Core namespace for Ensign's numerical algorithms and data structures. More...

Namespaces
namespace	gt
	Named and aggregated timers for profiling code sections.

namespace	IndexFunction
	Conversion and iteration helpers for multidimensional indices.

namespace	Matrix
	Dense matrix operations.

namespace	Tensor
	Tensor matricization, tensorization, and orthogonalization operations.

Classes
struct	external_node
	Represents a leaf tree node with a basis matrix. More...

struct	fft
	FFT for arbitrary dimensional data, specified by dim. More...

struct	internal_node
	Represents an internal tree node with a coefficient tensor. More...

struct	lr2
	Class to store the low-rank factors (X, S, V) that are used in the computation. More...

struct	multi_array
	Dense d-dimensional array stored contiguously in column-major order (i.e. More...

struct	nc_writer
	Writes simulation variables and dimension metadata to a NetCDF file. More...

struct	node
	Base class for a node in a tree tensor network. More...

struct	orthogonalize
	Orthogonalizes Q and returns the corresponding upper triangular matrix R. More...

struct	timer
	This timer class measures the elapsed time between two events. More...

Typedefs
template<size_t d>
using	fft3d = fft< d, 3 >

template<size_t d>
using	fft2d = fft< d, 2 >

template<size_t d>
using	fft1d = fft< d, 1 >

Functions
template<typename T , typename... Args>
std::unique_ptr< T >	make_unique_ptr (Args &&... args)

array< fftw_plan, 2 >	create_plans_1d (Index dims_, multi_array< double, 2 > &real, multi_array< complex< double >, 2 > &freq)
	Helper routines to create FFTW plans for 1d transforms.

array< fftw_plan, 2 >	create_plans_1d (Index dims_, multi_array< double, 1 > &real, multi_array< complex< double >, 1 > &freq)

array< fftw_plan, 2 >	create_plans_2d (array< Index, 2 > dims_, multi_array< double, 1 > &real, multi_array< complex< double >, 1 > &freq)
	Helper routines to create FFTW plans for 2d transforms.

array< fftw_plan, 2 >	create_plans_2d (array< Index, 2 > dims_, multi_array< double, 2 > &real, multi_array< complex< double >, 2 > &freq)

array< fftw_plan, 2 >	create_plans_3d (array< Index, 3 > dims_, multi_array< double, 2 > &real, multi_array< complex< double >, 2 > &freq)
	Helper routines to create FFTW plans for 3d transforms.

array< fftw_plan, 2 >	create_plans_3d (array< Index, 3 > dims_, multi_array< double, 1 > &real, multi_array< complex< double >, 1 > &freq)

array< fftw_plan, 2 >	create_plans_3d_adapt (array< Index, 3 > dims_, multi_array< double, 2 > &real, multi_array< complex< double >, 2 > &freq)

void	destroy_plans (array< fftw_plan, 2 > &plans)
	Helper function to destroy FFTW plans.

template<size_t d>
void	dump (string fn, const multi_array< double, d > &ma)

template<size_t d>
void	dump (string fn, const multi_array< complex< double >, d > &ma)

template<class T >
void	print (const multi_array< T, 2 > &ma)

template<class T , size_t d>
T	prod (array< T, d > a)

template<class T >
T	phi1 (T a)
	Computes (exp(z)-1)/z.

template<class T >
T	phi1_im (T a)
	Computes (exp(i a)-1)/(i a)

template<class T >
T	phi2_im (T a)
	Computes (exp(i a)-1-i a)/((i a)^2)

template<size_t d>
array< Index, d >	parse (string s)
	Parser for command line arguments separated by whitespaces.

template<class T >
double	max_err (T err, T diff)
	Maximum function which treats NaNs correctly.

template<class InputIt , class OutputIt >
void	remove_element (InputIt first, InputIt last, OutputIt d_first, const Index idx)

template<class T >
void	coeff (const multi_array< T, 2 > &a, const multi_array< T, 2 > &b, T w, multi_array< T, 2 > &out, const Ensign::Matrix::blas_ops &blas)
	Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) \,dx\).

