/usr/include/simbody/simmath/Differentiator.h is in libsimbody-dev 3.5.4+dfsg-1ubuntu2.
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#define SimTK_DIFFERENTIATOR_H_
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKmath *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2006-12 Stanford University and the Authors. *
* Authors: Michael Sherman *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
/** @file
* This is the header file that user code should include to pick up the
* SimTK Simmath numerical differentiation tools.
*/
#include "SimTKcommon.h"
#include "simmath/internal/common.h"
namespace SimTK {
/**
* Given a function f(y), where f, y or both can be vectors, calculate the
* derivative (gradient, Jacobian) df/dy.
*
* Calculation is done using numerical differencing, which should be considered
* a last resort for cases in which the analytic derivative is unavailable.
* (Note that you can obtain an analytic gradient automatically from the source
* code for f using automatic differentiation methods like complex step
* derivatives, ADIFOR, etc.).
*
* @par Theory and Implementation
*
* The SimTK::Differentiator class uses methods adapted from the book
* Practical Optimization by Gill, Murray, and Wright (1981), section 8.6
* (339ff) and Numerical Recipies in C++ 2nd ed. (2002) section 5.7 (192ff).
* Here is a summary:
* - We want to differentiate a function f(y) whose estimated relative
* accuracy eps is known (e.g. eps=1e-6). (We'll treat y as a scalar here
* but for vector y this is done for one element yi at a time.)
* - We need to know what perturbation h to use for calculating an estimate
* of df/dy that optimally balances roundoff error (h too small) with
* truncation error (h too big).
* - First guess at h depends on the order of the numerical method: either
* forward difference (1st order) or central difference (2nd order). For
* 1st order, h0=eps^(1/2); for 2nd order h0=eps^(1/3).
* - Now we have to make sure that we can compute y+h reliably. If y is very
* large, we can not allow h to be too small. We calculate a scaled
* perturbation h1=h0*max(y, 0.1). The 0.1 allows a small y to pull down
* the step size <em>a little</em>; but it is dangerous to go much lower
* because a very small y might just be zero plus noise.
* - Finally, the step size should be exactly representable as a power of 2.
* Conceptually, this is just h=(y+h1)-y although one must be careful to
* stop the compiler from cleverly "simplifying" this expression.
* Differentiator uses a C++ volatile variable for that purpose.
*
* Then the derivative, gradient element, or Jacobian column is computed
* as df/dy=[f(x+h)-f(x)]/h (1st order) or df/dy=[f(x+h)-f(x-h)]/(2h)
* (2nd order).
*/
class SimTK_SIMMATH_EXPORT Differentiator {
public:
// This are local classes within Differentiator; defined below.
class ScalarFunction; // ordinary scalar function of a scalar
class GradientFunction; // scalar function of vector
class JacobianFunction; // vector function of vector
class Function; // abstraction of the above
// These are the exceptions that can be thrown by this class.
class OpNotAllowedForFunctionOfThisShape;
class UserFunctionThrewAnException;
class UserFunctionReturnedNonzeroStatus;
class UnknownMethodSpecified;
enum Method {
UnspecifiedMethod=0,
ForwardDifference=1,
CentralDifference=2
};
static bool isValidMethod(Method);
static const char* getMethodName(Method);
static int getMethodOrder(Method);
virtual ~Differentiator();
explicit Differentiator(const Function& f,
Method defaultMethod=UnspecifiedMethod);
// You can change the default method; normally it is ForwardDifference.
// If you set it to 'UnspecifiedMethod' it goes back to the original default.
Differentiator& setDefaultMethod(Method);
Method getDefaultMethod() const;
// These are the real routines, which are efficient and flexible
// but somewhat messy to use.
void calcDerivative(Real y0, Real fy0, Real& dfdy,
Method=UnspecifiedMethod) const;
void calcGradient (const Vector& y0, Real fy0, Vector& gf,
Method=UnspecifiedMethod) const;
void calcJacobian (const Vector& y0, const Vector& fy0, Matrix& dfdy,
Method=UnspecifiedMethod) const;
// These provide a simpler though less efficient interface. They will
// do some heap allocation, and will make an initial unperturbed call
// to the user function.
