sfad_example.cpp

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// @HEADER
// *****************************************************************************
//                           Sacado Package
//
// Copyright 2006 NTESS and the Sacado contributors.
// SPDX-License-Identifier: LGPL-2.1-or-later
// *****************************************************************************
// @HEADER

// sfad_example
//
//  usage: 
//     sfad_example
//
//  output:  
//     prints the results of differentiating a simple function with forward
//     mode AD using the Sacado::Fad::SFad class (uses static memory allocation
//     for the number of derivative components, meaning this must be known
//     at compile time.

#include <iostream>
#include <iomanip>

#include "Sacado.hpp"

// The function to differentiate
template <typename ScalarT>
ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
  ScalarT r = c*std::log(b+1.)/std::sin(a);

  return r;
}

// The analytic derivative of func(a,b,c) with respect to a and b
void func_deriv(double a, double b, double c, double& drda, double& drdb)
{
  drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2.))*std::cos(a);
  drdb = c / ((b+1.)*std::sin(a));
}

int main(int argc, char **argv)
{
  double pi = std::atan(1.0)*4.0;

  // Values of function arguments
  double a = pi/4;
  double b = 2.0;
  double c = 3.0;

  // Number of independent variables
  int num_deriv = 2;    // Must be == 2 (see below)

  // Fad objects
  Sacado::Fad::SFad<double,2> afad(num_deriv, 0, a); // First (0) indep. var
  Sacado::Fad::SFad<double,2> bfad(num_deriv, 1, b); // Second (1) indep. var
  Sacado::Fad::SFad<double,2> cfad(c);               // Passive variable
  Sacado::Fad::SFad<double,2> rfad;                  // Result

  // Compute function
  double r = func(a, b, c);

  // Compute derivative analytically
  double drda, drdb;
  func_deriv(a, b, c, drda, drdb);

  // Compute function and derivative with AD
  rfad = func(afad, bfad, cfad);

  // Extract value and derivatives
  double r_ad = rfad.val();     // r
  double drda_ad = rfad.dx(0);  // dr/da
  double drdb_ad = rfad.dx(1);  // dr/db

  // Print the results
  int p = 4;
  int w = p+7;
  std::cout.setf(std::ios::scientific);
  std::cout.precision(p);
  std::cout << "    r =  " << r << " (original) == " << std::setw(w) << r_ad
      << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
      << "dr/da = " << std::setw(w) << drda << " (analytic) == " 
      << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w) 
      << drda - drda_ad << std::endl
      << "dr/db = " << std::setw(w) << drdb << " (analytic) == " 
      << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w) 
      << drdb - drdb_ad << std::endl;

  double tol = 1.0e-14;
  if (std::fabs(r - r_ad)       < tol &&
      std::fabs(drda - drda_ad) < tol &&
      std::fabs(drdb - drdb_ad) < tol) {
    std::cout << "\nExample passed!" << std::endl;
    return 0;
  }
  else {
    std::cout <<"\nSomething is wrong, example failed!" << std::endl;
    return 1;
  }
}