General mathematical functions

Function(*args) Function base class.
SymbolicFunction(*args) Symbolic function.
TranslationFunction(*args) Translation function.
LinearFunction(*args) Linear numerical math function.
QuadraticFunction(*args) Quadratic function.
DatabaseFunction(*args) Pre-evaluated function.
PythonFunction(*args) Override Function from Python.
OpenTURNSPythonFunction([n, p]) Override Function from Python.
MemoizeFunction(*args) Function which keep tracks of input and output.

Algebra of functions

AggregatedFunction(*args) Aggregated function.
ComposedFunction(*args) Composed function.
DualLinearCombinationFunction(*args) Linear combination of functions with vectorial weights.
IndicatorFunction(*args) Indicator function.
LinearCombinationFunction(*args) Linear combination of functions.
ParametricFunction(*args) Parametric function.
ProductFunction(*args) Product function.
PointToPointEvaluation(*args) Evaluation of the composition f \circ g where g acts on points and f produces points.
FieldToFieldConnection(*args) Composition function f \circ g where g acts on fields and f produces fields.
FieldToPointConnection(*args) Composition function f \circ g where g acts on fields and f produces points.
PointToFieldConnection(*args) Composition function f \circ g where g acts on points and f produces fields.
PointToPointConnection(*args) Composition function f \circ g where g acts on points and f produces points.

Field and mixed functions

Refer to Field functions.

FieldFunction(*args) Function mapping a field to a field.
FieldToPointFunction(*args) Function mapping a field into a point.
PointToFieldFunction(*args) Function mapping a point into a field.
PythonFieldFunction(*args) Override FieldFunction from Python.
ValueFunction(*args) Function mapping a field to a field.
VertexValueFunction(*args) Function mapping a field to a field.
PythonFieldFunction(*args) Override FieldFunction from Python.
PythonFieldToPointFunction(*args) Override FieldToPointFunction from Python.
PythonPointToFieldFunction(*args) Override PointToFieldFunction from Python.
OpenTURNSPythonFieldFunction(inputMesh, …) Override FieldFunction from Python.
OpenTURNSPythonFieldToPointFunction(…) Override FieldToPointFunction from Python.
OpenTURNSPythonPointToFieldFunction(…) Override PointToFieldFunction from Python.
P1LagrangeInterpolation(*args) P1 interpolation of values between two meshes.

Collection of functions

Basis(*args) Basis.
OrthogonalBasis(*args) Orthogonal basis.
BasisSequence(*args) Sequence of basis.

Finite differentiation schemes

CenteredFiniteDifferenceGradient(*args) First order centered finite-difference scheme.
CenteredFiniteDifferenceHessian(*args) Second order centered finite-difference scheme.
FiniteDifferenceGradient(*args) Base class for first order finite-difference schemes.
FiniteDifferenceHessian(*args) Base class for second order centered finite-difference scheme.
NonCenteredFiniteDifferenceGradient(*args) First order non-centered finite-difference scheme.
FiniteDifferenceStep(*args) Base class to define finite difference steps.
ConstantStep(*args) Constant step.
BlendedStep(*args) Blended step.

Evaluation functions

EvaluationImplementation(*args) Numerical math evaluation implementation.
AggregatedEvaluation(*args) Aggregated numerical math evaluation implementation.
SymbolicEvaluation(*args) Proxy of C++ OT::SymbolicEvaluation.
ComposedEvaluation(*args) Proxy of C++ OT::ComposedEvaluation.
DatabaseEvaluation(*args) Data based math evaluation implementation.
DualLinearCombinationEvaluation(*args) Dual linear combination evaluation implementation.
IndicatorEvaluation(*args) Proxy of C++ OT::IndicatorEvaluation.
LinearCombinationEvaluation(*args) Proxy of C++ OT::LinearCombinationEvaluation.
LinearEvaluation(*args) Linear numerical math evaluation implementation.
MarginalTransformationEvaluation(*args) Marginal transformation evaluation.
NoEvaluation(*args) Proxy of C++ OT::NoEvaluation.
ParametricEvaluation(*args) Proxy of C++ OT::ParametricEvaluation.
PiecewiseHermiteEvaluation(*args) Proxy of C++ OT::PiecewiseHermiteEvaluation.
PiecewiseLinearEvaluation(*args) Proxy of C++ OT::PiecewiseLinearEvaluation.
P1LagrangeEvaluation(*args) Data based math evaluation implementation.
ProductEvaluation(*args) Proxy of C++ OT::ProductEvaluation.
ProductPolynomialEvaluation(*args) Product polynomial evaluation implementation.
QuadraticEvaluation(*args) Proxy of C++ OT::QuadraticEvaluation.

Gradient functions

GradientImplementation(*args) Numerical math gradient implementation.
SymbolicGradient(*args) Proxy of C++ OT::SymbolicGradient.
ComposedGradient(*args) Proxy of C++ OT::ComposedGradient.
ConstantGradient(*args) Proxy of C++ OT::ConstantGradient.
DualLinearCombinationGradient(*args) Dual linear combination gradient implementation.
LinearCombinationGradient(*args) Proxy of C++ OT::LinearCombinationGradient.
LinearGradient(*args) Linear numerical math gradient implementation.
NoGradient(*args) Proxy of C++ OT::NoGradient.
ParametricGradient(*args) Proxy of C++ OT::ParametricGradient.
ProductGradient(*args) Proxy of C++ OT::ProductGradient.

