Files
file	ManagedMemory.h
	Base class and operators for managed-memory objects.

file	matrix.h

file	matrix3.h
	3x3 matrices with CPU and GPU operators

file	RadialFunction.h

file	scalar.h
	Complex numbers with CPU and GPU operators.

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

file	ScalarFieldArray.h
	Variable length arrays of ScalarField and ScalarFieldTildeArray, and their operators.

file	tensor3.h
	Symmetric traceless tensor with CPU and GPU operators.

file	vector3.h
	3-vector with CPU and GPU operators

file	VectorField.h
	Fixed-length multiplet of ScalarField and ScalarFieldTilde, and specialization to vector fields (3-component)

file	ColumnBundle.h

Classes
class	ManagedMemoryBase
	Base class for managed-memory objects (that could potentially live on GPUs as well) with unspecified data type. More...

class	ManagedMemory< T >
	Base class for managed memory of a specified data type. More...

struct	ManagedArray< T >

struct	IndexArray
	Managed array of integers (indices) More...

struct	IndexVecArray
	Managed array of integer vectors. More...

class	diagMatrix
	Real diagonal matrix. More...

class	matrix
	General complex matrix. More...

struct	matrixScaledTransOp
	Matrix with pending scale, submatrix and/or transpose operations. More...

class	tiledBlockMatrix
	A block matrix formed by repeating (tiling) a dense matrix along the diagonal. More...

class	matrix3< scalar >
	3x3 matrix More...

struct	symmetricMatrix3< scalar >
	Symmetric matrix that stores only non-redundant entries (with limited operations) More...

struct	SpaceGroupOp
	Space group operation r -> rot * r + a in real-space lattice coordinates. More...

struct	RadialFunctionG
	G-space radial function stored on a uniform grid (of \|G\|) More...

struct	RadialFunctionR
	A function on a non-uniform real-space radial grid. More...

struct	array< T, N >

struct	complex
	Complex number (need to define our own because we need operators for gpu code as well) More...

struct	FieldData< T >
	ManagedMemory wrapper with gridInfo and pending scale factor for ScalarField* classes. 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	scaled< T >
	Template to avoid (delay) scaling operations on linear objects. More...

class	tensor3< scalar >
	Symmetric traceless rank-2 tensor in 3D. More...

class	vector3< scalar >
	Generic 3-vector. More...

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

class	ColumnBundle
	Wavefunction data structure. More...

struct	ColumnBundleMatrixProduct
	ColumnBundle with a pending matrix multiply (on the right side) More...

Macros
#define	MUL_MAT_VEC(retType)

#define	MUL_VEC_MAT(retType)

#define	MUL_MAT_MAT(retType)

#define	__hostanddev__ inline

#define	TptrCollection std::vector<std::shared_ptr<T> >
	shorthand for templates below (undef'd at end of file)

#define	LOOP5(code) { for(int k=0; k<5; k++) { code } }

#define	LOOP3(code) { for(int k=0; k<3; k++) { code } }

#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 std::vector< ScalarField >	ScalarFieldArray
	dynamic size collection of real space scalar fields

typedef std::vector< ScalarFieldTilde >	ScalarFieldTildeArray
	dynamic size collection of reciprocal space scalar fields

typedef std::vector< complexScalarField >	complexScalarFieldArray
	dynamic size collection of complex scalar fields

typedef std::vector< complexScalarFieldTilde >	complexScalarFieldTildeArray
	dynamic size collection of reciprocal complex scalar fields

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
template<typename T >
void	memcpy (ManagedMemory< T > &, const ManagedMemory< T > &)
	copy entire object over

void	scale (double alpha, ManagedMemory< double > &y)

void	scale (double alpha, ManagedMemory< complex > &y)
	scale y *= alpha

void	scale (complex alpha, ManagedMemory< complex > &y)
	scale y *= alpha

void	scale (const ManagedMemory< complex > &x, ManagedMemory< complex > &y)
	scale y *= alpha

void	axpy (complex alpha, const ManagedMemory< complex > &x, ManagedMemory< complex > &y)
	scale y *= x elementwise More...

double	nrm2 (const ManagedMemory< complex > &)
	2-norm, pretending it is a vector

complex	dotc (const ManagedMemory< complex > &a, const ManagedMemory< complex > &b)
	return a^H b

matrix	conj (const scaled< matrix > &A)
	return element-wise complex conjugate of A

matrixScaledTransOp	dagger (const matrixScaledTransOp &A)
	return hermitian adjoint of A

matrixScaledTransOp	transpose (const matrixScaledTransOp &A)
	return transpose of A

matrix	dagger_symmetrize (const matrixScaledTransOp &A)

matrix	transpose_symmetrize (const matrixScaledTransOp &A)
	return adjoint symmetric part: (A + Adag)/2

double	nrm2 (const matrixScaledTransOp &A)
	return transpose symmetric part: (A + AT)/2 More...

