hesopcheck.cpp

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// ***********************************************************************
//
//                           Sacado Package
//                 Copyright (2007) Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
// (etphipp@sandia.gov).
//
// ***********************************************************************
// @HEADER

// Individually check concistency among Hv products via rad2.h, trad2.hpp,
// Fad<Rad> and Rad<Fad> for all unary and binary ops.

#include <cstdio>
#include <float.h>  // for DBL_MAX
#include "Sacado_MathFunctions.hpp"
#include "Sacado_trad.hpp"
#include "Sacado_trad2.hpp"
#include "Sacado_rad2.hpp"
#include "Sacado_Fad_SFad.hpp"

typedef Sacado::Rad2d::ADvar ADVar;
typedef Sacado::Rad2::ADvar<double> DADVar;
typedef Sacado::Rad::ADvar<double> DReal;
typedef Sacado::Fad::SFad<DReal,1> FDReal;
typedef Sacado::Fad::SFad<double,1> FReal;
typedef Sacado::Rad::ADvar<FReal> AFReal;

#define UF(T,f,fn) T fn(T &x) { return f(x); }

#define UF4(f) UF(ADVar,f,f ## _ADV) UF(DADVar,f,f ## _DADV) UF(FDReal,f,f ## _FDR) UF(AFReal,f,f ## _AFR)

UF4(abs)
UF4(acos)
UF4(acosh)
UF4(asin)
UF4(asinh)
UF4(atan)
UF4(atanh)
UF4(cos)
UF4(cosh)
UF4(exp)
UF4(fabs)
UF4(log)
UF4(log10)
UF4(sin)
UF4(sinh)
UF4(sqrt)
UF4(tan)
UF4(tanh)

#undef UF
#define UF(T,f,fn) T fn(T &x, T &y) { return f(x,y); }

UF4(atan2)
UF4(pow)

typedef ADVar (*ADVar_uf )(ADVar  &);
typedef DADVar  (*DADVar_uf)(DADVar &);
typedef FDReal  (*FDReal_uf)(FDReal &);
typedef AFReal  (*AFReal_uf)(AFReal &);

typedef ADVar (*ADVar_uf2 )(ADVar  &, ADVar  &);
typedef DADVar  (*DADVar_uf2)(DADVar &, DADVar &);
typedef FDReal  (*FDReal_uf2)(FDReal &, FDReal &);
typedef AFReal  (*AFReal_uf2)(AFReal &, AFReal &);

static double
  dom_acosh[] = { 1., DBL_MAX },
  dom_all[] = { -DBL_MAX, DBL_MAX },
  dom_invtrig[] = { -1., 1. },
  dom_log[] = { DBL_MIN, DBL_MAX };

 struct
Func4 {
  const char *name;
  const double *dom;
  ADVar_uf  f1;
  DADVar_uf f2;
  FDReal_uf f3;
  AFReal_uf f4;
  };

#define U4f(f,d) { #f, d, f ## _ADV, f ## _DADV, f ## _FDR, f ## _AFR }

static Func4 UT[] = {
  U4f(abs,   dom_all),
  U4f(acos,  dom_invtrig),
  U4f(acosh, dom_acosh),
  U4f(asin,  dom_invtrig),
  U4f(asinh, dom_all),
  U4f(atan,  dom_all),
  U4f(atanh, dom_invtrig),
  U4f(cos,   dom_all),
  U4f(cosh,  dom_all),
  U4f(exp,   dom_all),
  U4f(fabs,  dom_all),
  U4f(log,   dom_log),
  U4f(log10, dom_log),
  U4f(sin,   dom_all),
  U4f(sinh,  dom_all),
  U4f(sqrt,  dom_log),
  U4f(tan,   dom_all),
  U4f(tanh,  dom_all)
  };

 struct
Func42 {
  const char *name;
  const double *xdom;
  ADVar_uf2  f1;
  DADVar_uf2 f2;
  FDReal_uf2 f3;
  AFReal_uf2 f4;
  };

static Func42 UT2[] = {
  U4f(atan2, dom_all),
  U4f(pow,   dom_log)
  };