template<class T >
void	coeff (const multi_array< T, 2 > &a, const multi_array< T, 2 > &b, const multi_array< T, 1 > &w, multi_array< T, 2 > &out, const Ensign::Matrix::blas_ops &blas)
	Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) \,dx\).

template<class T >
void	integrate (const multi_array< T, 2 > &a, T w, multi_array< T, 1 > &out, const Ensign::Matrix::blas_ops &blas)
	Computes an approximation to the integral \(\int a_i(x) \,dx\).

template<class T >
void	integrate (const multi_array< T, 2 > &a, const multi_array< T, 1 > &w, multi_array< T, 1 > &out, const Ensign::Matrix::blas_ops &blas)
	Computes an approximation to the integral \(\int a_i(x) \,dx\).

template<class T >
void	coeff (const multi_array< T, 2 > &a, const multi_array< T, 2 > &b, const multi_array< T, 2 > &c, T w, multi_array< T, 3 > &out, const Ensign::Matrix::blas_ops &blas)
	Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) b_k(x) \,dx\).

void	deim_ext (const multi_array< double, 2 > &_U, Index r, multi_array< Index, 1 > &I)

double	colloquation_to_lr (const multi_array< double, 2 > &f_I, multi_array< double, 2 > &f_J, const multi_array< Index, 1 > &I, multi_array< double, 2 > &X, multi_array< double, 2 > &L, Matrix::blas_ops &blas)

double	colloquation_to_lr (const multi_array< double, 2 > &f_I, multi_array< double, 2 > &f_J, const multi_array< Index, 1 > &I, lr2< double > &f, Matrix::blas_ops &blas)

template<class T , class IP >
void	lr_add (T alpha, const lr2< T > &A, T beta, const lr2< T > &B, lr2< T > &out, IP inner_product_X, IP inner_product_V, const Ensign::Matrix::blas_ops &blas)
	Add two low-rank representations together.

template<class T , class IP >
void	lr_add (T alpha, const lr2< T > &A, T beta, const lr2< T > &B, T gamma, const lr2< T > &C, lr2< T > &out, IP inner_product_X, IP inner_product_V, const Ensign::Matrix::blas_ops &blas)
	Add three low-rank representations together.

template<class T , class IP >
void	lr_mul (const lr2< T > &A, const lr2< T > &B, lr2< T > &out, IP inner_product_X, IP inner_product_V, const Ensign::Matrix::blas_ops &blas)
	Multiplies two low-rank representations together.

template<class T >
void	lr_truncate (const lr2< T > &in, lr2< T > &out, const Ensign::Matrix::blas_ops &blas)
	Truncate a low-rank representation inplace to a fixed rank r.

template<class T >
double	lr_inner_product (const lr2< T > &A, const lr2< T > &B, T w, const Ensign::Matrix::blas_ops &blas)
	Computes the inner product of two low-rank representations.

template<class T >
double	lr_norm_sq (const lr2< T > &A, const Ensign::Matrix::blas_ops &blas)
	Computes the norm of a low-rank representations.

template<class T , class IP >
void	initialize (lr2< T > &lr, vector< const T * > X, vector< const T * > V, IP inner_product_X, IP inner_product_V, const Ensign::Matrix::blas_ops &blas)
	Initializes (an already allocated) lr2 to \(\sum_i X_i V_i\).

template<class T >
void	initialize (lr2< T > &lr, vector< const T * > X, vector< const T * > V, array< double, 3 > h_xx, array< double, 3 > h_vv, const Ensign::Matrix::blas_ops &blas)

template<class T >
std::function< T(T , T )>	inner_product_from_const_weight (T w, Index N)
	Return an inner product function object for use in, e.g., in gram_schmidt.

template<class T >
std::function< T(T , T )>	inner_product_from_weight (const T *w, Index N)
	Return an inner product function object for use in, e.g., in gram_schmidt.

Detailed Description

Core namespace for Ensign's numerical algorithms and data structures.

