Difference between revisions of "cpp/numeric/valarray/sinh"
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{{cpp/title|sinh{{small|(std::valarray)}}}} | {{cpp/title|sinh{{small|(std::valarray)}}}} | ||
{{cpp/numeric/valarray/navbar}} | {{cpp/numeric/valarray/navbar}} | ||
| − | {{ddcl | header=valarray | 1= | + | {{ddcl|header=valarray|1= |
template< class T > | template< class T > | ||
valarray<T> sinh( const valarray<T>& va ); | valarray<T> sinh( const valarray<T>& va ); | ||
}} | }} | ||
| − | For each element in {{ | + | For each element in {{c|va}} computes hyperbolic sine of the value of the element. |
===Parameters=== | ===Parameters=== | ||
{{par begin}} | {{par begin}} | ||
| − | {{par | va | value array to apply the operation to}} | + | {{par|va|value array to apply the operation to}} |
{{par end}} | {{par end}} | ||
===Return value=== | ===Return value=== | ||
| − | Value array containing hyperbolic sine of the values in {{ | + | Value array containing hyperbolic sine of the values in {{c|va}}. |
===Notes=== | ===Notes=== | ||
| Line 22: | Line 22: | ||
===Possible implementation=== | ===Possible implementation=== | ||
| − | {{ | + | {{cpp/numeric/valarray/impl|sinh}} |
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| − | }} | + | |
===Example=== | ===Example=== | ||
| − | {{example | + | {{example |
| − | + | |code= | |
#include <cmath> | #include <cmath> | ||
| + | #include <complex> | ||
#include <iomanip> | #include <iomanip> | ||
#include <iostream> | #include <iostream> | ||
#include <valarray> | #include <valarray> | ||
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template<typename T> | template<typename T> | ||
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{ | { | ||
std::cout << title << " : " << std::right; | std::cout << title << " : " << std::right; | ||
| − | for (T x : va) | + | for (T x : va) |
| − | std::cout << std::fixed << x << | + | std::cout << std::fixed << x << ' '; |
| − | + | ||
std::cout << '\n'; | std::cout << '\n'; | ||
} | } | ||
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// Hyperbolic sine is sinh(z) = (eᶻ - e⁻ᶻ) / 2. | // Hyperbolic sine is sinh(z) = (eᶻ - e⁻ᶻ) / 2. | ||
| − | const std::valarray<T> sinh_z { std::sinh(z) }; | + | const std::valarray<T> sinh_z{std::sinh(z)}; |
| − | const std::valarray<T> e_z { std::exp(z) }; | + | const std::valarray<T> e_z{std::exp(z)}; |
| − | const std::valarray<T> e_neg_z { std::exp(-z) }; | + | const std::valarray<T> e_neg_z{std::exp(-z)}; |
| − | const std::valarray<T> sinh_def { (e_z - e_neg_z) / 2.0f }; | + | const std::valarray<T> sinh_def{(e_z - e_neg_z) / 2.0f}; |
show("n ", z); | show("n ", z); | ||
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int main() | int main() | ||
{ | { | ||
| − | sinh_for(std::valarray<float>{ -.2f, -.1f, 0.f, .1f, .2f, INFINITY }); | + | sinh_for(std::valarray<float>{-.2f, -.1f, 0.f, .1f, .2f, INFINITY}); |
| − | sinh_for(std::valarray<std::complex<double>>{ {-.2,-.1}, {. | + | sinh_for(std::valarray<std::complex<double>>{<!---->{-.2,-.1}, {.2,.1}<!---->}); |
} | } | ||
| − | + | |output= | |
n : -0.200000 -0.100000 0.000000 0.100000 0.200000 inf | n : -0.200000 -0.100000 0.000000 0.100000 0.200000 inf | ||
sinh(n) : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf | sinh(n) : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf | ||
(eⁿ-e⁻ⁿ)/2 : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf | (eⁿ-e⁻ⁿ)/2 : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf | ||
| − | n : (-0.200000,-0.100000) (0. | + | n : (-0.200000,-0.100000) (0.200000,0.100000) |
| − | sinh(n) : (-0.200330,-0.101837) (0. | + | sinh(n) : (-0.200330,-0.101837) (0.200330,0.101837) |
