private double[] Compute(OptMultivariateFunction function, OptMultivariateGradient gradient, double tolerance, double factr, ref int nMax)
{
double f = 0;
BFGSTask TASK = BFGSTask.START;
BFGSTask Csave = BFGSTask.START;
int iprint = 0;
bool Continue = true;
int funcEvaluations = 0;
while (Continue)
{
this._SETULB.Run(this._NumFreeVariables, this.M, ref this._FreeVariables, 0, this._LowerBounds, 0, this._UpperBounds, 0,
this._NBD, 0, ref f, ref this._GradientArray, 0, factr, tolerance, ref WA, 0, ref IWA, 0, ref TASK, iprint, ref Csave,
ref LSAVE, 0, ref this.ISAVE, 0, ref DSAVE, 0);
if (funcEvaluations <= nMax)
{
if (TASK == BFGSTask.FG || TASK == BFGSTask.FG_LNSRCH || TASK == BFGSTask.FG_ST || TASK == BFGSTask.FG_START)
{
// c the minimization routine has returned to request the
// c function f and gradient g values at the current x.
// c Compute function value f for the sample problem.
this.UpdateExternalVariables();
funcEvaluations++;
f = function(this._ExternalVariables);
this._ExternalGradientArray = gradient(this._ExternalVariables);
this.UpdateInternalGradient();
// c go back to the minimization routine.
Continue = true;
}
else if (TASK == BFGSTask.NEW_X)
{
Continue = true;
}
else
{
Continue = false;
}
}
else
{
Continue = false;
}
}
this.UpdateExternalVariables();
nMax = funcEvaluations;
return(this._ExternalVariables);
}
public void Run(int N, int M, double FACTR, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref BFGSTask TASK, ref int INFO, ref int K)
{
#region Variables
int I = 0;
#endregion
#region Array Index Correction
int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
#endregion
#region Prolog
// c ************
// c
// c Subroutine errclb
// c
// c This subroutine checks the validity of the input data.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
// c Check the input arguments for errors.
#endregion
#region Body
if (N <= 0) TASK = BFGSTask.ERROR;
if (M <= 0) TASK = BFGSTask.ERROR;
if (FACTR < ZERO) TASK = BFGSTask.ERROR;
// c Check the validity of the arrays nbd(i), u(i), and l(i).
for (I = 1; I <= N; I++)
{
if (NBD[I + o_nbd] < 0 || NBD[I + o_nbd] > 3)
{
// c return
//"ERROR: INVALID NBD";
TASK = BFGSTask.ERROR;
INFO = - 6;
K = I;
}
if (NBD[I + o_nbd] == 2)
{
if (L[I + o_l] > U[I + o_u])
{
// c return
//"ERROR: NO FEASIBLE SOLUTION"
TASK = BFGSTask.ERROR;
INFO = - 7;
K = I;
}
}
}
return;
#endregion
}
/// <param name="F">
/// is a double precision variable.
/// On initial entry f is the value of the function at 0.
/// On subsequent entries f is the value of the
/// function at stp.
/// On exit f is the value of the function at stp.
///</param>
/// <param name="G">
/// is a double precision variable.
/// On initial entry g is the derivative of the function at 0.
/// On subsequent entries g is the derivative of the
/// function at stp.
/// On exit g is the derivative of the function at stp.
///
/// stp is a double precision variable.
/// On entry stp is the current estimate of a satisfactory
/// step. On initial entry, a positive initial estimate
/// must be provided.
/// On exit stp is the current estimate of a satisfactory step
/// if task = 'FG'. If task = 'CONV' then stp satisfies
/// the sufficient decrease and curvature condition.
///
/// ftol is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///
/// gtol is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///
/// xtol is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STP">
/// is a double precision variable.
/// On entry stp is the current estimate of a satisfactory
/// step. On initial entry, a positive initial estimate
/// must be provided.
/// On exit stp is the current estimate of a satisfactory step
/// if task = 'FG'. If task = 'CONV' then stp satisfies
/// the sufficient decrease and curvature condition.
///
/// ftol is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///
/// gtol is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///
/// xtol is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="FTOL">
/// is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///</param>
/// <param name="GTOL">
/// is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///</param>
/// <param name="XTOL">
/// is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STPMIN">
/// is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STPMAX">
/// is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="TASK">
/// = 'START'
///</param>
/// <param name="ISAVE">
/// is an integer work array of dimension 2.
///</param>
/// <param name="DSAVE">
/// is a double precision work array of dimension 13.
///</param>
public void Run(double F, double G, ref double STP, double FTOL, double GTOL, double XTOL
, double STPMIN, double STPMAX, ref BFGSTask TASK, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
bool BRACKT = false; int STAGE = 0; double FINIT = 0; double FTEST = 0; double FM = 0; double FX = 0; double FXM = 0;
double FY = 0;double FYM = 0; double GINIT = 0; double GTEST = 0; double GM = 0; double GX = 0; double GXM = 0;
double GY = 0;double GYM = 0; double STX = 0; double STY = 0; double STMIN = 0; double STMAX = 0; double WIDTH = 0;
double WIDTH1 = 0;
#endregion
#region Array Index Correction
int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c **********
// c
// c Subroutine dcsrch
// c
// c This subroutine finds a step that satisfies a sufficient
// c decrease condition and a curvature condition.
// c
// c Each call of the subroutine updates an interval with
// c endpoints stx and sty. The interval is initially chosen
// c so that it contains a minimizer of the modified function
// c
// c psi(stp) = f(stp) - f(0) - ftol*stp*f'(0).
// c
// c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the
// c interval is chosen so that it contains a minimizer of f.
// c
// c The algorithm is designed to find a step that satisfies
// c the sufficient decrease condition
// c
// c f(stp) <= f(0) + ftol*stp*f'(0),
// c
// c and the curvature condition
// c
// c abs(f'(stp)) <= gtol*abs(f'(0)).
// c
// c If ftol is less than gtol and if, for example, the function
// c is bounded below, then there is always a step which satisfies
// c both conditions.
// c
// c If no step can be found that satisfies both conditions, then
// c the algorithm stops with a warning. In this case stp only
// c satisfies the sufficient decrease condition.
// c
// c A typical invocation of dcsrch has the following outline:
// c
// c task = 'START'
// c 10 continue
// c call dcsrch( ... )
// c if (task .eq. 'FG') then
// c Evaluate the function and the gradient at stp
// c goto 10
// c end if
// c
// c NOTE: The user must no alter work arrays between calls.
// c
// c The subroutine statement is
// c
// c subroutine dcsrch(f,g,stp,ftol,gtol,xtol,stpmin,stpmax,
// c task,isave,dsave)
// c where
// c
// c f is a double precision variable.
// c On initial entry f is the value of the function at 0.
// c On subsequent entries f is the value of the
// c function at stp.
// c On exit f is the value of the function at stp.
// c
// c g is a double precision variable.
// c On initial entry g is the derivative of the function at 0.
// c On subsequent entries g is the derivative of the
// c function at stp.
// c On exit g is the derivative of the function at stp.
// c
// c stp is a double precision variable.
