madness::GaussianConvolution1D< Q > Class Template Reference

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 >:

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, 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)

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)

where

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

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::KernelRange::N(), 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.

Referenced by main(), madness::test_rnlp_rangelimited(), and madness::test_rnlp_rangelimited_erf().

Member Data Documentation

coeff

template<typename Q >

const Q madness::GaussianConvolution1D< Q >::coeff

Coefficient.

Referenced by madness::GaussianConvolution1D< Q >::rnlp().

expnt

template<typename Q >

const double madness::GaussianConvolution1D< Q >::expnt

Exponent.

Referenced by madness::GaussianConvolution1D< Q >::issmall(), and madness::GaussianConvolution1D< Q >::rnlp().

m

template<typename Q >

const int madness::GaussianConvolution1D< Q >::m

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

Referenced by madness::GaussianConvolution1D< Q >::rnlp().

natlev

template<typename Q >

const Level madness::GaussianConvolution1D< Q >::natlev

Level to evaluate.

Referenced by madness::GaussianConvolution1D< Q >::natural_level().

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The documentation for this class was generated from the following file:

• convolution1d.h