void IGradient::Gradient(const RnFunction *f, double step, const DoubleVector &x, DoubleVector &g)
{
double h = step;
for (unsigned int i=0; i<g.length(); i++)
{
double cx = x[i];
const_cast<DoubleVector&>(x)[i] = cx - h;
double f1 = f->fx(x);
const_cast<DoubleVector&>(x)[i] = cx + h;
double f2 = f->fx(x);
const_cast<DoubleVector&>(x)[i] = cx;
g[i] = (f2 - f1) / (2.0 * h);
}
}
void HeatControl2Delta::gradient(const DoubleVector& x, DoubleVector& g)
{
px = &x;
DoubleMatrix u;
IParabolicEquation2D::calculateMVD(u, h1, h2, ht, N1, N2, M, a1, a2);
pu = &u;
DoubleCube psi;
IBackwardParabolicEquation2D::calculateMVD(psi, h1, h2, ht, N1, N2, M, a1, a2);
for (unsigned int i=0; i<g.length(); i++) g[i] = 0.0;
for (unsigned int k=M; k!=(unsigned int)0-1; k--)
{
calculateGX(x, psi.matrix(k), g, k);
//calculateGF(x, psi[k], g, k);
}
// for (unsigned int k=0; k<=M; k++)
// {
// unsigned int i1 = (unsigned int)round(E[0]/h1);
// unsigned int j1 = (unsigned int)round(E[1]/h2);
// g[0*(M+1)+k] = -psi[k][j1][i1] + 2.0*alpha*(v[0*(M+1)+k] - v1(k*ht));
// unsigned int i2 = (unsigned int)round(E[2]/h1);
// unsigned int j2 = (unsigned int)round(E[3]/h2);
// g[1*(M+1)+k] = -psi[k][j2][i2] + 2.0*alpha*(v[1*(M+1)+k] - v2(k*ht));
// unsigned int i3 = (unsigned int)round(E[4]/h1);
// unsigned int j3 = (unsigned int)round(E[5]/h2);
// g[2*(M+1)+k] = -psi[k][j3][i3] + 2.0*alpha*(v[2*(M+1)+k] - v3(k*ht));
// }
psi.clear();
// IGradient::Gradient(this, 0.0001, x, g);
}
void IFunctional::gradient(const DoubleVector &pv, DoubleVector &g) const
{
IFunctional *ifunc = const_cast<IFunctional*>(this);
unsigned int L = mTimeDimension.sizeN();
double ht = mTimeDimension.step();
ifunc->fromVector(pv, ifunc->mParameter);
forward->setParameter(mParameter);
backward->setParameter(mParameter);
DoubleMatrix u;
DoubleMatrix p;
vector<ExtendedSpaceNode2D> u_info;
forward->calculateMVD(u, u_info, true);
backward->u = &u;
backward->U = &ifunc->U;
backward->info = &u_info;
vector<ExtendedSpaceNode2D> p_info;
backward->calculateMVD(p, p_info, true);
g.clear();
g.resize(pv.length(), 0.0);
unsigned int gi = 0;
// k
if (optimizeK)
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
ExtendedSpaceNode2D &pi = p_info[i];
for (unsigned int j=0; j<mParameter.Lo; j++)
{
ExtendedSpaceNode2D &uj = u_info[j];
double grad_Kij = 0.0;
grad_Kij += 0.5 * (pi.value(0)+2.0*r*gpi(i,0,u_info)*sgn(g0i(i,0,u_info))) * (uj.value(0) - mParameter.z.at(i,j));
for (unsigned int m=1; m<=L-1; m++)
{
grad_Kij += (pi.value(m)+2.0*r*gpi(i,m,u_info)*sgn(g0i(i,m,u_info))) * (uj.value(m) - mParameter.z.at(i,j));
}
grad_Kij += 0.5 * (pi.value(L)+2.0*r*gpi(i,L,u_info)*sgn(g0i(i,L,u_info))) * (uj.value(L) - mParameter.z.at(i,j));
grad_Kij *= -ht;
g[gi++] = grad_Kij + 2.0*regEpsilon*(mParameter.k.at(i,j) - mParameter0.k.at(i,j));
}
}
}
else
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
for (unsigned int j=0; j<mParameter.Lo; j++)
{
g[gi++] = 0.0;
}
}
}
// z
if (optimizeZ)
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