// c On entry stp is the current estimate of a satisfactory
// c step. On initial entry, a positive initial estimate
// c must be provided.
// c On exit stp is the current estimate of a satisfactory step
// c if task = 'FG'. If task = 'CONV' then stp satisfies
// c the sufficient decrease and curvature condition.
// c
// c ftol is a double precision variable.
// c On entry ftol specifies a nonnegative tolerance for the
// c sufficient decrease condition.
// c On exit ftol is unchanged.
// c
// c gtol is a double precision variable.
// c On entry gtol specifies a nonnegative tolerance for the
// c curvature condition.
// c On exit gtol is unchanged.
// c
// c xtol is a double precision variable.
// c On entry xtol specifies a nonnegative relative tolerance
// c for an acceptable step. The subroutine exits with a
// c warning if the relative difference between sty and stx
// c is less than xtol.
// c On exit xtol is unchanged.
// c
// c stpmin is a double precision variable.
// c On entry stpmin is a nonnegative lower bound for the step.
// c On exit stpmin is unchanged.
// c
// c stpmax is a double precision variable.
// c On entry stpmax is a nonnegative upper bound for the step.
// c On exit stpmax is unchanged.
// c
// c task is a character variable of length at least 60.
// c On initial entry task must be set to 'START'.
// c On exit task indicates the required action:
// c
// c If task(1:2) = 'FG' then evaluate the function and
// c derivative at stp and call dcsrch again.
// c
// c If task(1:4) = 'CONV' then the search is successful.
// c
// c If task(1:4) = 'WARN' then the subroutine is not able
// c to satisfy the convergence conditions. The exit value of
// c stp contains the best point found during the search.
// c
// c If task(1:5) = 'ERROR' then there is an error in the
// c input arguments.
// c
// c On exit with convergence, a warning or an error, the
// c variable task contains additional information.
// c
// c isave is an integer work array of dimension 2.
// c
// c dsave is a double precision work array of dimension 13.
// c
// c Subprograms called
// c
// c MINPACK-2 ... dcstep
// c
// c MINPACK-1 Project. June 1983.
// c Argonne National Laboratory.
// c Jorge J. More' and David J. Thuente.
// c
// c MINPACK-2 Project. October 1993.
// c Argonne National Laboratory and University of Minnesota.
// c Brett M. Averick, Richard G. Carter, and Jorge J. More'.
// c
// c **********
// c Initialization block.
#endregion
#region Body
if (TASK == BFGSTask.START)
{
// c Check the input arguments for errors.
//if (STP < STPMIN) FortranLib.Copy(ref TASK , "ERROR: STP .LT. STPMIN");
//if (STP > STPMAX) FortranLib.Copy(ref TASK , "ERROR: STP .GT. STPMAX");
//if (G >= ZERO) FortranLib.Copy(ref TASK , "ERROR: INITIAL G .GE. ZERO");
//if (FTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: FTOL .LT. ZERO");
//if (GTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: GTOL .LT. ZERO");
//if (XTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: XTOL .LT. ZERO");
//if (STPMIN < ZERO) FortranLib.Copy(ref TASK , "ERROR: STPMIN .LT. ZERO");
//if (STPMAX < STPMIN) FortranLib.Copy(ref TASK , "ERROR: STPMAX .LT. STPMIN");
if (STP < STPMIN)
{
TASK = BFGSTask.ERROR;;
}
if (STP > STPMAX)
{
TASK = BFGSTask.ERROR;
}
if (G >= ZERO)
{
TASK = BFGSTask.ERROR;
}
if (FTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (GTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (XTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (STPMIN < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (STPMAX < STPMIN)
{
TASK = BFGSTask.ERROR;
}
// c Exit if there are errors on input.
if (TASK == BFGSTask.ERROR) return;
// c Initialize local variables.
BRACKT = false;
STAGE = 1;
FINIT = F;
GINIT = G;
GTEST = FTOL * GINIT;
WIDTH = STPMAX - STPMIN;
WIDTH1 = WIDTH / P5;
// c The variables stx, fx, gx contain the values of the step,
// c function, and derivative at the best step.
// c The variables sty, fy, gy contain the value of the step,
// c function, and derivative at sty.
// c The variables stp, f, g contain the values of the step,
// c function, and derivative at stp.
STX = ZERO;
FX = FINIT;
GX = GINIT;
STY = ZERO;
FY = FINIT;
GY = GINIT;
STMIN = ZERO;
STMAX = STP + XTRAPU * STP;
TASK = BFGSTask.FG;
goto LABEL1000;
}
else
{
// c Restore local variables.
if (ISAVE[1 + o_isave] == 1)
{
BRACKT = true;
}
else
{
BRACKT = false;
}
STAGE = ISAVE[2 + o_isave];
GINIT = DSAVE[1 + o_dsave];
GTEST = DSAVE[2 + o_dsave];
GX = DSAVE[3 + o_dsave];
GY = DSAVE[4 + o_dsave];
FINIT = DSAVE[5 + o_dsave];
FX = DSAVE[6 + o_dsave];
FY = DSAVE[7 + o_dsave];
STX = DSAVE[8 + o_dsave];
STY = DSAVE[9 + o_dsave];
STMIN = DSAVE[10 + o_dsave];
STMAX = DSAVE[11 + o_dsave];
WIDTH = DSAVE[12 + o_dsave];
WIDTH1 = DSAVE[13 + o_dsave];
}
// c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the
// c algorithm enters the second stage.
FTEST = FINIT + STP * GTEST;
if (STAGE == 1 && F <= FTEST && G >= ZERO) STAGE = 2;
// c Test for warnings.
//if (BRACKT && (STP <= STMIN || STP >= STMAX)) FortranLib.Copy(ref TASK , "WARNING: ROUNDING ERRORS PREVENT PROGRESS");
//if (BRACKT && STMAX - STMIN <= XTOL * STMAX) FortranLib.Copy(ref TASK , "WARNING: XTOL TEST SATISFIED");
//if (STP == STPMAX && F <= FTEST && G <= GTEST) FortranLib.Copy(ref TASK , "WARNING: STP = STPMAX");
//if (STP == STPMIN && (F > FTEST || G >= GTEST)) FortranLib.Copy(ref TASK , "WARNING: STP = STPMIN");
if (BRACKT && (STP <= STMIN || STP >= STMAX))
{
TASK = BFGSTask.WARNING;
}
if (BRACKT && STMAX - STMIN <= XTOL * STMAX)
{
TASK = BFGSTask.WARNING;
}
if (STP == STPMAX && F <= FTEST && G <= GTEST)
{
TASK = BFGSTask.WARNING;
}
if (STP == STPMIN && (F > FTEST || G >= GTEST))
{
TASK = BFGSTask.WARNING;
}
// c Test for convergence.
if (F <= FTEST && Math.Abs(G) <= GTOL * (-GINIT)) TASK = BFGSTask.CONV;
// c Test for termination.
if (TASK == BFGSTask.WARNING || TASK == BFGSTask.CONV) goto LABEL1000;
// c A modified function is used to predict the step during the
// c first stage if a lower function value has been obtained but
// c the decrease is not sufficient.
if (STAGE == 1 && F <= FX && F > FTEST)
{
// c Define the modified function and derivative values.
