hila Namespace Reference

Invert diagonal + const. matrix using Sherman-Morrison formula. More...

Classes
struct	base_type_struct
struct	contains_type
struct	inner_type_struct
class	input
	hila::input - Class for parsing runtime parameter files. More...
struct	is_arithmetic
struct	is_avx_vector
struct	is_complex_or_arithmetic
	hila::is_complex_or_arithmetic<T>::value More...
struct	is_field_class_type
struct	is_field_type
struct	is_vectorizable_type
	is_vectorizable_type<T>::value is always false if the target is not vectorizable More...
class	k_binning
class	timer
struct	timer_value
	This file defines timer class and other timing related utilities. More...
struct	vector_info

Typedefs
template<typename A , typename B >
using	type_plus = decltype(std::declval< A >()+std::declval< B >())

Enumerations
enum class	bc
	list of field boundary conditions - used only if SPECIAL_BOUNDARY_CONDITIONS defined

Functions
bool	bc_need_communication (hila::bc bc)
	False if we have b.c. which does not require communication.
template<typename T >
T	broadcast (const T &var, int rank=0)
	Version of broadcast with non-modifiable var.
template<typename T >
void	broadcast (std::vector< T > &list, int rank=0)
	Broadcast for std::vector.
template<typename T >
T	broadcast (T &var, int rank=0)
	Broadcast the value of var to all MPI ranks from rank (default=0).
template<typename T >
void	broadcast (T *var, int rank=0)
	Bare pointers cannot be broadcast.
template<typename T , typename U >
void	broadcast2 (T &t, U &u, int rank=0)
	and broadcast with two values
template<typename T >
void	broadcast_array (T *var, int n, int rank=0)
	Broadcast for arrays where size must be known and same for all nodes.
void	check_that_rng_is_initialized ()
	Check if RNG is initialized, do what the name says.
void	error (const char *msg)
	Print message and force quit.
void	finishrun ()
	Normal, controlled exit - all nodes must call this. Prints timing information and information about communications.
void	free_device_rng ()
	Free GPU RNG state, does nothing on non-GPU archs.
template<typename T >
T	gaussian_random ()
	Template function T hila::gaussian_random<T>(),generates gaussian random value of type T, with variance \(1\).
template<typename T , std::enable_if_t< std::is_arithmetic< T >::value, int > = 0>
T	gaussian_random (out_only T &val, double w=1.0)
	Template function const T & hila::gaussian_random(T & variable,double width=1)
double	gaussrand ()
	Gaussian random generation routine.
double	gaussrand2 (double &out2)
	hila::gaussrand2 returns 2 Gaussian distributed random numbers with variance \(1.0\).
template<typename T >
hila::arithmetic_type< T >	get_number_in_var (const T &var, int i)
double	gettime ()
void	initialize (int argc, char **argv)
	Read in command line arguments. Initialise default stream and MPI communication.
void	initialize_device_rng (uint64_t seed)
	Initialize device random number generator on GPUs, if application run on GPU platform. No effect on other archs.
void	initialize_host_rng (uint64_t seed)
	Initialize host (CPU) random number generator separately, done implicitly by seed_random()
bool	is_device_rng_on ()
	Check if the RNG on GPU is allocated and ready to use.
bool	is_rng_seeded ()
	Check if RNG is seeded already.
int	myrank ()
	rank of this node
int	number_of_nodes ()
	how many nodes there are
template<typename T >
std::string	prettyprint (const Complex< T > &A, int prec=8)
	Return well formatted Complex number as std::string.
template<int n, int m, typename T , typename MT >
std::string	prettyprint (const Matrix_t< n, m, T, MT > &A, int prec=8)
	Formats Matrix_t object in a human readable way.
double	random ()
	Real valued uniform random number generator.
template<typename T >
T	random ()
	Template function T hila::random<T>() without argument.
template<typename T , std::enable_if_t< std::is_arithmetic< T >::value, int > = 0>
T	random (out_only T &val)
	Template function const T & hila::random(T & var) sets the argument to a random value, and return a constant reference to it.
template<typename T >
T	reduce_node_sum (T &var, bool allreduce=true)
	Reduce single variable across nodes.
template<typename T >
void	reduce_node_sum (T *value, int send_count, bool allreduce=true)
	Reduce an array across nodes.
void	seed_random (uint64_t seed, bool device_rng=true)
	Seed random generators with 64-bit unsigned value. On MPI shuffles the seed so that different MPI ranks are seeded with different values.
void	set_allreduce (bool on=true)
	set allreduce on (default) or off on the next reduction
uint64_t	shuffle_rng_seed (uint64_t seed)
	Random shuffling of rng seed for MPI nodes.
void	synchronize ()
	synchronize mpi
void	terminate (int status)
template<int n, int m, typename T >
std::string	to_string (const Array< n, m, T > &A, int prec=8, char separator=' ')
	Converts Array object to string.
template<typename T >
std::string	to_string (const Complex< T > &A, int prec=8, char separator=' ')
	Return Complex number as std::string.
template<int n, int m, typename T , typename MT >
std::string	to_string (const Matrix_t< n, m, T, MT > &A, int prec=8, char separator=' ')
	Converts Matrix_t object to string.
template<typename T , std::enable_if_t< hila::is_arithmetic< T >::value, int > = 0>
std::string	to_string (const T v, int prec=8, char separator=' ')
	convert to string: separator does nothing, but for compatibility w. other to_strings