Hessian functions

HessianImplementation(*args) Numerical math hessian implementation.
SymbolicHessian(*args) Proxy of C++ OT::SymbolicHessian.
ComposedHessian(*args) Proxy of C++ OT::ComposedHessian.
ConstantHessian(*args) Proxy of C++ OT::ConstantHessian.
DualLinearCombinationHessian(*args) Dual linear combination hessian implementation.
LinearCombinationHessian(*args) Proxy of C++ OT::LinearCombinationHessian.
NoHessian(*args) Proxy of C++ OT::NoHessian.
ParametricHessian(*args) Proxy of C++ OT::ParametricHessian.
ProductHessian(*args) Proxy of C++ OT::ProductHessian.

Differential equation solvers

ODESolver(*args) ODE solver base class.
RungeKutta(*args) Runge-Kutta fourth-order method.
Fehlberg(*args) Adaptive order Fehlberg method.

Special constants & functions

Numerical constants

Special functions

Special functions are implemented as C++ static methods and are hence casted as Python functions.

SpecFunc_BesselI0(x) Modified first kind Bessel function of order 0.
SpecFunc_BesselI1(x) Modified first kind Bessel function of order 1.
SpecFunc_BesselK(nu, x) Modified second kind Bessel function of order \nu.
SpecFunc_Beta(a, b) Beta function \mathrm{B}.
SpecFunc_BinomialCoefficient(n, k) Binomial coefficient.
SpecFunc_BitCount(n) Compute the number of bits set to 1 in an integer.
SpecFunc_Cbrt(x) Cubit root function.
SpecFunc_Dawson(*args) Dawson function.
SpecFunc_Debye(x, n) Debye function of order n.
SpecFunc_DiGamma(x) Digamma function.
SpecFunc_DiGammaInv(a) Inverse of the DiGamma function.
SpecFunc_DiLog(x) Dilogarithm function.
SpecFunc_Ei(*args) Exponential integral function.
SpecFunc_Erf(*args) Error function Erf.
SpecFunc_ErfC(*args) Complementary error function ErfC.
SpecFunc_ErfCX(*args) ErfCX function.
SpecFunc_ErfI(*args) Imaginary error function ErfI.
SpecFunc_ErfInverse(x) Inverse of the error function Erf.
SpecFunc_Expm1(z) Expm1 function.
SpecFunc_Faddeeva(z) Complex Faddeeva function.
SpecFunc_FaddeevaIm(x) Imaginary part of the Faddeeva function.
SpecFunc_Gamma(*args) Gamma function \Gamma.
SpecFunc_GammaCorrection(a) GammaCorrection function.
SpecFunc_HyperGeom_1_1(*args) Hypergeometric function of type (1,1).
SpecFunc_HyperGeom_2_1(p1, p2, q1, x) Hypergeometric function of type (2,1).
SpecFunc_HyperGeom_2_2(p1, p2, q1, q2, x) Hypergeometric function of type (2,2).
SpecFunc_IGamma1pm1(a) IGamma1pm1 function.
SpecFunc_IncompleteBeta(a, b, x[, tail]) Incomplete Beta function.
SpecFunc_IncompleteBetaInverse(a, b, x[, tail]) Inverse of the incomplete Beta function.
SpecFunc_IncompleteGamma(a, x[, tail]) Incomplete Gamma function.
SpecFunc_IncompleteGammaInverse(a, x[, tail]) Inverse of the incomplete Gamma function with respect to x.
SpecFunc_IsNormal(value) Check for non-NaN and non-Inf values.
SpecFunc_LambertW(x[, principal]) Lambert W function.
SpecFunc_LnBeta(a, b) Logarithm of the Beta function.
SpecFunc_LnGamma(a) Logarithm of the Gamma function.
SpecFunc_Log1MExp(x) Log1MExp function.
SpecFunc_Log1p(z) Log1p function.
SpecFunc_Log2(n) Integer base 2 logarithm of n.
SpecFunc_LogBesselI0(x) Logarithm of the modified first kind Bessel function of order 0.
SpecFunc_LogBesselI1(x) Logarithm of the modified first kind Bessel function of order 1.
SpecFunc_LogBesselK(nu, x) Logarithm of the modified second kind Bessel function of order \nu.
SpecFunc_LogBeta(a, b) Logarithm of the Beta function.
SpecFunc_LogGamma(*args) Logarithm of the Gamma function.
SpecFunc_LogGamma1p(a) LogGamma1p function.
SpecFunc_NextPowerOfTwo(n) Smallest power of two greater or equal to the given n.
SpecFunc_Psi(x) Psi function.
SpecFunc_RegularizedIncompleteBeta(a, b, x) Regularized incomplete Beta function.
SpecFunc_RegularizedIncompleteBetaInverse(a, b, x) Inverse of the regularized incomplete Beta function.
SpecFunc_RegularizedIncompleteGamma(a, x[, tail]) Regularized incomplete Gamma function.
SpecFunc_RegularizedIncompleteGammaInverse(a, x) Inverse of the regularized incomplete Gamma function.
SpecFunc_TriGamma(x) TriGamma function.
TimerCallback(duration) Time stopping criterion.

External code coupling

These methods are dedicated to coupling external codes by means of text files.

coupling_tools.replace(infile, outfile, …) Replace values in a file using delimiters.
coupling_tools.execute(cmd[, workdir, …]) Launch an external process.
coupling_tools.get_value(filename[, token, …]) Get a value from a file using a delimiter and/or offsets.
coupling_tools.get_line_col(filename[, …]) Get a value at specific line/columns coordinates.
coupling_tools.get_regex(filename, patterns) Get values from a file using regex.
coupling_tools.get(filename[, tokens, …]) Get several values from a file using delimiters and/or offsets.

1-D functions

UniVariateFunction(*args) Base class for univariate functions.