ExtendedSpaceNode2D &pi = p_info[i];
for (unsigned int j=0; j<mParameter.Lo; j++)
{
double grad_Zij = 0.0;
grad_Zij += 0.5 * (pi.value(0)+2.0*r*gpi(i,0,u_info)*sgn(g0i(i,0,u_info))) * mParameter.k.at(i,j);
for (unsigned int m=1; m<=L-1; m++)
{
grad_Zij += (pi.value(m)+2.0*r*gpi(i,m,u_info)*sgn(g0i(i,m,u_info))) * mParameter.k.at(i,j);
}
grad_Zij += 0.5 * (pi.value(L)+2.0*r*gpi(i,L,u_info)*sgn(g0i(i,L,u_info))) * mParameter.k.at(i,j);
grad_Zij *= ht;
g[gi++] = grad_Zij + 2.0*regEpsilon*(mParameter.z[i][j] - mParameter0.z[i][j]);
}
}
}
else
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
for (unsigned int j=0; j<mParameter.Lo; j++)
{
g[gi++] = 0.0;
}
}
}
// xi
if (optimizeO)
{
for (unsigned int j=0; j<mParameter.Lo; j++)
{
ExtendedSpaceNode2D &uj = u_info[j];
double gradXijX = 0.0;
double gradXijY = 0.0;
double vi = 0.0;
vi = 0.0;
for (unsigned int i=0; i<mParameter.Lc; i++) vi += mParameter.k.at(i,j) * (p_info[i].value(0)+2.0*r*gpi(i,0,u_info)*sgn(g0i(i,0,u_info)));
gradXijX += 0.5 * uj.valueDx(0) * vi;
gradXijY += 0.5 * uj.valueDy(0) * vi;
for (unsigned int m=1; m<=L-1; m++)
{
vi = 0.0;
for (unsigned int i=0; i<mParameter.Lc; i++) vi += mParameter.k.at(i,j)*(p_info[i].value(m)+2.0*r*gpi(i,m,u_info)*sgn(g0i(i,m,u_info)));
gradXijX += uj.valueDx(m) * vi;
gradXijY += uj.valueDy(m) * vi;
}
vi = 0.0;
for (unsigned int i=0; i<mParameter.Lc; i++) vi += mParameter.k.at(i,j)*(p_info[i].value(L)+2.0*r*gpi(i,L,u_info)*sgn(g0i(i,L,u_info)));
gradXijX += 0.5 * uj.valueDx(L) * vi;
gradXijY += 0.5 * uj.valueDy(L) * vi;
gradXijX *= -ht;
gradXijY *= -ht;
g[gi++] = gradXijX + 2.0*regEpsilon*(mParameter.xi[j].x - mParameter0.xi[j].x);
g[gi++] = gradXijY + 2.0*regEpsilon*(mParameter.xi[j].y - mParameter0.xi[j].y);
}
}
else
{
for (unsigned int j=0; j<mParameter.Lo; j++)
{
g[gi++] = 0.0;
g[gi++] = 0.0;
}
}
// eta
if (optimizeC)
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
ExtendedSpaceNode2D &pi = p_info[i];
double grad_EtaiX = 0.0;
double grad_EtaiY = 0.0;
double vi = 0.0;
vi = 0.0;
for (unsigned int j=0; j<mParameter.Lo; j++) vi += mParameter.k.at(i,j) * (u_info[j].value(0) - mParameter.z.at(i,j));
grad_EtaiX += 0.5 * pi.valueDx(0) * vi;
grad_EtaiY += 0.5 * pi.valueDy(0) * vi;
for (unsigned int m=1; m<=L-1; m++)
{
vi = 0.0;
for (unsigned int j=0; j<mParameter.Lo; j++) vi += mParameter.k.at(i,j) * (u_info[j].value(m) - mParameter.z.at(i,j));
grad_EtaiX += pi.valueDx(m) * vi;
grad_EtaiY += pi.valueDy(m) * vi;
}
vi = 0.0;
for (unsigned int j=0; j<mParameter.Lo; j++) vi += mParameter.k.at(i,j) * (u_info[j].value(L) - mParameter.z.at(i,j));
grad_EtaiX += 0.5 * pi.valueDx(L) * vi;
grad_EtaiY += 0.5 * pi.valueDy(L) * vi;
grad_EtaiX *= -ht;
grad_EtaiY *= -ht;
g[gi++] = grad_EtaiX + 2.0*regEpsilon*(mParameter.eta[i].x - mParameter0.eta[i].x);
g[gi++] = grad_EtaiY + 2.0*regEpsilon*(mParameter.eta[i].y - mParameter0.eta[i].y);
}
}
else
{
for (unsigned int i=0; i<mParameter.Lc; i++)
{
g[gi++] = 0.0;
g[gi++] = 0.0;
}
}
u_info.clear();
p_info.clear();
}