Real calcDerivative(Real y0, Method=UnspecifiedMethod) const;
Vector calcGradient (const Vector& y0, Method=UnspecifiedMethod) const;
Matrix calcJacobian (const Vector& y0, Method=UnspecifiedMethod) const;
// Statistics (mutable)
void resetAllStatistics(); // reset all stats to zero
int getNumDifferentiations() const; // total # calls of calcWhatever
int getNumDifferentiationFailures() const; // # of those that failed
int getNumCallsToUserFunction() const; // total # calls to user function
// This is a local class.
class DifferentiatorRep;
private:
// opaque implementation for binary compatibility
DifferentiatorRep* rep;
};
/**
* This abstract class defines a function to be differentiated (repeatedly)
* by a Differentiator object. Users should not access this class directly;
* instead, use one of the specialized function classes ScalarFunction,
* GradientFunction, or JacobianFunction depending on the type of function
* you want to differentiate.
*
* The Differentiator class will assume the function is calculated to
* about machine accuracy unless told otherwise. But if f is the result of some
* approximate calculation (for example, it came from another Differentiator
* approximation, or from numerical integration), we will need to know that in
* order to have a reasonable crack at calculating df.
*/
class SimTK_SIMMATH_EXPORT Differentiator::Function {
public:
Function& setNumFunctions(int);
Function& setNumParameters(int);
Function& setEstimatedAccuracy(Real);
// These values are fixed after construction.
int getNumFunctions() const;
int getNumParameters() const;
Real getEstimatedAccuracy() const; // approx. "roundoff" in f calculation
// Statistics (mutable)
void resetAllStatistics();
int getNumCalls() const; // # evaluations of this function since reset
int getNumFailures() const; // # of calls which failed
// This is the declaration of a local class name.
class FunctionRep;
protected:
Function();
~Function();
// opaque implementation for binary compatibility
FunctionRep* rep;
private:
// suppress copy constructor and copy assignment
// This is a workaround for a Visual Studio 2015 bug where
// the old-style C++03 deletion method didn't work.
#if defined(_MSC_VER) && (_MSC_VER >= 1900)
Function(const Function&) = delete;
Function& operator=(const Function&) = delete;
#else
Function(const Function&);
Function& operator=(const Function&);
#endif
friend class Differentiator;
};
/**
* Derive a concrete class from this one if you have a scalar function
* of a single scalar variable that you want to differentiate.
*/
class SimTK_SIMMATH_EXPORT Differentiator::ScalarFunction : public Differentiator::Function {
public:
virtual int f(Real x, Real& fx) const=0;
protected:
explicit ScalarFunction(Real acc=-1);
virtual ~ScalarFunction() { }
private:
// suppress copy constructor and copy assignment
ScalarFunction(const Function&);
ScalarFunction& operator=(const Function&);
};
/**
* Derive a concrete class from this one if you have a scalar function
* of multiple variables that you want to differentiate. This is the typical
* form for an optimization objective function, for example.
*/
class SimTK_SIMMATH_EXPORT Differentiator::GradientFunction : public Differentiator::Function {
public:
virtual int f(const Vector& y, Real& fy) const=0;
protected:
explicit GradientFunction(int ny=-1, Real acc=-1);
virtual ~GradientFunction() { }
private:
// suppress copy constructor and copy assignment
GradientFunction(const GradientFunction&);
GradientFunction& operator=(const GradientFunction&);
};
/**
* Derive a concrete class from this one if you have a set of functions
* (i.e., a vector-valued function) of multiple variables that you want
* to differentiate. This is the typical form for a multibody system, for example.
*/
class SimTK_SIMMATH_EXPORT Differentiator::JacobianFunction : public Differentiator::Function {
public:
virtual int f(const Vector& y, Vector& fy) const=0;
protected:
explicit JacobianFunction(int nf=-1, int ny=-1, Real acc=-1);
virtual ~JacobianFunction() { }
private:
// suppress copy constructor and copy assignment
JacobianFunction(const JacobianFunction&);
JacobianFunction& operator=(const JacobianFunction&);
};
} // namespace SimTK
#endif // SimTK_DIFFERENTIATOR_H_
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