std::laguerre, std::laguerref, std::laguerrel - cppreference.com (original) (raw)
| Defined in header | ||
|---|---|---|
| (1) | ||
| float laguerre ( unsigned int n, float x ); double laguerre ( unsigned int n, double x ); long double laguerre ( unsigned int n, long double x ); | (since C++17) (until C++23) | |
| /* floating-point-type */ laguerre( unsigned int n, /* floating-point-type */ x ); | (since C++23) | |
| float laguerref( unsigned int n, float x ); | (2) | (since C++17) |
| long double laguerrel( unsigned int n, long double x ); | (3) | (since C++17) |
| Additional overloads | ||
| Defined in header | ||
| template< class Integer > double laguerre ( unsigned int n, Integer x ); | (A) | (since C++17) |
1-3) Computes the non-associated Laguerre polynomials of the degree n and argument x. The library provides overloads of std::laguerre for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.
Contents
[edit] Parameters
| n | - | the degree of the polynomial, an unsigned integer value |
|---|---|---|
| x | - | the argument, a floating-point or integer value |
[edit] Return value
If no errors occur, value of the nonassociated Laguerre polynomial of x, that is (xn
_e_-x), is returned.
[edit] 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 x is negative, a domain error may occur
- If n is greater or equal than 128, the behavior is implementation-defined
[edit] 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.
The Laguerre polynomials are the polynomial solutions of the equation .
The first few are:
| Function | Polynomial |
|---|---|
| laguerre(0, x) | 1 |
| laguerre(1, x) | -x + 1 |
| laguerre(2, x) | 12(x2 - 4x + 2) |
| laguerre(3, x) | 16(-x3 - 9x2 - 18x + 6) |
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::laguerre(int_num, num) has the same effect as std::laguerre(int_num, static_cast<double>(num)).
[edit] Example
#include #include double L1(double x) { return -x + 1; } double L2(double x) { return 0.5 * (x * x - 4 * x + 2); } int main() { // spot-checks std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\n' << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\n' << std::laguerre(3, 0.0) << '=' << 1.0 << '\n'; }
Output: