxpy() for GPU data pointers.
void	eblas_scatter_zaxpy_gpu (const int Nindex, complex a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_scatter_zaxpy() for GPU data pointers.
void	eblas_scatter_daxpy_gpu (const int Nindex, double a, const int *index, const double *x, double *y, const double *w=0)
	Equivalent of eblas_scatter_daxpy() for GPU data pointers.
void	eblas_gather_zdaxpy_gpu (const int Nindex, double a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_gather_zdaxpy() for GPU data pointers.
void	eblas_gather_zaxpy_gpu (const int Nindex, complex a, const int *index, const complex *x, complex *y, bool conjx=false, const complex *w=0, bool conjw=false)
	Equivalent of eblas_gather_zaxpy() for GPU data pointers.
void	eblas_gather_daxpy_gpu (const int Nindex, double a, const int *index, const double *x, double *y, const double *w=0)
	Equivalent of eblas_gather_daxpy() for GPU data pointers.
void	eblas_accumNorm (int N, const double &a, const complex *x, double *y)
	Accumulate elementwise norm of a complex array x into y i.e. y += a x conj(x) More...
void	eblas_accumProd (int N, const double &a, const complex *xU, const complex *xC, double *yRe, double *yIm)
	Accumulate elementwise product of two complex arrays xU and xC into real and imaginary parts yRe and yIm i.e. (yRe + i yIm) += a xU conj(xC) More...
void	eblas_accumProdComplex (int N, const double &a, const complex *xU, const complex *xC, complex *y)
	Accumulate elementwise product of two complex arrays xU and xC into y. More...
void	eblas_accumNorm_gpu (int N, const double &a, const complex *x, double *y)
	Equivalent of eblas_accumNorm() for GPU data pointers.
void	eblas_accumProd_gpu (int N, const double &a, const complex *xU, const complex *xC, double *yRe, double *yIm)
	Equivalent of eblas_accumProd() for GPU data pointers.
void	eblas_accumProdComplex_gpu (int N, const double &a, const complex *xU, const complex *xC, complex *y)
	Equivalent of eblas_accumProd() for GPU data pointers.
void	eblas_symmetrize (int N, int n, const int *symmIndex, double *x)
	Symmetrize an array x, using N n-fold equivalence classes in symmIndex. More...
void	eblas_symmetrize (int N, int n, const int *symmIndex, complex *x)
	Equivalent of eblas_symmetrize() for complex data pointers.
void	eblas_symmetrize_gpu (int N, int n, const int *symmIndex, double *x)
	Equivalent of eblas_symmetrize() for real GPU data pointers.
void	eblas_symmetrize_gpu (int N, int n, const int *symmIndex, complex *x)
	Equivalent of eblas_symmetrize() for complex GPU data pointers.
void	eblas_symmetrize (int N, int n, const int *symmIndex, const int *symmMult, const complex *phase, complex *x)
	Symmetrize a complex array x with phase factors, using N n-fold equivalence classes in symmIndex (useful for space group symmetrization in reciprocal space) More...
void	eblas_symmetrize_gpu (int N, int n, const int *symmIndex, const int *symmMult, const complex *phase, complex *x)
	Equivalent of eblas_symmetrize() for complex GPU data pointers.
void	eblas_symmetrize (int N, int n, const int *symmIndex, const int *symmMult, const complex *phase, const matrix3<> *rotSpin, std::vector< complex * > x)
	Symmetrize a quadruplet of complex arrays with phase factors, using N n-fold equivalence classes in symmIndex (useful for space group symmetrization of spin density matrices in reciprocal space) More...
void	eblas_symmetrize_gpu (int N, int n, const int *symmIndex, const int *symmMult, const complex *phase, const matrix3<> *rotSpin, std::vector< complex * > x)
