/usr/include/trilinos/ROL_ObjectiveDef.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
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//
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// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// Questions? Contact lead developers:
// Drew Kouri (dpkouri@sandia.gov) and
// Denis Ridzal (dridzal@sandia.gov)
//
// ************************************************************************
// @HEADER
#ifndef ROL_OBJECTIVE_DEF_H
#define ROL_OBJECTIVE_DEF_H
/** \class ROL::Objective
\brief Provides the definition of the objective function interface.
*/
namespace ROL {
template <class Real>
Real Objective<Real>::dirDeriv( const Vector<Real> &x, const Vector<Real> &d, Real &tol) {
Real ftol = std::sqrt(ROL_EPSILON<Real>());
Teuchos::RCP<Vector<Real> > xd = d.clone();
xd->set(x);
xd->axpy(tol, d);
return (this->value(*xd,ftol) - this->value(x,ftol)) / tol;
}
template <class Real>
void Objective<Real>::gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
g.zero();
Real deriv = 0.0, h = 0.0, xi = 0.0;
for (int i = 0; i < g.dimension(); i++) {
xi = std::abs(x.dot(*x.basis(i)));
h = ((xi < ROL_EPSILON<Real>()) ? 1. : xi)*tol;
deriv = this->dirDeriv(x,*x.basis(i),h);
g.axpy(deriv,*g.basis(i));
}
}
template <class Real>
void Objective<Real>::hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
Real zero(0), one(1);
// Get Step Length
if ( v.norm() == zero ) {
hv.zero();
}
else {
Real gtol = std::sqrt(ROL_EPSILON<Real>());
Real h = std::max(one,x.norm()/v.norm())*tol;
//Real h = 2.0/(v.norm()*v.norm())*tol;
// Compute Gradient at x
Teuchos::RCP<Vector<Real> > g = hv.clone();
this->gradient(*g,x,gtol);
// Compute New Step x + h*v
Teuchos::RCP<Vector<Real> > xnew = x.clone();
xnew->set(x);
xnew->axpy(h,v);
this->update(*xnew);
// Compute Gradient at x + h*v
hv.zero();
this->gradient(hv,*xnew,gtol);
// Compute Newton Quotient
hv.axpy(-one,*g);
hv.scale(one/h);
}
}
template <class Real>
std::vector<std::vector<Real> > Objective<Real>::checkGradient( const Vector<Real> &x,
const Vector<Real> &g,
const Vector<Real> &d,
const bool printToStream,
std::ostream & outStream,
const int numSteps,
const int order ) {
std::vector<Real> steps(numSteps);
for(int i=0;i<numSteps;++i) {
steps[i] = pow(10,-i);
}
return checkGradient(x,g,d,steps,printToStream,outStream,order);
} // checkGradient
template <class Real>
std::vector<std::vector<Real> > Objective<Real>::checkGradient( const Vector<Real> &x,
const Vector<Real> &g,
const Vector<Real> &d,
const std::vector<Real> &steps,
const bool printToStream,
std::ostream & outStream,
const int order ) {
TEUCHOS_TEST_FOR_EXCEPTION( order<1 || order>4, std::invalid_argument,
"Error: finite difference order must be 1,2,3, or 4" );
using Finite_Difference_Arrays::shifts;
using Finite_Difference_Arrays::weights;
Real tol = std::sqrt(ROL_EPSILON<Real>());
int numSteps = steps.size();
int numVals = 4;
std::vector<Real> tmp(numVals);
std::vector<std::vector<Real> > gCheck(numSteps, tmp);
// Save the format state of the original outStream.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(outStream);
// Evaluate objective value at x.
this->update(x);
Real val = this->value(x,tol);
// Compute gradient at x.
Teuchos::RCP<Vector<Real> > gtmp = g.clone();
this->update(x);
this->gradient(*gtmp, x, tol);
Real dtg = d.dot(gtmp->dual());
// Temporary vectors.
Teuchos::RCP<Vector<Real> > xnew = x.clone();
for (int i=0; i<numSteps; i++) {
Real eta = steps[i];
xnew->set(x);
// Compute gradient, finite-difference gradient, and absolute error.
gCheck[i][0] = eta;
gCheck[i][1] = dtg;
gCheck[i][2] = weights[order-1][0] * val;
for(int j=0; j<order; ++j) {
// Evaluate at x <- x+eta*c_i*d.
xnew->axpy(eta*shifts[order-1][j], d);
// Only evaluate at shifts where the weight is nonzero
if( weights[order-1][j+1] != 0 ) {
this->update(*xnew);
gCheck[i][2] += weights[order-1][j+1] * this->value(*xnew,tol);
}
}
gCheck[i][2] /= eta;
gCheck[i][3] = std::abs(gCheck[i][2] - gCheck[i][1]);
if (printToStream) {
if (i==0) {
outStream << std::right
<< std::setw(20) << "Step size"
<< std::setw(20) << "grad'*dir"
<< std::setw(20) << "FD approx"
<< std::setw(20) << "abs error"
<< "\n"
<< std::setw(20) << "---------"
<< std::setw(20) << "---------"
<< std::setw(20) << "---------"
<< std::setw(20) << "---------"
<< "\n";
}
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << gCheck[i][0]
<< std::setw(20) << gCheck[i][1]
<< std::setw(20) << gCheck[i][2]
<< std::setw(20) << gCheck[i][3]
<< "\n";
}
}
// Reset format state of outStream.