FM = F - STP * GTEST;
FXM = FX - STX * GTEST;
FYM = FY - STY * GTEST;
GM = G - GTEST;
GXM = GX - GTEST;
GYM = GY - GTEST;
// c Call dcstep to update stx, sty, and to compute the new step.
this._dcstep.Run(ref STX, ref FXM, ref GXM, ref STY, ref FYM, ref GYM
, ref STP, FM, GM, ref BRACKT, STMIN, STMAX);
// c Reset the function and derivative values for f.
FX = FXM + STX * GTEST;
FY = FYM + STY * GTEST;
GX = GXM + GTEST;
GY = GYM + GTEST;
}
else
{
// c Call dcstep to update stx, sty, and to compute the new step.
this._dcstep.Run(ref STX, ref FX, ref GX, ref STY, ref FY, ref GY
, ref STP, F, G, ref BRACKT, STMIN, STMAX);
}
// c Decide if a bisection step is needed.
if (BRACKT)
{
if (Math.Abs(STY - STX) >= P66 * WIDTH1) STP = STX + P5 * (STY - STX);
WIDTH1 = WIDTH;
WIDTH = Math.Abs(STY - STX);
}
// c Set the minimum and maximum steps allowed for stp.
if (BRACKT)
{
STMIN = Math.Min(STX, STY);
STMAX = Math.Max(STX, STY);
}
else
{
STMIN = STP + XTRAPL * (STP - STX);
STMAX = STP + XTRAPU * (STP - STX);
}
// c Force the step to be within the bounds stpmax and stpmin.
STP = Math.Max(STP, STPMIN);
STP = Math.Min(STP, STPMAX);
// c If further progress is not possible, let stp be the best
// c point obtained during the search.
if (BRACKT && (STP <= STMIN || STP >= STMAX) || (BRACKT && STMAX - STMIN <= XTOL * STMAX)) STP = STX;
// c Obtain another function and derivative.
TASK = BFGSTask.FG;
LABEL1000:;
// c Save local variables.
if (BRACKT)
{
ISAVE[1 + o_isave] = 1;
}
else
{
ISAVE[1 + o_isave] = 0;
}
ISAVE[2 + o_isave] = STAGE;
DSAVE[1 + o_dsave] = GINIT;
DSAVE[2 + o_dsave] = GTEST;
DSAVE[3 + o_dsave] = GX;
DSAVE[4 + o_dsave] = GY;
DSAVE[5 + o_dsave] = FINIT;
DSAVE[6 + o_dsave] = FX;
DSAVE[7 + o_dsave] = FY;
DSAVE[8 + o_dsave] = STX;
DSAVE[9 + o_dsave] = STY;
DSAVE[10 + o_dsave] = STMIN;
DSAVE[11 + o_dsave] = STMAX;
DSAVE[12 + o_dsave] = WIDTH;
DSAVE[13 + o_dsave] = WIDTH1;
#endregion
}
public void Run(int N, int M, double FACTR, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref BFGSTask TASK, ref int INFO, ref int K)
{
#region Variables
int I = 0;
#endregion
#region Array Index Correction
int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
#endregion
#region Prolog
// c ************
// c
// c Subroutine errclb
// c
// c This subroutine checks the validity of the input data.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
// c Check the input arguments for errors.
#endregion
#region Body
if (N <= 0)
{
TASK = BFGSTask.ERROR;
}
if (M <= 0)
{
TASK = BFGSTask.ERROR;
}
if (FACTR < ZERO)
{
TASK = BFGSTask.ERROR;
}
// c Check the validity of the arrays nbd(i), u(i), and l(i).
for (I = 1; I <= N; I++)
{
if (NBD[I + o_nbd] < 0 || NBD[I + o_nbd] > 3)
{
// c return
//"ERROR: INVALID NBD";
TASK = BFGSTask.ERROR;
INFO = -6;
K = I;
}
if (NBD[I + o_nbd] == 2)
{
if (L[I + o_l] > U[I + o_u])
{
// c return
//"ERROR: NO FEASIBLE SOLUTION"
TASK = BFGSTask.ERROR;
INFO = -7;
K = I;
}
}
}
return;
#endregion
}
/// <param name="F">
/// is a double precision variable.
/// On initial entry f is the value of the function at 0.
/// On subsequent entries f is the value of the
/// function at stp.
/// On exit f is the value of the function at stp.
///</param>
/// <param name="G">
/// is a double precision variable.
/// On initial entry g is the derivative of the function at 0.
/// On subsequent entries g is the derivative of the
/// function at stp.
/// On exit g is the derivative of the function at stp.
///
/// stp is a double precision variable.
/// On entry stp is the current estimate of a satisfactory
/// step. On initial entry, a positive initial estimate
/// must be provided.
/// On exit stp is the current estimate of a satisfactory step
/// if task = 'FG'. If task = 'CONV' then stp satisfies
/// the sufficient decrease and curvature condition.
///
/// ftol is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///
/// gtol is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///
/// xtol is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STP">
/// is a double precision variable.
/// On entry stp is the current estimate of a satisfactory
/// step. On initial entry, a positive initial estimate
/// must be provided.
/// On exit stp is the current estimate of a satisfactory step
/// if task = 'FG'. If task = 'CONV' then stp satisfies
/// the sufficient decrease and curvature condition.
///
/// ftol is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///
/// gtol is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///
/// xtol is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="FTOL">
/// is a double precision variable.
/// On entry ftol specifies a nonnegative tolerance for the
/// sufficient decrease condition.
/// On exit ftol is unchanged.
///</param>
/// <param name="GTOL">
/// is a double precision variable.
/// On entry gtol specifies a nonnegative tolerance for the
/// curvature condition.
/// On exit gtol is unchanged.
///</param>
/// <param name="XTOL">
/// is a double precision variable.
/// On entry xtol specifies a nonnegative relative tolerance
/// for an acceptable step. The subroutine exits with a
/// warning if the relative difference between sty and stx
/// is less than xtol.
/// On exit xtol is unchanged.
///
/// stpmin is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STPMIN">
/// is a double precision variable.
/// On entry stpmin is a nonnegative lower bound for the step.
/// On exit stpmin is unchanged.
///
/// stpmax is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="STPMAX">
/// is a double precision variable.
/// On entry stpmax is a nonnegative upper bound for the step.
/// On exit stpmax is unchanged.
///
/// task is a character variable of length at least 60.
/// On initial entry task must be set to 'START'.
/// On exit task indicates the required action:
///
/// If task(1:2) = 'FG' then evaluate the function and
/// derivative at stp and call dcsrch again.
///
/// If task(1:4) = 'CONV' then the search is successful.
///
/// If task(1:4) = 'WARN' then the subroutine is not able
/// to satisfy the convergence conditions. The exit value of
/// stp contains the best point found during the search.
///
/// If task(1:5) = 'ERROR' then there is an error in the
/// input arguments.
///
/// On exit with convergence, a warning or an error, the
/// variable task contains additional information.