Variables
logger_class	log
	Now declare the logger.
std::ostream	out
	this is our default output file stream
std::ostream	out0
	This writes output only from main process (node 0)
std::ofstream	output_file
	this is just a hook to store output file, if it is in use
std::vector< timer * >	timer_list = {}
	Timer routines - for high-resolution event timing.

Detailed Description

Invert diagonal + const. matrix using Sherman-Morrison formula.

Implement hila::swap() for Fields too, equivalent to std::swap()

define hila::direction_name() and hila::prettyprint(Direction)

let us house the partitions-struct here

////////////////////////////////////////////////////////////////////////////// Function hila::to_string

Convert to string for "pretty" printing

Sherman-Morrison formula (generalized to complex) is (A + u v^*)^-1 = A^-1 - A^-1 u v^* A^-1/(1 + v^* A^-1 u) where A invertible matrix and u,v vectors.

Specialize this here for the case where A is diagonal and u = v = sqrt(c) [1 1 1 ..]^T i.e. invert M = (A + C), where C is constant matrix. Let now B = A^-1, result is M^{-1}_ij = B_i delta_ij - c B_i B_j / (1 + c Tr B) or M^{-1} = B - c Bv Bv^T / (1 + c Tr B) where Bv = B [1 1 1 ..]^T, i.e. Bv_i = B_ii.

Inverse exists if (1 + c Tr B) != 0.

FFT_complex_to_real; Field must be a complex-valued field, result is a real field of the same number type Not optimized, should not be used on a hot path

Because the complex field must have the property f(-x) = f(L-x) = f(x)^*, only half of the values in input field are significant, the routine does the appropriate symmetrization.

Routine hila::FFT_complex_to_real_site(CoordinateVector cv) gives the significant values at location cv: = +1 significant complex value, = 0 significant real part, imag ignored = -1 value ignored here Example: in 2d 8x8 lattice the sites are: (* = (0,0), value 0)

• + + + - - - - - - - 0 + + + 0
• + + + - - - - - - - + + + + +
• + + + - - - - after centering - - - + + + + + 0 + + + 0 - - - (0,0) to center - - - + + + + +
• + + + + - - - --------------—> - - - * + + + 0
• + + + + - - - - - - - + + + -
• + + + + - - - - - - - + + + -
• + + + 0 - - - - - - - + + + -

This file implements "hila::has_unary_minus<T>::value" -conditional, which is false if the type T does not implement -T (unary -) operator, i.e. T T::operator-() const { .. } This is needed for antiperiodic b.c. Note that this gives false for unsigned type, whereas c++ allows -unsigned

Parameter file input system Check input.h for user instructions

Time related routines (runtime - timing - timelimit) Check timing.h for details

Typedef Documentation

type_plus

template<typename A , typename B >

using hila::type_plus = typedef decltype(std::declval<A>() + std::declval<B>())

Helper operations to make generic templates for arithmetic operators e.g. hila::type_plus<A,B> gives the type of the operator a + b, where a is of type A and b type B.

Definition at line 103 of file type_tools.h.

Function Documentation

broadcast()

template<typename T >

T hila::broadcast	(	T &	var,
		int	rank = 0
	)

Broadcast the value of var to all MPI ranks from rank (default=0).

NOTE: the function must be called by all MPI ranks, otherwise the program will deadlock.

The type of the variable var can be any standard plain datatype (trivial type), std::string or std::vector.

For trivial types, the input var can be non-modifiable value. In this case the broadcast value is obtained from the broadcast return value.

Example:

auto rnd = hila::broadcast(hila::random());    // all MPI ranks get the same random value

Parameters

var	variable to be synchronized across the full
rank	MPI rank from which the

Returns

template <typename T>

Definition at line 153 of file com_mpi.h.

check_that_rng_is_initialized()

void hila::check_that_rng_is_initialized

(

)

Check if RNG is initialized, do what the name says.

program quits with error message if RNG is not initialized. It also quit with error messages if the device RNG is not initialized.

Definition at line 252 of file random.cpp.

free_device_rng()

void hila::free_device_rng

(

)

Free GPU RNG state, does nothing on non-GPU archs.

hila::random() does not work inside onsites() after this, unless seeded again using initialize_device_rng(). Frees the memory RNG takes on the device.

