diplib/library/numeric.h file

Numeric algorithms and constants unrelated to images. This file is always included through diplib.h. See Numeric algorithms and constants.

Contents

Classes

struct dip::GaussianParameters
Parameters defining a 1D Gaussian. Returned by dip::GaussianMixtureModel. more...
class dip::ThinPlateSpline
Fits a thin plate spline function to a set of points. Useful for interpolation of scattered points. more...

Enums

enum class dip::Option::DecompositionMethod: uint8
Select the algorithm to use with dip::SymmetricEigenDecomposition2 and dip::SymmetricEigenDecomposition3. more...
enum class dip::Option::Periodicity: uint8
Select if the operation is periodic or not. Used in dip::GaussianMixtureModel. more...

Functions

template<typename T>
auto dip::abs(T value) -> T constexpr
constexpr version of std::abs. Prefer std::abs outside of constexpr functions.
auto dip::ApproximatelyEquals(dip::dfloat lhs, dip::dfloat rhs, dip::dfloat tolerance = 1e-6) -> bool constexpr
Approximate floating-point equality: abs(lhs-rhs)/lhs <= tolerance.
auto dip::BesselJ0(dip::dfloat x) -> dip::dfloat
Computes the Bessel function J of the order 0 (with around 7 digits of precision).
auto dip::BesselJ1(dip::dfloat x) -> dip::dfloat
Computes the Bessel function J of the order 1 (with around 7 digits of precision).
auto dip::BesselJN(dip::dfloat x, dip::uint n) -> dip::dfloat
Computes the Bessel function J of the order n (with around 7 digits of precision).
auto dip::BesselY0(dip::dfloat x) -> dip::dfloat
Computes the Bessel function Y of the order 0 (with around 7 digits of precision).
auto dip::BesselY1(dip::dfloat x) -> dip::dfloat
Computes the Bessel function Y of the order 1 (with around 7 digits of precision).
auto dip::BesselYN(dip::dfloat x, dip::uint n) -> dip::dfloat
Computes the Bessel function Y of the order n (with around 7 digits of precision).
template<typename T, typename <SFINAE>>
auto dip::ceil_cast(T v) -> dip::sint constexpr
Fast ceil operation, without checks, returning a dip::sint.
template<typename T>
auto dip::clamp(T const& v, T const& lo, T const& hi) -> T const& constexpr
Clamps a value between a min and max value (a.k.a. clip, saturate, etc.).
template<typename T, bool inverse = false, typename <SFINAE>>
auto dip::consistent_round(T v) -> dip::sint constexpr
Consistent rounding, without checks, returning a dip::sint. more...
auto dip::Determinant(dip::uint n, dip::ConstSampleIterator input) -> dip::dfloat
Computes the determinant of a square, real-valued matrix. more...
auto dip::Determinant(dip::uint n, dip::ConstSampleIterator input) -> dip::dcomplex
Computes the determinant of a square, complex-valued matrix. more...
template<typename T>
auto dip::DeterminantDiagonal(dip::uint n, dip::ConstSampleIterator input) -> T
Computes the determinant of a diagonal matrix. more...
template<typename T, <SFINAE> = 0>
auto dip::div_ceil(T lhs, T rhs) -> T constexpr
Integer division, unsigned, return ceil.
template<typename T, <SFINAE> = 0>
auto dip::div_floor(T lhs, T rhs) -> T constexpr
Integer division, unsigned, return floor.
template<typename T, typename <SFINAE> = T>
auto dip::div_round(T lhs, T rhs) -> T constexpr
Integer division, return rounded.
void dip::EigenDecomposition(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr)
Finds the eigenvalues and eigenvectors of a square, real-valued matrix. more...
void dip::EigenDecomposition(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr)
Finds the eigenvalues and eigenvectors of a square, complex-valued matrix. more...
template<typename T, typename <SFINAE>>
auto dip::floor_cast(T v) -> dip::sint constexpr
Fast floor operation, without checks, returning a dip::sint.
auto dip::GaussianMixtureModel(dip::ConstSampleIterator data, dip::SampleIterator responsibilities, dip::uint size, dip::uint numberOfGaussians, dip::uint maxIter = 20, dip::Option::Periodicity periodicity = Option::Periodicity::NOT_PERIODIC) -> std::vector<GaussianParameters>
Determines the parameters for a Gaussian Mixture Model. more...
auto dip::gcd(dip::uint a, dip::uint b) -> dip::uint constexpr
Compute the greatest common denominator of two positive integers.
auto dip::HypersphereSurface(dip::uint n, dip::dfloat r) -> dip::dfloat constexpr
Computes the surface area of an n-dimensional hypersphere with radius r.
auto dip::HypersphereVolume(dip::uint n, dip::dfloat r) -> dip::dfloat constexpr
Computes the volume of an n-dimensional hypersphere with radius r.
void dip::Inverse(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output)
Computes the inverse of a square, real-valued matrix. more...
void dip::Inverse(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output)
Computes the inverse of a square, complex-valued matrix. more...
void dip::LargestEigenvector(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator vector)
Finds the largest eigenvector of a symmetric, real-valued matrix. more...
auto dip::LengthUnicode(dip::String const& string) -> dip::uint
Counts the length of a (UTF-8 encoded) Unicode string.
template<typename T>
auto dip::maximum_gauss_truncation() -> dip::dfloat constexpr
