\( n\times m \) Array type More...

#include <array.h>

Public Member Functions
	Array ()=default
	Default constructor.

	Array (const Array< n, m, T > &v)=default
	Copy constructor.

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>
	Array (const S rhs)
	Scalar constructor.

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>
	Array (std::initializer_list< S > rhs)
	Initializer list constructor.

Matrix< n, m, T > &	asMatrix ()
	Cast Array to Matrix.

Vector< n, T > &	asVector ()
	Cast Array1D to Vector.

constexpr int	columns () const
	Returns number of columns.

Array< n, m, T >	conj () const
	Returns element wise Complex conjugate of Array.

template<int q = n, int p = m, std::enable_if_t<(q==1\|\|p==1), int > = 0>
T &	e (const int i)
	Standard array indexing operation for 1D Array.

template<int q = n, int p = m, std::enable_if_t<(q==1\|\|p==1), int > = 0>
T	e (const int i) const
	Const overload.

T &	e (const int i, const int j)
	Const overload.

T	e (const int i, const int j) const
	Standard array indexing operation for 2D Array.

Array< n, m, T > &	gaussian_random (double width=1.0)
	Fill Array with Gaussian random elements.

Array< n, m, hila::arithmetic_type< T > >	imag () const
	return imaginary part

template<typename S , int n1, int m1>
bool	operator!= (const Array< n1, m1, S > &rhs) const
	Compare non-equality of two Arrays.

template<int n, int m, typename T >
Array< n, m, T >	operator* (Array< n, m, T > a, const Array< n, m, T > &b)
	Multiplication operator.

template<typename S , std::enable_if_t< std::is_convertible< hila::type_mul< T, S >, T >::value, int > = 0>
Array< n, m, T > &	operator*= (const Array< n, m, S > &rhs) &
	Multiply assign scalar or array.

template<typename S , std::enable_if_t< std::is_convertible< hila::type_mul< T, S >, T >::value, int > = 0>
Array< n, m, T > &	*operator=** (const S rhs) &
	multiply assign with scalar

Array< n, m, T >	operator+ () const
	Unary + operator.

template<int n, int m, typename A , typename B >
auto	operator+ (const Array< n, m, A > &a, const Array< n, m, B > &b)
	Addition operator.

template<typename S , std::enable_if_t< std::is_convertible< S, T >::value, int > = 0>
Array< n, m, T > &	operator+= (const Array< n, m, S > &rhs) &
	Add assign operator with Array or scalar.

Array< n, m, T >	operator- () const
	Unary - operator.

template<int n, int m, typename A , typename B >
auto	operator- (const Array< n, m, A > &a, const Array< n, m, B > &b)
	Subtraction operator.

template<typename S , std::enable_if_t< std::is_convertible< S, T >::value, int > = 0>
Array< n, m, T > &	operator-= (const Array< n, m, S > &rhs) &
	Subtract assign operator with Array or scalar.

template<int n, int m, typename A , typename B >
auto	operator/ (const Array< n, m, A > &a, const Array< n, m, B > &b)
	Division operator.

template<typename S , std::enable_if_t< std::is_convertible< hila::type_div< T, S >, T >::value, int > = 0>
Array< n, m, T > &	operator/= (const Array< n, m, S > &rhs) &
	Division assign with array or scalar.

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>
Array< n, m, T > &	operator= (const S rhs) &
	Scalar assignment operator.

template<typename S , int n1, int m1>
bool	operator== (const Array< n1, m1, S > &rhs) const
	Compare equality of Arrays.

Array< n, m, T > &	random ()
	Fill Array with random elements.

Array< n, m, hila::arithmetic_type< T > >	real () const
	Returns real part of Array.

constexpr int	rows () const
	Returns number of rows.

template<int q = n, int p = m, std::enable_if_t< q==1, int > = 0>
constexpr int	size () const
	Returns size of Vector Array or square Array.

template<int N>
Array< n, m, T >	sort (Vector< N, int > &permutation, hila::sort order=hila::sort::ascending) const
	implement sort as casting to array

hila::arithmetic_type< T >	squarenorm () const
	calculate square norm - sum of squared elements

std::string	str (int prec=8, char separator=' ') const
	Convert to string for printing.

Related Symbols

(Note that these are not member symbols.)

Arithmetic operations

all operations are applied linearly to the Array A

Most functions are self explanitory, but if necessary function will have a detailed section with additional information.

