Math routines. More...
Functions | |
| COMPILER_FUNCTIONAL double | BinomialCoefficient (int n, int k) |
| Computes the binomial coefficient, n choose k for nonnegative integers n and k. | |
| double | ClampNonNegative (double d) |
| Forces a number to be non-negative, turning negative numbers into zero. | |
| double | ClampNonPositive (double d) |
| Forces a number to be non-positive, turning positive numbers into zero. | |
| double | ClampRange (double value, double range_min, double range_max) |
| Clips a number between a particular range. | |
| COMPILER_FUNCTIONAL double | Factorial (int d) |
| Computes the factorial of an integer. | |
| unsigned | IntLog2 (unsigned i) |
| Finds the log base 2 of an integer. | |
| template<typename TAnyIntegerType > | |
| bool | IsPowerTwo (TAnyIntegerType i) |
| void | MakeIdentityPermutation (index_t size, ArrayList< index_t > *result) |
| Creates an identity permutation where the element i equals i. | |
| void | MakeIdentityPermutation (index_t size, index_t *array) |
| Creates an identity permutation where the element i equals i. | |
| void | MakeInversePermutation (const ArrayList< index_t > &original, ArrayList< index_t > *reverse) |
| Inverts or transposes an existing permutation. | |
| void | MakeInversePermutation (index_t size, const index_t *original, index_t *reverse) |
| Inverts or transposes an existing permutation. | |
| void | MakeRandomPermutation (index_t size, ArrayList< index_t > *result) |
| Creates a random permutation over integers 0 throush size - 1. | |
| void | MakeRandomPermutation (index_t size, index_t *array) |
| Creates a random permutation and stores it in an existing C array (power user version). | |
| double | Mean (Vector V) |
| Computes the mean value of a vector. | |
| template<int t_numerator, int t_denominator> | |
| double | Pow (double d) |
| Calculates a relatively small power using template metaprogramming. | |
| template<int t_numerator, int t_denominator> | |
| double | PowAbs (double d) |
| Calculates a small power of the absolute value of a number using template metaprogramming. | |
| int | RandInt (int lo, int hi_exclusive) |
| Generates a uniform random integer. | |
| int | RandInt (int hi_exclusive) |
| Generates a uniform random integer. | |
| double | Random (double lo, double hi) |
| Generates a uniform random number in the specified range. | |
| double | Random () |
| Generates a uniform random number between 0 and 1. | |
| int64 | RoundInt (double d) |
| Rounds a double-precision to an integer, casting it too. | |
| double | Sigmoid (double x) |
| Computes the sigmoid function of a real number x Sigmoid(x) = 1/[1+exp(-x)]. | |
| double | SphereVolume (double r, int d) |
| Computes the hyper-volume of a hyper-sphere of dimension d. | |
| template<typename T > | |
| T | Sqr (T v) |
| Squares a number. | |
| double | Std (Vector V) |
| Computes the standard deviation of a vector. | |
| double | Var (Vector V) |
| Computes the variance of a vector using "corrected two-pass algorithm". | |
Variables | |
| const double | E = 2.7182818284590452354 |
| Base of the natural logarithm. | |
| const double | LN_10 = 2.30258509299404568402 |
| Natural log of 10. | |
| const double | LN_2 = 0.69314718055994530942 |
| Natural log of 2. | |
| const double | LOG10_E = 0.43429448190325182765 |
| Log base 10 of E. | |
| const double | LOG2_E = 1.4426950408889634074 |
| Log base 2 of E. | |
| const double | PI = 3.141592653589793238462643383279 |
| The ratio of the circumference of a circle to its diameter. | |
| const double | PI_2 = 1.57079632679489661923 |
| The ratio of the circumference of a circle to its radius. | |
| const double | SQRT2 = 1.41421356237309504880 |
| The square root of 2. | |
Math routines.
The hope is that this should contain most of the useful math routines you can think of. Currently, this is very sparse.
| COMPILER_FUNCTIONAL double math::BinomialCoefficient | ( | int | n, | |
| int | k | |||
| ) |
Computes the binomial coefficient, n choose k for nonnegative integers n and k.
| n | the first nonnegative integer argument | |
| k | the second nonnegative integer argument |
Definition at line 43 of file discrete.cc.