Typedef Documentation

◆ fft1d

template<size_t d>

using Ensign::fft1d = typedef fft<d, 1>

Definition at line 52 of file fft.hpp.

◆ fft2d

template<size_t d>

using Ensign::fft2d = typedef fft<d, 2>

Definition at line 49 of file fft.hpp.

◆ fft3d

template<size_t d>

using Ensign::fft3d = typedef fft<d, 3>

Definition at line 46 of file fft.hpp.

Function Documentation

◆ coeff() [1/3]

template<class T >

void Ensign::coeff	(	const multi_array< T, 2 > &	a,
		const multi_array< T, 2 > &	b,
		const multi_array< T, 1 > &	w,
		multi_array< T, 2 > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) \,dx\).

If a and b are of size (n,r) then w must be of size n. The weight w can be used as a pure weight (in a quadrature sense) but also can incooperate a x dependent function.

◆ coeff() [2/3]

template<class T >

void Ensign::coeff	(	const multi_array< T, 2 > &	a,
		const multi_array< T, 2 > &	b,
		const multi_array< T, 2 > &	c,
		T	w,
		multi_array< T, 3 > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) b_k(x) \,dx\).

This function assumes that w is a constant weight.

◆ coeff() [3/3]

template<class T >

void Ensign::coeff	(	const multi_array< T, 2 > &	a,
		const multi_array< T, 2 > &	b,
		T	w,
		multi_array< T, 2 > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes a low-rank coefficient that approximates \(\int a_i(x) b_j(x) \,dx\).

This functions assumes that w is a constant weight.

◆ colloquation_to_lr() [1/2]

double Ensign::colloquation_to_lr	(	const multi_array< double, 2 > &	f_I,
		multi_array< double, 2 > &	f_J,
		const multi_array< Index, 1 > &	I,
		lr2< double > &	f,
		Matrix::blas_ops &	blas
	)

◆ colloquation_to_lr() [2/2]

double Ensign::colloquation_to_lr	(	const multi_array< double, 2 > &	f_I,
		multi_array< double, 2 > &	f_J,
		const multi_array< Index, 1 > &	I,
		multi_array< double, 2 > &	X,
		multi_array< double, 2 > &	L,
		Matrix::blas_ops &	blas
	)

◆ create_plans_1d() [1/2]

array< fftw_plan, 2 > Ensign::create_plans_1d	(	Index	dims_,
		multi_array< double, 1 > &	real,
		multi_array< complex< double >, 1 > &	freq
	)

◆ create_plans_1d() [2/2]

array< fftw_plan, 2 > Ensign::create_plans_1d	(	Index	dims_,
		multi_array< double, 2 > &	real,
		multi_array< complex< double >, 2 > &	freq
	)

Helper routines to create FFTW plans for 1d transforms.

◆ create_plans_2d() [1/2]

array< fftw_plan, 2 > Ensign::create_plans_2d	(	array< Index, 2 >	dims_,
		multi_array< double, 1 > &	real,
		multi_array< complex< double >, 1 > &	freq
	)

Helper routines to create FFTW plans for 2d transforms.

◆ create_plans_2d() [2/2]

array< fftw_plan, 2 > Ensign::create_plans_2d	(	array< Index, 2 >	dims_,
		multi_array< double, 2 > &	real,
		multi_array< complex< double >, 2 > &	freq
	)

◆ create_plans_3d() [1/2]

array< fftw_plan, 2 > Ensign::create_plans_3d	(	array< Index, 3 >	dims_,
		multi_array< double, 1 > &	real,
		multi_array< complex< double >, 1 > &	freq
	)

◆ create_plans_3d() [2/2]

array< fftw_plan, 2 > Ensign::create_plans_3d	(	array< Index, 3 >	dims_,
		multi_array< double, 2 > &	real,
		multi_array< complex< double >, 2 > &	freq
	)

Helper routines to create FFTW plans for 3d transforms.