///
/// isave is an integer work array of dimension 2.
///
/// dsave is a double precision work array of dimension 13.
///
/// Subprograms called
///
/// MINPACK-2 ... dcstep
///
/// MINPACK-1 Project. June 1983.
/// Argonne National Laboratory.
/// Jorge J. More' and David J. Thuente.
///
/// MINPACK-2 Project. October 1993.
/// Argonne National Laboratory and University of Minnesota.
/// Brett M. Averick, Richard G. Carter, and Jorge J. More'.
///
/// **********
///
///
///
///
/// Initialization block.
///</param>
/// <param name="TASK">
/// = 'START'
///</param>
/// <param name="ISAVE">
/// is an integer work array of dimension 2.
///</param>
/// <param name="DSAVE">
/// is a double precision work array of dimension 13.
///</param>
public void Run(double F, double G, ref double STP, double FTOL, double GTOL, double XTOL
, double STPMIN, double STPMAX, ref BFGSTask TASK, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
bool BRACKT = false; int STAGE = 0; double FINIT = 0; double FTEST = 0; double FM = 0; double FX = 0; double FXM = 0;
double FY = 0; double FYM = 0; double GINIT = 0; double GTEST = 0; double GM = 0; double GX = 0; double GXM = 0;
double GY = 0; double GYM = 0; double STX = 0; double STY = 0; double STMIN = 0; double STMAX = 0; double WIDTH = 0;
double WIDTH1 = 0;
#endregion
#region Array Index Correction
int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c **********
// c
// c Subroutine dcsrch
// c
// c This subroutine finds a step that satisfies a sufficient
// c decrease condition and a curvature condition.
// c
// c Each call of the subroutine updates an interval with
// c endpoints stx and sty. The interval is initially chosen
// c so that it contains a minimizer of the modified function
// c
// c psi(stp) = f(stp) - f(0) - ftol*stp*f'(0).
// c
// c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the
// c interval is chosen so that it contains a minimizer of f.
// c
// c The algorithm is designed to find a step that satisfies
// c the sufficient decrease condition
// c
// c f(stp) <= f(0) + ftol*stp*f'(0),
// c
// c and the curvature condition
// c
// c abs(f'(stp)) <= gtol*abs(f'(0)).
// c
// c If ftol is less than gtol and if, for example, the function
// c is bounded below, then there is always a step which satisfies
// c both conditions.
// c
// c If no step can be found that satisfies both conditions, then
// c the algorithm stops with a warning. In this case stp only
// c satisfies the sufficient decrease condition.
// c
// c A typical invocation of dcsrch has the following outline:
// c
// c task = 'START'
// c 10 continue
// c call dcsrch( ... )
// c if (task .eq. 'FG') then
// c Evaluate the function and the gradient at stp
// c goto 10
// c end if
// c
// c NOTE: The user must no alter work arrays between calls.
// c
// c The subroutine statement is
// c
// c subroutine dcsrch(f,g,stp,ftol,gtol,xtol,stpmin,stpmax,
// c task,isave,dsave)
// c where
// c
// c f is a double precision variable.
// c On initial entry f is the value of the function at 0.
// c On subsequent entries f is the value of the
// c function at stp.
// c On exit f is the value of the function at stp.
// c
// c g is a double precision variable.
// c On initial entry g is the derivative of the function at 0.
// c On subsequent entries g is the derivative of the
// c function at stp.
// c On exit g is the derivative of the function at stp.
// c
// c stp is a double precision variable.
// c On entry stp is the current estimate of a satisfactory
// c step. On initial entry, a positive initial estimate
// c must be provided.
// c On exit stp is the current estimate of a satisfactory step
// c if task = 'FG'. If task = 'CONV' then stp satisfies
// c the sufficient decrease and curvature condition.
// c
// c ftol is a double precision variable.
// c On entry ftol specifies a nonnegative tolerance for the
// c sufficient decrease condition.
// c On exit ftol is unchanged.
// c
// c gtol is a double precision variable.
// c On entry gtol specifies a nonnegative tolerance for the
// c curvature condition.
// c On exit gtol is unchanged.
// c
// c xtol is a double precision variable.
// c On entry xtol specifies a nonnegative relative tolerance
// c for an acceptable step. The subroutine exits with a
// c warning if the relative difference between sty and stx
// c is less than xtol.
// c On exit xtol is unchanged.
// c
// c stpmin is a double precision variable.
// c On entry stpmin is a nonnegative lower bound for the step.
// c On exit stpmin is unchanged.
// c
// c stpmax is a double precision variable.
// c On entry stpmax is a nonnegative upper bound for the step.
// c On exit stpmax is unchanged.
// c
// c task is a character variable of length at least 60.
// c On initial entry task must be set to 'START'.
// c On exit task indicates the required action:
// c
// c If task(1:2) = 'FG' then evaluate the function and
// c derivative at stp and call dcsrch again.
// c
// c If task(1:4) = 'CONV' then the search is successful.
// c
// c If task(1:4) = 'WARN' then the subroutine is not able
// c to satisfy the convergence conditions. The exit value of
// c stp contains the best point found during the search.
// c
// c If task(1:5) = 'ERROR' then there is an error in the
// c input arguments.
// c
// c On exit with convergence, a warning or an error, the
// c variable task contains additional information.
// c
// c isave is an integer work array of dimension 2.
// c
// c dsave is a double precision work array of dimension 13.
// c
// c Subprograms called
// c
// c MINPACK-2 ... dcstep
// c
// c MINPACK-1 Project. June 1983.
// c Argonne National Laboratory.
// c Jorge J. More' and David J. Thuente.
// c
// c MINPACK-2 Project. October 1993.
// c Argonne National Laboratory and University of Minnesota.
// c Brett M. Averick, Richard G. Carter, and Jorge J. More'.
// c
// c **********
// c Initialization block.
#endregion
#region Body
if (TASK == BFGSTask.START)
{
// c Check the input arguments for errors.
//if (STP < STPMIN) FortranLib.Copy(ref TASK , "ERROR: STP .LT. STPMIN");
//if (STP > STPMAX) FortranLib.Copy(ref TASK , "ERROR: STP .GT. STPMAX");
//if (G >= ZERO) FortranLib.Copy(ref TASK , "ERROR: INITIAL G .GE. ZERO");
//if (FTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: FTOL .LT. ZERO");
//if (GTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: GTOL .LT. ZERO");
//if (XTOL < ZERO) FortranLib.Copy(ref TASK , "ERROR: XTOL .LT. ZERO");
//if (STPMIN < ZERO) FortranLib.Copy(ref TASK , "ERROR: STPMIN .LT. ZERO");
//if (STPMAX < STPMIN) FortranLib.Copy(ref TASK , "ERROR: STPMAX .LT. STPMIN");
if (STP < STPMIN)
{
TASK = BFGSTask.ERROR;;
}
if (STP > STPMAX)
{
TASK = BFGSTask.ERROR;
}
if (G >= ZERO)
{
TASK = BFGSTask.ERROR;
}
if (FTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (GTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (XTOL < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (STPMIN < ZERO)
{
TASK = BFGSTask.ERROR;
}
if (STPMAX < STPMIN)
{
TASK = BFGSTask.ERROR;
}
// c Exit if there are errors on input.
if (TASK == BFGSTask.ERROR)
{
return;
}
// c Initialize local variables.