	Equivalent of eblas_symmetrize() for complex GPU data pointers.
template<typename T >
void	eblas_copy (T *dest, const T *src, int N)
	Copy a data array. More...
template<typename T >
void	eblas_zero (int N, T *x)
	Zero a data array. More...
void	eblas_dscal (int N, double a, double *x, int incx)
	Scale a real array: threaded wrapper to the cblas_dscal BLAS1 function.
void	eblas_zdscal (int N, double a, complex *x, int incx)
	Scale a complex array by a real scale factor: threaded wrapper to the cblas_zdscal BLAS1 function.
void	eblas_zscal (int N, const complex &a, complex *x, int incx)
	Scale a complex array by a complex scale factor: threaded wrapper to the cblas_zscal BLAS1 function.
void	eblas_daxpy (int N, double a, const double *x, int incx, double *y, int incy)
	Scaled-accumulate on real arrays: threaded wrapper to the cblas_daxpy BLAS1 function.
void	eblas_zaxpy (int N, const complex &a, const complex *x, int incx, complex *y, int incy)
	Scaled-accumulate on complex arrays: threaded wrapper to the cblas_zaxpy BLAS1 function.
complex	eblas_zdotc (int N, const complex *x, int incx, const complex *y, int incy)
	Dot product of complex arrays: threaded wrapper to the cblas_zdotc BLAS1 function.
double	eblas_ddot (int N, const double *x, int incx, const double *y, int ncy)
	Dot product of real arrays: threaded wrapper to the cblas_ddot BLAS1 function.
double	eblas_dznrm2 (int N, const complex *x, int incx)
	2-norm of a complex array: threaded wrapper to the cblas_dznrm2 BLAS1 function
double	eblas_dnrm2 (int N, const double *x, int incx)
	2-norm of a real array: threaded wrapper to the cblas_dnrm2 BLAS1 function
template<typename T >
void	eblas_copy_gpu (T *dest, const T *src, int N)
	Equivalent of eblas_copy() for GPU data pointers.
template<typename T >
void	eblas_zero_gpu (int N, T *x)
	Equivalent of eblas_zero() for GPU data pointers.
void	eblas_dscal_gpu (int N, double a, double *x, int incx)
	Equivalent of eblas_dscal() for GPU data pointers.
void	eblas_zdscal_gpu (int N, double a, complex *x, int incx)
	Equivalent of eblas_zdscal() for GPU data pointers.
void	eblas_zscal_gpu (int N, const complex &a, complex *x, int incx)
	Equivalent of eblas_zscal for GPU data pointers.
void	eblas_daxpy_gpu (int N, double a, const double *x, int incx, double *y, int incy)
	Equivalent of eblas_daxpy() for GPU data pointers.
void	eblas_zaxpy_gpu (int N, const complex &a, const complex *x, int incx, complex *y, int incy)
	Equivalent of eblas_zaxpy() for GPU data pointers.
complex	eblas_zdotc_gpu (int N, const complex *x, int incx, const complex *y, int incy)
	Equivalent of eblas_zdotc() for GPU data pointers.
double	eblas_ddot_gpu (int N, const double *x, int incx, const double *y, int incy)
	Equivalent of eblas_ddot() for GPU data pointers.
double	eblas_dznrm2_gpu (int N, const complex *x, int incx)
	Equivalent of eblas_dznrm2() for GPU data pointers.
double	eblas_dnrm2_gpu (int N, const double *x, int incx)
	Equivalent of eblas_dnrm2() for GPU data pointers.
void	eblas_capMinMax (const int N, double *x, double &xMin, double &xMax, double capLo=-DBL_MAX, double capHi=+DBL_MAX)
	Find the minimum and maximum of a data array and optionally cap it from above and/or below. More...
void	eblas_capMinMax_gpu (const int N, double *x, double &xMin, double &xMax, double capLo=-DBL_MAX, double capHi=+DBL_MAX)
	Equivalent of eblas_capMinMax() for GPU data pointers.
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

