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Mathematical Functions | ![]() |
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Namespaces | |
namespace | vigra::detail |
namespace | vigra::detail |
namespace | vigra::detail |
namespace | vigra::detail |
namespace | vigra::detail |
Classes | |
class | BSpline |
class | BSplineBase |
class | CatmullRomSpline |
class | CoscotFunction |
class | Gaussian |
Functions | |
float | round (float t) |
template<class T> NumericTraits< T >::Promote | sq (T t) |
Int32 | sqrti (Int32 v) |
UInt32 | sqrti (UInt32 v) |
double | hypot (double a, double b) |
template<class T> T | sign (T t) |
template<class T1, class T2> T1 | sign (T1 t1, T2 t2) |
NormTraits< T >::SquaredNormType | squaredNorm (T const &t) |
template<class T> NormTraits< T >::NormType | norm (T const &t) |
double | ellipticIntegralF (double x, double k) |
double | ellipticIntegralE (double x, double k) |
double | erf (double x) |
double | chi2 (unsigned int degreesOfFreedom, double arg, double accuracy=1e-7) |
double | chi2CDF (unsigned int degreesOfFreedom, double arg, double accuracy=1e-7) |
double | noncentralChi2 (unsigned int degreesOfFreedom, double noncentrality, double arg, double accuracy=1e-7) |
double | noncentralChi2CDF (unsigned int degreesOfFreedom, double noncentrality, double arg, double accuracy=1e-7) |
double | noncentralChi2CDFApprox (unsigned int degreesOfFreedom, double noncentrality, double arg) |
template<class T1, class T2> bool | closeAtTolerance (T1 l, T2 r, typename PromoteTraits< T1, T2 >::Promote epsilon) |
template<typename IntType> IntType | gcd (IntType n, IntType m) |
template<typename IntType> IntType | lcm (IntType n, IntType m) |
result_type | operator() (argument_type x) const |
Detailed Description |
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Value: inline NormTraits<T>::SquaredNormType squaredNorm(T t) { return sq(t); } \ inline NormTraits<T>::NormType norm(T t) { return abs(t); } |
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Chi square distribution.
Computes the density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg by calling
#include "vigra/mathutil.hxx" |
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Cumulative chi square distribution.
Computes the cumulative density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg by calling
#include "vigra/mathutil.hxx" |
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Tolerance based floating-point comparison. Check whether two floating point numbers are equal within the given tolerance. This is useful because floating point numbers that should be equal in theory are rarely exactly equal in practice. If the tolerance epsilon is not given, twice the machine epsilon is used.
#include "vigra/mathutil.hxx" |
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The incomplete elliptic integral of the second kind. Computes
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according to the algorithm given in Press et al. "Numerical Recipes". The complete elliptic integral of the second kind is simply Note: In some libraries (e.g. Mathematica), the second parameter of the elliptic integral functions must be k^2 rather than k. Check the documentation when results disagree!
#include "vigra/mathutil.hxx" |
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The incomplete elliptic integral of the first kind. Computes
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according to the algorithm given in Press et al. "Numerical Recipes". Note: In some libraries (e.g. Mathematica), the second parameter of the elliptic integral functions must be k^2 rather than k. Check the documentation when results disagree!
#include "vigra/mathutil.hxx" |
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The error function.
If
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according to the formula given in Press et al. "Numerical Recipes".
#include "vigra/mathutil.hxx" |
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Calculate the greatest common divisor. This function works for arbitrary integer types, including user-defined (e.g. infinite precision) ones.
#include "vigra/rational.hxx" |
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Compute the Euclidean distance (length of the hypothenuse of a right-angled triangle). The hypot() function returns the sqrt(a*a + b*b). It is implemented in a way that minimizes round-off error.
#include "vigra/mathutil.hxx" |
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Calculate the lowest common multiple. This function works for arbitrary integer types, including user-defined (e.g. infinite precision) ones.
#include "vigra/rational.hxx" |
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Non-central chi square distribution. Computes the density of a non-central chi square distribution with degreesOfFreedom, noncentrality parameter noncentrality and tolerance accuracy at the given argument arg. It uses Algorithm AS 231 from Appl. Statist. (1987) Vol.36, No.3 (code ported from http://lib.stat.cmu.edu/apstat/231). The algorithm has linear complexity in the number of degrees of freedom.
#include "vigra/mathutil.hxx" |
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Cumulative non-central chi square distribution. Computes the cumulative density of a chi square distribution with degreesOfFreedom, noncentrality parameter noncentrality and tolerance accuracy at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg It uses Algorithm AS 231 from Appl. Statist. (1987) Vol.36, No.3 (code ported from http://lib.stat.cmu.edu/apstat/231). The algorithm has linear complexity in the number of degrees of freedom (see noncentralChi2CDFApprox() for a constant-time algorithm).
#include "vigra/mathutil.hxx" |
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Cumulative non-central chi square distribution (approximate). Computes approximate values of the cumulative density of a chi square distribution with degreesOfFreedom, and noncentrality parameter noncentrality at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg It uses the approximate transform into a normal distribution due to Wilson and Hilferty (see Abramovitz, Stegun: "Handbook of Mathematical Functions", formula 26.3.32). The algorithm's running time is independent of the inputs, i.e. is should be used when noncentralChi2CDF() is too slow, and approximate values are sufficient. The accuracy is only about 0.1 for few degrees of freedom, but reaches about 0.001 above dof = 5.
#include "vigra/mathutil.hxx" |
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The norm of a numerical object.
For scalar types: implemented as
#include "vigra/mathutil.hxx" |
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function (functor) call |
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The rounding function.
Defined for all floating point types. Rounds towards the nearest integer such that
#include "vigra/mathutil.hxx" |
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The binary sign function. Transfers the sign of t2 to t1.
#include "vigra/mathutil.hxx" |
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The sign function. Returns 1, 0, or -1 depending on the sign of t.
#include "vigra/mathutil.hxx" |
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The square function. sq(x) is needed so often that it makes sense to define it as a function.
#include "vigra/mathutil.hxx" |
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Unsigned integer square root. Useful for fast fixed-point computations.
#include "vigra/mathutil.hxx" |
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Signed integer square root. Useful for fast fixed-point computations.
#include "vigra/mathutil.hxx" |
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The squared norm of a numerical object.
For scalar types: equals |
© Ullrich Köthe (koethe@informatik.uni-hamburg.de) |
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