Definition at line 106 of file hila_gpu.cpp.

gaussian_random() [1/2]

template<typename T >

T hila::gaussian_random

(

)

Template function T hila::gaussian_random<T>(),generates gaussian random value of type T, with variance \(1\).

For example,

auto n = hila::gaussian_random<Complex<double>>().abs();

calculates the norm of a gaussian random complex value.

Note

there is no width/variance parameter, because of danger of confusion with above hila::gaussian_random(value)

Definition at line 183 of file random.h.

gaussian_random() [2/2]

template<typename T , std::enable_if_t< std::is_arithmetic< T >::value, int > = 0>

T hila::gaussian_random	(	out_only T &	val,
		double	w = 1.0
	)

Template function const T & hila::gaussian_random(T & variable,double width=1)

Sets the argument to a gaussian random value, and return a constant reference to it. Optional second argument width sets the \(variance=width^{2}\) ( \(default==1\))

For example:

Complex<double> c;
auto n = sqr(hila::gaussian_random(c));

sets the variable c to complex gaussian random value and stores its square in n.

This function is for hila classes relies on the existence of method T::gaussian_random(). The advantage for this function over class function T::random() is that the argument can be of elementary arithmetic type.

Returns

T by reference

Definition at line 158 of file random.h.

gaussrand()

double hila::gaussrand

(

)

Gaussian random generation routine.

By default these gives random numbers with variance \(1.0\) and expectation value \(0.0\), i.e.

\[ e^{-(\frac{x^{2}}{2})} \]

with variance

\[ < x^{2}-0.0> = 1 \]

If you want random numbers with variance \( \sigma^{2} \), multiply the result by \( \sqrt{\sigma^{2}} \) i.e.,

sqrt(sigma * sigma) * gaussrand();

Returns

double

Definition at line 212 of file random.cpp.

gaussrand2()

double hila::gaussrand2

(

double &

out2

)

hila::gaussrand2 returns 2 Gaussian distributed random numbers with variance \(1.0\).

Useful because Box-Muller algorithm computes 2 values at the same time.

Definition at line 177 of file random.cpp.

get_number_in_var()

template<typename T >

hila::arithmetic_type< T > hila::get_number_in_var ( const T &  var, int  i  )

inline

Access variables as if arrays of scalar_type numbers

Definition at line 118 of file type_tools.h.

gettime()

double hila::gettime

(

)

Use clock_gettime() to get the accurate time (alternative: use gettimeofday() or MPI_Wtime()) gettime returns the time in secs since program start

Definition at line 163 of file timing.cpp.

initialize()

void hila::initialize	(	int	argc,
		char **	argv
	)

Read in command line arguments. Initialise default stream and MPI communication.

Parameters

argc	Number of command line arguments
argv	List of command line arguments

Definition at line 65 of file initialize.cpp.

initialize_device_rng()

void hila::initialize_device_rng

(

uint64_t

seed

)

Initialize device random number generator on GPUs, if application run on GPU platform. No effect on other archs.

This function shuffles the seed for different MPI ranks on MPI. Called by seed_random() unless its 2nd argument is hila::device_rng_off. This can reinitialize device RNG free'd by free_device_rng().

Definition at line 70 of file hila_gpu.cpp.

initialize_host_rng()

void hila::initialize_host_rng

(

uint64_t

seed

)

Initialize host (CPU) random number generator separately, done implicitly by seed_random()

Parameters

seed	unsigned int_64

Note

On MPI, this function shuffles different seed values for all MPI ranks.

Definition at line 61 of file random.cpp.

is_device_rng_on()

bool hila::is_device_rng_on

(

)

Check if the RNG on GPU is allocated and ready to use.

Returns true on non-GPU archs.

Definition at line 57 of file hila_gpu.cpp.

is_rng_seeded()

bool hila::is_rng_seeded

(

)

Check if RNG is seeded already.

Returns

bool

Definition at line 239 of file random.cpp.

myrank()

int hila::myrank

(

)

rank of this node

Return my node number - take care to return the previous node number if mpi is being torn down (used in destructors)

Definition at line 235 of file com_mpi.cpp.

number_of_nodes()

int hila::number_of_nodes

(

)

how many nodes there are

Return number of nodes or "pseudo-nodes".

Definition at line 246 of file com_mpi.cpp.

prettyprint() [1/2]

template<typename T >

std::string hila::prettyprint	(	const Complex< T > &	A,
		int	prec = 8
	)

Return well formatted Complex number as std::string.

