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Difference between revisions of "cpp/numeric/special functions/expint"

From cppreference.com
m (Typo Gompetz -> Gompertz)
m (→‎Example: +`expint` outline.)
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===Example===
 
===Example===
 
{{example|code=
 
{{example|code=
−
#include <cmath>
+
{{cpp/numeric/draw_vbars}}
−
#include <iostream>
+
 
 
int main()
 
int main()
 
{
 
{
Line 46: Line 46:
 
               << "Ei(1) = " << std::expint(1) << '\n'
 
               << "Ei(1) = " << std::expint(1) << '\n'
 
               << "Gompertz constant = " << -std::exp(1)*std::expint(-1) << '\n';
 
               << "Gompertz constant = " << -std::exp(1)*std::expint(-1) << '\n';
 +
 +
    std::vector<float> v;         
 +
    for (float x{1.f}; x < 8.8f; x += 0.3565f)
 +
        v.push_back(std::expint(x));
 +
    draw_vbars<9,1,1>(v);
 
}
 
}
−
|output=
+
|output=<nowiki/>
 
Ei(0) = -inf
 
Ei(0) = -inf
 
Ei(1) = 1.89512
 
Ei(1) = 1.89512
 
Gompertz constant = 0.596347
 
Gompertz constant = 0.596347
 +
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 +
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▁ ▁ ▁ ▁ ▁ ▁ ▁ ▂ ▂ ▃ ▃ ▄ ▆ ▇ █ █ █ █ █ █ █ █ ┴ 1.89512
 
}}
 
}}
  

Revision as of 05:45, 24 June 2022

 
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Mathematical special functions
 
Defined in header <cmath>
double      expint( double arg );

float       expint( float arg );
long double expint( long double arg );
float       expintf( float arg );

long double expintl( long double arg );
 (1) (since C++17)
double      expint( IntegralType arg );
 (2) (since C++17)
1) Computes the exponential integral of arg.
2) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

Contents

Parameters

arg - value of a floating-point or Integral type

Return value

If no errors occur, value of the exponential integral of arg, that is -∫∞-arg
e-t
t
dt, is returned.

Error handling

Errors may be reported as specified in math_errhandling

  • If the argument is NaN, NaN is returned and domain error is not reported
  • If the argument is ±0, -∞ is returned

Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.

An implementation of this function is also available in boost.math

Example

Run this code
template<int Height = 5, int BarWidth = 1, int Padding = 1, int Offset = 0, class Seq>
void draw_vbars(Seq&& s, const bool DrawMinMax = true)
{
    static_assert(0 < Height and 0 < BarWidth and 0 <= Padding and 0 <= Offset);
 
    auto cout_n = [](auto&& v, int n = 1)
    {
        while (n-- > 0)
            std::cout << v;
    };
 
    const auto [min, max] = std::minmax_element(std::cbegin(s), std::cend(s));
 
    std::vector<std::div_t> qr;
    for (typedef decltype(*std::cbegin(s)) V; V e : s)
        qr.push_back(std::div(std::lerp(V(0), 8 * Height,
                                        (e - *min) / (*max - *min)), 8));
 
    for (auto h{Height}; h-- > 0; cout_n('\n'))
    {
        cout_n(' ', Offset);
 
        for (auto dv : qr)
        {
            const auto q{dv.quot}, r{dv.rem};
            unsigned char d[]{0xe2, 0x96, 0x88, 0}; // Full Block: '█'
            q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0;
            cout_n(d, BarWidth), cout_n(' ', Padding);
        }
 
        if (DrawMinMax && Height > 1)
            Height - 1 == h ? std::cout << "┬ " << *max:
                          h ? std::cout << "│ "
                            : std::cout << "┴ " << *min;
    }
}
 
int main()
{
    std::cout << "Ei(0) = " << std::expint(0) << '\n'
              << "Ei(1) = " << std::expint(1) << '\n'
              << "Gompertz constant = " << -std::exp(1)*std::expint(-1) << '\n';
 
    std::vector<float> v;          
    for (float x{1.f}; x < 8.8f; x += 0.3565f)
        v.push_back(std::expint(x));
    draw_vbars<9,1,1>(v);
}

Output: 

Ei(0) = -inf
Ei(1) = 1.89512
Gompertz constant = 0.596347
                                          █ ┬ 666.505
                                          █ │
                                        ▆ █ │
                                        █ █ │
                                      █ █ █ │
                                    ▆ █ █ █ │
                                ▁ ▆ █ █ █ █ │
                            ▂ ▅ █ █ █ █ █ █ │
▁ ▁ ▁ ▁ ▁ ▁ ▁ ▂ ▂ ▃ ▃ ▄ ▆ ▇ █ █ █ █ █ █ █ █ ┴ 1.89512

External links

Weisstein, Eric W. "Exponential Integral." From MathWorld--A Wolfram Web Resource.

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