Referenced by SeriesExpansionAux::Init(), and MultSeriesExpansionAux::Init().
| double math::ClampNonNegative | ( | double | d | ) | [inline] |
Forces a number to be non-negative, turning negative numbers into zero.
Avoids branching costs (yes, we've discovered measurable improvements).
Definition at line 87 of file math_lib.h.
Referenced by DBallBound< TMetric, TPoint >::MinDistance(), DBallBound< TMetric, TPoint >::MinimaxDistance(), DBallBound< TMetric, TPoint >::MinToMid(), and DBallBound< TMetric, TPoint >::RangeDistance().
| double math::ClampNonPositive | ( | double | d | ) | [inline] |
Forces a number to be non-positive, turning positive numbers into zero.
Avoids branching costs (yes, we've discovered measurable improvements).
Definition at line 96 of file math_lib.h.
| double math::ClampRange | ( | double | value, | |
| double | range_min, | |||
| double | range_max | |||
| ) | [inline] |
Clips a number between a particular range.
| value | the number to clip | |
| range_min | the first of the range | |
| range_max | the last of the range |
Definition at line 108 of file math_lib.h.
| COMPILER_FUNCTIONAL double math::Factorial | ( | int | d | ) |
Computes the factorial of an integer.
Definition at line 64 of file discrete.cc.
| unsigned math::IntLog2 | ( | unsigned | i | ) | [inline] |
Finds the log base 2 of an integer.
This integer must absolutely be a power of 2.
Definition at line 139 of file discrete.h.
| void math::MakeIdentityPermutation | ( | index_t | size, | |
| ArrayList< index_t > * | result | |||
| ) | [inline] |
Creates an identity permutation where the element i equals i.
For instance, result[0] == 0, result[1] == 1, result[2] == 2, etc.
| size | the size to initialize the result to | |
| result | will be initialized to the identity permutation |
Definition at line 85 of file discrete.h.
References ArrayList< TElem >::begin(), ArrayList< TElem >::Init(), and MakeIdentityPermutation().
| void math::MakeIdentityPermutation | ( | index_t | size, | |
| index_t * | array | |||
| ) |
Creates an identity permutation where the element i equals i.
Low-level pointer version -- preferably use the ArrayList version instead.
For instance, result[0] == 0, result[1] == 1, result[2] == 2, etc.
| size | the number of elements in the permutation | |
| array | a place to store the permutation |
Definition at line 76 of file discrete.cc.
Referenced by MakeIdentityPermutation(), GeneralCrossValidator< TLearner >::Run(), and SimpleCrossValidator< TClassifier >::Run().
| void math::MakeInversePermutation | ( | const ArrayList< index_t > & | original, | |
| ArrayList< index_t > * | reverse | |||
| ) | [inline] |
Inverts or transposes an existing permutation.
Definition at line 123 of file discrete.h.
References ArrayList< TElem >::begin(), ArrayList< TElem >::Init(), MakeInversePermutation(), and ArrayList< TElem >::size().
| void math::MakeInversePermutation | ( | index_t | size, | |
| const index_t * | original, | |||
| index_t * | reverse | |||
| ) |
Inverts or transposes an existing permutation.
Definition at line 100 of file discrete.cc.
Referenced by MakeInversePermutation().
| void math::MakeRandomPermutation | ( | index_t | size, | |
| ArrayList< index_t > * | result | |||
| ) | [inline] |
Creates a random permutation over integers 0 throush size - 1.
| size | the number of elements | |
| result | will be initialized to a permutation array |
Definition at line 108 of file discrete.h.
References ArrayList< TElem >::begin(), ArrayList< TElem >::Init(), and MakeRandomPermutation().
| void math::MakeRandomPermutation | ( | index_t | size, | |
| index_t * | array | |||
| ) |
Creates a random permutation and stores it in an existing C array (power user version).
The random permutation is over the integers 0 through size - 1.
| size | the number of elements | |
| array | the array to store a permutation in |
Definition at line 82 of file discrete.cc.