| − | (eⁿ-e⁻ⁿ)/2 : (-0.200330,-0.101837) (0. | + | (eⁿ-e⁻ⁿ)/2 : (-0.200330,-0.101837) (0.200330,0.101837) |
}} | }} | ||
===See also=== | ===See also=== | ||
{{dsc begin}} | {{dsc begin}} | ||
| − | {{dsc inc | cpp/numeric/valarray/dsc cosh}} | + | {{dsc inc|cpp/numeric/valarray/dsc cosh}} |
| − | {{dsc inc | cpp/numeric/valarray/dsc tanh}} | + | {{dsc inc|cpp/numeric/valarray/dsc tanh}} |
| − | {{dsc inc | cpp/numeric/math/dsc sinh}} | + | {{dsc inc|cpp/numeric/math/dsc sinh}} |
| − | {{dsc inc | cpp/numeric/complex/dsc sinh}} | + | {{dsc inc|cpp/numeric/complex/dsc sinh}} |
{{dsc end}} | {{dsc end}} | ||
| − | + | {{langlinks|de|es|fr|it|ja|pt|ru|zh}} | |
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Latest revision as of 03:20, 17 October 2023
| Defined in header <valarray>
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| template< class T > valarray<T> sinh( const valarray<T>& va ); |
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For each element in va computes hyperbolic sine of the value of the element.
Contents |
[edit] Parameters
| va | - | value array to apply the operation to |
[edit] Return value
Value array containing hyperbolic sine of the values in va.
[edit] Notes
Unqualified function (sinh) is used to perform the computation. If such function is not available, std::sinh is used due to argument-dependent lookup.
The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:
- All const member functions of std::valarray are provided.
- std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
- For every function taking a const std::valarray<T>& except begin() and end()(since C++11), identical functions taking the replacement types shall be added;
- For every function taking two const std::valarray<T>& arguments, identical functions taking every combination of const std::valarray<T>& and replacement types shall be added.
- The return type does not add more than two levels of template nesting over the most deeply-nested argument type.
[edit] Possible implementation
template<class T> valarray<T> sinh(const valarray<T>& va) { valarray<T> other = va; for (T& i : other) i = sinh(i); return other; // proxy object may be returned } |
[edit] Example
Run this code
#include <cmath> #include <complex> #include <iomanip> #include <iostream> #include <valarray> template<typename T> void show(char const* title, const std::valarray<T>& va) { std::cout << title << " : " << std::right; for (T x : va) std::cout << std::fixed << x << ' '; std::cout << '\n'; } template<typename T> void sinh_for(std::valarray<T> const& z) { // Hyperbolic sine is sinh(z) = (eᶻ - e⁻ᶻ) / 2. const std::valarray<T> sinh_z{std::sinh(z)}; const std::valarray<T> e_z{std::exp(z)}; const std::valarray<T> e_neg_z{std::exp(-z)}; const std::valarray<T> sinh_def{(e_z - e_neg_z) / 2.0f}; show("n ", z); show("sinh(n) ", sinh_z); show("(eⁿ-e⁻ⁿ)/2", sinh_def); std::cout.put('\n'); } int main() { sinh_for(std::valarray<float>{-.2f, -.1f, 0.f, .1f, .2f, INFINITY}); sinh_for(std::valarray<std::complex<double>>{{-.2,-.1}, {.2,.1}}); }
Output:
n : -0.200000 -0.100000 0.000000 0.100000 0.200000 inf sinh(n) : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf (eⁿ-e⁻ⁿ)/2 : -0.201336 -0.100167 0.000000 0.100167 0.201336 inf n : (-0.200000,-0.100000) (0.200000,0.100000) sinh(n) : (-0.200330,-0.101837) (0.200330,0.101837) (eⁿ-e⁻ⁿ)/2 : (-0.200330,-0.101837) (0.200330,0.101837)
[edit] See also
| applies the function std::cosh to each element of valarray (function template) | |
| applies the function std::tanh to each element of valarray (function template) | |
| (C++11)(C++11) |
computes hyperbolic sine (sinh(x)) (function) |
| computes hyperbolic sine of a complex number (sinh(z)) (function template) |
