/*************************************************************************
Returns norm of bounded anti-gradient.
Bounded antigradient is a vector obtained from anti-gradient by zeroing
components which point outwards:
result = norm(v)
v[i]=0 if ((-g[i]<0)and(x[i]=bndl[i])) or
((-g[i]>0)and(x[i]=bndu[i]))
v[i]=-g[i] otherwise
This function may be used to check a stopping criterion.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
private static double asaboundedantigradnorm(minasastate state)
{
double result = 0;
int i = 0;
double v = 0;
result = 0;
for(i=0; i<=state.n-1; i++)
{
v = -state.g[i];
if( (double)(state.x[i])==(double)(state.bndl[i]) && (double)(-state.g[i])<(double)(0) )
{
v = 0;
}
if( (double)(state.x[i])==(double)(state.bndu[i]) && (double)(-state.g[i])>(double)(0) )
{
v = 0;
}
result = result+math.sqr(v);
}
result = Math.Sqrt(result);
return result;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
public static void minasaresultsbuf(minasastate state,
ref double[] x,
minasareport rep)
{
int i = 0;
int i_ = 0;
if( alglib.ap.len(x)<state.n )
{
x = new double[state.n];
}
for(i_=0; i_<=state.n-1;i_++)
{
x[i_] = state.x[i_];
}
rep.iterationscount = state.repiterationscount;
rep.nfev = state.repnfev;
rep.terminationtype = state.repterminationtype;
rep.activeconstraints = 0;
for(i=0; i<=state.n-1; i++)
{
if( (double)(state.ak[i])==(double)(0) )
{
rep.activeconstraints = rep.activeconstraints+1;
}
}
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasarestartfrom(minasastate state,
double[] x,
double[] bndl,
double[] bndu)
{
int i_ = 0;
alglib.ap.assert(alglib.ap.len(x)>=state.n, "MinASARestartFrom: Length(X)<N!");
alglib.ap.assert(apserv.isfinitevector(x, state.n), "MinASARestartFrom: X contains infinite or NaN values!");
alglib.ap.assert(alglib.ap.len(bndl)>=state.n, "MinASARestartFrom: Length(BndL)<N!");
alglib.ap.assert(apserv.isfinitevector(bndl, state.n), "MinASARestartFrom: BndL contains infinite or NaN values!");
alglib.ap.assert(alglib.ap.len(bndu)>=state.n, "MinASARestartFrom: Length(BndU)<N!");
alglib.ap.assert(apserv.isfinitevector(bndu, state.n), "MinASARestartFrom: BndU contains infinite or NaN values!");
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = x[i_];
}
for(i_=0; i_<=state.n-1;i_++)
{
state.bndl[i_] = bndl[i_];
}
for(i_=0; i_<=state.n-1;i_++)
{
state.bndu[i_] = bndu[i_];
}
state.laststep = 0;
state.rstate.ia = new int[3+1];
state.rstate.ba = new bool[1+1];
state.rstate.ra = new double[2+1];
state.rstate.stage = -1;
clearrequestfields(state);
}
/*************************************************************************
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
public static bool minasaiteration(minasastate state)
{
bool result = new bool();
int n = 0;
int i = 0;
double betak = 0;
double v = 0;
double vv = 0;
int mcinfo = 0;
bool b = new bool();
bool stepfound = new bool();
int diffcnt = 0;
int i_ = 0;
//
// Reverse communication preparations
// I know it looks ugly, but it works the same way
// anywhere from C++ to Python.