Template Parameters

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

Parameters

a	Input array

Returns: Array<n, m, T>

template<int n, int m, typename T >

Array< n, m, T > sqrt (Array< n, m, T > a)

Square root.

template<int n, int m, typename T >

Array< n, m, T > cbrt (Array< n, m, T > a)

Cuberoot.

template<int n, int m, typename T >

Array< n, m, T > exp (Array< n, m, T > a)

Exponential.

template<int n, int m, typename T >

Array< n, m, T > log (Array< n, m, T > a)

Logarithm.

template<int n, int m, typename T >

Array< n, m, T > sin (Array< n, m, T > a)

Sine.

template<int n, int m, typename T >

Array< n, m, T > cos (Array< n, m, T > a)

Cosine.

template<int n, int m, typename T >

Array< n, m, T > tan (Array< n, m, T > a)

Tangent.

template<int n, int m, typename T >

Array< n, m, T > asin (Array< n, m, T > a)

Inverse Sine.

template<int n, int m, typename T >

Array< n, m, T > acos (Array< n, m, T > a)

Inverse Cosine.

template<int n, int m, typename T >

Array< n, m, T > atan (Array< n, m, T > a)

Inverse Tangent.

template<int n, int m, typename T >

Array< n, m, T > sinh (Array< n, m, T > a)

Hyperbolic Sine.

template<int n, int m, typename T >

Array< n, m, T > cosh (Array< n, m, T > a)

Hyperbolic Cosine.

template<int n, int m, typename T >

Array< n, m, T > tanh (Array< n, m, T > a)

Hyperbolic tangent.

template<int n, int m, typename T >

Array< n, m, T > asinh (Array< n, m, T > a)

Inverse Hyperbolic Sine.

template<int n, int m, typename T >

Array< n, m, T > acosh (Array< n, m, T > a)

Inverse Hyperbolic Cosine.

template<int n, int m, typename T >

Array< n, m, T > atanh (Array< n, m, T > a)

Inverse Hyperbolic Tangent.

template<int n, int m, typename T >

Array< n, m, T > pow (Array< n, m, T > a, int b)

Power.

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

Array< n, m, T > round (Array< n, m, T > a)

Rounding.

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

Array< n, m, T > floor (Array< n, m, T > a)

Floor.

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

Array< n, m, T > ceil (Array< n, m, T > a)

Ceiling.

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

Array< n, m, T > trunc (Array< n, m, T > a)

Truncation.

Detailed Description

template<const int n, const int m, typename T>
class Array< n, m, T >

\( n\times m \) Array type

Acts as array class which stores data in a simple C style array.

Main functionality which the Array class offers is to supplement the fall backs of storing information in a Matrix data structure.

For example assigning a value to each element with the Matrix class is not directly possible using the assignment operator=. This is because assignment with matrices is defined as \( M = a = a*I \) where M is a general matrix, a is a scalar and I an identity matrix. The result would only assign a to the diagonal elements.

Unlike the Matrix object, the Array object assigns element wise. This allows filling the Array with the assignment operator. Additionally element wise operations are useable as long as they are defined for the Array type. For example the operation:

Array<n,m,double> m.random();

sin(m);

Array

Array type

Definition array.h:43

Array::random

Array< n, m, T > & random()

Fill Array with random elements.

Definition array.h:625

Array::sin

Array< n, m, T > sin(Array< n, m, T > a)

Sine.

Definition array.h:1081

is defined, since the \(sin\) function is defined for doubles.

The above operation would not work for matrices, but with casting operations. Matrix::asArray and Array::asMatrix one can take full advantage of element wise operations.

Template Parameters

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

Definition at line 43 of file array.h.

Constructor & Destructor Documentation

◆ Array() [1/4]

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

Array< n, m, T >::Array ( )

default

Default constructor.

The following ways of constructing a matrix are:

Allocates undefined \( n\times m\) Array.

Array<n,m,MyType> A;

◆ Array() [2/4]

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

Array< n, m, T >::Array ( const Array< n, m, T > & v )

default

Copy constructor.

Construction from previously defined Array.

Array<n,m,MyOtherType> A_0;
//
// A_0 is filled with content
//
Array<n,m,MyType> A = A_0;

Parameters

v	Array to assign

◆ Array() [3/4]

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

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>

Array< n, m, T >::Array ( const S rhs )

inlineexplicit

Scalar constructor.

Construct with given scalar which is assigned to all elements in array

MyType x = hila::random();

Array<n,m,MyType> A = x;

Complex

Complex definition.