BRACKT = false;
STAGE = 1;
FINIT = F;
GINIT = G;
GTEST = FTOL * GINIT;
WIDTH = STPMAX - STPMIN;
WIDTH1 = WIDTH / P5;
// c The variables stx, fx, gx contain the values of the step,
// c function, and derivative at the best step.
// c The variables sty, fy, gy contain the value of the step,
// c function, and derivative at sty.
// c The variables stp, f, g contain the values of the step,
// c function, and derivative at stp.
STX = ZERO;
FX = FINIT;
GX = GINIT;
STY = ZERO;
FY = FINIT;
GY = GINIT;
STMIN = ZERO;
STMAX = STP + XTRAPU * STP;
TASK = BFGSTask.FG;
goto LABEL1000;
}
else
{
// c Restore local variables.
if (ISAVE[1 + o_isave] == 1)
{
BRACKT = true;
}
else
{
BRACKT = false;
}
STAGE = ISAVE[2 + o_isave];
GINIT = DSAVE[1 + o_dsave];
GTEST = DSAVE[2 + o_dsave];
GX = DSAVE[3 + o_dsave];
GY = DSAVE[4 + o_dsave];
FINIT = DSAVE[5 + o_dsave];
FX = DSAVE[6 + o_dsave];
FY = DSAVE[7 + o_dsave];
STX = DSAVE[8 + o_dsave];
STY = DSAVE[9 + o_dsave];
STMIN = DSAVE[10 + o_dsave];
STMAX = DSAVE[11 + o_dsave];
WIDTH = DSAVE[12 + o_dsave];
WIDTH1 = DSAVE[13 + o_dsave];
}
// c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the
// c algorithm enters the second stage.
FTEST = FINIT + STP * GTEST;
if (STAGE == 1 && F <= FTEST && G >= ZERO)
{
STAGE = 2;
}
// c Test for warnings.
//if (BRACKT && (STP <= STMIN || STP >= STMAX)) FortranLib.Copy(ref TASK , "WARNING: ROUNDING ERRORS PREVENT PROGRESS");
//if (BRACKT && STMAX - STMIN <= XTOL * STMAX) FortranLib.Copy(ref TASK , "WARNING: XTOL TEST SATISFIED");
//if (STP == STPMAX && F <= FTEST && G <= GTEST) FortranLib.Copy(ref TASK , "WARNING: STP = STPMAX");
//if (STP == STPMIN && (F > FTEST || G >= GTEST)) FortranLib.Copy(ref TASK , "WARNING: STP = STPMIN");
if (BRACKT && (STP <= STMIN || STP >= STMAX))
{
TASK = BFGSTask.WARNING;
}
if (BRACKT && STMAX - STMIN <= XTOL * STMAX)
{
TASK = BFGSTask.WARNING;
}
if (STP == STPMAX && F <= FTEST && G <= GTEST)
{
TASK = BFGSTask.WARNING;
}
if (STP == STPMIN && (F > FTEST || G >= GTEST))
{
TASK = BFGSTask.WARNING;
}
// c Test for convergence.
if (F <= FTEST && Math.Abs(G) <= GTOL * (-GINIT))
{
TASK = BFGSTask.CONV;
}
// c Test for termination.
if (TASK == BFGSTask.WARNING || TASK == BFGSTask.CONV)
{
goto LABEL1000;
}
// c A modified function is used to predict the step during the
// c first stage if a lower function value has been obtained but
// c the decrease is not sufficient.
if (STAGE == 1 && F <= FX && F > FTEST)
{
// c Define the modified function and derivative values.
FM = F - STP * GTEST;
FXM = FX - STX * GTEST;
FYM = FY - STY * GTEST;
GM = G - GTEST;
GXM = GX - GTEST;
GYM = GY - GTEST;
// c Call dcstep to update stx, sty, and to compute the new step.
this._dcstep.Run(ref STX, ref FXM, ref GXM, ref STY, ref FYM, ref GYM
, ref STP, FM, GM, ref BRACKT, STMIN, STMAX);
// c Reset the function and derivative values for f.
FX = FXM + STX * GTEST;
FY = FYM + STY * GTEST;
GX = GXM + GTEST;
GY = GYM + GTEST;
}
else
{
// c Call dcstep to update stx, sty, and to compute the new step.
this._dcstep.Run(ref STX, ref FX, ref GX, ref STY, ref FY, ref GY
, ref STP, F, G, ref BRACKT, STMIN, STMAX);
}
// c Decide if a bisection step is needed.
if (BRACKT)
{
if (Math.Abs(STY - STX) >= P66 * WIDTH1)
{
STP = STX + P5 * (STY - STX);
}
WIDTH1 = WIDTH;
WIDTH = Math.Abs(STY - STX);
}
// c Set the minimum and maximum steps allowed for stp.
if (BRACKT)
{
STMIN = Math.Min(STX, STY);
STMAX = Math.Max(STX, STY);
}
else
{
STMIN = STP + XTRAPL * (STP - STX);
STMAX = STP + XTRAPU * (STP - STX);
}
// c Force the step to be within the bounds stpmax and stpmin.
STP = Math.Max(STP, STPMIN);
STP = Math.Min(STP, STPMAX);
// c If further progress is not possible, let stp be the best
// c point obtained during the search.
if (BRACKT && (STP <= STMIN || STP >= STMAX) || (BRACKT && STMAX - STMIN <= XTOL * STMAX))
{
STP = STX;
}
// c Obtain another function and derivative.
TASK = BFGSTask.FG;
LABEL1000 :;
// c Save local variables.
if (BRACKT)
{
ISAVE[1 + o_isave] = 1;
}
else
{
ISAVE[1 + o_isave] = 0;
}
ISAVE[2 + o_isave] = STAGE;
DSAVE[1 + o_dsave] = GINIT;
DSAVE[2 + o_dsave] = GTEST;
DSAVE[3 + o_dsave] = GX;
DSAVE[4 + o_dsave] = GY;
DSAVE[5 + o_dsave] = FINIT;
DSAVE[6 + o_dsave] = FX;
DSAVE[7 + o_dsave] = FY;
DSAVE[8 + o_dsave] = STX;
DSAVE[9 + o_dsave] = STY;
DSAVE[10 + o_dsave] = STMIN;
DSAVE[11 + o_dsave] = STMAX;
DSAVE[12 + o_dsave] = WIDTH;
DSAVE[13 + o_dsave] = WIDTH1;
#endregion
}
public void Run(int N, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd, ref double[] X, int offset_x, double F
, ref double FOLD, ref double GD, ref double GDOLD, double[] G, int offset_g, double[] D, int offset_d, ref double[] R, int offset_r
, ref double[] T, int offset_t, double[] Z, int offset_z, ref double STP, ref double DNORM, ref double DTD, ref double XSTEP
, ref double STPMX, int ITER, ref int IFUN, ref int IBACK, ref int NFGV, ref int INFO
, ref BFGSTask TASK, bool BOXED, bool CNSTND, ref BFGSTask CSAVE, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
int I = 0; double DDOT = 0; double A1 = 0; double A2 = 0;
#endregion
#region Array Index Correction
int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd; int o_x = -1 + offset_x;
int o_g = -1 + offset_g; int o_d = -1 + offset_d; int o_r = -1 + offset_r; int o_t = -1 + offset_t;
int o_z = -1 + offset_z; int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c **********
// c
// c Subroutine lnsrlb
// c
// c This subroutine calls subroutine dcsrch from the Minpack2 library
// c to perform the line search. Subroutine dscrch is safeguarded so
// c that all trial points lie within the feasible region.
