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nilss.cpp
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nilss.cpp
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#include <cmath>
#include <iostream>
#include <Eigen/Dense>
#include "nilss.h"
#include "nilss_solver.h"
using namespace nilss;
NILSS::NILSS(int nHomoAdjoint, int nStateVariables,
int nDesignVariables, const double * dotProductWeights)
: nHomo_(nHomoAdjoint), size_(nStateVariables), nGrad_(nDesignVariables)
{
for (int i = 0; i < size_; ++i) {
dotWeights_.push_back(dotProductWeights[i]);
}
}
double NILSS::dotProd_(const double * y1, const double * y2) const
{
double dot = 0;
for (int i = 0; i < size_; ++ i) {
dot += dotWeights_[i] * y1[i] * y2[i];
}
return dot;
}
void NILSS::axpy_(double * y, const double * x, double a) const
{
for (int i = 0; i < size_; ++ i) {
y[i] += a * x[i];
}
}
void NILSS::scale_(double * y, double a) const
{
for (int i = 0; i < size_; ++ i) {
y[i] *= a;
}
}
void NILSS::checkpoint(double * y, const double * grad)
{
double * p_y[nHomo_ + 1];
const double * p_grad[nHomo_ + 1];
for (int i = 0; i <= nHomo_; ++ i) {
p_y[i] = y + i * size_;
p_grad[i] = grad + i * nGrad_;
}
checkpoint(p_y, p_grad);
}
void NILSS::checkpoint(double * const * y, const double * const * grad)
{
// Gram Schmidt orthonormalization
R_.emplace_back(nHomo_, nHomo_);
Eigen::MatrixXd & R = R_.back();
for (int i = 0; i < nHomo_; ++ i) {
R.col(i).setZero();
for (int j = 0; j < i; ++j) {
R(j,i) = dotProd_(y[i], y[j]);
axpy_(y[i], y[j], -R(j,i));
}
R(i,i) = sqrt(dotProd_(y[i], y[i]));
scale_(y[i], 1.0/R(i,i));
}
// Orthogonalization
b_.emplace_back(nHomo_);
Eigen::VectorXd & b = b_.back();
b.setZero();
for (int j = 0; j < nHomo_; ++j) {
b(j) = dotProd_(y[j], y[nHomo_]);
axpy_(y[nHomo_], y[j], -b(j));
}
// Store gradient
stored_grad_.emplace_back(nHomo_ + 1, nGrad_); // homo and inhomo
Eigen::MatrixXd & stored_grad = stored_grad_.back();
for (int i = 0; i <= nHomo_; ++i) {
for (int j = 0; j < nGrad_; ++j) {
stored_grad(i,j) = grad[i][j];
}
}
}
double NILSS::window_(double x) const
{
const double PI = atan(1.0) * 4;
double s = sin(x * PI);
return s * s;
}
void NILSS::gradient(double * gradient) const
{
std::vector<Eigen::MatrixXd> identities;
std::vector<Eigen::VectorXd> zeros;
identities.reserve(R_.size() + 1);
zeros.reserve(R_.size() + 1);
for (size_t i = 0; i <= R_.size(); ++ i) {
double window = window_((double)i / R_.size());
identities.emplace_back(nHomo_, nHomo_);
identities.back().setIdentity();
identities.back() *= window;
zeros.emplace_back(nHomo_);
zeros.back().setZero();
}
std::vector<Eigen::VectorXd> a;
nilss_solve(R_, identities, b_, zeros, a);
assert(a.size() == stored_grad_.size() + 1);
assert(a.size() == R_.size() + 1);
Eigen::VectorXd window(R_.size());
for (size_t i = 0; i < R_.size(); ++ i) {
window(i) = window_((double)i / (R_.size() - 1));
}
window /= window.mean();
// combine the gradients
Eigen::VectorXd grad(nGrad_);
grad.setZero();
for (size_t i = 0; i < R_.size(); ++ i) {
auto gradi = window(i) * stored_grad_[i];
for (int j = 0; j <= nHomo_; ++ j) {
double aij = (j < nHomo_) ? a[i](j) : 1.0;
grad += aij * gradi.row(j);
}
}
for (int i = 0; i < nGrad_; ++i) {
gradient[i] = grad(i);
}
}