Maximum meaningful truncation value for a Gaussian. Larger truncation values will lead to differences of more than one machine epsilon between the middle and the ends of the Gaussian. T must be a floating-point type.
auto dip::modulo(dip::uint value, dip::uint period) -> dip::uint constexpr
Integer modulo, result is always positive, as opposed to % operator.
auto dip::modulo(dip::sint value, dip::sint period) -> dip::sint constexpr
Integer modulo, result is always positive, as opposed to % operator.
template<typename T>
auto dip::Norm(dip::uint n, dip::ConstSampleIterator input) -> dip::FloatType
Computes the norm of a vector. more...
auto dip::Phi(dip::dfloat x) -> dip::dfloat
Computes phi, the integral of the PDF of a Normal distribution with unit variance and zero mean from minus infinity to x.
auto dip::Phi(dip::dfloat x, dip::dfloat m, dip::dfloat s) -> dip::dfloat
Computes phi, the integral of the PDF of a Normal distribution with standard deviation s and mean m from minus infinity to x.
auto dip::pow10(dip::sint power) -> dip::dfloat constexpr
Computes integer powers of 10, assuming the power is relatively small.
template<typename T>
auto dip::Product(dip::uint n, dip::ConstSampleIterator input) -> T
Computes the product of the values of a vector. more...
void dip::PseudoInverse(dip::uint m, dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output, dip::dfloat tolerance = 1e-7)
Computes the Moore-Penrose pseudo-inverse of a real-valued matrix, using the Jacobi SVD decomposition. more...
void dip::PseudoInverse(dip::uint m, dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output, dip::dfloat tolerance = 1e-7)
Computes the Moore-Penrose pseudo-inverse of a complex-valued matrix, using the Jacobi SVD decomposition. more...
auto dip::Rank(dip::uint m, dip::uint n, dip::ConstSampleIterator input) -> dip::uint
Computes the rank of a real-valued matrix. more...
auto dip::Rank(dip::uint m, dip::uint n, dip::ConstSampleIterator input) -> dip::uint
Computes the rank of a complex-valued matrix. more...
auto dip::RankFromPercentile(dip::dfloat percentile, dip::uint n) -> dip::uint constexpr
Computes the rank (index into array) for a given percentile and an array of length n. more...
template<typename T, typename <SFINAE>>
auto dip::round_cast(T v) -> dip::sint
Fast round operation, without checks, returning a dip::sint.
auto dip::Sinc(dip::dfloat x) -> dip::dfloat
Computes the sinc function.
void dip::SingularValueDecomposition(dip::uint m, dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output, dip::SampleIterator U = nullptr, dip::SampleIterator V = nullptr)
Computes the “thin” singular value decomposition of a real-valued matrix more...
void dip::SingularValueDecomposition(dip::uint m, dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator output, dip::SampleIterator U = nullptr, dip::SampleIterator V = nullptr)
Computes the “thin” singular value decomposition of a complex-valued matrix more...
void dip::SmallestEigenvector(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator vector)
Finds the smallest eigenvector of a symmetric, real-valued matrix. more...
void dip::Solve(dip::uint m, dip::uint n, dip::ConstSampleIterator A, dip::ConstSampleIterator b, dip::SampleIterator output)
Solves a system of real-valued equations, using the Jacobi SVD decomposition. more...
template<typename T>
auto dip::SquareNorm(dip::uint n, dip::ConstSampleIterator input) -> dip::FloatType
Computes the square norm of a vector. more...
template<typename T>
auto dip::Sum(dip::uint n, dip::ConstSampleIterator input) -> T
Computes the sum of the values of a vector. more...
template<typename T>
auto dip::SumAbsSquare(dip::uint n, dip::ConstSampleIterator input) -> dip::FloatType
Computes the sum of the square of the values of a vector. more...
void dip::SymmetricEigenDecomposition(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr)
Finds the eigenvalues and eigenvectors of a symmetric, real-valued matrix. more...
void dip::SymmetricEigenDecomposition2(dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr, dip::Option::DecompositionMethod method = Option::DecompositionMethod::PRECISE)
Finds the eigenvalues and eigenvectors of a 2x2 symmetric, real-valued matrix.
void dip::SymmetricEigenDecomposition3(dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr, dip::Option::DecompositionMethod method = Option::DecompositionMethod::PRECISE)
Finds the eigenvalues and eigenvectors of a 3x3 symmetric, real-valued matrix.
void dip::SymmetricEigenDecompositionPacked(dip::uint n, dip::ConstSampleIterator input, dip::SampleIterator lambdas, dip::SampleIterator vectors = nullptr)
Finds the eigenvalues and eigenvectors of a symmetric, real-valued matrix, where only the unique values are given. more...
template<typename T>
auto dip::Trace(dip::uint n, dip::ConstSampleIterator input) -> T
Computes the trace of a square matrix. more...
template<typename T>
auto dip::TraceDiagonal(dip::uint n, dip::ConstSampleIterator input) -> T
Computes the trace of a diagonal matrix. more...

Variables

dip::dfloat const dip::infinity = std::numeric_limits::infinity() constexpr
Infinity.
dip::dfloat const dip::nan = std::numeric_limits::quiet_NaN() constexpr
A NaN value.
dip::dfloat const dip::pi = 3.14159265358979323846264338327950288 constexpr
The constant π.