//
// This code initializes locals by:
// * random values determined during code
// generation - on first subroutine call
// * values from previous call - on subsequent calls
//
if( state.rstate.stage>=0 )
{
n = state.rstate.ia[0];
i = state.rstate.ia[1];
mcinfo = state.rstate.ia[2];
diffcnt = state.rstate.ia[3];
b = state.rstate.ba[0];
stepfound = state.rstate.ba[1];
betak = state.rstate.ra[0];
v = state.rstate.ra[1];
vv = state.rstate.ra[2];
}
else
{
n = -983;
i = -989;
mcinfo = -834;
diffcnt = 900;
b = true;
stepfound = false;
betak = 214;
v = -338;
vv = -686;
}
if( state.rstate.stage==0 )
{
goto lbl_0;
}
if( state.rstate.stage==1 )
{
goto lbl_1;
}
if( state.rstate.stage==2 )
{
goto lbl_2;
}
if( state.rstate.stage==3 )
{
goto lbl_3;
}
if( state.rstate.stage==4 )
{
goto lbl_4;
}
if( state.rstate.stage==5 )
{
goto lbl_5;
}
if( state.rstate.stage==6 )
{
goto lbl_6;
}
if( state.rstate.stage==7 )
{
goto lbl_7;
}
if( state.rstate.stage==8 )
{
goto lbl_8;
}
if( state.rstate.stage==9 )
{
goto lbl_9;
}
if( state.rstate.stage==10 )
{
goto lbl_10;
}
if( state.rstate.stage==11 )
{
goto lbl_11;
}
if( state.rstate.stage==12 )
{
goto lbl_12;
}
if( state.rstate.stage==13 )
{
goto lbl_13;
}
if( state.rstate.stage==14 )
{
goto lbl_14;
}
//
// Routine body
//
//
// Prepare
//
n = state.n;
state.repterminationtype = 0;
state.repiterationscount = 0;
state.repnfev = 0;
state.debugrestartscount = 0;
state.cgtype = 1;
for(i_=0; i_<=n-1;i_++)
{
state.xk[i_] = state.x[i_];
}
for(i=0; i<=n-1; i++)
{
if( (double)(state.xk[i])==(double)(state.bndl[i]) || (double)(state.xk[i])==(double)(state.bndu[i]) )
{
state.ak[i] = 0;
}
else
{
state.ak[i] = 1;
}
}
state.mu = 0.1;
state.curalgo = 0;
//
// Calculate F/G, initialize algorithm
//
clearrequestfields(state);
state.needfg = true;
state.rstate.stage = 0;
goto lbl_rcomm;
lbl_0:
state.needfg = false;
if( !state.xrep )
{
goto lbl_15;
}
//
// progress report
//
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 1;
goto lbl_rcomm;
lbl_1:
state.xupdated = false;
lbl_15:
if( (double)(asaboundedantigradnorm(state))<=(double)(state.epsg) )
{
state.repterminationtype = 4;
result = false;
return result;
}
state.repnfev = state.repnfev+1;
//
// Main cycle
//
// At the beginning of new iteration:
// * CurAlgo stores current algorithm selector
// * State.XK, State.F and State.G store current X/F/G
// * State.AK stores current set of active constraints
//
lbl_17:
if( false )
{
goto lbl_18;
}
//
// GPA algorithm
//
if( state.curalgo!=0 )
{
goto lbl_19;
}
state.k = 0;
state.acount = 0;
lbl_21:
if( false )
{
goto lbl_22;
}
//
// Determine Dk = proj(xk - gk)-xk
//
for(i=0; i<=n-1; i++)
{
state.d[i] = apserv.boundval(state.xk[i]-state.g[i], state.bndl[i], state.bndu[i])-state.xk[i];
}
//
// Armijo line search.
// * exact search with alpha=1 is tried first,
// 'exact' means that we evaluate f() EXACTLY at
// bound(x-g,bndl,bndu), without intermediate floating
// point operations.
// * alpha<1 are tried if explicit search wasn't successful
// Result is placed into XN.
//
// Two types of search are needed because we can't
// just use second type with alpha=1 because in finite
// precision arithmetics (x1-x0)+x0 may differ from x1.
// So while x1 is correctly bounded (it lie EXACTLY on
// boundary, if it is active), (x1-x0)+x0 may be
// not bounded.
//
v = 0.0;
for(i_=0; i_<=n-1;i_++)
{
v += state.d[i_]*state.g[i_];
}
state.dginit = v;
state.finit = state.f;
if( !((double)(asad1norm(state))<=(double)(state.stpmax) || (double)(state.stpmax)==(double)(0)) )
{
goto lbl_23;
}
//
// Try alpha=1 step first
//
for(i=0; i<=n-1; i++)
{
state.x[i] = apserv.boundval(state.xk[i]-state.g[i], state.bndl[i], state.bndu[i]);
}
clearrequestfields(state);
state.needfg = true;
state.rstate.stage = 2;
goto lbl_rcomm;
lbl_2:
state.needfg = false;
state.repnfev = state.repnfev+1;
stepfound = (double)(state.f)<=(double)(state.finit+gpaftol*state.dginit);
goto lbl_24;
lbl_23:
stepfound = false;
lbl_24:
if( !stepfound )
{
goto lbl_25;
}
//
// we are at the boundary(ies)
//
for(i_=0; i_<=n-1;i_++)
{
state.xn[i_] = state.x[i_];
}
state.stp = 1;
goto lbl_26;
lbl_25:
//
// alpha=1 is too large, try smaller values
//
state.stp = 1;
linmin.linminnormalized(ref state.d, ref state.stp, n);
state.dginit = state.dginit/state.stp;
state.stp = gpadecay*state.stp;
if( (double)(state.stpmax)>(double)(0) )
{
state.stp = Math.Min(state.stp, state.stpmax);
}
lbl_27:
if( false )
{
goto lbl_28;
}
v = state.stp;
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xk[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.x[i_] + v*state.d[i_];
}
clearrequestfields(state);
state.needfg = true;
state.rstate.stage = 3;
goto lbl_rcomm;
lbl_3:
state.needfg = false;
state.repnfev = state.repnfev+1;
if( (double)(state.stp)<=(double)(stpmin) )
{
goto lbl_28;
}
if( (double)(state.f)<=(double)(state.finit+state.stp*gpaftol*state.dginit) )
{
goto lbl_28;
}
state.stp = state.stp*gpadecay;
goto lbl_27;
lbl_28:
for(i_=0; i_<=n-1;i_++)
{
state.xn[i_] = state.x[i_];
}
lbl_26:
state.repiterationscount = state.repiterationscount+1;
if( !state.xrep )
{
goto lbl_29;
}
//
// progress report
//
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 4;
goto lbl_rcomm;
lbl_4:
state.xupdated = false;
lbl_29:
//
// Calculate new set of active constraints.