Function Documentation

checkSymmetry()

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

dot()

template<typename T >

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

Parameters

Y	Generic inner product for complex types

eblas_accumNorm()

void eblas_accumNorm	(	int	N,
		const double &	a,
		const complex *	x,
		double *	y
	)

Accumulate elementwise norm of a complex array x into y i.e. y += a x conj(x)

Parameters

N	Length of array
a	scale factor
x	Input complex data array
y	Ouput real data array

eblas_accumProd()

void eblas_accumProd	(	int	N,
		const double &	a,
		const complex *	xU,
		const complex *	xC,
		double *	yRe,
		double *	yIm
	)

Accumulate elementwise product of two complex arrays xU and xC into real and imaginary parts yRe and yIm i.e. (yRe + i yIm) += a xU conj(xC)

Parameters

N	Length of array
a	scale factor
xU	Unconjugated input complex data array
xC	Conjugated input complex data array
yRe	Ouput real-part data array
yIm	Ouput imaginary-part data array

eblas_accumProdComplex()

void eblas_accumProdComplex	(	int	N,
		const double &	a,
		const complex *	xU,
		const complex *	xC,
		complex *	y
	)

Accumulate elementwise product of two complex arrays xU and xC into y.

Parameters

N	Length of array
a	scale factor
xU	Unconjugated input complex data array
xC	Conjugated input complex data array
y	Output complex data array

eblas_capMinMax()

void eblas_capMinMax	(	const int	N,
		double *	x,
		double &	xMin,
		double &	xMax,
		double	capLo = -DBL_MAX,
		double	capHi = +DBL_MAX
	)

Find the minimum and maximum of a data array and optionally cap it from above and/or below.

Parameters

N	Length of data array
x	Input data array, that might be modified if capLo or capHi are finite
xMin	On output, the minimum of the input data array
xMax	On output, the maximum of the input data array
capLo	If finite, cap the data array on output from below at this value (no capping for the default value)
capHi	If finite, cap the data array on output from above at this value (no capping for the default value)

eblas_copy()

template<typename T >

void eblas_copy	(	T *	dest,
		const T *	src,
		int	N
	)

Copy a data array.

Template Parameters

T	Data type of the input and output arrays

Parameters

dest	Destination data pointer
src	Source data pointer
N	Number of elements of the data type T to copy

eblas_div()

template<typename Ty , typename Tx >

void eblas_div	(	const int	N,
		const Tx *	X,
		const int	incX,
		Ty *	Y,
		const int	incY
	)

Templated elementwise divide Y /= X for arrays X, Y.

Template Parameters

Ty	primiitive data-type for array Y
Tx	primiitive data-type for array X

Parameters

N	number of elements in X and Y
X	pointer to the first element of array X
incX	stride along the X array
Y	pointer to the first element of array Y
incY	stride along the Y array (must be non-zero)

eblas_gather_zdaxpy()

void eblas_gather_zdaxpy	(	const int	Nindex,
		double	a,
		const int *	index,
		const complex *	x,
		complex *	y,
		bool	conjx = false,
		const complex *	w = 0,
		bool	conjw = false
	)

Gather y += a * x(index)

Parameters

Nindex	Length of index array
a	Scale factor (real)
index	0-based index array (with length at least Nindex)
x	Input array that is sampled with the index array (with length at least max(index)+1)
y	Output array that is sampled consecutively (with length at least Nindex)
conjx	If true, use conj(x) instead of x
w	Optional array that is sampled consecutively and multiplies x elementwise
conjw	If true, use conj(w) instead of w

eblas_lincomb()

void eblas_lincomb	(	const int	N,
		const complex &	sX,
		const complex *	X,
		const int	incX,
		const complex &	sY,
		const complex *	Y,
		const int	incY,
		complex *	Z,
		const int	incZ
	)

Elementwise linear combination Z = sX * X + sY * Y.

Parameters

N	Number of elements in X, Y and X
sX	Scale factor for input X
X	Data pointer for input X
incX	Pointer increment for input X
sY	Scale factor for input Y
Y	Data pointer for input Y
incY	Pointer increment for input Y
Z	Data pointer for input Z
incZ	Pointer increment for input Z

eblas_mul()

template<typename Ty , typename Tx >

void eblas_mul	(	const int	N,
		const Tx *	X,
		const int	incX,
		Ty *	Y,
		const int	incY
	)

Templated elementwise multiply Y *= X for arrays X, Y.

