ad_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

// Brief demo of Fad and Rad for computing first derivatives

#include <Sacado_No_Kokkos.hpp>   // for FAD and RAD
#include <cstdio>   // nicer than streams in some respects
using std::printf;

using namespace std;

// Typedefs reduce gobbledygook below

typedef Sacado::Fad::DFad<double>   F;  // FAD with # of ind. vars given later
typedef Sacado::Fad::SFad<double,2> F2; // FAD with # of ind. vars fixed at 2
typedef Sacado::Rad::ADvar<double>  R;  // for RAD

template <typename T>
const T func2(T &a, T &b) // sample function of 2 variables
{ return sqrt(a*a + 2*b*b); }

template <typename T>
const T func(int n, T *x) // sample function of n variables
        // == func2 when n == 2
{
  int i;
  T t = 0;
  for(i = 1; i < n; i++)
    t += i*x[i]*x[i];
  return sqrt(t);
  }

// demo of FAD (forward-mode AD), with general number of ind. vars

 void
Fad_demo()
{
  F a, b, x[5], y;
  int i, n;

  printf("Fad_demo...\n\n");

  // first try n == 2
  a = 1.;
  b = 2.;
  // indicate the independent variables, and initialize their partials to 1:
  a.diff(0,2);  // 0 ==> this is the first independent var., of 2
  b.diff(1,2);  // 1 ==> this is the second ind. var.
  
  y = func2(a,b);

  printf("func2(%g,%g) = %g\n", a.val(), b.val(), y.val());

  printf("partials of func2 = %g, %g\n", y.dx(0), y.dx(1));

  // When we know the result was not constant (i.e., did involve ind. vars)
  // or when hasFastAccess() is true, we access partials more quickly
  // by using member function fastAccessDx rather than dx

  if (y.hasFastAccess())
    printf("Repeat with fastAccess: partials of func2 = %g, %g\n",
      y.fastAccessDx(0), y.fastAccessDx(1));

  // Similar exercise with general n, in this case n == 5
  n = 5;
  for(i = 0; i < n; i++) {
    x[i] = i;
    x[i].diff(i, n);
    }
  y = func(n, x);
  printf("\nfunc(5,x) for x = (0,1,2,3,4) = %g\n", y.val());
  for(i = 0; i < n; i++)
    printf("d func / d x[%d] = %g == %g\n", i, y.dx(i), y.fastAccessDx(i));
  }

// Fad_demo2 == repeat first part of Fad_Demo with type F2 instead of F
// i.e., with fixed-size allocations

 void
Fad2_demo()
{
  F2 a, b, y;

  printf("\n\nFad2_demo...\n\n");

  a = 1.;
  b = 2.;
  // indicate the independent variables, and initialize their partials to 1:
  a.diff(0,2);  // 0 ==> this is the first independent var., of 2
  b.diff(1,2);  // 1 ==> this is the second ind. var.
  
  y = func2(a,b);

  printf("func2(%g,%g) = %g\n", a.val(), b.val(), y.val());

  printf("partials of func2 = %g, %g\n", y.dx(0), y.dx(1));

  if (y.hasFastAccess())
    printf("Repeat with fastAccess: partials of func2 = %g, %g\n",
      y.fastAccessDx(0), y.fastAccessDx(1));
  }

// Fad_demo3 == repeat of Fad_Demo2 with a different constructor, one that
// indicates the independent variables and their initial values
// and removes the need to invoke .diff()

 void
Fad3_demo()
{
  F2 a(2,0,1.), b(2,1,2.), y;

  printf("\n\nFad3_demo...\n\n");

  y = func2(a,b);

  printf("func2(%g,%g) = %g\n", a.val(), b.val(), y.val());

  printf("partials of func2 = %g, %g\n", y.dx(0), y.dx(1));

  if (y.hasFastAccess())
    printf("Repeat with fastAccess: partials of func2 = %g, %g\n",
      y.fastAccessDx(0), y.fastAccessDx(1));
  }

// Rad_demo == repeat of Fad_Demo with type R instead of F,
// i.e., with reverse-mode rather than forward-mode AD

 void
Rad_demo()
{
  R a, b, x[5], y;
  int i, n;

  printf("\n\nRad_demo...\n\n");

  // first try n == 2
  a = 1.;
  b = 2.;
  
  y = func2(a,b);

  R::Gradcomp();  // do the reverse sweep

  printf("func2(%g,%g) = %g\n", a.val(), b.val(), y.val());

  printf("partials of func2 = %g, %g\n", a.adj(), b.adj());

  // Similar exercise with general n, in this case n == 5
  n = 5;
  for(i = 0; i < n; i++)
    x[i] = i;
  y = func(n, x);
  printf("\nfunc(5,x) for x = (0,1,2,3,4) = %g\n", y.val());

  // the .val() values are always available; we must call Gradcomp
  // before accessing the adjoints, i.e., the .adj() values...

  R::Gradcomp();
  
  for(i = 0; i < n; i++)
    printf("d func / d x[%d] = %g\n", i, x[i].adj());
  }

 int
main()
{
  Fad_demo();
  Fad2_demo();
  Fad3_demo();
  Rad_demo();
  return 0;
  }