// c
// c Subprograms called:
// c
// c Minpack2 Library ... dcsrch.
// c
// c Linpack ... dtrsl, ddot.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c **********
#endregion
#region Body
if (TASK == BFGSTask.FG_LNSRCH) goto LABEL556;
DTD = this._ddot.Run(N, D, offset_d, 1, D, offset_d, 1);
DNORM = Math.Sqrt(DTD);
// c Determine the maximum step length.
STPMX = BIG;
if (CNSTND)
{
if (ITER == 0)
{
STPMX = ONE;
}
else
{
for (I = 1; I <= N; I++)
{
A1 = D[I + o_d];
if (NBD[I + o_nbd] != 0)
{
if (A1 < ZERO && NBD[I + o_nbd] <= 2)
{
A2 = L[I + o_l] - X[I + o_x];
if (A2 >= ZERO)
{
STPMX = ZERO;
}
else
{
if (A1 * STPMX < A2)
{
STPMX = A2 / A1;
}
}
}
else
{
if (A1 > ZERO && NBD[I + o_nbd] >= 2)
{
A2 = U[I + o_u] - X[I + o_x];
if (A2 <= ZERO)
{
STPMX = ZERO;
}
else
{
if (A1 * STPMX > A2)
{
STPMX = A2 / A1;
}
}
}
}
}
}
}
}
if (ITER == 0 && !BOXED)
{
STP = Math.Min(ONE / DNORM, STPMX);
}
else
{
STP = ONE;
}
this._dcopy.Run(N, X, offset_x, 1, ref T, offset_t, 1);
this._dcopy.Run(N, G, offset_g, 1, ref R, offset_r, 1);
FOLD = F;
IFUN = 0;
IBACK = 0;
CSAVE = BFGSTask.START;
LABEL556:;
GD = this._ddot.Run(N, G, offset_g, 1, D, offset_d, 1);
if (IFUN == 0)
{
GDOLD = GD;
if (GD >= ZERO)
{
// c the directional derivative >=0.
// c Line search is impossible.
INFO = - 4;
return;
}
}
this._dcsrch.Run(F, GD, ref STP, FTOL, GTOL, XTOL
, ZERO, STPMX, ref CSAVE, ref ISAVE, offset_isave, ref DSAVE, offset_dsave);
XSTEP = STP * DNORM;
if (CSAVE != BFGSTask.CONV && CSAVE != BFGSTask.WARNING)
{
TASK = BFGSTask.FG_LNSRCH;
IFUN += 1;
NFGV += 1;
IBACK = IFUN - 1;
if (STP == ONE)
{
this._dcopy.Run(N, Z, offset_z, 1, ref X, offset_x, 1);
}
else
{
for (I = 1; I <= N; I++)
{
X[I + o_x] = STP * D[I + o_d] + T[I + o_t];
}
}
}
else
{
TASK = BFGSTask.NEW_X;
}
return;
#endregion
}
public void Run(int N, double[] X, int offset_x, double F, BFGSTask TASK, int IPRINT, int INFO
, int ITFILE, int ITER, int NFGV, int NINTOL, int NSKIP, int NACT
, double SBGNRM, double TIME, int NINT, BFGSWord WORD, int IBACK, double STP
, double XSTEP, int K, double CACHYT, double SBTIME, double LNSCHT)
{
#region Variables
int I = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x;
#endregion
#region Prolog
// c ************
// c
// c Subroutine prn3lb
// c
// c This subroutine prints out information when either a built-in
// c convergence test is satisfied or when an error message is
// c generated.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.ERROR)
{
goto LABEL999;
}
if (IPRINT >= 0)
{
//ERROR-ERROR WRITE (6,3003);
//ERROR-ERROR WRITE (6,3004);
//ERROR-ERROR WRITE(6,3005) N,ITER,NFGV,NINTOL,NSKIP,NACT,SBGNRM,F;
if (IPRINT >= 100)
{
//ERROR-ERROR WRITE (6,1004) 'X =',(X(I),I = 1,N);
}
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,*)' F =',F
}
}
LABEL999 :;
if (IPRINT >= 0)
{
//ERROR-ERROR WRITE (6,3009) TASK;
if (INFO != 0)
{
if (INFO == -1)
{
; //ERROR-ERRORWRITE(6,9011)
}
if (INFO == -2)
{
; //ERROR-ERRORWRITE(6,9012)
}
if (INFO == -3)
{
; //ERROR-ERRORWRITE(6,9013)
}
if (INFO == -4)
{
; //ERROR-ERRORWRITE(6,9014)
}
if (INFO == -5)
{
; //ERROR-ERRORWRITE(6,9015)
}
if (INFO == -6)
{
; //ERROR-ERRORWRITE(6,*)' Input nbd(',K,') is invalid.'
}
if (INFO == -7)
{
; //ERROR-ERRORWRITE(6,*)' l(',K,') > u(',K,'). No feasible solution.'
}
if (INFO == -8)
{
; //ERROR-ERRORWRITE(6,9018)
}
if (INFO == -9)
{
; //ERROR-ERRORWRITE(6,9019)
}
}
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,3007)CACHYT,SBTIME,LNSCHT
}
//ERROR-ERROR WRITE (6,3008) TIME;
if (IPRINT >= 1)
{
if (INFO == -4 || INFO == -9)
{
//ERROR-ERROR WRITE (ITFILE,3002)ITER,NFGV,NINT,NACT,WORD,IBACK,STP,XSTEP;
}
//ERROR-ERROR WRITE (ITFILE,3009) TASK;
if (INFO != 0)
{
if (INFO == -1)
{
; //ERROR-ERRORWRITE(ITFILE,9011)
}
if (INFO == -2)
{
; //ERROR-ERRORWRITE(ITFILE,9012)
}
if (INFO == -3)
{
; //ERROR-ERRORWRITE(ITFILE,9013)
}
if (INFO == -4)
{
; //ERROR-ERRORWRITE(ITFILE,9014)
}
if (INFO == -5)
{
; //ERROR-ERRORWRITE(ITFILE,9015)
}
if (INFO == -8)
{
; //ERROR-ERRORWRITE(ITFILE,9018)
}
if (INFO == -9)
{
; //ERROR-ERRORWRITE(ITFILE,9019)
}
}
//ERROR-ERROR WRITE (ITFILE,3008) TIME;
}
}
return;
#endregion
}
/// <param name="N">
/// is an integer variable.