// Reset counter if active set was changed.
// Prepare for the new iteration
//
for(i=0; i<=n-1; i++)
{
if( (double)(state.xn[i])==(double)(state.bndl[i]) || (double)(state.xn[i])==(double)(state.bndu[i]) )
{
state.an[i] = 0;
}
else
{
state.an[i] = 1;
}
}
for(i=0; i<=n-1; i++)
{
if( (double)(state.ak[i])!=(double)(state.an[i]) )
{
state.acount = -1;
break;
}
}
state.acount = state.acount+1;
for(i_=0; i_<=n-1;i_++)
{
state.xk[i_] = state.xn[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.ak[i_] = state.an[i_];
}
//
// Stopping conditions
//
if( !(state.repiterationscount>=state.maxits && state.maxits>0) )
{
goto lbl_31;
}
//
// Too many iterations
//
state.repterminationtype = 5;
if( !state.xrep )
{
goto lbl_33;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 5;
goto lbl_rcomm;
lbl_5:
state.xupdated = false;
lbl_33:
result = false;
return result;
lbl_31:
if( (double)(asaboundedantigradnorm(state))>(double)(state.epsg) )
{
goto lbl_35;
}
//
// Gradient is small enough
//
state.repterminationtype = 4;
if( !state.xrep )
{
goto lbl_37;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 6;
goto lbl_rcomm;
lbl_6:
state.xupdated = false;
lbl_37:
result = false;
return result;
lbl_35:
v = 0.0;
for(i_=0; i_<=n-1;i_++)
{
v += state.d[i_]*state.d[i_];
}
if( (double)(Math.Sqrt(v)*state.stp)>(double)(state.epsx) )
{
goto lbl_39;
}
//
// Step size is too small, no further improvement is
// possible
//
state.repterminationtype = 2;
if( !state.xrep )
{
goto lbl_41;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 7;
goto lbl_rcomm;
lbl_7:
state.xupdated = false;
lbl_41:
result = false;
return result;
lbl_39:
if( (double)(state.finit-state.f)>(double)(state.epsf*Math.Max(Math.Abs(state.finit), Math.Max(Math.Abs(state.f), 1.0))) )
{
goto lbl_43;
}
//
// F(k+1)-F(k) is small enough
//
state.repterminationtype = 1;
if( !state.xrep )
{
goto lbl_45;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 8;
goto lbl_rcomm;
lbl_8:
state.xupdated = false;
lbl_45:
result = false;
return result;
lbl_43:
//
// Decide - should we switch algorithm or not
//
if( asauisempty(state) )
{
if( (double)(asaginorm(state))>=(double)(state.mu*asad1norm(state)) )
{
state.curalgo = 1;
goto lbl_22;
}
else
{
state.mu = state.mu*asarho;
}
}
else
{
if( state.acount==n1 )
{
if( (double)(asaginorm(state))>=(double)(state.mu*asad1norm(state)) )
{
state.curalgo = 1;
goto lbl_22;
}
}
}
//
// Next iteration
//
state.k = state.k+1;
goto lbl_21;
lbl_22:
lbl_19:
//
// CG algorithm
//
if( state.curalgo!=1 )
{
goto lbl_47;
}
//
// first, check that there are non-active constraints.
