Examples

This section illustrates how to use the numericalderivative algorithms.

• A simple demonstration of the methods
  • Define the function
  • SteplemanWinarsky
  • DumontetVignes
  • GillMurraySaundersWright
  • ShiXieXuanNocedalForward
  • ShiXieXuanNocedalGeneral
  • Function with extra arguments
• Applies Stepleman & Winarsky method to an OpenTURNS function
  • Chaboche model
  • Compute the step of a ot.Function using Stepleman & Winarsky
  • Cantilever beam model
  • Fire satellite model
• Use the benchmark problems
• Use the finite differences formulas
  • References
  • Compute the first derivative using forward F.D. formula
  • Compute the exact step for the forward F.D. formula
  • Central F.D. formula for first derivative
  • Central F.D. formula for second derivative
  • Central F.D. formula for third derivative
• Use the generalized finite differences formulas
  • References
  • Compute the first derivative using forward F.D. formula
  • Compute the exact step for the forward F.D. formula
  • Compute the coefficients of several central F.D. formulas
  • Compute the coefficients of several forward F.D. formulas
• Convergence of the generalized finite differences formulas
  • References

Dumontet & Vignes

• Experiments with Dumontet & Vignes method
  • References
  • Use the method on a simple problem
  • Useful functions
  • Plot the L ratio for various problems
  • Plot the error depending on the step
  • Compute the lower and upper bounds of the third derivative
  • Plot the lower and upper bounds of the third derivative
  • See the history of steps during the bissection search
• Benchmark Dumontet & Vignes method
  • References

Gill, Murray, Saunders & Wright

• Experiment with Gill, Murray, Saunders and Wright method
  • References
  • Use the method on a simple problem
  • Test the method on the exponential problem
  • Benchmark the method on a collection of test points
  • Plot the condition error depending on the step
  • Plot the error depending on the step
  • See the history of steps during the bissection search
• Benchmark Gill, Murray, Saunders and Wright method
  • References

Stepleman & Winarsky

• Experiment with Stepleman & Winarsky method
  • References
  • Use the method on a simple problem
  • Use the method on the ScaledExponentialProblem
  • Plot the error vs h
  • Plot the absolute difference depending on the step
  • Plot the criterion depending on the step
  • Compute reference step
  • Plot number of lost digits vs h
  • Use the bisection search
  • See the history of steps during the search
• Plot Stepleman & Winarsky's method
  • References
• Benchmark Stepleman & Winarsky's method
  • References
  • Compute the first derivative
  • Perform the benchmark

Shi, Xie, Xuan & Nocedal

• Experiment with Shi, Xie, Xuan & Nocedal forward method
  • References
  • Use the method on a simple problem
  • Use the method on the ScaledExponentialProblem
  • Plot the error vs h
  • Plot the criterion depending on the step
  • See the history of steps during the search
• Benchmark Shi, Xie, Xuan & Nocedal's forward method
  • Compute the first derivative
  • Perform the benchmark
• Experiment with Shi, Xie, Xuan & Nocedal general method
  • References
  • Use the method on a simple problem
  • Use the method on the ScaledExponentialProblem
  • Plot the error vs h
  • Plot the criterion depending on the step
  • See the history of steps during the search
• Benchmark Shi, Xie, Xuan & Nocedal's general method
  • Compute the first derivative
  • Perform the benchmark