Template Parameters

Ty	primiitive data-type for array Y
Tx	primiitive data-type for array X

Parameters

N	number of elements in X and Y
X	pointer to the first element of array X
incX	stride along the X array
Y	pointer to the first element of array Y
incY	stride along the Y array (must be non-zero)

eblas_scatter_zdaxpy()

void eblas_scatter_zdaxpy	(	const int	Nindex,
		double	a,
		const int *	index,
		const complex *	x,
		complex *	y,
		bool	conjx = false,
		const complex *	w = 0,
		bool	conjw = false
	)

Scatter y(index) += a * x.

Parameters

Nindex	Length of index array
a	Scale factor (real)
index	0-based index array (with length at least Nindex)
x	Input array that is sampled consecutively (with length at least Nindex)
y	Output array that is sampled with the index array (with length at least max(index)+1)
conjx	If true, use conj(x) instead of x
w	Optional array that is sampled consecutively and multiplies x elementwise
conjw	If true, use conj(w) instead of w

eblas_symmetrize() [1/3]

void eblas_symmetrize	(	int	N,
		int	n,
		const int *	symmIndex,
		const int *	symmMult,
		const complex *	phase,
		complex *	x
	)

Symmetrize a complex array x with phase factors, using N n-fold equivalence classes in symmIndex (useful for space group symmetrization in reciprocal space)

Parameters

N	Length of array x
n	Length of symmetry equivalence classes
symmIndex	Every consecutive set of n indices in this array forms an equivalence class
symmMult	Multiplicity per equivalence class (number of repetitions of each element in orbit)
phase	Phase factors corresponding to each entry in symmIndex
x	Data array to be symmetrized in place

eblas_symmetrize() [2/3]

void eblas_symmetrize	(	int	N,
		int	n,
		const int *	symmIndex,
		const int *	symmMult,
		const complex *	phase,
		const matrix3<> *	rotSpin,
		std::vector< complex * >	x
	)

Symmetrize a quadruplet of complex arrays with phase factors, using N n-fold equivalence classes in symmIndex (useful for space group symmetrization of spin density matrices in reciprocal space)

Parameters

N	Length of array x
n	Length of symmetry equivalence classes
symmIndex	Every consecutive set of n indices in this array forms an equivalence class
symmMult	Multiplicity per equivalence class (number of repetitions of each element in orbit)
phase	Phase factors corresponding to each entry in symmIndex
rotSpin	Cartesian pseudo-vector (eg. spin) rotations corresponding to each symmetry operation
x	Data array to be symmetrized in place

eblas_symmetrize() [3/3]

void eblas_symmetrize	(	int	N,
		int	n,
		const int *	symmIndex,
		double *	x
	)

Symmetrize an array x, using N n-fold equivalence classes in symmIndex.

Parameters

N	Length of array x
n	Length of symmetry equivalence classes
symmIndex	Every consecutive set of n indices in this array forms an equivalence class
x	Data array to be symmetrized in place

eblas_zero()

template<typename T >

void eblas_zero	(	int	N,
		T *	x
	)

Zero a data array.

Template Parameters

T	Data type of the array

Parameters

N	Number of elements to zero
x	Data pointer

nrm2()

template<typename T >

double nrm2

(

const Tptr &

X

)

Parameters

X	Generic 2-norm for complex types

removePhase()

void removePhase	(	size_t	N,
		complex *	data,
		double &	meanPhase,
		double &	sigmaPhase,
		double &	rmsImagErr
	)

Convert a complex wavefunction to a real one with optimum phase choice Store the phase statistics before conversion in meanPhase and sigmaPhase and the relative rms imaginary part truncated during conversion in rmsImagErr (Useful for getting real wavefunctions in gamma point only calculations or Wannier functions)

sum()

template<typename T >

complex sum

(

const Tptr &

X

)

Parameters

X	Generic sum for complex types