Definition cmplx.h:58

hila::random

double random()

Real valued uniform random number generator.

Definition hila_gpu.cpp:121

Template Parameters

S	Type for scalar

Parameters

rhs	Scalar to assign

Definition at line 104 of file array.h.

◆ Array() [4/4]

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

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>

Array< n, m, T >::Array ( std::initializer_list< S > rhs )

inline

Initializer list constructor.

Construction from c++ initializer list.

Array<2,2,int> A = {1, 0

0, 1};

Template Parameters

S	Element type of initializer list

Parameters

rhs	Initializer list to assign

Definition at line 132 of file array.h.

Member Function Documentation

◆ asMatrix()

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

Matrix< n, m, T > & Array< n, m, T >::asMatrix ( )

inline

Cast Array to Matrix.

Returns: Matrix<n, m, T>&

Definition at line 232 of file array.h.

◆ asVector()

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

Vector< n, T > & Array< n, m, T >::asVector ( )

inline

Cast Array1D to Vector.

asMatrix will perform the same operation.

Returns: Vector<n, T>&

Definition at line 247 of file array.h.

◆ columns()

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

constexpr int Array< n, m, T >::columns ( ) const

inlineconstexpr

Returns number of columns.

Returns: constexpr int

Definition at line 153 of file array.h.

◆ conj()

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

Array< n, m, T > Array< n, m, T >::conj ( ) const

inline

Returns element wise Complex conjugate of Array.

Returns: Array<n, m, T>

Definition at line 582 of file array.h.

◆ e() [1/2]

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

template<int q = n, int p = m, std::enable_if_t<(q==1||p==1), int > = 0>

T & Array< n, m, T >::e ( const int i )

inline

Standard array indexing operation for 1D Array.

Example for Vector Array:

Array1d<n,MyType> A;

MyType a = A.e(i); // i <= n

Array::e

T e(const int i, const int j) const

Standard array indexing operation for 2D Array.

Definition array.h:195

Parameters

i	Vector index type

Returns: T matrix element type

Definition at line 223 of file array.h.

◆ e() [2/2]

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

T Array< n, m, T >::e	(	const int	i,
		const int	j
	)		const

inline

Standard array indexing operation for 2D Array.

Accessing singular elements is insufficient, but matrix elements are often quite small.

Example for 2D Array:

Array<n,m,MyType> A;

MyType a = A.e(i,j); // i <= n, j <= m

Parameters

i	row index
j	column index

Returns: T matrix element type

Definition at line 195 of file array.h.

◆ gaussian_random()

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

Array< n, m, T > & Array< n, m, T >::gaussian_random ( double width = 1.0 )

inline

Fill Array with Gaussian random elements.

Parameters

width

Returns: Array<n, m, T>&

Definition at line 638 of file array.h.

◆ operator!=()

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

template<typename S , int n1, int m1>

bool Array< n, m, T >::operator!= ( const Array< n1, m1, S > & rhs ) const

inline

Compare non-equality of two Arrays.

Negation of operator==()

Template Parameters

S
n1
m1

Parameters

rhs

Returns: true; false

Definition at line 389 of file array.h.

◆ operator*()

template<int n, int m, typename T >

Array< n, m, T > operator*	(	Array< n, m, T >	a,
		const Array< n, m, T > &	b
	)

inline

Multiplication operator.

Defined for the following operations

Array*Array:

NOTE: Arrays must share same dimensionality

Array<n,m,MyType> A, B, C;
A = 2;
B = 3;
C = A*B; // C is uniformly 6

Scalar * Array / Array * Scalar:

NOTE: Exact definition exist in overloaded functions that can be viewed in source code.

Array<n,m,MyType> A,B;

A = 2;

B = A*3; // B is uniformly 6

Template Parameters

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

Parameters

a
b

Returns: Array<n, m, T>

Definition at line 862 of file array.h.

◆ operator*=()

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

template<typename S , std::enable_if_t< std::is_convertible< hila::type_mul< T, S >, T >::value, int > = 0>

Array< n, m, T > & Array< n, m, T >::operator*= ( const Array< n, m, S > & rhs ) &

inline

Multiply assign scalar or array.

Multiplication works element wise

Multiply assign operator can be used in the following ways

Multiply assign Array:

Array<n,m,MyType> A,B;
A = 2;
B = 2;
A *= B; \\ A is uniformly 4

Multiply assign scalar:

Array<n,m,MyType> A = 1;
 
A *= 2 ; \\ A is uniformly 2

Template Parameters

S

Parameters

rhs

Returns: Array<n, m, T>&

Definition at line 513 of file array.h.