matrix &	*operator=** (matrix &m, double s)

scaled< matrix >	operator* (double s, const matrix &m)

scaled< matrix >	operator* (const matrix &m, double s)

scaled< matrix >	operator- (const matrix &m)

matrix &	*operator=** (matrix &m, complex s)

matrix	operator* (complex s, const matrix &m)

matrix	operator* (const matrix &m, complex s)

diagMatrix	operator* (double s, const diagMatrix &m)

diagMatrix	operator* (const diagMatrix &m, double s)

diagMatrix	operator- (const diagMatrix &m)

matrix	operator* (const matrixScaledTransOp &, const matrixScaledTransOp &)

matrix	operator* (const diagMatrix &, const matrix &)

matrix	operator* (const matrix &, const diagMatrix &)

matrix	operator* (const std::vector< complex > &d, const matrix &m)

matrix	operator* (const matrix &m, const std::vector< complex > &d)

diagMatrix	operator* (const diagMatrix &, const diagMatrix &)

matrix &	operator+= (matrix &m1, const matrix &m2)

matrix &	operator-= (matrix &m1, const matrix &m2)

matrix	operator+ (const matrix &m1, const matrix &m2)

matrix	operator- (const matrix &m1, const matrix &m2)

void	axpy (double alpha, const diagMatrix &x, matrix &y)

matrix &	operator+= (matrix &m, const diagMatrix &d)

matrix &	operator-= (matrix &m, const diagMatrix &d)

matrix	operator+ (const matrix &m, const diagMatrix &d)

matrix	operator+ (const diagMatrix &d, const matrix &m)

matrix	operator- (const matrix &m, const diagMatrix &d)

matrix	operator- (const diagMatrix &d, const matrix &m)

void	axpy (double alpha, const diagMatrix &x, diagMatrix &y)

diagMatrix &	operator+= (diagMatrix &d1, const diagMatrix &d2)

diagMatrix &	operator-= (diagMatrix &d1, const diagMatrix &d2)

diagMatrix	operator+ (const diagMatrix &d1, const diagMatrix &d2)

diagMatrix	operator- (const diagMatrix &d1, const diagMatrix &d2)

diagMatrix	clone (const diagMatrix &x)

matrix	clone (const matrix &x)

double	dot (const diagMatrix &x, const diagMatrix &y)

double	dot (const matrix &x, const matrix &y)

void	randomize (diagMatrix &x)

void	randomize (matrix &x)

diagMatrix	diagDot (const matrix &X, const matrix &Y)
	Compute diag(dagger(X)*Y) efficiently (avoid the off-diagonals)

matrix	inv (const matrix &A)
	Compute / apply inverse: More...

diagMatrix	inv (const diagMatrix &A)
	inverse of diagonal matrix

matrix	invTriangular (const matrix &T, bool upper)
	return inv(T) for triangular matrix T (upper/lower for upper=true/false)

matrix	invApply (const matrix &A, const matrix &b)
	return inv(A) * b (A must be hermitian, positive-definite)

matrix	LU (const matrix &A)
	Compute the LU decomposition of the matrix.

matrix	cholesky (const matrix &A, bool upper)

complex	det (const matrix &A)

double	det (const diagMatrix &A)
	Compute the determinant of an diagonal matrix A.

matrix	pow (const matrix &A, double exponent, matrix Aevecs=0, diagMatrix Aeigs=0, bool *isSingular=0)

matrix	invsqrt (const matrix &A, matrix Aevecs=0, diagMatrix Aeigs=0, bool *isSingular=0)

matrix	orthoMatrix (const matrix &A)

matrix	cis (const matrix &A, matrix Aevecs=0, diagMatrix Aeigs=0)
	Compute cis(A) = exp(iota A) and optionally the eigensystem of A (if non-null)

matrix	cisInv (const matrix &A, matrix Bevecs=0, diagMatrix Beigs=0)

matrix	sqrt_grad (const matrix &grad_sqrtA, const matrix &Aevecs, const diagMatrix &Aeigs)
	Return gradient w.r.t A given gradient w.r.t sqrt(A) and A's eigensystem.

matrix	cis_grad (const matrix &grad_cisA, const matrix &Aevecs, const diagMatrix &Aeigs)
	Return gradient w.r.t A given gradient w.r.t cis(A) and A's eigensystem.

complex	trace (const matrix &m)
	trace of matrix

double	trace (const diagMatrix &m)
	trace of diagonal matrix

double	nrm2 (const diagMatrix &m)
	RMS of matrix entries.