outStream.copyfmt(oldFormatState);
return gCheck;
} // checkGradient
template <class Real>
std::vector<std::vector<Real> > Objective<Real>::checkHessVec( const Vector<Real> &x,
const Vector<Real> &hv,
const Vector<Real> &v,
const bool printToStream,
std::ostream & outStream,
const int numSteps,
const int order ) {
std::vector<Real> steps(numSteps);
for(int i=0;i<numSteps;++i) {
steps[i] = pow(10,-i);
}
return checkHessVec(x,hv,v,steps,printToStream,outStream,order);
} // checkHessVec
template <class Real>
std::vector<std::vector<Real> > Objective<Real>::checkHessVec( const Vector<Real> &x,
const Vector<Real> &hv,
const Vector<Real> &v,
const std::vector<Real> &steps,
const bool printToStream,
std::ostream & outStream,
const int order ) {
TEUCHOS_TEST_FOR_EXCEPTION( order<1 || order>4, std::invalid_argument,
"Error: finite difference order must be 1,2,3, or 4" );
using Finite_Difference_Arrays::shifts;
using Finite_Difference_Arrays::weights;
Real tol = std::sqrt(ROL_EPSILON<Real>());
int numSteps = steps.size();
int numVals = 4;
std::vector<Real> tmp(numVals);
std::vector<std::vector<Real> > hvCheck(numSteps, tmp);
// Save the format state of the original outStream.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(outStream);
// Compute gradient at x.
Teuchos::RCP<Vector<Real> > g = hv.clone();
this->update(x);
this->gradient(*g, x, tol);
// Compute (Hessian at x) times (vector v).
Teuchos::RCP<Vector<Real> > Hv = hv.clone();
this->hessVec(*Hv, v, x, tol);
Real normHv = Hv->norm();
// Temporary vectors.
Teuchos::RCP<Vector<Real> > gdif = hv.clone();
Teuchos::RCP<Vector<Real> > gnew = hv.clone();
Teuchos::RCP<Vector<Real> > xnew = x.clone();
for (int i=0; i<numSteps; i++) {
Real eta = steps[i];
// Evaluate objective value at x+eta*d.
xnew->set(x);
gdif->set(*g);
gdif->scale(weights[order-1][0]);
for(int j=0; j<order; ++j) {
// Evaluate at x <- x+eta*c_i*d.
xnew->axpy(eta*shifts[order-1][j], v);
// Only evaluate at shifts where the weight is nonzero
if( weights[order-1][j+1] != 0 ) {
this->update(*xnew);
this->gradient(*gnew, *xnew, tol);
gdif->axpy(weights[order-1][j+1],*gnew);
}
}
gdif->scale(1.0/eta);
// Compute norms of hessvec, finite-difference hessvec, and error.
hvCheck[i][0] = eta;
hvCheck[i][1] = normHv;
hvCheck[i][2] = gdif->norm();
gdif->axpy(-1.0, *Hv);
hvCheck[i][3] = gdif->norm();
if (printToStream) {
if (i==0) {
outStream << std::right
<< std::setw(20) << "Step size"
<< std::setw(20) << "norm(Hess*vec)"
<< std::setw(20) << "norm(FD approx)"
<< std::setw(20) << "norm(abs error)"
<< "\n"
<< std::setw(20) << "---------"
<< std::setw(20) << "--------------"
<< std::setw(20) << "---------------"
<< std::setw(20) << "---------------"
<< "\n";
}
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << hvCheck[i][0]
<< std::setw(20) << hvCheck[i][1]
<< std::setw(20) << hvCheck[i][2]
<< std::setw(20) << hvCheck[i][3]
<< "\n";
}
}
// Reset format state of outStream.
outStream.copyfmt(oldFormatState);
return hvCheck;
} // checkHessVec
template<class Real>
std::vector<Real> Objective<Real>::checkHessSym( const Vector<Real> &x,
const Vector<Real> &hv,
const Vector<Real> &v,
const Vector<Real> &w,
const bool printToStream,
std::ostream & outStream ) {
Real tol = std::sqrt(ROL_EPSILON<Real>());
// Compute (Hessian at x) times (vector v).
Teuchos::RCP<Vector<Real> > h = hv.clone();
this->hessVec(*h, v, x, tol);
Real wHv = w.dot(h->dual());
this->hessVec(*h, w, x, tol);
Real vHw = v.dot(h->dual());
std::vector<Real> hsymCheck(3, 0);
hsymCheck[0] = wHv;
hsymCheck[1] = vHw;
hsymCheck[2] = std::abs(vHw-wHv);
// Save the format state of the original outStream.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(outStream);
if (printToStream) {
outStream << std::right
<< std::setw(20) << "<w, H(x)v>"
<< std::setw(20) << "<v, H(x)w>"
<< std::setw(20) << "abs error"
<< "\n";
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << hsymCheck[0]
<< std::setw(20) << hsymCheck[1]
<< std::setw(20) << hsymCheck[2]
<< "\n";
}
// Reset format state of outStream.
outStream.copyfmt(oldFormatState);
return hsymCheck;
} // checkHessSym
} // namespace ROL
#endif
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