// move to GPA algorithm, if all constraints are active
//
b = true;
for(i=0; i<=n-1; i++)
{
if( (double)(state.ak[i])!=(double)(0) )
{
b = false;
break;
}
}
if( b )
{
state.curalgo = 0;
goto lbl_17;
}
//
// CG iterations
//
state.fold = state.f;
for(i_=0; i_<=n-1;i_++)
{
state.xk[i_] = state.x[i_];
}
for(i=0; i<=n-1; i++)
{
state.dk[i] = -(state.g[i]*state.ak[i]);
state.gc[i] = state.g[i]*state.ak[i];
}
lbl_49:
if( false )
{
goto lbl_50;
}
//
// Store G[k] for later calculation of Y[k]
//
for(i=0; i<=n-1; i++)
{
state.yk[i] = -state.gc[i];
}
//
// Make a CG step in direction given by DK[]:
// * calculate step. Step projection into feasible set
// is used. It has several benefits: a) step may be
// found with usual line search, b) multiple constraints
// may be activated with one step, c) activated constraints
// are detected in a natural way - just compare x[i] with
// bounds
// * update active set, set B to True, if there
// were changes in the set.
//
for(i_=0; i_<=n-1;i_++)
{
state.d[i_] = state.dk[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.xn[i_] = state.xk[i_];
}
state.mcstage = 0;
state.stp = 1;
linmin.linminnormalized(ref state.d, ref state.stp, n);
if( (double)(state.laststep)!=(double)(0) )
{
state.stp = state.laststep;
}
linmin.mcsrch(n, ref state.xn, ref state.f, ref state.gc, state.d, ref state.stp, state.stpmax, gtol, ref mcinfo, ref state.nfev, ref state.work, state.lstate, ref state.mcstage);
lbl_51:
if( state.mcstage==0 )
{
goto lbl_52;
}
//
// preprocess data: bound State.XN so it belongs to the
// feasible set and store it in the State.X
//
for(i=0; i<=n-1; i++)
{
state.x[i] = apserv.boundval(state.xn[i], state.bndl[i], state.bndu[i]);
}
//
// RComm
//
clearrequestfields(state);
state.needfg = true;
state.rstate.stage = 9;
goto lbl_rcomm;
lbl_9:
state.needfg = false;
//
// postprocess data: zero components of G corresponding to
// the active constraints
//
for(i=0; i<=n-1; i++)
{
if( (double)(state.x[i])==(double)(state.bndl[i]) || (double)(state.x[i])==(double)(state.bndu[i]) )
{
state.gc[i] = 0;
}
else
{
state.gc[i] = state.g[i];
}
}
linmin.mcsrch(n, ref state.xn, ref state.f, ref state.gc, state.d, ref state.stp, state.stpmax, gtol, ref mcinfo, ref state.nfev, ref state.work, state.lstate, ref state.mcstage);
goto lbl_51;
lbl_52:
diffcnt = 0;
for(i=0; i<=n-1; i++)
{
//
// XN contains unprojected result, project it,
// save copy to X (will be used for progress reporting)
//
state.xn[i] = apserv.boundval(state.xn[i], state.bndl[i], state.bndu[i]);
//
// update active set
//
if( (double)(state.xn[i])==(double)(state.bndl[i]) || (double)(state.xn[i])==(double)(state.bndu[i]) )
{
state.an[i] = 0;
}
else
{
state.an[i] = 1;
}
if( (double)(state.an[i])!=(double)(state.ak[i]) )
{
diffcnt = diffcnt+1;
}
state.ak[i] = state.an[i];
}
for(i_=0; i_<=n-1;i_++)
{
state.xk[i_] = state.xn[i_];
}
state.repnfev = state.repnfev+state.nfev;
state.repiterationscount = state.repiterationscount+1;
if( !state.xrep )
{
goto lbl_53;
}
//
// progress report
//
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 10;
goto lbl_rcomm;
lbl_10:
state.xupdated = false;
lbl_53:
//
// Update info about step length
//
v = 0.0;
for(i_=0; i_<=n-1;i_++)
{
v += state.d[i_]*state.d[i_];
}
state.laststep = Math.Sqrt(v)*state.stp;
//
// Check stopping conditions.
//
if( (double)(asaboundedantigradnorm(state))>(double)(state.epsg) )
{
goto lbl_55;
}
//
// Gradient is small enough
//
state.repterminationtype = 4;
if( !state.xrep )
{
goto lbl_57;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 11;
goto lbl_rcomm;
lbl_11:
state.xupdated = false;
lbl_57:
result = false;
return result;
lbl_55:
if( !(state.repiterationscount>=state.maxits && state.maxits>0) )
{
goto lbl_59;
}
//
// Too many iterations
//
state.repterminationtype = 5;
if( !state.xrep )
{
goto lbl_61;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 12;
goto lbl_rcomm;
lbl_12:
state.xupdated = false;
lbl_61:
result = false;
return result;
lbl_59:
if( !((double)(asaginorm(state))>=(double)(state.mu*asad1norm(state)) && diffcnt==0) )
{
goto lbl_63;
}
//
// These conditions (EpsF/EpsX) are explicitly or implicitly
// related to the current step size and influenced
// by changes in the active constraints.