diagMatrix	diag (const matrix &m)
	obtain the real diagonal part of a hermitian matrix

diagMatrix	eye (int N)
	identity

matrix	zeroes (int nRows, int nCols)
	a dense-matrix of zeroes

matrix	operator* (const matrix &m, const tiledBlockMatrix &tbm)
	multiply dense matrix by block matrix

template<typename scalar >
__hostanddev__ matrix3< scalar >	operator* (scalar s, const matrix3< scalar > &m)

template<typename scalar >
__hostanddev__ matrix3< scalar >	outer (const vector3< scalar > &a, const vector3< scalar > &b)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const matrix3< scalar > &m, const vector3< scalar > &v)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const matrix3< scalar > &m, const vector3< int > &v)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const matrix3< int > &m, const vector3< scalar > &v)

__hostanddev__ vector3< int >	operator* (const matrix3< int > &m, const vector3< int > &v)

__hostanddev__ vector3< complex >	operator* (const matrix3< complex > &m, const vector3<> &v)

__hostanddev__ vector3< complex >	operator* (const matrix3<> &m, const vector3< complex > &v)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< scalar > &v, const matrix3< scalar > &m)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< int > &v, const matrix3< scalar > &m)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< scalar > &v, const matrix3< int > &m)

__hostanddev__ vector3< int >	operator* (const vector3< int > &v, const matrix3< int > &m)

__hostanddev__ vector3< complex >	operator* (const vector3<> &v, const matrix3< complex > &m)

__hostanddev__ vector3< complex >	operator* (const vector3< complex > &v, const matrix3<> &m)

template<typename scalar >
__hostanddev__ matrix3< scalar >	operator* (const matrix3< scalar > &m, const matrix3< scalar > &n)

template<typename scalar >
__hostanddev__ matrix3< scalar >	operator* (const matrix3< scalar > &m, const matrix3< int > &n)

template<typename scalar >
__hostanddev__ matrix3< scalar >	operator* (const matrix3< int > &m, const matrix3< scalar > &n)

__hostanddev__ matrix3< int >	operator* (const matrix3< int > &m, const matrix3< int > &n)

template<typename scalar >
__hostanddev__ matrix3< scalar > &	*operator=** (matrix3< scalar > &m, const matrix3< scalar > &n)

template<typename scalar >
__hostanddev__ matrix3< scalar >	Diag (vector3< scalar > v)

template<typename scalar >
__hostanddev__ scalar	trace (const matrix3< scalar > &m)
	Trace of matrix.

template<typename scalar >
__hostanddev__ scalar	det (const matrix3< scalar > &m)
	Determinant of matrix.

template<typename scalar >
__hostanddev__ matrix3< scalar >	adjugate (const matrix3< scalar > &m)

__hostanddev__ matrix3	inv (const matrix3<> &m)

template<typename scalar >
__hostanddev__ scalar	nrm2sq (const matrix3< scalar > &m)
	square of 2-norm of matrix

template<typename scalar >
__hostanddev__ double	nrm2 (const matrix3< scalar > &m)
	2-norm of matrix

__hostanddev__ matrix3	rotation (double theta, int axis)
	Create a rotation matrix.

template<typename scalar >
__hostanddev__ symmetricMatrix3< scalar >	operator* (scalar s, symmetricMatrix3< scalar > m)
	Scale.

template<typename scalar >
__hostanddev__ symmetricMatrix3< scalar >	outer (const vector3< scalar > &v)
	Symmetric outer product of vector.

template<class T >
T	ceildiv (T num, T den)
	Ceiling of a positive integer division, templated over int types.

template<class T >
T	floorMultiple (T num, T den)
	Return largest multiple of den smaller than num, templated over int types.

__hostanddev__ double	real (const complex &c)
	real part

__hostanddev__ double	imag (const complex &c)
	imaginary part

__hostanddev__ double	norm (const complex &c)
	absolute value squared

__hostanddev__ double	abs (const complex &c)
	absolute value

__hostanddev__ double	arg (const complex &c)
	argument (phase angle)

__hostanddev__ complex	conj (const complex &c)
	complex conjugate

__hostanddev__ double	conj (const double &c)
	identity operation provided to ease templating over complex and double

__hostanddev__ complex	operator+ (double r, const complex &c)

__hostanddev__ complex	operator- (double r, const complex &c)

__hostanddev__ complex	operator* (double r, const complex &c)

__hostanddev__ complex	cis (double x)
	Compute cis(x) = exp(iota x) = cos(x) + iota sin(x)

template<typename T >
std::vector< typename T::DataType * >	dataPref (TptrCollection &x)
	Extract a std::vector of data pointers from a ScalarFieldArray.

template<typename T >
std::vector< const typename T::DataType * >	constDataPref (const TptrCollection &x)
	Extract a std::vector of const data pointers from a const ScalarFieldArray.

template<typename T >
TptrCollection	clone (const TptrCollection &x)
	Create a copy of the data (note operator= references same data since Tptr's are pointers!)

template<typename T >
TptrCollection &	operator*= (TptrCollection &x, double alpha)
	Scale.