/// On entry n is the number of variables.
/// On exit n is unchanged.
///</param>
/// <param name="M">
/// is an integer variable.
/// On entry m is the maximum number of variable metric
/// corrections allowed in the limited memory matrix.
/// On exit m is unchanged.
///</param>
/// <param name="X">
/// is a double precision array of dimension n.
/// On entry x is an approximation to the solution.
/// On exit x is the current approximation.
///</param>
/// <param name="L">
/// is a double precision array of dimension n.
/// On entry l is the lower bound of x.
/// On exit l is unchanged.
///</param>
/// <param name="U">
/// is a double precision array of dimension n.
/// On entry u is the upper bound of x.
/// On exit u is unchanged.
///</param>
/// <param name="NBD">
/// is an integer array of dimension n.
/// On entry nbd represents the type of bounds imposed on the
/// variables, and must be specified as follows:
/// nbd(i)=0 if x(i) is unbounded,
/// 1 if x(i) has only a lower bound,
/// 2 if x(i) has both lower and upper bounds,
/// 3 if x(i) has only an upper bound.
/// On exit nbd is unchanged.
///</param>
/// <param name="F">
/// is a double precision variable.
/// On first entry f is unspecified.
/// On final exit f is the value of the function at x.
///</param>
/// <param name="G">
/// is a double precision array of dimension n.
/// On first entry g is unspecified.
/// On final exit g is the value of the gradient at x.
///</param>
/// <param name="FACTR">
/// is a double precision variable.
/// On entry factr .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} .LE. factr*epsmch
///
/// where epsmch is the machine precision, which is automatically
/// generated by the code.
/// On exit factr is unchanged.
///</param>
/// <param name="PGTOL">
/// is a double precision variable.
/// On entry pgtol .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// max{|proj g_i | i = 1, ..., n} .LE. pgtol
///
/// where pg_i is the ith component of the projected gradient.
/// On exit pgtol is unchanged.
///</param>
/// <param name="WN">
/// is a double precision working array of dimension 2m x 2m
/// used to store the LEL^T factorization of the indefinite matrix
/// K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
/// [L_a -R_z theta*S'AA'S ]
///
/// where E = [-I 0]
/// [ 0 I]
///</param>
/// <param name="SND">
/// is a double precision working array of dimension 2m x 2m
/// used to store the lower triangular part of
/// N = [Y' ZZ'Y L_a'+R_z']
/// [L_a +R_z S'AA'S ]
///</param>
/// <param name="Z">
/// is used at different times to store the Cauchy point and
///</param>
/// <param name="INDEX">
/// is an integer working array of dimension n.
/// In subroutine freev, index is used to store the free and fixed
/// variables at the Generalized Cauchy Point (GCP).
///</param>
/// <param name="IWHERE">
/// is an integer working array of dimension n used to record
/// the status of the vector x for GCP computation.
/// iwhere(i)=0 or -3 if x(i) is free and has bounds,
/// 1 if x(i) is fixed at l(i), and l(i) .ne. u(i)
/// 2 if x(i) is fixed at u(i), and u(i) .ne. l(i)
/// 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i)
/// -1 if x(i) is always free, i.e., no bounds on it.
///</param>
/// <param name="INDX2">
/// is an integer working array of dimension n.
/// Within subroutine cauchy, indx2 corresponds to the array iorder.
/// In subroutine freev, a list of variables entering and leaving
/// the free set is stored in indx2, and it is passed on to
/// subroutine formk with this information.
///</param>
/// <param name="TASK">
/// is a working string of characters of length 60 indicating
/// the current job when entering and leaving this subroutine.
///</param>
/// <param name="IPRINT">
/// is an INTEGER variable that must be set by the user.
/// It controls the frequency and type of output generated:
/// iprint.LT.0 no output is generated;
/// iprint=0 print only one line at the last iteration;
/// 0.LT.iprint.LT.99 print also f and |proj g| every iprint iterations;
/// iprint=99 print details of every iteration except n-vectors;
/// iprint=100 print also the changes of active set and final x;
/// iprint.GT.100 print details of every iteration including x and g;
/// When iprint .GT. 0, the file iterate.dat will be created to
/// summarize the iteration.
///</param>
/// <param name="CSAVE">
/// is a working string of characters of length 60.
///</param>
/// <param name="LSAVE">
/// is a logical working array of dimension 4.
///</param>
/// <param name="ISAVE">
/// is an integer working array of dimension 23.
///</param>
/// <param name="DSAVE">
/// is a double precision working array of dimension 29.
///
///</param>
public void Run(int N, int M, ref double[] X, int offset_x, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref double F, ref double[] G, int offset_g, double FACTR, double PGTOL, ref double[] WS, int offset_ws, ref double[] WY, int offset_wy
, ref double[] SY, int offset_sy, ref double[] SS, int offset_ss, double[] YY, int offset_yy, ref double[] WT, int offset_wt, ref double[] WN, int offset_wn, ref double[] SND, int offset_snd
, ref double[] Z, int offset_z, ref double[] R, int offset_r, ref double[] D, int offset_d, ref double[] T, int offset_t, ref double[] WA, int offset_wa, double[] SG, int offset_sg
, double[] SGO, int offset_sgo, double[] YG, int offset_yg, double[] YGO, int offset_ygo, ref int[] INDEX, int offset_index, ref int[] IWHERE, int offset_iwhere, ref int[] INDX2, int offset_indx2
, ref BFGSTask TASK, int IPRINT, ref BFGSTask CSAVE, ref bool[] LSAVE, int offset_lsave, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
BFGSWord WORD = BFGSWord.aaa;
bool PRJCTD = false; bool CNSTND = false; bool BOXED = false; bool UPDATD = false; bool WRK = false;
int I = 0; int K = 0; int NINTOL = 0; int ITFILE = 0; int IBACK = 0; int NSKIP = 0;
int HEAD = 0;int COL = 0; int ITER = 0; int ITAIL = 0; int IUPDAT = 0; int NINT = 0; int NFGV = 0; int INFO = 0;
int IFUN = 0;int IWORD = 0; int NFREE = 0; int NACT = 0; int ILEAVE = 0; int NENTER = 0; double THETA = 0;
double FOLD = 0;double DDOT = 0; double DR = 0; double RR = 0; double TOL = 0; double DPMEPS = 0; double XSTEP = 0;
double SBGNRM = 0;double DDUM = 0; double DNORM = 0; double DTD = 0; double EPSMCH = 0; double CPU1 = 0;
double CPU2 = 0;double CACHYT = 0; double SBTIME = 0; double LNSCHT = 0; double TIME1 = 0; double TIME2 = 0;
double GD = 0;double GDOLD = 0; double STP = 0; double STPMX = 0; double TIME = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x; int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
int o_g = -1 + offset_g; int o_ws = -1 - N + offset_ws; int o_wy = -1 - N + offset_wy;
int o_sy = -1 - M + offset_sy; int o_ss = -1 - M + offset_ss; int o_yy = -1 - M + offset_yy;
int o_wt = -1 - M + offset_wt; int o_wn = -1 - (2*M) + offset_wn; int o_snd = -1 - (2*M) + offset_snd;
int o_z = -1 + offset_z; int o_r = -1 + offset_r; int o_d = -1 + offset_d; int o_t = -1 + offset_t;
int o_wa = -1 + offset_wa; int o_sg = -1 + offset_sg; int o_sgo = -1 + offset_sgo; int o_yg = -1 + offset_yg;
int o_ygo = -1 + offset_ygo; int o_index = -1 + offset_index; int o_iwhere = -1 + offset_iwhere;
int o_indx2 = -1 + offset_indx2; int o_lsave = -1 + offset_lsave; int o_isave = -1 + offset_isave;
int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c ************
// c
// c Subroutine mainlb
// c
// c This subroutine solves bound constrained optimization problems by
// c using the compact formula of the limited memory BFGS updates.
