std::log(std::complex)
From cppreference.com
| Defined in header <complex>
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| template< class T > complex<T> log( const complex<T>& z ); |
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Computes complex natural (base e) logarithm of a complex value z with a branch cut along the negative real axis.
Contents |
[edit] Parameters
| z | - | complex value |
[edit] Return value
If no errors occur, the complex natural logarithm of z is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.
If z is a negative real number, std::imag(std::log(x)) equals pi.
[edit] Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floating-point arithmetic,
- The function is continuous onto the branch cut taking into account the sign of imaginary part
- std::log(std::conj(z)) == std::conj(std::log(z))
- If
zis(-0,+0), the result is(-∞,π)and FE_DIVBYZERO is raised - If
zis(+0,+0), the result is(-∞,+0)and FE_DIVBYZERO is raised - If
zis(x,+∞)(for any finite x), the result is(+∞,π/2) - If
zis(x,NaN)(for any finite x), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(-∞,y)(for any finite positive y), the result is(-∞,π) - If
zis(+∞,y)(for any finite positive 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) - 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
The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ
[edit] Example
Run this code
#include <iostream> #include <cmath> #include <complex> int main() { std::complex<double> z(0, 1); // // r = 1, θ = pi/2 std::cout << "2*log" << z << " = " << 2.*std::log(z) << '\n'; std::complex<double> z2(sqrt(2)/2, sqrt(2)/2); // r = 1, θ = pi/4 std::cout << "4*log" << z2 << " = " << 4.*std::log(z2) << '\n'; std::complex<double> z3(-1, 0); // r = 1, θ = pi std::cout << "log" << z3 << " = " << std::log(z3) << '\n'; std::complex<double> z4(-1, -0.0); // the other side of the cut std::cout << "log" << z4 << " (the other side of the cut) = " << std::log(z4) << '\n'; }
Output:
2*log(0,1) = (0,3.14159) 4*log(0.707107,0.707107) = (0,3.14159) log(-1,0) = (0,3.14159) log(-1,-0) (the other side of the cut) = (0,-3.14159)
[edit] See also
| complex common logarithm with the branch cuts along the negative real axis (function template) | |
| complex base e exponential (function template) | |
| computes natural (base e) logarithm (to base e) (ln(x)) (function) | |
| applies the function std::log to each element of valarray (function template) | |
| C documentation for clog
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