//
// For these reasons they are checked only when we don't
// want to 'unstick' at the end of the iteration and there
// were no changes in the active set.
//
// NOTE: consition |G|>=Mu*|D1| must be exactly opposite
// to the condition used to switch back to GPA. At least
// one inequality must be strict, otherwise infinite cycle
// may occur when |G|=Mu*|D1| (we DON'T test stopping
// conditions and we DON'T switch to GPA, so we cycle
// indefinitely).
//
if( (double)(state.fold-state.f)>(double)(state.epsf*Math.Max(Math.Abs(state.fold), Math.Max(Math.Abs(state.f), 1.0))) )
{
goto lbl_65;
}
//
// F(k+1)-F(k) is small enough
//
state.repterminationtype = 1;
if( !state.xrep )
{
goto lbl_67;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 13;
goto lbl_rcomm;
lbl_13:
state.xupdated = false;
lbl_67:
result = false;
return result;
lbl_65:
if( (double)(state.laststep)>(double)(state.epsx) )
{
goto lbl_69;
}
//
// X(k+1)-X(k) is small enough
//
state.repterminationtype = 2;
if( !state.xrep )
{
goto lbl_71;
}
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 14;
goto lbl_rcomm;
lbl_14:
state.xupdated = false;
lbl_71:
result = false;
return result;
lbl_69:
lbl_63:
//
// Check conditions for switching
//
if( (double)(asaginorm(state))<(double)(state.mu*asad1norm(state)) )
{
state.curalgo = 0;
goto lbl_50;
}
if( diffcnt>0 )
{
if( asauisempty(state) || diffcnt>=n2 )
{
state.curalgo = 1;
}
else
{
state.curalgo = 0;
}
goto lbl_50;
}
//
// Calculate D(k+1)
//
// Line search may result in:
// * maximum feasible step being taken (already processed)
// * point satisfying Wolfe conditions
// * some kind of error (CG is restarted by assigning 0.0 to Beta)
//
if( mcinfo==1 )
{
//
// Standard Wolfe conditions are satisfied:
// * calculate Y[K] and BetaK
//
for(i_=0; i_<=n-1;i_++)
{
state.yk[i_] = state.yk[i_] + state.gc[i_];
}
vv = 0.0;
for(i_=0; i_<=n-1;i_++)
{
vv += state.yk[i_]*state.dk[i_];
}
v = 0.0;
for(i_=0; i_<=n-1;i_++)
{
v += state.gc[i_]*state.gc[i_];
}
state.betady = v/vv;
v = 0.0;
for(i_=0; i_<=n-1;i_++)
{
v += state.gc[i_]*state.yk[i_];
}
state.betahs = v/vv;
if( state.cgtype==0 )
{
betak = state.betady;
}
if( state.cgtype==1 )
{
betak = Math.Max(0, Math.Min(state.betady, state.betahs));
}
}
else
{
//
// Something is wrong (may be function is too wild or too flat).
//
// We'll set BetaK=0, which will restart CG algorithm.
// We can stop later (during normal checks) if stopping conditions are met.
//
betak = 0;
state.debugrestartscount = state.debugrestartscount+1;
}
for(i_=0; i_<=n-1;i_++)
{
state.dn[i_] = -state.gc[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.dn[i_] = state.dn[i_] + betak*state.dk[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.dk[i_] = state.dn[i_];
}
//
// update other information
//
state.fold = state.f;
state.k = state.k+1;
goto lbl_49;
lbl_50:
lbl_47:
goto lbl_17;
lbl_18:
result = false;
return result;
//
// Saving state
//
lbl_rcomm:
result = true;
state.rstate.ia[0] = n;
state.rstate.ia[1] = i;
state.rstate.ia[2] = mcinfo;
state.rstate.ia[3] = diffcnt;
state.rstate.ba[0] = b;
state.rstate.ba[1] = stepfound;
state.rstate.ra[0] = betak;
state.rstate.ra[1] = v;
state.rstate.ra[2] = vv;
return result;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
public static void minasaresults(minasastate state,
ref double[] x,
minasareport rep)
{
x = new double[0];
minasaresultsbuf(state, ref x, rep);
}
/*************************************************************************
Returns True, if U set is empty.
