1D convolution with (derivative) Gaussian; coeff and expnt given in simulation coordinates [0,1] More...

#include <convolution1d.h>

Inheritance diagram for madness::GaussianConvolution1D< Q >:

Collaboration diagram for madness::GaussianConvolution1D< Q >:

[legend]

Public Member Functions
	GaussianConvolution1D (int k, Q coeff, double expnt, int m, bool periodic, double bloch_k=0.0, KernelRange rng={})

virtual	~GaussianConvolution1D ()

bool	issmall (Level n, Translation lx) const final

virtual Level	natural_level () const final
	Returns the level for projection.

Tensor< Q >	rnlp (Level n, const Translation lx) const final
	Compute the projection of the operator onto the double order polynomials.

Public Member Functions inherited from madness::Convolution1D< Q >
	Convolution1D (int k, int npt, int maxR, double bloch_k=0.0, KernelRange rng={})

virtual	~Convolution1D ()

bool	get_issmall (Level n, Translation lx) const

const Tensor< Q > &	get_rnlp (Level n, Translation lx) const

bool	lattice_summed () const

const ConvolutionData1D< Q > *	mod_nonstandard (const Key< 2 > &op_key) const
	Returns a pointer to the cached modified make_nonstandard form of the operator.

const ConvolutionData1D< Q > *	nonstandard (Level n, Translation lx) const
	Returns a pointer to the cached make_nonstandard form of the operator.

Q	phase (double R) const

bool	range_restricted () const

const Tensor< Q > &	rnlij (Level n, Translation lx, bool do_transpose=false) const
	Computes the transition matrix elements for the convolution for n,l.

bool	rnlp_is_zero (Level n, Translation l) const

Public Attributes
const Q	coeff
	Coefficient.

const double	expnt
	Exponent.

const int	m
	Order of derivative (0, 1, or 2 only)

const Level	natlev
	Level to evaluate.

Public Attributes inherited from madness::Convolution1D< Q >
double	bloch_k
	k in exp(i k R) Bloch phase factor folded into lattice sum

Tensor< double >	c

Tensor< double >	hg

Tensor< double >	hgT

Tensor< double >	hgT2k

int	k
	Wavelet order.

int	maxR
	Number of lattice translations for sum.

SimpleCache< ConvolutionData1D< Q >, 2 >	mod_ns_cache

int	npt
	Number of quadrature points (is this used?)

SimpleCache< ConvolutionData1D< Q >, 1 >	ns_cache

Tensor< double >	quad_w

Tensor< double >	quad_x

KernelRange	range
	if range is nonnull, kernel range limited to to range (in simulation cell units), useful for finite-range convolutions with periodic functions

SimpleCache< Tensor< Q >, 1 >	rnlij_cache

SimpleCache< Tensor< Q >, 1 >	rnlp_cache

Static Private Member Functions
static int	maxR (bool periodic, double expnt, const KernelRange &rng={})

Additional Inherited Members
Public Types inherited from madness::Convolution1D< Q >
typedef Q	opT
	The apply function uses this to infer resultT=opT*inputT.

Detailed Description

template<typename Q>
class madness::GaussianConvolution1D< Q >

1D convolution with (derivative) Gaussian; coeff and expnt given in simulation coordinates [0,1]

Note that the derivative is computed in simulation coordinates so you must be careful to scale the coefficients correctly.

Constructor & Destructor Documentation

◆ GaussianConvolution1D()

template<typename Q >

madness::GaussianConvolution1D< Q >::GaussianConvolution1D	(	int	k,
		Q	coeff,
		double	expnt,
		int	m,
		bool	periodic,
		double	bloch_k = `0.0`,
		KernelRange	rng = `{}`
	)

inlineexplicit

◆ ~GaussianConvolution1D()

template<typename Q >

virtual madness::GaussianConvolution1D< Q >::~GaussianConvolution1D ( )

inlinevirtual

Member Function Documentation

◆ issmall()

template<typename Q >

bool madness::GaussianConvolution1D< Q >::issmall	(	Level	n,
		Translation	lx
	)		const

inlinefinalvirtual

Returns: true if the block of [r^n_l]_ij is expected to be small

Implements madness::Convolution1D< Q >.

References beta, madness::GaussianConvolution1D< Q >::expnt, madness::nonlinear_vector_solver(), and pow().

◆ maxR()

template<typename Q >

static int madness::GaussianConvolution1D< Q >::maxR	(	bool	periodic,
		double	expnt,
		const KernelRange &	rng = `{}`
	)

inlinestaticprivate

◆ natural_level()

template<typename Q >

virtual Level madness::GaussianConvolution1D< Q >::natural_level ( ) const

inlinefinalvirtual

Returns the level for projection.

Reimplemented from madness::Convolution1D< Q >.

References madness::GaussianConvolution1D< Q >::natlev.

◆ rnlp()

template<typename Q >

Tensor< Q > madness::GaussianConvolution1D< Q >::rnlp	(	Level	n,
		const Translation	lx
	)		const

inlinefinalvirtual

Compute the projection of the operator onto the double order polynomials.

The returned reference is to a cached tensor ... if you want to modify it, take a copy first.

Return in v[p] p=0..2*k-1

r(n,l,p) = 2^(-n) * int(K(2^(-n)*(z+l)) * phi(p,z), z=0..1)

p

char * p(char *buf, const char *name, int k, int initial_level, double thresh, int order)

Definition derivatives.cc:72

K

vecfuncT K(vecfuncT &ket, vecfuncT &bra, vecfuncT &vf)

The kernel is coeff*exp(-expnt*z^2)*z^m (with m>0). This is equivalent to

r(n,l,p) = 2^(-n*(m+1))*coeff * int( ((d/dz)^m exp(-beta*z^2)) * phi(p,z-l), z=l..l+1)

madness::GaussianConvolution1D::m

const int m

Order of derivative (0, 1, or 2 only)

Definition convolution1d.h:754

madness::GaussianConvolution1D::coeff

const Q coeff

Coefficient.

Definition convolution1d.h:751

beta

const double beta

Definition gygi_soltion.cc:62

madness::nonlinear_vector_solver

static XNonlinearSolver< std::vector< Function< T, NDIM > >, T, vector_function_allocator< T, NDIM > > nonlinear_vector_solver(World &world, const long nvec)

Definition nonlinsol.h:371

d

static const double d

Definition nonlinschro.cc:121

where

beta = alpha * 2^(-2*n)

alpha

static const double alpha

Definition testcosine.cc:10

Implements madness::Convolution1D< Q >.

References std::abs(), beta, madness::GaussianConvolution1D< Q >::coeff, e(), madness::GaussianConvolution1D< Q >::expnt, madness::KernelRange::finite(), madness::KernelRange::finite_hard(), madness::KernelRange::finite_soft(), h(), madness::KernelRange::iextent_x2(), madness::Convolution1D< Q >::k, L, madness::legendre_scaling_functions(), madness::GaussianConvolution1D< Q >::m, MADNESS_ASSERT, madness::MAXK, madness::KernelRange::N(), madness::nonlinear_vector_solver(), madness::Convolution1D< Q >::npt, p(), pow(), Q(), madness::Convolution1D< Q >::quad_w, madness::Convolution1D< Q >::quad_x, madness::Convolution1D< Q >::range, madness::Convolution1D< Q >::rnlp_is_zero(), madness::KernelRange::sigma(), v, madness::KernelRange::value(), and x0.