#undef U4f
#undef UF4
#undef UF

 static int
differ(double a, double b)
{
  double d = a - b;;
  if (d == 0.)
    return 0;
  if (d < 0.)
    d = -d;
  if (a < 0.)
    a = -a;
  if (b < 0.)
    b = - b;
  return d > 5e-15 * (a + b);
  }

 static char *progname;

 static int
usage(int rc)
{
  fprintf(rc ? stderr : stdout, "Usage: %s [-v]\n\
  to compare consistency among several schemes for Hessian-vector computations.\n\
  -v ==> verbose (show results)\n\
  No -v ==> just print OK if all goes well; otherwise complain.\n", progname);
  return rc;
  }

 int
main(int argc, char **argv)
{
  Func4 *f, *fe;
  Func42 *f2, *f2e;
  char *s;
  double a, *ap, c, h[4], h1[4], v[3];
  int b0, b1, b2, k, verbose;
  static double unopargs[] = { .7, -.9, 2.5, -4.2, .1, .3, 1.2, -2.4, 0. };
  static double binargs[] = { .1,.2,  -.3,.4, -.5,-.6,  .7,-.8,
          1.1,2.2, -2.3,3.4, -2.5,-3.6, 2.7,-3.8, 0.};

#define Dcl(T,T1) T x ## T1, y ## T1, z ## T1
  Dcl(ADVar,  ADV);
  Dcl(DADVar, DADV);
  Dcl(FDReal, FDR);
  Dcl(AFReal, AFR);
#undef  Dcl
  ADVar *pADV[2];
  DADVar *pDADV[2];
  DReal tDR;
  FDReal tfFDR;
  FReal  tfFR;

  progname = argv[0];
  verbose = 0;
  if (argc > 1) {
    if (argc > 2 || *(s = argv[1]) != '-')
      return usage(1);
    switch(s[1]) {
     case 'h':
     case '?':
      return usage(s[2] != 0);
     case '-':
      if (!s[2])
        break;
      return usage(strcmp(s,"--help") ? 1 : 0);
     case 'v':
      if (!s[2]) {
        verbose = 1;
        break;
        }
     default:
      return usage(1);
     }
    }

  v[0] = v[2] = 1.;
  v[1] = 0.;
#define In(T) p ## T[0] = &x ## T; p ## T[1] = &z ## T
  In(ADV);
  In(DADV);
#undef  In
  b0 = b1 = b2 = 0;
  fe = UT + sizeof(UT)/sizeof(UT[0]);
  for(ap = unopargs; (a = *ap++) != 0.; )
      for(f = UT; f < fe; f++) {
    if (a < f->dom[0] || a > f->dom[1])
      continue;
    xADV = a;
    yADV = f->f1(xADV);
    ADVar::Gradcomp();
    ADVar::Hvprod(1,pADV,v,h);
    if (verbose) {
      printf("%s(%g) = %g\n", f->name, xADV.val(), yADV.val());
      printf("%s' = %g\n", f->name, xADV.adj());
      printf("%s\" = %g\n", f->name, h[0]);
      }
    xDADV = a;
    yDADV = f->f2(xDADV);
    DADVar::Gradcomp();
    if (differ(yDADV.val(), yADV.val())) {
      ++b0;
      printf("%s(%g): yADV = %g, yDADV = %g, diff = %.2g\n",
        f->name, a, yADV.val(), yDADV.val(),
        yADV.val() - yDADV.val());
      }
    if (differ(xADV.adj(), xDADV.adj())) {
      ++b1;
      printf("%s'(%g): ADV ==> %g, DADV ==> %g, diff = %.2g\n",
        f->name, a, xADV.adj(), xDADV.adj(),
        xADV.adj() - xDADV.adj());
      }
    DADVar::Hvprod(1,pDADV,v,h1);
    if (differ(h[0], h1[0])) {
      ++b2;
      printf("%s\"(%g): ADV ==> %g, DADV ==> %g, diff = %.2g\n",
        f->name, a, h[0], h1[0], h[0] - h1[0]);
      }

    tfFDR = 0.;
    tfFDR.diff(0,1);
    xFDR = a + tfFDR*v[0];
    yFDR = f->f3(xFDR);
    tDR = yFDR.dx(0);
    DReal::Gradcomp();

    if (differ(yFDR.val().val(), yADV.val())) {
      ++b0;
      printf("%s(%g): yFDR = %g, yADV = %g, diff = %.2g\n",
        f->name, a, yFDR.val().val(), yADV.val(),
        yFDR.val().val() - yADV.val());
      }
    if (differ(xFDR.val().adj(), h[0])) {
      ++b2;
      printf("%s\"(%g): FDR ==> %g, ADV ==> %g, diff = %.2g\n",
        f->name, a, xFDR.val().adj(), h[0],
        xFDR.val().adj() - h[0]);
      }

