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interior.h
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interior.h
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extern "C" {
#include "ldl.h"
#include "amd.h"
}
struct NRldl {
Doub Info [AMD_INFO];
Int lnz,n,nz;
VecInt PP,PPinv,PPattern,LLnz,LLp,PParent,FFlag,*LLi;
VecDoub YY,DD,*LLx;
Doub *Ax, *Lx, *B, *D, *X, *Y;
Int *Ai, *Ap, *Li, *Lp, *P, *Pinv, *Flag,*Pattern, *Lnz, *Parent;
NRldl(NRsparseMat &adat);
void order();
void factorize();
void solve(VecDoub_O &y,VecDoub &rhs);
~NRldl();
};
Doub dotprod(VecDoub_I &x, VecDoub_I &y)
{
Doub sum=0.0;
for (Int i=0;i<x.size();i++)
sum += x[i]*y[i];
return sum;
}
Int intpt(const NRsparseMat &a, VecDoub_I &b, VecDoub_I &c, VecDoub_O &x)
{
const Int MAXITS=200;
const Doub EPS=1.0e-6;
const Doub SIGMA=0.9;
const Doub DELTA=0.02;
const Doub BIG=numeric_limits<Doub>::max();
Int i,j,iter,status;
Int m=a.nrows;
Int n=a.ncols;
VecDoub y(m),z(n),ax(m),aty(n),rp(m),rd(n),d(n),dx(n),dy(m),dz(n),
rhs(m),tempm(m),tempn(n);
NRsparseMat at=a.transpose();
ADAT adat(a,at);
NRldl solver(adat.ref());
solver.order();
Doub rpfact=1.0+sqrt(dotprod(b,b));
Doub rdfact=1.0+sqrt(dotprod(c,c));
for (j=0;j<n;j++) {
x[j]=1000.0;
z[j]=1000.0;
}
for (i=0;i<m;i++) {
y[i]=1000.0;
}
Doub normrp_old=BIG;
Doub normrd_old=BIG;
cout << setw(4) << "iter" << setw(12) << "Primal obj." << setw(9) <<
"||r_p||" << setw(13) << "Dual obj." << setw(11) << "||r_d||" <<
setw(13) << "duality gap" << setw(16) << "normalized gap" << endl;
cout << scientific << setprecision(4);
for (iter=0;iter<MAXITS;iter++) {
ax=a.ax(x);
for (i=0;i<m;i++)
rp[i]=ax[i]-b[i];
Doub normrp=sqrt(dotprod(rp,rp))/rpfact;
aty=at.ax(y);
for (j=0;j<n;j++)
rd[j]=aty[j]+z[j]-c[j];
Doub normrd=sqrt(dotprod(rd,rd))/rdfact;
Doub gamma=dotprod(x,z);
Doub mu=DELTA*gamma/n;
Doub primal_obj=dotprod(c,x);
Doub dual_obj=dotprod(b,y);
Doub gamma_norm=gamma/(1.0+abs(primal_obj));
cout << setw(3) << iter << setw(12) << primal_obj << setw(12) <<
normrp << setw(12) << dual_obj << setw(12) << normrd << setw(12)
<< gamma << setw(12) << gamma_norm<<endl;
if (normrp < EPS && normrd < EPS && gamma_norm < EPS)
return status=0;
if (normrp > 1000*normrp_old && normrp > EPS)
return status=1;
if (normrd > 1000*normrd_old && normrd > EPS)
return status=2;
for (j=0;j<n;j++)
d[j]=x[j]/z[j];
adat.updateD(d);
solver.factorize();
for (j=0;j<n;j++)
tempn[j]=x[j]-mu/z[j]-d[j]*rd[j];
tempm=a.ax(tempn);
for (i=0;i<m;i++)
rhs[i]=-rp[i]+tempm[i];
solver.solve(dy,rhs);
tempn=at.ax(dy);
for (j=0;j<n;j++)
dz[j]=-tempn[j]-rd[j];
for (j=0;j<n;j++)
dx[j]=-d[j]*dz[j]+mu/z[j]-x[j];
Doub alpha_p=1.0;
for (j=0;j<n;j++)
if (x[j]+alpha_p*dx[j] < 0.0)
alpha_p=-x[j]/dx[j];
Doub alpha_d=1.0;
for (j=0;j<n;j++)
if (z[j]+alpha_d*dz[j] < 0.0)
alpha_d=-z[j]/dz[j];
alpha_p = MIN(alpha_p*SIGMA,1.0);
alpha_d = MIN(alpha_d*SIGMA,1.0);
for (j=0;j<n;j++) {
x[j]+=alpha_p*dx[j];
z[j]+=alpha_d*dz[j];
}
for (i=0;i<m;i++)
y[i]+=alpha_d*dy[i];
normrp_old=normrp;
normrd_old=normrd;
}
return status=3;
}
NRldl::NRldl(NRsparseMat &adat) : n(adat.ncols), nz(adat.nvals),
Ap(&adat.col_ptr[0]), Ai(&adat.row_ind[0]), Ax(&adat.val[0]),
PP(n),PPinv(n),PPattern(n),LLnz(n),LLp(n+1),PParent(n),FFlag(n),
YY(n),DD(n),Y(&YY[0]),D(&DD[0]),P(&PP[0]),Pinv(&PPinv[0]),
Pattern(&PPattern[0]),Lnz(&LLnz[0]),Lp(&LLp[0]),Parent(&PParent[0]),
Flag(&FFlag[0]) {}
void NRldl::order() {
if (amd_order (n, Ap, Ai, P, (Doub *) NULL, Info) != AMD_OK)
throw("call to AMD failed");
amd_control ((Doub *) NULL);
//amd_info (Info);
ldl_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv);
lnz = Lp [n];
/* find # of nonzeros in L, and flop count for ldl_numeric */
Doub flops = 0 ;
for (Int j = 0 ; j < n ; j++)
flops += ((Doub) Lnz [j]) * (Lnz [j] + 2) ;
cout << "Nz in L: " << lnz << " Flop count: " << flops << endl;
/* -------------------------------------------------------------- */
/* allocate remainder of L, of size lnz */
/* -------------------------------------------------------------- */
LLi=new VecInt(lnz);
LLx=new VecDoub(lnz);
Li=&(*LLi)[0];
Lx=&(*LLx)[0];
}
void NRldl::factorize() {
/* -------------------------------------------------------------- */
/* numeric factorization to get Li, Lx, and D */
/* -------------------------------------------------------------- */
Int dd = ldl_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D,
Y, Flag, Pattern, P, Pinv) ;
if (dd != n)
throw("Factorization failed since diagonal is zero.");
}
void NRldl::solve(VecDoub_O &y,VecDoub &rhs) {
B=&rhs[0];
X=&y[0];
/* solve Ax=b */
/* the factorization is LDL' = PAP' */
ldl_perm (n, Y, B, P) ; /* y = Pb */
ldl_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */
ldl_dsolve (n, Y, D) ; /* y = D\y */
ldl_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */
ldl_permt (n, X, Y, P) ; /* x = P'y */
}
NRldl::~NRldl() {
delete LLx;
delete LLi;
}