◆ operator+() [1/2]

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

Array< n, m, T > Array< n, m, T >::operator+ ( ) const

inline

Unary + operator.

Equivalent to identity operator meaning that Arrat stays as is.

Returns: const Array<n, m, T>

Definition at line 301 of file array.h.

◆ operator+() [2/2]

template<int n, int m, typename A , typename B >

auto operator+	(	const Array< n, m, A > &	a,
		const Array< n, m, B > &	b
	)

inline

Addition operator.

Defined for the following operations

Array + Array:

NOTE: Arrays must share same dimensionality

Array<n,m,MyType> A, B, C;
A = 1;
B = 1;
C = A + B; // C is uniformly 2

Scalar + Array / Array + Scalar:

NOTE: Exact definition exist in overloaded functions that can be viewed in source code.

Array<n,m,MyType> A,B;

A = 1;

B = A + 1; // B is uniformly 2

Template Parameters

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

Parameters

a
b

Returns: Array<n, m, T>

Definition at line 741 of file array.h.

◆ operator+=()

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

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

Array< n, m, T > & Array< n, m, T >::operator+= ( const Array< n, m, S > & rhs ) &

inline

Add assign operator with Array or scalar.

Add assign operator can be used in the following ways

Add assign Array:

Requires that Arrays have same dimensions

Array<n,m,MyType> A,B;
A = 1;
B = 1;
A += B; \\ A is uniformly 2

Add assign scalar:

Adds scalar \( a \) to Array uniformly

Array<n,m,MyType> A = 1;

A += 1 ; \\ A is uniformly 2

Template Parameters

S	Element type of rhs

Parameters

rhs	Array to add

Returns: Array<n, m, T>

Definition at line 423 of file array.h.

◆ operator-() [1/2]

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

Array< n, m, T > Array< n, m, T >::operator- ( ) const

inline

Unary - operator.

Returns Array with the signs of all the elements in the Arrat flipped.

Returns: Array<n,m,T>

Definition at line 287 of file array.h.

◆ operator-() [2/2]

template<int n, int m, typename A , typename B >

auto operator-	(	const Array< n, m, A > &	a,
		const Array< n, m, B > &	b
	)

inline

Subtraction operator.

Defined for the following operations

Array - Array:

NOTE: Arrays must share same dimensionality

Array<n,m,MyType> A, B, C;
A = 2;
B = 1;
C = A - B; // C is uniformly 2

Scalar - Array / Array - Scalar:

NOTE: Exact definition exist in overloaded functions that can be viewed in source code.

Array<n,m,MyType> A,B;

A = 2;

B = A - 1; // B is uniformly 2

Template Parameters

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

Parameters

a
b

Returns: Array<n, m, T>

Definition at line 782 of file array.h.

◆ operator-=()

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

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

Array< n, m, T > & Array< n, m, T >::operator-= ( const Array< n, m, S > & rhs ) &

inline

Subtract assign operator with Array or scalar.

Subtract assign operator can be used in the following ways

Subtract assign Array:

Array<n,m,MyType> A,B;
A = 3;
B = 1;
A -= B; \\ A is uniformly 2

Subtract assign scalar:

Subtract scalar uniformly from square matrix

A<n,m,MyType> A = 3;

A -= 1 ; \\ A is uniformly 2

Template Parameters

S

Parameters

rhs

Returns: Array<n, m, T>&

Definition at line 457 of file array.h.

◆ operator/()

template<int n, int m, typename A , typename B >

auto operator/	(	const Array< n, m, A > &	a,
		const Array< n, m, B > &	b
	)

inline

Division operator.

Defined for the following operations

Array/Array:

NOTE: Arrays must share same dimensionality

Array<n,m,MyType> A, B, C;
A = 4;
B = 2;
C = A/B; // C is uniformly 2

Scalar / Array / Array / Scalar:

NOTE: Exact definition exist in overloaded functions that can be viewed in source code.

Array<n,m,MyType> A,B;

A = 4;

B = A/2; // B is uniformly 2

Template Parameters

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

Parameters

a
b

Returns: Array<n, m, T>

Definition at line 917 of file array.h.

◆ operator/=()

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

template<typename S , std::enable_if_t< std::is_convertible< hila::type_div< T, S >, T >::value, int > = 0>

Array< n, m, T > & Array< n, m, T >::operator/= ( const Array< n, m, S > & rhs ) &

inline

Division assign with array or scalar.

