Detailed Description

Various mathematical functions that can be applied to arrays and views.

Mathematical functions are (mostly) implemented as lazy expressions. That means they do not return the result right away but the following proxy object instead:

nda::expr_call: A lazy function call expression.

This lazy function call expression satisfies the nda::Array concept and can therefore be used to assign to or construct nda::basic_array and nda::basic_array_view objects. Another way to evaluate lazy expressions is with nda::make_regular:

#include <nda/nda.hpp>
#include <iostream>
 
int main() {
  // create an array A
  auto A = nda::array<int, 2>({{1, 2}, {3, 4}});
 
  // square the elements of A
  auto ex = nda::pow(A, 2); // ex is a lazy expression
 
  // evaluate the lazy expression by constructing a new array
  nda::array<int, 2> A_sq = ex;
  std::cout << A_sq << std::endl;
 
  // evaluate the lazy expression using nda::make_regular
  std::cout << nda::make_regular(ex) << std::endl;
}

Output:

[[1,4]
 [9,16]]
 
[[1,4]
 [9,16]]

All functions also accept scalars. For the <cmath> functions, the scalar overloads are the std ones, while nda::conj, nda::real, nda::imag, nda::abs2, nda::reciprocal, nda::max and nda::min provide their own. The exception is nda::isnan for complex scalars, which is not covered by std::isnan and is true if either component is NaN.

Classes
struct	nda::expr_call< F, As >
	A lazy function call expression on arrays/views. More...
struct	nda::mapped< F >
	Functor that is returned by the nda::map function. More...

Functions
template<Array A>
auto	nda::abs (A &&a)
	Function abs for nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::abs (S s)
	Function abs for nda::Scalar types (uses std::abs).
template<ArrayOrScalar A>
auto	nda::abs2 (A &&a)
	Function abs2 for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::acos (A &&a)
	Function acos for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::acos (S s)
	Function acos for nda::Scalar types (uses std::acos).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::asin (A &&a)
	Function asin for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::asin (S s)
	Function asin for nda::Scalar types (uses std::asin).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::atan (A &&a)
	Function atan for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::atan (S s)
	Function atan for nda::Scalar types (uses std::atan).
template<ArrayOrScalar A>
decltype(auto)	nda::conj (A &&a)
	Function conj for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types with a complex value type).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::cos (A &&a)
	Function cos for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::cos (S s)
	Function cos for nda::Scalar types (uses std::cos).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::cosh (A &&a)
	Function cosh for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::cosh (S s)
	Function cosh for nda::Scalar types (uses std::cosh).
template<ArrayOfRank< 2 > M>
ArrayOfRank< 2 > auto	nda::dagger (M const &m)
	Get the conjugate transpose of 2-dimensional array/view.
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::exp (A &&a)
	Function exp for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::exp (S s)
	Function exp for nda::Scalar types (uses std::exp).
template<Array A>
auto	nda::floor (A &&a)
	Function floor for nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::floor (S s)
	Function floor for nda::Scalar types (uses std::floor).
template<ArrayOfRank< 2 > A>
auto	nda::frobenius_norm (A const &a)
	Calculate the Frobenius norm of a 2-dimensional array.
template<ArrayOrScalar A>
auto	nda::imag (A &&a)
	Function imag for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<typename A> requires (Array<A> \|\| is_complex_v<A>)
auto	nda::isnan (A &&a)
	Function isnan for nda::Array types and complex nda::Scalar types (lazy and coefficient-wise for nda::Array types).
template<Scalar S> requires (not is_complex_v<S>)
auto	nda::isnan (S s)
	Function isnan for real nda::Scalar types (uses std::isnan).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::log (A &&a)
	Function log for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::log (S s)
	Function log for nda::Scalar types (uses std::log).
template<class F>
mapped< F >	nda::map (F f)
	Create a lazy function call expression on arrays/views.
template<ArrayOrScalar A, ArrayOrScalar B> requires (((Scalar<A> && Scalar<B>) \|\| (Array<A> && Array<B> && get_rank<A> == get_rank<B>)) && !is_complex_v<get_value_t<A>> && !is_complex_v<get_value_t<B>>)
auto	nda::max (A &&a, B &&b)
	Function max for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<ArrayOrScalar A, ArrayOrScalar B> requires (((Scalar<A> && Scalar<B>) \|\| (Array<A> && Array<B> && get_rank<A> == get_rank<B>)) && !is_complex_v<get_value_t<A>> && !is_complex_v<get_value_t<B>>)
auto	nda::min (A &&a, B &&b)
	Function min for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<Array A, Scalar S>
auto	nda::pow (A &&a, S p)
	Function pow for nda::Array types (lazy and coefficient-wise).
template<Scalar S, Scalar P>
auto	nda::pow (S s, P p)
	Function pow for nda::Scalar types (uses std::pow).
template<ArrayOrScalar A>
auto	nda::real (A &&a)
	Function real for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<ArrayOrScalar A>
auto	nda::reciprocal (A &&a)
	Reciprocal function for nda::ArrayOrScalar types (lazy and coefficient-wise for nda::Array types).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::sin (A &&a)
	Function sin for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::sin (S s)
	Function sin for nda::Scalar types (uses std::sin).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::sinh (A &&a)
	Function sinh for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::sinh (S s)
	Function sinh for nda::Scalar types (uses std::sinh).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::sqrt (A &&a)
	Function sqrt for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::sqrt (S s)
	Function sqrt for nda::Scalar types (uses std::sqrt).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::tan (A &&a)
	Function tan for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::tan (S s)
	Function tan for nda::Scalar types (uses std::tan).
template<Array A> requires (get_algebra<A> != 'M')
auto	nda::tanh (A &&a)
	Function tanh for non-matrix nda::Array types (lazy and coefficient-wise).
template<Scalar S>
auto	nda::tanh (S s)
	Function tanh for nda::Scalar types (uses std::tanh).
template<ArrayOfRank< 2 > M>
auto	nda::trace (M const &m)
	Get the trace of a 2-dimensional square array/view.

Function Documentation

◆ abs()

template<Array A>

auto nda::abs ( A && a )

Detailed Description

Classes

Functions

Function Documentation

◆ abs()

◆ abs2()

◆ acos()

◆ asin()

◆ atan()

◆ conj()

◆ cos()

◆ cosh()

◆ dagger()

◆ exp()

◆ floor()

◆ frobenius_norm()

◆ imag()

◆ isnan()

◆ log()

◆ map()

◆ max()

◆ min()

◆ pow()

◆ real()

◆ reciprocal()

◆ sin()

◆ sinh()

◆ sqrt()

◆ tan()

◆ tanh()

◆ trace()