template<class T >
TptrCollection	operator* (const TptrCollection &in, double scaleFac)

template<class T >
TptrCollection	operator* (double scaleFac, const TptrCollection &in)

template<class T >
TptrCollection	operator* (TptrCollection &&in, double scaleFac)
	Add (destructible input)

template<class T >
TptrCollection	operator* (double scaleFac, TptrCollection &&in)
	Add (destructible input)

template<typename T >
void	axpy (double alpha, const TptrCollection &x, TptrCollection &y)
	y += alpha x

ScalarFieldArray	operator* (const ScalarFieldArray &x, const ScalarFieldArray &y)
	elementise multiply

ScalarFieldArray	operator* (ScalarFieldArray &&x, const ScalarFieldArray &y)

ScalarFieldArray	operator* (const ScalarFieldArray &x, ScalarFieldArray &&y)

ScalarFieldArray &	*operator=** (ScalarFieldArray &y, const ScalarField &x)

ScalarFieldArray	operator* (const ScalarField &x, ScalarFieldArray &&y)

ScalarFieldArray	operator* (ScalarFieldArray &&y, const ScalarField &x)

ScalarFieldArray	operator* (const ScalarField &x, const ScalarFieldArray &y)

ScalarFieldArray	operator* (const ScalarFieldArray &y, const ScalarField &x)

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

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

template<class T >
TptrCollection	operator+ (const TptrCollection &in1, const TptrCollection &in2)

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

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

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

template<class T >
TptrCollection	operator- (const TptrCollection &in1, const TptrCollection &in2)

template<class T >
TptrCollection	operator- (const TptrCollection &in1, TptrCollection &&in2)
	Add (destructible inputs)

template<class T >
TptrCollection	operator- (TptrCollection &&in1, const TptrCollection &in2)
	Add (destructible inputs)

template<class T >
TptrCollection	operator- (TptrCollection &&in1, TptrCollection &&in2)
	Add (destructible inputs)

template<typename T >
double	dot (const TptrCollection &x, const TptrCollection &y)
	Inner product.

ScalarFieldTildeArray	lGradient (const ScalarFieldTilde &, int l)
	spherical tensor gradient of order l (2l+1 outputs, multiplied by Ylm(Ghat) (iG)^l)

ScalarFieldTilde	lDivergence (const ScalarFieldTildeArray &, int l)
	spherical tensor divergence of order l (2l+1 inputs, multiplied by Ylm(Ghat) (iG)^l, and summed)

matrix3	lGradientStress (const RadialFunctionG &, const ScalarFieldTilde &, const ScalarFieldTilde &, int l, int m)
	Stress corresponding to lGradient and a convolution.

template<typename T >
void	initZero (TptrCollection &x)
	Initialize (non-null) data to zero.

template<typename T >
void	nullToZero (TptrCollection &x, const GridInfo &gInfo, int N=0)

template<typename T >
void	initRandomFlat (TptrCollection &x)
	Initialize to random numbers (uniform on 0 to 1)

template<typename T >
void	randomize (TptrCollection &x)
	Initialize to normal random numbers:

template<typename T >
void	loadFromFile (TptrCollection &x, const char *filename)
	Load an array of scalar fields from a file.

template<typename T >
void	saveToFile (const TptrCollection &x, const char *filename)
	Save an array of scalar fields to a file.

ScalarFieldArray	I (ScalarFieldTildeArray &&X)

ScalarFieldArray	I (const ScalarFieldTildeArray &X)
	Reciprocal to real space.

ScalarFieldTildeArray	J (const ScalarFieldArray &X)

ScalarFieldTildeArray	Idag (const ScalarFieldArray &X)

ScalarFieldArray	Jdag (ScalarFieldTildeArray &&X)

ScalarFieldArray	Jdag (const ScalarFieldTildeArray &X)
	Hermitian conjugate of J.

ScalarFieldArray	Real (const complexScalarFieldArray X)

ScalarFieldArray	Imag (const complexScalarFieldArray X)

complexScalarFieldArray	Complex (const ScalarFieldArray re, const ScalarFieldArray im)

complexScalarFieldArray	Complex (const ScalarFieldArray re)

complexScalarFieldArray	conj (const complexScalarFieldArray X)

template<typename T >
T &	operator+= (T &y, const scaled< T > &x)

template<typename T >
T &	operator-= (T &y, const scaled< T > &x)

template<typename T >
T	operator+ (const scaled< T > &x, const scaled< T > &y)

template<typename T >
T	operator- (const scaled< T > &x, const scaled< T > &y)

template<typename T >
scaled< T >	operator- (const scaled< T > &x)

template<typename T >
scaled< T >	operator* (double s, const scaled< T > &x)

template<typename T >
scaled< T >	operator* (const scaled< T > &x, double s)

template<typename scalar >
__hostanddev__ tensor3< scalar >	operator* (scalar s, const tensor3< scalar > &a)

template<typename scalar >
__hostanddev__ tensor3< scalar >	operator* (const tensor3< scalar > &a, scalar s)

template<typename scalar >
__hostanddev__ tensor3< scalar >	loadTensor (const tensor3< const scalar * > &tArr, int i)
	Load tensor from a constant tensor field.