◆ create_plans_3d_adapt()

array< fftw_plan, 2 > Ensign::create_plans_3d_adapt	(	array< Index, 3 >	dims_,
		multi_array< double, 2 > &	real,
		multi_array< complex< double >, 2 > &	freq
	)

◆ deim_ext()

void Ensign::deim_ext	(	const multi_array< double, 2 > &	_U,
		Index	r,
		multi_array< Index, 1 > &	I
	)

◆ destroy_plans()

void Ensign::destroy_plans ( array< fftw_plan, 2 > & plans )

Helper function to destroy FFTW plans.

◆ dump() [1/2]

template<size_t d>

void Ensign::dump	(	string	fn,
		const multi_array< complex< double >, d > &	ma
	)

Definition at line 506 of file storage.hpp.

◆ dump() [2/2]

template<size_t d>

void Ensign::dump	(	string	fn,
		const multi_array< double, d > &	ma
	)

Definition at line 494 of file storage.hpp.

◆ initialize() [1/2]

template<class T >

void Ensign::initialize	(	lr2< T > &	lr,
		vector< const T * >	X,
		vector< const T * >	V,
		array< double, 3 >	h_xx,
		array< double, 3 >	h_vv,
		const Ensign::Matrix::blas_ops &	blas
	)

◆ initialize() [2/2]

template<class T , class IP >

void Ensign::initialize	(	lr2< T > &	lr,
		vector< const T * >	X,
		vector< const T * >	V,
		IP	inner_product_X,
		IP	inner_product_V,
		const Ensign::Matrix::blas_ops &	blas
	)

Initializes (an already allocated) lr2 to \(\sum_i X_i V_i\).

The rank r is taken from the initialized lr. If X.size() and V.size() are smaller than r, the remaining basis functions are initialized in a random manner (subject (to the orthogonality condition). X.size() == V.size() is required.

◆ inner_product_from_const_weight()

template<class T >

std::function< T(T , T )> Ensign::inner_product_from_const_weight	(	T	w,
		Index	N
	)

Return an inner product function object for use in, e.g., in gram_schmidt.

◆ inner_product_from_weight()

template<class T >

std::function< T(T , T )> Ensign::inner_product_from_weight	(	const T *	w,
		Index	N
	)

Return an inner product function object for use in, e.g., in gram_schmidt.

◆ integrate() [1/2]

template<class T >

void Ensign::integrate	(	const multi_array< T, 2 > &	a,
		const multi_array< T, 1 > &	w,
		multi_array< T, 1 > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes an approximation to the integral \(\int a_i(x) \,dx\).

If a is of size (n,r) then w must be a contiguous memory region of size n. The weight w can be used as a pure weight (in a quadrature sense) but also can incooperate a x dependent function.

◆ integrate() [2/2]

template<class T >

void Ensign::integrate	(	const multi_array< T, 2 > &	a,
		T	w,
		multi_array< T, 1 > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes an approximation to the integral \(\int a_i(x) \,dx\).

This function assumes that w is a constant weight.

◆ lr_add() [1/2]

template<class T , class IP >

void Ensign::lr_add	(	T	alpha,
		const lr2< T > &	A,
		T	beta,
		const lr2< T > &	B,
		lr2< T > &	out,
		IP	inner_product_X,
		IP	inner_product_V,
		const Ensign::Matrix::blas_ops &	blas
	)

Add two low-rank representations together.

Note that no truncation is performed by this function. To do that call lr_truncate.

◆ lr_add() [2/2]

template<class T , class IP >

void Ensign::lr_add	(	T	alpha,
		const lr2< T > &	A,
		T	beta,
		const lr2< T > &	B,
		T	gamma,
		const lr2< T > &	C,
		lr2< T > &	out,
		IP	inner_product_X,
		IP	inner_product_V,
		const Ensign::Matrix::blas_ops &	blas
	)

Add three low-rank representations together.

Note that no truncation is performed by this function. To do that call lr_truncate.

◆ lr_inner_product()

template<class T >

double Ensign::lr_inner_product	(	const lr2< T > &	A,
		const lr2< T > &	B,
		T	w,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes the inner product of two low-rank representations.