Division works element wise

Division assign operator can be used in the following ways

Division assign Array:

Array<n,m,MyType> A,B;
A = 2;
B = 2;
A /= B; \\ A is uniformly 1

Division assign scalar:

Array<n,m,MyType> A = 2;
 
A /= 2 ; \\ A is uniformly 1

Template Parameters

S

Parameters

rhs

Returns: Array<n, m, T>&

Definition at line 559 of file array.h.

◆ operator=()

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

template<typename S , std::enable_if_t< hila::is_assignable< T &, S >::value, int > = 0>

Array< n, m, T > & Array< n, m, T >::operator= ( const S rhs ) &

inline

Scalar assignment operator.

The following ways to assign an Array are:

Assignment from Array:

Array<n,m,MyType> A_0;
.
. A_0 has values assigned to it
.
Array<n,m,MyType> A; \\ undefined matrix
A = A_0; \\ Assignment from A_0

Assignment from scalar:

Assignment from scalar assigns the scalar uniformly to the array

MyType a = hila::random;
Array<n,m,MyType> A;
A = a;

Definition at line 334 of file array.h.

◆ operator==()

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

template<typename S , int n1, int m1>

bool Array< n, m, T >::operator== ( const Array< n1, m1, S > & rhs ) const

inline

Compare equality of Arrays.

Two Arrays are equal iff Arrays are of same dimension and all elements compare to equal Note: Complex == scalar if arithmetic value is equal

Template Parameters

S

Parameters

rhs

Returns: true if equal

Definition at line 363 of file array.h.

◆ random()

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

Array< n, m, T > & Array< n, m, T >::random ( )

inline

Fill Array with random elements.

Returns: Array<n, m, T>&

Definition at line 625 of file array.h.

◆ real()

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

Array< n, m, hila::arithmetic_type< T > > Array< n, m, T >::real ( ) const

inline

Returns real part of Array.

Returns: Array<n, m, T>

Definition at line 594 of file array.h.

◆ rows()

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

constexpr int Array< n, m, T >::rows ( ) const

inlineconstexpr

Returns number of rows.

Returns: constexpr int

Definition at line 145 of file array.h.

◆ size()

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

template<int q = n, int p = m, std::enable_if_t< q==1, int > = 0>

constexpr int Array< n, m, T >::size ( ) const

inlineconstexpr

Returns size of Vector Array or square Array.

Template Parameters

q	Number of rows n
p	Number of columns m

Returns: constexpr int

Definition at line 165 of file array.h.

Friends And Related Symbol Documentation

◆ ceil()

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

Array< n, m, T > ceil ( Array< n, m, T > a )

Ceiling function if T is arithmetic type

Template Parameters

T	Array element type, must be arithmetic type

Definition at line 1256 of file array.h.

◆ floor()

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

Array< n, m, T > floor ( Array< n, m, T > a )

Flooring function if T is arithmetic type

Template Parameters

T	Array element type, must be arithmetic type

Definition at line 1244 of file array.h.

◆ pow()

template<int n, int m, typename T >

Array< n, m, T > pow	(	Array< n, m, T >	a,
		int	b
	)

Array can be raised homogeneously to the power of a integer or scalar b or Array can be raised to the power of another Array b element wise.

Parameters

b	Array, Integer or Real scalar to raise to the power of

Definition at line 1206 of file array.h.

◆ round()

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

Array< n, m, T > round ( Array< n, m, T > a )

Rounding function if T is arithmetic type

Template Parameters

T	Array element type, must be arithmetic type

Definition at line 1232 of file array.h.

◆ trunc()

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

Array< n, m, T > trunc ( Array< n, m, T > a )

Truncation function if T is arithmetic type

Template Parameters

T	Array element type, must be arithmetic type

Definition at line 1268 of file array.h.

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

array.h

Public Member Functions

Related Symbols

Detailed Description

Constructor & Destructor Documentation

◆ Array() [1/4]

◆ Array() [2/4]

◆ Array() [3/4]

◆ Array() [4/4]

Member Function Documentation

◆ asMatrix()

◆ asVector()

◆ columns()

◆ conj()

◆ e() [1/2]

◆ e() [2/2]

◆ gaussian_random()

◆ operator!=()

◆ operator*()

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ random()

◆ real()

◆ rows()

◆ size()

Friends And Related Symbol Documentation

◆ ceil()

◆ floor()

◆ pow()

◆ round()

◆ trunc()