template<typename scalar >
__hostanddev__ tensor3< scalar >	loadTensor (const tensor3< scalar * > &tArr, int i)
	Load tensor from a tensor field.

template<typename scalar >
__hostanddev__ void	storeTensor (const tensor3< scalar > &t, tensor3< scalar * > &tArr, int i)
	Store tensor to a tensor field.

template<typename scalar >
__hostanddev__ void	accumTensor (const tensor3< scalar > &t, tensor3< scalar * > &tArr, int i)
	Accumulate tensor onto a tensor field.

template<typename scalar >
__hostanddev__ vector3< scalar >	operator+ (scalar s, const vector3< scalar > &a)

__hostanddev__ vector3< int >	operator+ (int s, const vector3< int > &a)

__hostanddev__ vector3< int >	operator+ (const vector3< int > &a, int s)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator+ (const vector3< scalar > &a, int s)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator+ (int s, const vector3< scalar > &a)

__hostanddev__ vector3	operator+ (vector3<> a, vector3< int > b)

__hostanddev__ vector3	operator+ (vector3< int > a, vector3<> b)

template<typename scalar >
__hostanddev__ vector3< scalar > &	*operator=** (vector3< scalar > &a, scalar s)

template<typename scalar >
__hostanddev__ vector3< scalar > &	*operator=** (vector3< scalar > &a, double s)

template<typename scalar >
__hostanddev__ vector3< scalar > &	*operator=** (vector3< scalar > &a, int s)

__hostanddev__ vector3 &	*operator=** (vector3<> &a, double s)

__hostanddev__ vector3 &	*operator=** (vector3<> &a, int s)

__hostanddev__ vector3< int > &	*operator=** (vector3< int > &a, int s)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (scalar s, const vector3< scalar > &a)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< scalar > &a, scalar s)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (double s, const vector3< scalar > &a)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< scalar > &a, double s)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (int s, const vector3< scalar > &a)

template<typename scalar >
__hostanddev__ vector3< scalar >	operator* (const vector3< scalar > &a, int s)

__hostanddev__ vector3	operator* (double s, const vector3<> &a)

__hostanddev__ vector3	operator* (const vector3<> &a, double s)

__hostanddev__ vector3	operator* (double s, const vector3< int > &a)

__hostanddev__ vector3	operator* (const vector3< int > &a, double s)

__hostanddev__ vector3< complex >	operator* (complex s, const vector3<> &a)

__hostanddev__ vector3< complex >	operator* (const vector3<> &a, complex s)

__hostanddev__ vector3< complex >	operator* (complex s, const vector3< int > &a)

__hostanddev__ vector3< complex >	operator* (const vector3< int > &a, complex s)

template<typename scalar >
__hostanddev__ scalar	dot (const vector3< scalar > &a, const vector3< scalar > &b)

template<typename scalar >
__hostanddev__ scalar	dot (const vector3< double > &a, const vector3< scalar > &b)

template<typename scalar >
__hostanddev__ scalar	dot (const vector3< int > &a, const vector3< scalar > &b)

template<typename scalar >
__hostanddev__ scalar	dot (const vector3< scalar > &a, const vector3< double > &b)

template<typename scalar >
__hostanddev__ scalar	dot (const vector3< scalar > &a, const vector3< int > &b)

__hostanddev__ double	dot (const vector3< double > &a, const vector3< double > &b)

__hostanddev__ double	dot (const vector3< int > &a, const vector3< double > &b)

__hostanddev__ double	dot (const vector3< double > &a, const vector3< int > &b)

__hostanddev__ int	dot (const vector3< int > &a, const vector3< int > &b)

template<typename scalar >
__hostanddev__ vector3< scalar >	cross (const vector3< scalar > &a, const vector3< scalar > &b)
	cross product

template<typename scalar >
__hostanddev__ scalar	box (const vector3< scalar > &a, const vector3< scalar > &b, const vector3< scalar > &c)
	box product / triple product

__hostanddev__ vector3< double >	normalize (const vector3<> &v)
	normalise vector

__hostanddev__ vector3< int >	round (const vector3<> &v, double *err=0)
	Round vector3<> to vector3<int> (and optionally retrieve error)

__hostanddev__ double	circDistanceSquared (const vector3<> &a, const vector3<> &b)

template<typename T >
T	gcd (T x, T y)
	GCD of integers, templated over integer types.

template<typename T >
vector3< T >	gcdReduce (const vector3< T > &d)
	Reduce an integer vector by its gcd.

template<typename scalar >
__hostanddev__ vector3< scalar >	loadVector (const vector3< const scalar * > &vArr, int i)
	Load vector from a constant vector field.

template<typename scalar >
__hostanddev__ vector3< scalar >	loadVector (const vector3< scalar * > &vArr, int i)
	Load vector from a vector field.

template<typename scalar >
__hostanddev__ void	storeVector (const vector3< scalar > &v, vector3< scalar * > &vArr, int i)
	Store vector to a vector field.

template<typename scalar >
__hostanddev__ void	accumVector (const vector3< scalar > &v, vector3< scalar * > &vArr, int i)
	Accumulate vector onto a vector field.