◆ lr_mul()

template<class T , class IP >

void Ensign::lr_mul	(	const lr2< T > &	A,
		const lr2< T > &	B,
		lr2< T > &	out,
		IP	inner_product_X,
		IP	inner_product_V,
		const Ensign::Matrix::blas_ops &	blas
	)

Multiplies two low-rank representations together.

Note that no truncation is performed by this function. To do that call lr_truncate.

◆ lr_norm_sq()

template<class T >

double Ensign::lr_norm_sq	(	const lr2< T > &	A,
		const Ensign::Matrix::blas_ops &	blas
	)

Computes the norm of a low-rank representations.

This assumes that X and V are orthogonalized. Thus, no inner product needs to be passed to this function. The function simply computes \(\sum_{ij} S_{ij}^2\)

◆ lr_truncate()

template<class T >

void Ensign::lr_truncate	(	const lr2< T > &	in,
		lr2< T > &	out,
		const Ensign::Matrix::blas_ops &	blas
	)

Truncate a low-rank representation inplace to a fixed rank r.

The rank is determined by the size of out.

◆ make_unique_ptr()

template<typename T , typename... Args>

std::unique_ptr< T > Ensign::make_unique_ptr ( Args &&... args )

Definition at line 100 of file common.hpp.

◆ max_err()

template<class T >

double Ensign::max_err	(	T	err,
		T	diff
	)

Maximum function which treats NaNs correctly.

Definition at line 87 of file utility.hpp.

◆ parse()

template<size_t d>

array< Index, d > Ensign::parse ( string s )

Parser for command line arguments separated by whitespaces.

Definition at line 66 of file utility.hpp.

◆ phi1()

template<class T >

T Ensign::phi1 ( T a )

Computes (exp(z)-1)/z.

There is a removeable singularity at z=0.

Definition at line 26 of file utility.hpp.

◆ phi1_im()

template<class T >

T Ensign::phi1_im ( T a )

Computes (exp(i a)-1)/(i a)

There is a removeable singularity at a=0.

Definition at line 35 of file utility.hpp.

◆ phi2_im()

template<class T >

T Ensign::phi2_im ( T a )

Computes (exp(i a)-1-i a)/((i a)^2)

There is a removeable singularity at a=0.

Definition at line 48 of file utility.hpp.

◆ print()

template<class T >

void Ensign::print ( const multi_array< T, 2 > & ma )

Definition at line 518 of file storage.hpp.

◆ prod()

template<class T , size_t d>

T Ensign::prod ( array< T, d > a )

Definition at line 14 of file utility.hpp.

◆ remove_element()

template<class InputIt , class OutputIt >

void Ensign::remove_element	(	InputIt	first,
		InputIt	last,
		OutputIt	d_first,
		const Index	idx
	)

Definition at line 95 of file utility.hpp.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ fft1d

◆ fft2d

◆ fft3d

Function Documentation

◆ coeff() [1/3]

◆ coeff() [2/3]

◆ coeff() [3/3]

◆ colloquation_to_lr() [1/2]

◆ colloquation_to_lr() [2/2]

◆ create_plans_1d() [1/2]

◆ create_plans_1d() [2/2]

◆ create_plans_2d() [1/2]

◆ create_plans_2d() [2/2]

◆ create_plans_3d() [1/2]

◆ create_plans_3d() [2/2]

◆ create_plans_3d_adapt()

◆ deim_ext()

◆ destroy_plans()

◆ dump() [1/2]

◆ dump() [2/2]

◆ initialize() [1/2]

◆ initialize() [2/2]

◆ inner_product_from_const_weight()

◆ inner_product_from_weight()

◆ integrate() [1/2]

◆ integrate() [2/2]

◆ lr_add() [1/2]

◆ lr_add() [2/2]

◆ lr_inner_product()

◆ lr_mul()

◆ lr_norm_sq()

◆ lr_truncate()

◆ make_unique_ptr()

◆ max_err()

◆ parse()

◆ phi1()

◆ phi1_im()

◆ phi2_im()

◆ print()

◆ prod()

◆ remove_element()