    tfFR = 0.;
    tfFR.diff(0,1);
    xAFR = a + tfFR*v[0];
    yAFR = f->f4(xAFR);
    AFReal::Gradcomp();
    if (differ(yAFR.val().val(), yADV.val())) {
      ++b0;
      printf("%s(%g): yAFR = %g, yADV = %g, diff = %.2g\n",
        f->name, a, yAFR.val().val(), yADV.val(),
        yAFR.val().val() - yADV.val());
      }
    if (differ(xAFR.adj().val(), xADV.adj())) {
      ++b1;
      printf("%s'(%g): AFR ==> %g, ADV ==> %g, diff = %.2g\n",
        f->name, a, xAFR.adj().val(), xADV.adj(),
        xAFR.adj().val() - xADV.adj());
      }
    if (differ(xAFR.adj().dx(0), h[0])) {
      ++b2;
      printf("%s\"(%g): AFR ==> %g, ADV ==> %g, diff = %.2g\n",
        f->name, a, xAFR.adj().dx(0), h[0],
        xAFR.adj().dx(0) - h[0]);
      }
    }
  f2e = UT2 + sizeof(UT2)/sizeof(UT2[0]);
  for(ap = binargs; (a = *ap) != 0.; ap += 2) {
      c = ap[1];
      for(f2 = UT2; f2 < f2e; f2++) {
        if (a < f2->xdom[0] || a > f2->xdom[1])
      continue;
    xADV = a;
    zADV = c;
    yADV = f2->f1(xADV, zADV);
    ADVar::Gradcomp();
    ADVar::Hvprod(2,pADV,v,h);
    ADVar::Hvprod(2,pADV,v+1,h+2);
    if (verbose) {
      printf("%s(%g,%g) = %g\n", f2->name, xADV.val(), zADV.val(), yADV.val());
      printf("%s' = (%g, %g)\n", f2->name, xADV.adj(), zADV.adj());
      printf("%s\" = (%8g\t%g)\n(%8g\t%g)", f2->name, h[0],h[1],h[2],h[3]);
      }
    xDADV = a;
    zDADV = c;
    yDADV = f2->f2(xDADV, zDADV);
    DADVar::Gradcomp();
    if (differ(yDADV.val(), yADV.val())) {
      ++b0;
      printf("%s(%g,%g): yADV = %g, yDADV = %g, diff = %.2g\n",
        f2->name, a, c, yADV.val(), yDADV.val(),
        yADV.val() - yDADV.val());
      }
    if (differ(xADV.adj(), xDADV.adj()) || differ(zADV.adj(), zDADV.adj())) {
      ++b1;
      printf("%s'(%g,%g): ADV ==> (%g,%g) DADV ==> (%g,%g), diff = (%.2g,%.2g)\n",
        f2->name, a, c, xADV.adj(), zADV.adj(),
        xDADV.adj(), zDADV.adj(),
        xADV.adj() - xDADV.adj(), zADV.adj() - zDADV.adj());
      }
    DADVar::Hvprod(2,pDADV,v,h1);
    DADVar::Hvprod(2,pDADV,v+1,h1+2);
    for(k = 0; k < 4; k++)
      if (differ(h[k], h1[k])) {
        ++b2;
        printf("%s\"(%g,%g):\n ADV ==> (%8g\t%8g\t%8g\t%g)\n",
          f2->name, a, c, h[0], h[1], h[2], h[3]);
        printf("DADV ==> (%8g\t%8g\t%8g\t%g)\n",
          h1[0], h1[1], h1[2], h1[3]);
        printf("diff = (%.2g  %.2g  %.2g  %.2g)\n\n",
          h[0] - h1[0], h[1] - h1[1],
          h[2] - h1[2], h[3] - h1[3]);
        break;
        }
    tfFDR = 0.;
    tfFDR.diff(0,1);
    xFDR = a + tfFDR*v[0];
    zFDR = c + tfFDR*v[1];
    yFDR = f2->f3(xFDR, zFDR);
    tDR = yFDR.dx(0);
    DReal::Gradcomp();

