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 arg=0.0)
virtual	~GaussianConvolution1D ()
virtual Level	natural_level () const
	Returns the level for projection. More...
Tensor< Q >	rnlp (Level n, Translation lx) const
	Compute the projection of the operator onto the double order polynomials. More...
bool	issmall (Level n, Translation lx) const
	Returns true if the block is expected to be small. More...
Public Member Functions inherited from madness::Convolution1D< Q >
virtual	~Convolution1D ()
	Convolution1D (int k, int npt, int maxR, double arg=0.0)
bool	get_issmall (Level n, Translation lx) const
	Returns true if the block of rnlp is expected to be small including periodicity. More...
const Tensor< Q > &	rnlij (Level n, Translation lx, bool do_transpose=false) const
	Computes the transition matrix elements for the convolution for n,l. More...
const ConvolutionData1D< Q > *	mod_nonstandard (const Key< 2 > &op_key) const
	Returns a pointer to the cached modified nonstandard form of the operator. More...
const ConvolutionData1D< Q > *	nonstandard (Level n, Translation lx) const
	Returns a pointer to the cached nonstandard form of the operator. More...
Q	phase (double R) const
Q	phase (double_complex R) const
const Tensor< Q > &	get_rnlp (Level n, Translation lx) const

Public Attributes
const Q	coeff
	Coefficient. More...
const double	expnt
	Exponent. More...
const Level	natlev
	Level to evaluate. More...
const int	m
	Order of derivative (0, 1, or 2 only) More...
Public Attributes inherited from madness::Convolution1D< Q >
int	k
	Wavelet order. More...
int	npt
	Number of quadrature points (is this used?) More...
int	maxR
	Number of lattice translations for sum. More...
Tensor< double >	quad_x
Tensor< double >	quad_w
Tensor< double >	c
Tensor< double >	hgT
Tensor< double >	hg
Tensor< double >	hgT2k
double	arg
SimpleCache< Tensor< Q >, 1 >	rnlp_cache
SimpleCache< Tensor< Q >, 1 >	rnlij_cache
SimpleCache< ConvolutionData1D < Q >, 1 >	ns_cache
SimpleCache< ConvolutionData1D < Q >, 2 >	mod_ns_cache

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

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

template<typename Q >

madness::GaussianConvolution1D< Q >::GaussianConvolution1D ( int  k, Q  coeff, double  expnt, int  m, bool  periodic, double  arg = 0.0  )

inlineexplicit

template<typename Q >

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

inlinevirtual

Member Function Documentation

template<typename Q >

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

inlinevirtual

Returns true if the block is expected to be small.

Implements madness::Convolution1D< Q >.

References beta.

template<typename Q >

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

inlinevirtual

Returns the level for projection.

Reimplemented from madness::Convolution1D< Q >.

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

template<typename Q >

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

inlinevirtual

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 beta, mpfr::exp(), madness::GaussianConvolution1D< Q >::expnt, madness::Convolution1D< Q >::k, madness::legendre_scaling_functions(), mpfr::log(), madness::Convolution1D< Q >::npt, madness::Convolution1D< Q >::quad_w, madness::Convolution1D< Q >::quad_x, and sqrt().

Member Data Documentation

template<typename Q >

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

Coefficient.

template<typename Q >

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

Exponent.

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

template<typename Q >

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

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

template<typename Q >

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

Level to evaluate.

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

---

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

• convolution1d.h