* State.X is used as point,
* State.G - as gradient,
* D is calculated within function (because State.D may have different
meaning depending on current optimization algorithm)
For a meaning of U see 'NEW ACTIVE SET ALGORITHM FOR BOX CONSTRAINED
OPTIMIZATION' by WILLIAM W. HAGER AND HONGCHAO ZHANG.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
private static bool asauisempty(minasastate state)
{
bool result = new bool();
int i = 0;
double d = 0;
double d2 = 0;
double d32 = 0;
d = asad1norm(state);
d2 = Math.Sqrt(d);
d32 = d*d2;
result = true;
for(i=0; i<=state.n-1; i++)
{
if( (double)(Math.Abs(state.g[i]))>=(double)(d2) && (double)(Math.Min(state.x[i]-state.bndl[i], state.bndu[i]-state.x[i]))>=(double)(d32) )
{
result = false;
return result;
}
}
return result;
}
/*************************************************************************
NONLINEAR BOUND CONSTRAINED OPTIMIZATION USING
MODIFIED
WILLIAM W. HAGER AND HONGCHAO ZHANG
ACTIVE SET ALGORITHM
The subroutine minimizes function F(x) of N arguments with bound
constraints: BndL[i] <= x[i] <= BndU[i]
This method is globally convergent as long as grad(f) is Lipschitz
continuous on a level set: L = { x : f(x)<=f(x0) }.
INPUT PARAMETERS:
N - problem dimension. N>0
X - initial solution approximation, array[0..N-1].
BndL - lower bounds, array[0..N-1].
all elements MUST be specified, i.e. all variables are
bounded. However, if some (all) variables are unbounded,
you may specify very small number as bound: -1000, -1.0E6
or -1.0E300, or something like that.
BndU - upper bounds, array[0..N-1].
all elements MUST be specified, i.e. all variables are
bounded. However, if some (all) variables are unbounded,
you may specify very large number as bound: +1000, +1.0E6
or +1.0E300, or something like that.
EpsG - positive number which defines a precision of search. The
subroutine finishes its work if the condition ||G|| < EpsG is
satisfied, where ||.|| means Euclidian norm, G - gradient, X -
current approximation.
EpsF - positive number which defines a precision of search. The
subroutine finishes its work if on iteration number k+1 the
condition |F(k+1)-F(k)| <= EpsF*max{|F(k)|, |F(k+1)|, 1} is
satisfied.
EpsX - positive number which defines a precision of search. The
subroutine finishes its work if on iteration number k+1 the
condition |X(k+1)-X(k)| <= EpsX is fulfilled.
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
OUTPUT PARAMETERS:
State - structure used for reverse communication.
This function initializes State structure with default optimization
parameters (stopping conditions, step size, etc.). Use MinASASet??????()
functions to tune optimization parameters.
After all optimization parameters are tuned, you should use
MinASAIteration() function to advance algorithm iterations.
NOTES:
1. you may tune stopping conditions with MinASASetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinASASetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasacreate(int n,
ref double[] x,
ref double[] bndl,
ref double[] bndu,
ref minasastate state)
{
int i = 0;
int i_ = 0;
System.Diagnostics.Debug.Assert(n>=1, "MinASA: N too small!");
for(i=0; i<=n-1; i++)
{
System.Diagnostics.Debug.Assert((double)(bndl[i])<=(double)(bndu[i]), "MinASA: inconsistent bounds!");
System.Diagnostics.Debug.Assert((double)(bndl[i])<=(double)(x[i]), "MinASA: infeasible X!");
System.Diagnostics.Debug.Assert((double)(x[i])<=(double)(bndu[i]), "MinASA: infeasible X!");
}
//
// Initialize
//
state.n = n;
minasasetcond(ref state, 0, 0, 0, 0);
minasasetxrep(ref state, false);
minasasetstpmax(ref state, 0);
minasasetalgorithm(ref state, -1);
state.bndl = new double[n];
state.bndu = new double[n];
state.ak = new double[n];
state.xk = new double[n];
state.dk = new double[n];
state.an = new double[n];
state.xn = new double[n];
state.dn = new double[n];
state.x = new double[n];
state.d = new double[n];
state.g = new double[n];
state.gc = new double[n];
state.work = new double[n];
state.yk = new double[n];
for(i_=0; i_<=n-1;i_++)
{
state.bndl[i_] = bndl[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.bndu[i_] = bndu[i_];
}
//
// Prepare first run
//
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = x[i_];
}
state.rstate.ia = new int[3+1];
state.rstate.ba = new bool[1+1];
state.rstate.ra = new double[2+1];
state.rstate.stage = -1;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetcond(minasastate state,
double epsg,
double epsf,
double epsx,
int maxits)
{
alglib.ap.assert(math.isfinite(epsg), "MinASASetCond: EpsG is not finite number!");
alglib.ap.assert((double)(epsg)>=(double)(0), "MinASASetCond: negative EpsG!");
alglib.ap.assert(math.isfinite(epsf), "MinASASetCond: EpsF is not finite number!");
alglib.ap.assert((double)(epsf)>=(double)(0), "MinASASetCond: negative EpsF!");
alglib.ap.assert(math.isfinite(epsx), "MinASASetCond: EpsX is not finite number!");
