std::acos(std::complex)
From cppreference.com
| Defined in header <complex>
|
||
| template< class T > complex<T> acos( const complex<T>& z ); |
(since C++11) | |
Computes complex arc cosine of a complex value z. Branch cuts exist outside the interval [−1 ; +1] along the real axis.
Contents |
[edit] Parameters
| z | - | complex value |
[edit] Return value
If no errors occur, complex arc cosine of z is returned, in the range [0 ; ∞) along the real axis and in the range [−iπ ; iπ] along the imaginary axis.
[edit] Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floating-point arithmetic,
- std::acos(std::conj(z)) == std::conj(std::acos(z))
- If
zis(±0,+0), the result is(π/2,-0) - If
zis(±0,NaN), the result is(π/2,NaN) - If
zis(x,+∞)(for any finite x), the result is(π/2,-∞) - If
zis(x,NaN)(for any nonzero finite x), the result is(NaN,NaN)and FE_INVALID may be raised. - If
zis(-∞,y)(for any positive finite y), the result is(π,-∞) - If
zis(+∞,y)(for any positive finite y), the result is(+0,-∞) - If
zis(-∞,+∞), the result is(3π/4,-∞) - If
zis(+∞,+∞), the result is(π/4,-∞) - If
zis(±∞,NaN), the result is(NaN,±∞)(the sign of the imaginary part is unspecified) - If
zis(NaN,y)(for any finite y), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(NaN,+∞), the result is(NaN,-∞) - If
zis(NaN,NaN), the result is(NaN,NaN)
[edit] Notes
Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.
The mathematical definition of the principal value of arc cosine is acos z =| 1 |
| 2 |
)
For any z, acos(z) = π - acos(-z)
[edit] Example
Run this code
#include <iostream> #include <cmath> #include <complex> int main() { std::cout << std::fixed; std::complex<double> z1(-2, 0); std::cout << "acos" << z1 << " = " << std::acos(z1) << '\n'; std::complex<double> z2(-2, -0.0); std::cout << "acos" << z2 << " (the other side of the cut) = " << std::acos(z2) << '\n'; // for any z, acos(z) = pi - acos(-z) const double pi = std::acos(-1); std::complex<double> z3 = pi - std::acos(z2); std::cout << "cos(pi - acos" << z2 << ") = " << std::cos(z3) << '\n'; }
Output:
acos(-2.000000,0.000000) = (3.141593,-1.316958) acos(-2.000000,-0.000000) (the other side of the cut) = (3.141593,1.316958) cos(pi - acos(-2.000000,-0.000000)) = (2.000000,0.000000)
[edit] See also
| (C++11) |
computes arc sine of a complex number (arcsin(z)) (function template) |
| (C++11) |
computes arc tangent of a complex number (arctan(z)) (function template) |
| computes cosine of a complex number (cos(z)) (function template) | |
| computes arc cosine (arccos(x)) (function) | |
| applies the function std::acos to each element of valarray (function template) | |
| C documentation for cacos
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