Output is as "(A.re, A.im)"

Template Parameters

T	Arithmetic type of A

Parameters

A	Complex number to print
prec	Precision to print Complex number as

Returns

std::string

Definition at line 1420 of file cmplx.h.

prettyprint() [2/2]

template<int n, int m, typename T , typename MT >

std::string hila::prettyprint	(	const Matrix_t< n, m, T, MT > &	A,
		int	prec = 8
	)

Formats Matrix_t object in a human readable way.

Example 2 x 3 matrix is the following

Matrix<2, 3, double> W;
W.random();
hila::out0 << hila::prettyprint(W ,4) << '\n';
// Result:
// [ 0.8555 0.006359 0.3193 ]
// [  0.237   0.8871 0.8545 ]

Template Parameters

n	Number of rows
m	Number of columns
T	Matrix element type
MT	Matrix type

Parameters

A	Matrix to be formatted
prec	Precision of Matrix element

Returns

std::string

Definition at line 2617 of file matrix.h.

random() [1/3]

double hila::random

(

)

Real valued uniform random number generator.

Returns an uniform double precision random number in interval \([0,1)\).
This function can be called from outside or inside site loops (on GPU if the device rng is initialized).

Uses std::uniform_real_distribution

Returns

double

Definition at line 120 of file hila_gpu.cpp.

random() [2/3]

template<typename T >

T hila::random

(

)

Template function T hila::random<T>() without argument.

This is used to generate random value for type T without defined variable. Example:

auto n = hila::random<Complex<double>>().abs();

calculates the norm of a random complex value. hila::random<double>() is functionally equivalent to hila::random()

Definition at line 132 of file random.h.

random() [3/3]

template<typename T , std::enable_if_t< std::is_arithmetic< T >::value, int > = 0>

T hila::random

(

out_only T &

val

)

Template function const T & hila::random(T & var) sets the argument to a random value, and return a constant reference to it.

For example

Complex<double> c;
auto n = hila::random(c).abs();

sets the variable c to complex random value and calculates its absolute value. c.real() and c.imag() will be \(\in [0,1)\).

For hila classes relies on the existence of method T::random() (i.e. var.random()), this function typically sets the argument real numbers to interval \([0,1)\) if type T is arithmatic. if T is more commplicated classes such as SU<N,T>-matrix, this function sets the argument to valid random SU<N,T>.

Advantage of this function over class function T::random() is that the argument can be of elementary arithmetic type.

Definition at line 110 of file random.h.

seed_random()

void hila::seed_random	(	uint64_t	seed,
		bool	device_init = true
	)

Seed random generators with 64-bit unsigned value. On MPI shuffles the seed so that different MPI ranks are seeded with different values.

The optional 2nd argument indicates whether to initialize the RNG on GPU device: hila::device_rng_on (default) or hila::device_rng_off. This argument does nothing if no GPU platform. If hila::device_rng_off is used, onsites() -loops cannot contain random number calls (Runtime error will be flagged and program exits).

Seed is shuffled so that different nodes get different rng seeds. If seed == 0, seed is generated through using the time() -function.

Definition at line 86 of file random.cpp.

shuffle_rng_seed()

uint64_t hila::shuffle_rng_seed

(

uint64_t

seed

)

Random shuffling of rng seed for MPI nodes.

Do it in a manner makes it difficult to give the same seed by mistake and also avoids giving the same seed for 2 nodes For single MPI node seed remains unchanged

Definition at line 47 of file random.cpp.

terminate()

void hila::terminate

(

int

status

)

Force quit for multinode processes – kill all nodes No synchronisation done

Definition at line 289 of file initialize.cpp.

to_string() [1/3]

template<int n, int m, typename T >

std::string hila::to_string	(	const Array< n, m, T > &	A,
		int	prec = 8,
		char	separator = ' '
	)

Converts Array object to string.

Template Parameters

n	Number of rows
m	Number of columns
T	Array element type

Parameters

A	Array to convert to string
prec	Precision of T
separator	Separator between elements

Returns

std::string

Definition at line 934 of file array.h.

to_string() [2/3]

template<typename T >

std::string hila::to_string	(	const Complex< T > &	A,
		int	prec = 8,
		char	separator = ' '
	)

Return Complex number as std::string.

Template Parameters

T	Arithmetic type of A

Parameters

A	Complex number to convert
prec	Precision to represent Complex number at
separator	Separator for Complex number

Returns

std::string

Definition at line 1406 of file cmplx.h.

to_string() [3/3]

template<int n, int m, typename T , typename MT >

std::string hila::to_string	(	const Matrix_t< n, m, T, MT > &	A,
		int	prec = 8,
		char	separator = ' '
	)

Converts Matrix_t object to string.

Template Parameters

n	Number of rows
m	Number of columns
T	Matrix element type
MT	Matrix type

Parameters

A	Matrix to convert to string
prec	Precision of T
separator	Separator between elements

Returns

std::string

Definition at line 2582 of file matrix.h.