Functions¶

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 where acts on points and produces points. FieldToFieldConnection(*args) Composition function where acts on fields and produces fields. FieldToPointConnection(*args) Composition function where acts on fields and produces points. PointToFieldConnection(*args) Composition function where acts on points and produces fields. PointToPointConnection(*args) Composition function where acts on points and 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.

 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¶

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 . SpecFunc_Beta(a, b) Beta function . 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 . 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 . 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 . 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 . 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 . 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 . 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.