    if (differ(yFDR.val().val(), yADV.val())) {
      ++b0;
      printf("%s(%g,%g): yFDR = %g, yADV = %g, diff = %.2g\n",
        f2->name, a, c, yFDR.val().val(), yADV.val(),
        yFDR.val().val() - yADV.val());
      }
    if (differ(xFDR.val().adj(), h[0]) || differ(zFDR.val().adj(), h[1])) {
      ++b2;
      printf("%s\"(%g,%g) row 1:\nFDR ==> (%g,%g)\nADV ==> (%g,%g)\n",
        f2->name, a, c, xFDR.val().adj(), zFDR.val().adj(),
        h[0], h[1]);
      printf("diff = %.2g  %g\n\n",
        xFDR.val().adj() - h[0], zFDR.val().adj() - h[1]);
      }
    tfFDR.diff(0,1);
    xFDR = a + tfFDR*v[1];
    zFDR = c + tfFDR*v[2];
    yFDR = f2->f3(xFDR, zFDR);
    tDR = yFDR.dx(0);
    DReal::Gradcomp();
    if (differ(xFDR.val().adj(), h[2]) || differ(zFDR.val().adj(), h[3])) {
      ++b2;
      printf("%s\"(%g,%g) row 2:\nFDR ==> (%g,%g)\nADV ==> (%g,%g)\n",
        f2->name, a, c, xFDR.val().adj(), zFDR.val().adj(),
        h[2], h[3]);
      printf("diff = %.2g  %g\n\n",
        xFDR.val().adj() - h[2], zFDR.val().adj() - h[3]);
      }

    tfFR = 0.;
    tfFR.diff(0,1);
    xAFR = a + tfFR*v[0];
    zAFR = c + tfFR*v[1];
    yAFR = f2->f4(xAFR, zAFR);
    AFReal::Gradcomp();
    if (differ(yAFR.val().val(), yADV.val())) {
      ++b0;
      printf("%s(%g,%g): yAFR = %g, yADV = %g, diff = %.2g\n",
        f2->name, a, c, yAFR.val().val(), yADV.val(),
        yAFR.val().val() - yADV.val());
      }
    if (differ(xAFR.adj().val(), xADV.adj()) || differ(zAFR.adj().val(), zADV.adj())) {
      ++b1;
      printf("%s'(%g,%g):\n AFR ==> (%g,%g)\n ADV ==> (%g,%g)\n",
        f2->name, a, c, xAFR.adj().val(), zAFR.adj().val(),
        xADV.adj(), zADV.adj());
      printf(" diff = %.2g  %.2g\n\n",
        xAFR.adj().val() - xADV.adj(),
        zAFR.adj().val() - zADV.adj());
      }
    if (differ(xAFR.adj().dx(0), h[0]) || differ(zAFR.adj().dx(0), h[1])) {
      ++b2;
      printf("%s\"(%g,%g) row 1:\n AFR ==> (%g,%g)\n",
        f2->name, a, c, xAFR.adj().dx(0), zAFR.adj().dx(0));
      printf(" ADV = (%g,%g)\n diff = %.2g  %.2g\n\n", h[0], h[1],
        xAFR.adj().dx(0) - h[0],
        zAFR.adj().dx(0) - h[1]);
      }
    tfFR.diff(0,1);
    xAFR = a + tfFR*v[1];
    zAFR = c + tfFR*v[2];
    yAFR = f2->f4(xAFR, zAFR);
    AFReal::Gradcomp();
    if (differ(xAFR.adj().dx(0), h[2]) || differ(zAFR.adj().dx(0), h[3])) {
      ++b2;
      printf("%s\"(%g,%g) row 2:\n AFR ==> (%g,%g)\n",
        f2->name, a, c, xAFR.adj().dx(0), zAFR.adj().dx(0));
      printf(" ADV = (%g,%g)\n diff = %.2g  %.2g\n\n", h[2], h[3],
        xAFR.adj().dx(0) - h[2],
        zAFR.adj().dx(0) - h[3]);
      }
    }
      }
  k = b0 + b1 + b2;
  if (k || verbose) {
    s = progname;
    if (*s == '.' && s[1] == '/')
      for(s += 2; *s == '/'; ++s);
    printf("%s: %d errors seen.\n", s, k);
    k = 1;
    }
  else
    printf("OK\n");
  return k;
  }

---