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 &in1, TptrMul &&in2)
	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	lengthSquaredWeighted (const vector3<> &w, const VectorField &X)
	Elementwise length squared (weighted)

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

matrix3	dotOuter (const VectorField &X, const VectorField &Y)
	Compute m(i,j) = dot(X[i], Y[j])

matrix3	dotOuter (const VectorField &X, const VectorField &Y, const ScalarField &w)
	Compute m(i,j) = dot(X[i], w * Y[j])

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)
	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)
	Inverse transform transpose: PW basis -> real space (destructible input)

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

template<int N>
RptrMul	I (const GptrMul &X)
	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

VectorFieldTilde	operator* (const RadialFunctionG &, const VectorFieldTilde &)
	Convolve a vector field by a radial function (preserve input)

VectorFieldTilde	operator* (const RadialFunctionG &, VectorFieldTilde &&)
	Convolve a vector field by a radial function (destructible input)

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)

void	init (std::vector< ColumnBundle > &, int nbundles, int ncols=0, const Basis basis=0, const ElecInfo eInfo=0)
	Initialize an array of column bundles (with appropriate wavefunction sizes if ncols, basis, qnum and eInfo are all non-zero)

void	randomize (std::vector< ColumnBundle > &, const ElecInfo &eInfo)
	randomize an array of columnbundles

ColumnBundle	clone (const ColumnBundle &)

void	randomize (ColumnBundle &x)
	Copies the input. More...

double	dot (const ColumnBundle &x, const ColumnBundle &y)
	inner product

ColumnBundle &	operator+= (ColumnBundle &Y, const scaled< ColumnBundle > &X)

ColumnBundle &	operator-= (ColumnBundle &Y, const scaled< ColumnBundle > &X)

ColumnBundle	operator+ (const scaled< ColumnBundle > &Y1, const scaled< ColumnBundle > &Y2)

ColumnBundle	operator- (const scaled< ColumnBundle > &Y1, const scaled< ColumnBundle > &Y2)

ColumnBundle &	*operator=** (ColumnBundle &X, double s)

ColumnBundle	operator* (double s, ColumnBundle &&Y)

ColumnBundle	operator* (ColumnBundle &&Y, double s)

scaled< ColumnBundle >	operator* (double s, const ColumnBundle &Y)

scaled< ColumnBundle >	operator* (const ColumnBundle &Y, double s)

scaled< ColumnBundle >	operator- (const ColumnBundle &Y)

ColumnBundle &	*operator=** (ColumnBundle &X, complex s)

ColumnBundle	operator* (complex s, const ColumnBundle &Y)

ColumnBundle	operator* (const ColumnBundle &Y, complex s)

ColumnBundleMatrixProduct	operator* (const scaled< ColumnBundle > &sY, const matrixScaledTransOp &Mst)

ColumnBundle &	operator+= (ColumnBundle &Y, const ColumnBundleMatrixProduct &XM)

ColumnBundle &	operator-= (ColumnBundle &Y, const ColumnBundleMatrixProduct &XM)

ColumnBundle	operator+ (const ColumnBundleMatrixProduct &XM1, const ColumnBundleMatrixProduct &XM2)

ColumnBundle	operator- (const ColumnBundleMatrixProduct &XM1, const ColumnBundleMatrixProduct &XM2)

ColumnBundle	operator* (const scaled< ColumnBundle > &, const diagMatrix &)

matrix	operator^ (const scaled< ColumnBundle > &, const scaled< ColumnBundle > &)
	inner product

vector3< matrix >	spinOverlap (const scaled< ColumnBundle > &sY)
	spin-resolved inner product for a spinorial ColumnBundle

ColumnBundle	Idag_DiagV_I (const ColumnBundle &C, const ScalarFieldArray &V, const ColumnBundle *Cout=0)

ColumnBundle	Idag_DiagV_I (const ColumnBundle &C, const complexScalarFieldArray &V, const ColumnBundle *Cout=0)
	Same as above for complex potentials.

ColumnBundle	L (const ColumnBundle &Y)
	Apply Laplacian.