alglib.ap.assert((double)(epsx)>=(double)(0), "MinASASetCond: negative EpsX!");
alglib.ap.assert(maxits>=0, "MinASASetCond: negative MaxIts!");
if( (((double)(epsg)==(double)(0) && (double)(epsf)==(double)(0)) && (double)(epsx)==(double)(0)) && maxits==0 )
{
epsx = 1.0E-6;
}
state.epsg = epsg;
state.epsf = epsf;
state.epsx = epsx;
state.maxits = maxits;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetxrep(minasastate state,
bool needxrep)
{
state.xrep = needxrep;
}
public override alglib.apobject make_copy()
{
minasastate _result = new minasastate();
_result.n = n;
_result.epsg = epsg;
_result.epsf = epsf;
_result.epsx = epsx;
_result.maxits = maxits;
_result.xrep = xrep;
_result.stpmax = stpmax;
_result.cgtype = cgtype;
_result.k = k;
_result.nfev = nfev;
_result.mcstage = mcstage;
_result.bndl = (double[])bndl.Clone();
_result.bndu = (double[])bndu.Clone();
_result.curalgo = curalgo;
_result.acount = acount;
_result.mu = mu;
_result.finit = finit;
_result.dginit = dginit;
_result.ak = (double[])ak.Clone();
_result.xk = (double[])xk.Clone();
_result.dk = (double[])dk.Clone();
_result.an = (double[])an.Clone();
_result.xn = (double[])xn.Clone();
_result.dn = (double[])dn.Clone();
_result.d = (double[])d.Clone();
_result.fold = fold;
_result.stp = stp;
_result.work = (double[])work.Clone();
_result.yk = (double[])yk.Clone();
_result.gc = (double[])gc.Clone();
_result.laststep = laststep;
_result.x = (double[])x.Clone();
_result.f = f;
_result.g = (double[])g.Clone();
_result.needfg = needfg;
_result.xupdated = xupdated;
_result.rstate = (rcommstate)rstate.make_copy();
_result.repiterationscount = repiterationscount;
_result.repnfev = repnfev;
_result.repterminationtype = repterminationtype;
_result.debugrestartscount = debugrestartscount;
_result.lstate = (linmin.linminstate)lstate.make_copy();
_result.betahs = betahs;
_result.betady = betady;
return _result;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasacreate(int n,
double[] x,
double[] bndl,
double[] bndu,
minasastate state)
{
int i = 0;
alglib.ap.assert(n>=1, "MinASA: N too small!");
alglib.ap.assert(alglib.ap.len(x)>=n, "MinCGCreate: Length(X)<N!");
alglib.ap.assert(apserv.isfinitevector(x, n), "MinCGCreate: X contains infinite or NaN values!");
alglib.ap.assert(alglib.ap.len(bndl)>=n, "MinCGCreate: Length(BndL)<N!");
alglib.ap.assert(apserv.isfinitevector(bndl, n), "MinCGCreate: BndL contains infinite or NaN values!");
alglib.ap.assert(alglib.ap.len(bndu)>=n, "MinCGCreate: Length(BndU)<N!");
alglib.ap.assert(apserv.isfinitevector(bndu, n), "MinCGCreate: BndU contains infinite or NaN values!");
for(i=0; i<=n-1; i++)
{
alglib.ap.assert((double)(bndl[i])<=(double)(bndu[i]), "MinASA: inconsistent bounds!");
alglib.ap.assert((double)(bndl[i])<=(double)(x[i]), "MinASA: infeasible X!");
alglib.ap.assert((double)(x[i])<=(double)(bndu[i]), "MinASA: infeasible X!");
}
//
// Initialize
//
state.n = n;
minasasetcond(state, 0, 0, 0, 0);
minasasetxrep(state, false);
minasasetstpmax(state, 0);
minasasetalgorithm(state, -1);
state.bndl = new double[n];
state.bndu = new double[n];
state.ak = new double[n];
state.xk = new double[n];
state.dk = new double[n];
state.an = new double[n];
state.xn = new double[n];
state.dn = new double[n];
state.x = new double[n];
state.d = new double[n];
state.g = new double[n];
state.gc = new double[n];
state.work = new double[n];
state.yk = new double[n];
minasarestartfrom(state, x, bndl, bndu);
}
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state between calls and
which is used for reverse communication. Must be
initialized with MinCGCreate()
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetstpmax(ref minasastate state,
double stpmax)
{
System.Diagnostics.Debug.Assert((double)(stpmax)>=(double)(0), "MinASASetStpMax: StpMax<0!");
state.stpmax = stpmax;
}
/*************************************************************************
This function sets optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state between calls and
which is used for reverse communication. Must be
initialized with MinASACreate()
UAType - algorithm type:
* -1 automatic selection of the best algorithm
* 0 DY (Dai and Yuan) algorithm
* 1 Hybrid DY-HS algorithm
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetalgorithm(ref minasastate state,
int algotype)
{
System.Diagnostics.Debug.Assert(algotype>=-1 & algotype<=1, "MinASASetAlgorithm: incorrect AlgoType!");
if( algotype==-1 )
{
algotype = 1;
}
state.cgtype = algotype;
}
/*************************************************************************
This function sets stopping conditions for the ASA optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state between calls and
which is used for reverse communication. Must be initialized
with MinASACreate()
EpsG - >=0
The subroutine finishes its work if the condition
||G||<EpsG is satisfied, where ||.|| means Euclidian norm,
G - gradient.
