Difference between revisions of "cpp/numeric/math/erf"
From cppreference.com
m (+ link to C documentation) |
(+detail, borrow special values from C for the example) |
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| Line 3: | Line 3: | ||
{{dcl begin}} | {{dcl begin}} | ||
{{dcl header | cmath}} | {{dcl header | cmath}} | ||
| − | {{dcl | since=c++11 | | + | {{dcl | since=c++11 |num=1| |
float erf( float arg ); | float erf( float arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 | | + | {{dcl | since=c++11 |num=2| |
double erf( double arg ); | double erf( double arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 | | + | {{dcl | since=c++11 |num=3| |
long double erf( long double arg ); | long double erf( long double arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 | | + | {{dcl | since=c++11 |num=4| |
double erf( Integral arg ); | double erf( Integral arg ); | ||
}} | }} | ||
{{dcl end}} | {{dcl end}} | ||
| − | Computes the [[enwiki:Error function|error function]] of {{tt|arg}}. | + | @1-3@ Computes the [[enwiki:Error function|error function]] of {{tt|arg}}. |
| + | @4@ A set of overloads or a function template accepting an argument of any [[cpp/types/is_integral|integral type]]. Equivalent to 2) (the argument is cast to {{c|double}}). | ||
===Parameters=== | ===Parameters=== | ||
| Line 25: | Line 26: | ||
===Return value=== | ===Return value=== | ||
| + | If no errors occur, value of the error function of {{tt|arg}}, that is {{math|{{mfrac|2|{{mrad|π}}}}{{minteg|0|arg|{{mexp|-t{{su|p=2}}}}d''t''}}}}, is returned. | ||
| − | + | If a range error occurs due to underflow, the correct result (after rounding), that is {{math|{{mfrac|2*arg|{{mrad|π}}}}}} is returned | |
| + | |||
| + | ===Error handling=== | ||
| + | Errors are reported as specified in [[cpp/numeric/math/math_errhandling|math_errhandling]] | ||
| + | |||
| + | If the implementation supports IEEE floating-point arithmetic (IEC 60559), | ||
| + | * If the argument is ±0, ±0 is returned | ||
| + | * If the argument is ±∞, ±1 is returned | ||
| + | * If the argument is NaN, NaN is returned | ||
===Example=== | ===Example=== | ||
| Line 46: | Line 56: | ||
<< std::setw(5) << std::fixed << std::setprecision(2) | << std::setw(5) << std::fixed << std::setprecision(2) | ||
<< 100*phi(n, n+1) << "%\n"; | << 100*phi(n, n+1) << "%\n"; | ||
| + | |||
| + | std::cout << "special values:\n" | ||
| + | << "erf(-0) = " << std::erf(-0.0) << '\n' | ||
| + | << "erf(Inf) = " << std::erf(INFINITY) << '\n'; | ||
} | } | ||
| output= | | output= | ||
| Line 57: | Line 71: | ||
[ 2: 3]: 2.14% | [ 2: 3]: 2.14% | ||
[ 3: 4]: 0.13% | [ 3: 4]: 0.13% | ||
| + | special values: | ||
| + | erf(-0) = -0.00 | ||
| + | erf(Inf) = 1.00 | ||
}} | }} | ||
| − | |||
===See also=== | ===See also=== | ||
| − | |||
{{dsc begin}} | {{dsc begin}} | ||
{{dsc inc | cpp/numeric/math/dsc erfc}} | {{dsc inc | cpp/numeric/math/dsc erfc}} | ||
Revision as of 21:01, 6 June 2014
| Defined in header <cmath>
|
||
| float erf( float arg ); |
(1) | (since C++11) |
| double erf( double arg ); |
(2) | (since C++11) |
| long double erf( long double arg ); |
(3) | (since C++11) |
| double erf( Integral arg ); |
(4) | (since C++11) |
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).
Contents |
Parameters
| arg | - | value of a floating-point or Integral type |
Return value
If no errors occur, value of the error function ofarg, that is | 2 |
| √π |
| 2*arg |
| √π |
Error handling
Errors are reported as specified in math_errhandling
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- If the argument is ±0, ±0 is returned
- If the argument is ±∞, ±1 is returned
- If the argument is NaN, NaN is returned
Example
The following example calculates the probability that a normal variate is on the interval (x1, x2)
Run this code
#include <iostream> #include <cmath> #include <iomanip> double phi(double x1, double x2) { return (std::erf(x2/std::sqrt(2)) - std::erf(x1/std::sqrt(2)))/2; } int main() { std::cout << "normal variate probabilities:\n"; for(int n=-4; n<4; ++n) std::cout << "[" << std::setw(2) << n << ":" << std::setw(2) << n+1 << "]: " << std::setw(5) << std::fixed << std::setprecision(2) << 100*phi(n, n+1) << "%\n"; std::cout << "special values:\n" << "erf(-0) = " << std::erf(-0.0) << '\n' << "erf(Inf) = " << std::erf(INFINITY) << '\n'; }
Output:
normal variate probabilities: [-4:-3]: 0.13% [-3:-2]: 2.14% [-2:-1]: 13.59% [-1: 0]: 34.13% [ 0: 1]: 34.13% [ 1: 2]: 13.59% [ 2: 3]: 2.14% [ 3: 4]: 0.13% special values: erf(-0) = -0.00 erf(Inf) = 1.00
See also
| (C++11)(C++11)(C++11) |
complementary error function (function) |
| C documentation for erf
| |
External links
Weisstein, Eric W. "Erf." From MathWorld--A Wolfram Web Resource.