ColumnBundle	Linv (const ColumnBundle &Y)
	Apply Laplacian inverse.

matrix3	Lstress (const ColumnBundle &Y, const diagMatrix &F)
	Compute lattice vector derivative of Tr[Y^LYF] (used for KE stress calculation)

ColumnBundle	O (const ColumnBundle &Y, std::vector< matrix > *VdagY=0)
	Apply overlap (and optionally retrieve pseudopotential projections for later reuse)

ColumnBundle	D (const ColumnBundle &Y, int iDir)
	Compute the cartesian gradient of a column bundle in direction# iDir.

ColumnBundle	D (const ColumnBundle &in, const vector3<> &dir)
	Directional derivative of column bundle along (cartesian direction) dir.

ColumnBundle	DD (const ColumnBundle &Y, int iDir, int jDir)
	Compute second spatial derivative of a column bundle along directions# iDir, jDir.

void	precond_inv_kinetic (ColumnBundle &Y, double KErollover, bool sqrtop=false)
	Apply inverse kinetic preconditioner (Roughly inv((k+G)^2/2)) in-place.

diagMatrix	diagDot (const ColumnBundle &X, const ColumnBundle &Y)
	compute diag(X^Y) efficiently (avoid the off-diagonals)

void	precond_inv_kinetic_band (ColumnBundle &Y, const diagMatrix &KEref)
	In-place inverse kinetic preconditioner with band-by-band KE reference (Used by BandDavidson)

ColumnBundle	translate (ColumnBundle &&, vector3<> dr)
	translate a column-bundle by dr in lattice coordinates (destructible input)

ColumnBundle	translate (const ColumnBundle &, vector3<> dr)
	translate a column-bundle by dr in lattice coordinates (preserve input)

void	translateColumns (ColumnBundle &, const vector3<> *dr)
	translate each column of a column bundle by a different dr (in-place)

ColumnBundle	switchBasis (const ColumnBundle &, const Basis &)
	return wavefunction projected to a different basis

complex	traceinner (const diagMatrix &F, const ColumnBundle &X, const ColumnBundle &Y)
	Return trace(F*X^Y)

ScalarFieldArray	diagouterI (const diagMatrix &F, const ColumnBundle &X, int nDensities, const GridInfo *gInfoOut=0)

complexScalarFieldArray	diagouterI (const diagMatrix &F, const ColumnBundle &A, const ColumnBundle &B, int nDensities, const GridInfo *gInfoOut)

Detailed Description

Macro Definition Documentation

◆ MUL_MAT_MAT

#define MUL_MAT_MAT ( retType )

Value:

        matrix3<retType> ret; \
        for(int i=0; i<3; i++) \
                for(int j=0; j<3; j++) \
                        for(int k=0; k<3; k++) \
                                ret(i,j) += m(i,k) * n(k,j); \
        return ret;

◆ MUL_MAT_VEC

#define MUL_MAT_VEC ( retType )

Value:

        vector3<retType> ret; \
        for(int i=0; i<3; i++) \
                for(int j=0; j<3; j++) \
                        ret[i] += m(i,j) * v[j]; \
        return ret;

◆ MUL_VEC_MAT

#define MUL_VEC_MAT ( retType )

Value:

        vector3<retType> ret; \
        for(int i=0; i<3; i++) \
                for(int j=0; j<3; j++) \
                        ret[j] += v[i] * m(i,j); \
        return ret;

Function Documentation

◆ adjugate()

template<typename scalar >

__hostanddev__ matrix3<scalar> adjugate ( const matrix3< scalar > & m )

Parameters

m	Calculate adjugate (matrix of signed cofactors)

◆ axpy()

void axpy	(	complex	alpha,
		const ManagedMemory< complex > &	x,
		ManagedMemory< complex > &	y
	)

scale y *= x elementwise

standard blas y += alpha*x

◆ cholesky()

matrix cholesky	(	const matrix &	A,
		bool	upper
	)

Compute Cholesky decomposition of positive definite matrix. Result in upper- / lower-triangular part for upper = true / false.

◆ circDistanceSquared()

__hostanddev__ double circDistanceSquared	(	const vector3<> &	a,
		const vector3<> &	b
	)

Return squared distance between a and b, interpreted as coordinates on a unit S1xS1xS1 embedded in R^6 i.e. sum of squares of distances between each coordinate put on a circle. This is useful for checking distances in a periodic cell safely.

◆ cisInv()

matrix cisInv	(	const matrix &	A,
		matrix *	Bevecs = `0`,
		diagMatrix *	Beigs = `0`
	)

Inverse function of cis: find matrix B such that A = exp(iota B). A must be unitary. Optionally retrieve the eigensystem of the result (note the real eigenvalues are of the input, not the result)

◆ det()

complex det ( const matrix & A )

Compute the determinant of an arbitrary matrix A (via LU decomposition) If skipZeros is true, skips diagonal entries in the diagonal of the LU decomposition that are below a tolerance

◆ Diag()

template<typename scalar >

__hostanddev__ matrix3<scalar> Diag ( vector3< scalar > v )

Parameters

v	Construct diagonal matrix

◆ diagouterI()

ScalarFieldArray diagouterI	(	const diagMatrix &	F,
		const ColumnBundle &	X,
		int	nDensities,
		const GridInfo *	gInfoOut = `0`
	)

Returns diag((I*X)*F*(I*X)^) (Compute density from an orthonormal wavefunction ColumnBundle with some fillings F). nDensities is the number of scalar field in the output and controls how spin/spinors are handled: 1: return total density regardless of spin / spinor nature 2: return spin density in X.qnum->index()'th component of the output (valid for non-spinor X only) 4: return spin density-matrix (valid for spinor X only) If gInfoOut is specified, function ensures that the output is changed to that grid (in case tighter wfns grid is in use)

◆ I()

ScalarFieldArray I ( ScalarFieldTildeArray && X )

inline

Parameters

X	Reciprocal to real space

◆ Idag()

ScalarFieldTildeArray Idag ( const ScalarFieldArray & X )

inline

Parameters

X	Hermitian conjugate of I

◆ Idag_DiagV_I()

ColumnBundle Idag_DiagV_I	(	const ColumnBundle &	C,
		const ScalarFieldArray &	V,
		const ColumnBundle *	Cout = `0`
	)

Return Idag V .* I C (evaluated columnwise) The handling of the spin structure of V parallels that of diagouterI, with V.size() taking the role of nDensities If Cout is specified, return output at the k-point and basis of Cout, else use k-point and basis of C.

◆ inv() [1/2]

matrix inv ( const matrix & A )

Compute / apply inverse:

inverse of matrix

◆ inv() [2/2]

__hostanddev__ matrix3 inv ( const matrix3<> & m )

Parameters

m	Matrix inverse

◆ invsqrt()

matrix invsqrt	(	const matrix &	A,
		matrix *	Aevecs = `0`,
		diagMatrix *	Aeigs = `0`,
		bool *	isSingular = `0`
	)

Compute matrix A^-0.5 and optionally the eigensystem of A (if non-null). If isSingular is provided, function will set it to true and return rather than stack-tracing in singular cases.

◆ J()

ScalarFieldTildeArray J ( const ScalarFieldArray & X )

inline

Parameters

X	Real to reciprocal space

◆ Jdag()

ScalarFieldArray Jdag ( ScalarFieldTildeArray && X )

inline

Parameters

X	Hermitian conjugate of J

◆ nrm2()

double nrm2 ( const matrixScaledTransOp & A )

return transpose symmetric part: (A + AT)/2

return 2-norm (avoid explicit transpose or sub-matrix operations)

◆ nullToZero()

template<typename T >

void nullToZero	(	TptrCollection &	x,
		const GridInfo &	gInfo,
		int	N = `0`
	)

Allocate all null components and initialize them to zero If N is non-zero, resize collection to N scalar fields

◆ operator+()

template<class T >

TptrCollection operator+	(	const TptrCollection &	in1,
		const TptrCollection &	in2
	)

< Add (destructible inputs)

◆ operator-()

template<class T >

TptrCollection operator-	(	const TptrCollection &	in1,
		const TptrCollection &	in2
	)

< Add (destructible inputs)

◆ orthoMatrix()

matrix orthoMatrix ( const matrix & A )

Compute matrix that orthonormalizes hermitian matrix A using Cholesky decomposition (effectively the Gram-Schmidt scheme). This is a potentially much faster alternative to invsqrt, applicable when the transformation does not have to be symmetric.

◆ outer()

template<typename scalar >

__hostanddev__ matrix3<scalar> outer	(	const vector3< scalar > &	a,
		const vector3< scalar > &	b
	)

Parameters

b	outer product

◆ pow()

matrix pow	(	const matrix &	A,
		double	exponent,
		matrix *	Aevecs = `0`,
		diagMatrix *	Aeigs = `0`,
		bool *	isSingular = `0`
	)

Compute matrix A^exponent, and optionally the eigensystem of A (if non-null). If isSingular is provided, function will set it to true and return rather than stack-tracing in singular cases.

◆ randomize()

void randomize ( ColumnBundle & x )

Copies the input.

Initialize to random numbers

Files

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ MUL_MAT_MAT

◆ MUL_MAT_VEC

◆ MUL_VEC_MAT

Function Documentation

◆ adjugate()

◆ axpy()

◆ cholesky()

◆ circDistanceSquared()

◆ cisInv()

◆ det()

◆ Diag()

◆ diagouterI()

◆ I()

◆ Idag()

◆ Idag_DiagV_I()

◆ inv() [1/2]

◆ inv() [2/2]

◆ invsqrt()

◆ J()

◆ Jdag()

◆ nrm2()

◆ nullToZero()

◆ operator+()

◆ operator-()

◆ orthoMatrix()

◆ outer()

◆ pow()

◆ randomize()