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |X(k+1)-X(k)| <= EpsX is fulfilled.
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetcond(ref minasastate state,
double epsg,
double epsf,
double epsx,
int maxits)
{
System.Diagnostics.Debug.Assert((double)(epsg)>=(double)(0), "MinASASetCond: negative EpsG!");
System.Diagnostics.Debug.Assert((double)(epsf)>=(double)(0), "MinASASetCond: negative EpsF!");
System.Diagnostics.Debug.Assert((double)(epsx)>=(double)(0), "MinASASetCond: negative EpsX!");
System.Diagnostics.Debug.Assert(maxits>=0, "MinASASetCond: negative MaxIts!");
if( (double)(epsg)==(double)(0) & (double)(epsf)==(double)(0) & (double)(epsx)==(double)(0) & maxits==0 )
{
epsx = 1.0E-6;
}
state.epsg = epsg;
state.epsf = epsf;
state.epsx = epsx;
state.maxits = maxits;
}
/*************************************************************************
Returns norm of GI(x).
GI(x) is a gradient vector whose components associated with active
constraints are zeroed. It differs from bounded anti-gradient because
components of GI(x) are zeroed independently of sign(g[i]), and
anti-gradient's components are zeroed with respect to both constraint and
sign.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
private static double asaginorm(minasastate state)
{
double result = 0;
int i = 0;
result = 0;
for(i=0; i<=state.n-1; i++)
{
if( (double)(state.x[i])!=(double)(state.bndl[i]) && (double)(state.x[i])!=(double)(state.bndu[i]) )
{
result = result+math.sqr(state.g[i]);
}
}
result = Math.Sqrt(result);
return result;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetalgorithm(minasastate state,
int algotype)
{
alglib.ap.assert(algotype>=-1 && algotype<=1, "MinASASetAlgorithm: incorrect AlgoType!");
if( algotype==-1 )
{
algotype = 1;
}
state.cgtype = algotype;
}
/*************************************************************************
Returns norm(D1(State.X))
For a meaning of D1 see 'NEW ACTIVE SET ALGORITHM FOR BOX CONSTRAINED
OPTIMIZATION' by WILLIAM W. HAGER AND HONGCHAO ZHANG.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
private static double asad1norm(minasastate state)
{
double result = 0;
int i = 0;
result = 0;
for(i=0; i<=state.n-1; i++)
{
result = result+math.sqr(apserv.boundval(state.x[i]-state.g[i], state.bndl[i], state.bndu[i])-state.x[i]);
}
result = Math.Sqrt(result);
return result;
}
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
public static void minasasetstpmax(minasastate state,
double stpmax)
{
alglib.ap.assert(math.isfinite(stpmax), "MinASASetStpMax: StpMax is not finite!");
alglib.ap.assert((double)(stpmax)>=(double)(0), "MinASASetStpMax: StpMax<0!");
state.stpmax = stpmax;
}
/*************************************************************************
Clears request fileds (to be sure that we don't forgot to clear something)
*************************************************************************/
private static void clearrequestfields(minasastate state)
{
state.needfg = false;
state.xupdated = false;
}
/*************************************************************************
Returns True, if optimizer "want to unstick" from one of the active
constraints, i.e. there is such active constraint with index I that either
lower bound is active and g[i]<0, or upper bound is active and g[i]>0.
State.X is used as current point, State.X - as gradient.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
private static bool asawanttounstick(ref minasastate state)
{
bool result = new bool();
int i = 0;
result = false;
for(i=0; i<=state.n-1; i++)
{
if( (double)(state.x[i])==(double)(state.bndl[i]) & (double)(state.g[i])<(double)(0) )
{
result = true;
}
if( (double)(state.x[i])==(double)(state.bndu[i]) & (double)(state.g[i])>(double)(0) )
{
result = true;
}
if( result )
{
return result;
}
}
return result;
}