Referenced by MakeRandomPermutation(), GeneralCrossValidator< TLearner >::Run(), and SimpleCrossValidator< TClassifier >::Run().
| double math::Mean | ( | Vector | V | ) |
Computes the mean value of a vector.
Don't forget initializing V before using this function
| V | the input vector |
| double math::Pow | ( | double | d | ) | [inline] |
Calculates a relatively small power using template metaprogramming.
This allows a numerator and denominator. In the case where the numerator and denominator are equal, this will not do anything, or in the case where the denominator is one.
Definition at line 158 of file math_lib.h.
| double math::PowAbs | ( | double | d | ) | [inline] |
Calculates a small power of the absolute value of a number using template metaprogramming.
This allows a numerator and denominator. In the case where the numerator and denominator are equal, this will not do anything, or in the case where the denominator is one. For even powers, this will avoid calling the absolute value function.
Definition at line 172 of file math_lib.h.
| int math::RandInt | ( | int | lo, | |
| int | hi_exclusive | |||
| ) | [inline] |
Generates a uniform random integer.
Definition at line 141 of file math_lib.h.
| int math::RandInt | ( | int | hi_exclusive | ) | [inline] |
Generates a uniform random integer.
Definition at line 135 of file math_lib.h.
| double math::Random | ( | double | lo, | |
| double | hi | |||
| ) | [inline] |
Generates a uniform random number in the specified range.
Definition at line 128 of file math_lib.h.
References Random().
| double math::Random | ( | ) | [inline] |
Generates a uniform random number between 0 and 1.
Definition at line 121 of file math_lib.h.
Referenced by Random().
| int64 math::RoundInt | ( | double | d | ) | [inline] |
Rounds a double-precision to an integer, casting it too.
Definition at line 78 of file math_lib.h.
| double math::Sigmoid | ( | double | x | ) |
Computes the sigmoid function of a real number x Sigmoid(x) = 1/[1+exp(-x)].
| x | the input real number |
| COMPILER_FUNCTIONAL double math::SphereVolume | ( | double | r, | |
| int | d | |||
| ) |
Computes the hyper-volume of a hyper-sphere of dimension d.
| r | the radius of the hyper-sphere | |
| d | the number of dimensions |
Referenced by EpanKernel::CalcNormConstant().
| T math::Sqr | ( | T | v | ) | [inline] |
Squares a number.
Definition at line 71 of file math_lib.h.
Referenced by DHrectBound< t_pow >::CalculateMaxDistanceSq(), and DatasetScaler::StandardizeData().
| double math::Std | ( | Vector | V | ) |
Computes the standard deviation of a vector.
Don't forget initializing V before using this function.
| V | the input vector |
| double math::Var | ( | Vector | V | ) |
Computes the variance of a vector using "corrected two-pass algorithm".
See "Numerical Recipes in C" for reference. Don't forget initializing V before using this function.
| V | the input vector |
| const double math::E = 2.7182818284590452354 |
Base of the natural logarithm.
Definition at line 55 of file math_lib.h.
| const double math::LN_10 = 2.30258509299404568402 |
Natural log of 10.
Definition at line 63 of file math_lib.h.
| const double math::LN_2 = 0.69314718055994530942 |
Natural log of 2.
Definition at line 61 of file math_lib.h.
Referenced by GaussianStarKernel::Init().
| const double math::LOG10_E = 0.43429448190325182765 |
Log base 10 of E.
Definition at line 59 of file math_lib.h.
| const double math::LOG2_E = 1.4426950408889634074 |
Log base 2 of E.
Definition at line 57 of file math_lib.h.
| const double math::PI = 3.141592653589793238462643383279 |
The ratio of the circumference of a circle to its diameter.
Definition at line 65 of file math_lib.h.
Referenced by GaussianKernel::CalcNormConstant().
| const double math::PI_2 = 1.57079632679489661923 |
The ratio of the circumference of a circle to its radius.
Definition at line 67 of file math_lib.h.
Referenced by GaussianStarKernel::CalcNormConstant().
| const double math::SQRT2 = 1.41421356237309504880 |
The square root of 2.
Definition at line 53 of file math_lib.h.
1.6.3