// c
// c n is an integer variable.
// c On entry n is the number of variables.
// c On exit n is unchanged.
// c
// c m is an integer variable.
// c On entry m is the maximum number of variable metric
// c corrections allowed in the limited memory matrix.
// c On exit m is unchanged.
// c
// c x is a double precision array of dimension n.
// c On entry x is an approximation to the solution.
// c On exit x is the current approximation.
// c
// c l is a double precision array of dimension n.
// c On entry l is the lower bound of x.
// c On exit l is unchanged.
// c
// c u is a double precision array of dimension n.
// c On entry u is the upper bound of x.
// c On exit u is unchanged.
// c
// c nbd is an integer array of dimension n.
// c On entry nbd represents the type of bounds imposed on the
// c variables, and must be specified as follows:
// c nbd(i)=0 if x(i) is unbounded,
// c 1 if x(i) has only a lower bound,
// c 2 if x(i) has both lower and upper bounds,
// c 3 if x(i) has only an upper bound.
// c On exit nbd is unchanged.
// c
// c f is a double precision variable.
// c On first entry f is unspecified.
// c On final exit f is the value of the function at x.
// c
// c g is a double precision array of dimension n.
// c On first entry g is unspecified.
// c On final exit g is the value of the gradient at x.
// c
// c factr is a double precision variable.
// c On entry factr >= 0 is specified by the user. The iteration
// c will stop when
// c
// c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch
// c
// c where epsmch is the machine precision, which is automatically
// c generated by the code.
// c On exit factr is unchanged.
// c
// c pgtol is a double precision variable.
// c On entry pgtol >= 0 is specified by the user. The iteration
// c will stop when
// c
// c max{|proj g_i | i = 1, ..., n} <= pgtol
// c
// c where pg_i is the ith component of the projected gradient.
// c On exit pgtol is unchanged.
// c
// c ws, wy, sy, and wt are double precision working arrays used to
// c store the following information defining the limited memory
// c BFGS matrix:
// c ws, of dimension n x m, stores S, the matrix of s-vectors;
// c wy, of dimension n x m, stores Y, the matrix of y-vectors;
// c sy, of dimension m x m, stores S'Y;
// c ss, of dimension m x m, stores S'S;
// c yy, of dimension m x m, stores Y'Y;
// c wt, of dimension m x m, stores the Cholesky factorization
// c of (theta*S'S+LD^(-1)L'); see eq.
// c (2.26) in [3].
// c
// c wn is a double precision working array of dimension 2m x 2m
// c used to store the LEL^T factorization of the indefinite matrix
// c K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
// c [L_a -R_z theta*S'AA'S ]
// c
// c where E = [-I 0]
// c [ 0 I]
// c
// c snd is a double precision working array of dimension 2m x 2m
// c used to store the lower triangular part of
// c N = [Y' ZZ'Y L_a'+R_z']
// c [L_a +R_z S'AA'S ]
// c
// c z(n),r(n),d(n),t(n),wa(8*m) are double precision working arrays.
// c z is used at different times to store the Cauchy point and
// c the Newton point.
// c
// c sg(m),sgo(m),yg(m),ygo(m) are double precision working arrays.
// c
// c index is an integer working array of dimension n.
// c In subroutine freev, index is used to store the free and fixed
// c variables at the Generalized Cauchy Point (GCP).
// c
// c iwhere is an integer working array of dimension n used to record
// c the status of the vector x for GCP computation.
// c iwhere(i)=0 or -3 if x(i) is free and has bounds,
// c 1 if x(i) is fixed at l(i), and l(i) .ne. u(i)
// c 2 if x(i) is fixed at u(i), and u(i) .ne. l(i)
// c 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i)
// c -1 if x(i) is always free, i.e., no bounds on it.
// c
// c indx2 is an integer working array of dimension n.
// c Within subroutine cauchy, indx2 corresponds to the array iorder.
// c In subroutine freev, a list of variables entering and leaving
// c the free set is stored in indx2, and it is passed on to
// c subroutine formk with this information.
// c
// c task is a working string of characters of length 60 indicating
// c the current job when entering and leaving this subroutine.
// c
// c iprint is an INTEGER variable that must be set by the user.
// c It controls the frequency and type of output generated:
// c iprint<0 no output is generated;
// c iprint=0 print only one line at the last iteration;
// c 0<iprint<99 print also f and |proj g| every iprint iterations;
// c iprint=99 print details of every iteration except n-vectors;
// c iprint=100 print also the changes of active set and final x;
// c iprint>100 print details of every iteration including x and g;
// c When iprint > 0, the file iterate.dat will be created to
// c summarize the iteration.
// c
// c csave is a working string of characters of length 60.
// c
// c lsave is a logical working array of dimension 4.
// c
// c isave is an integer working array of dimension 23.
// c
// c dsave is a double precision working array of dimension 29.
// c
// c
// c Subprograms called
// c
// c L-BFGS-B Library ... cauchy, subsm, lnsrlb, formk,
// c
// c errclb, prn1lb, prn2lb, prn3lb, active, projgr,
// c
// c freev, cmprlb, matupd, formt.
// c
// c Minpack2 Library ... timer, dpmeps.
// c
// c Linpack Library ... dcopy, ddot.
// c
// c
// c References:
// c
// c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited
// c memory algorithm for bound constrained optimization'',
// c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208.
// c
// c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN
// c Subroutines for Large Scale Bound Constrained Optimization''
// c Tech. Report, NAM-11, EECS Department, Northwestern University,
// c 1994.
// c
// c [3] R. Byrd, J. Nocedal and R. Schnabel "Representations of
// c Quasi-Newton Matrices and their use in Limited Memory Methods'',
// c Mathematical Programming 63 (1994), no. 4, pp. 129-156.
// c
// c (Postscript files of these papers are available via anonymous
// c ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.)
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.START)
{
this._timer.Run(ref TIME1);
// c Generate the current machine precision.
EPSMCH = this._dpmeps.Run();
// c Initialize counters and scalars when task='START'.
// c for the limited memory BFGS matrices:
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
// c for operation counts:
ITER = 0;
NFGV = 0;
NINT = 0;
NINTOL = 0;
NSKIP = 0;
NFREE = N;
// c for stopping tolerance:
TOL = FACTR * EPSMCH;
// c for measuring running time:
CACHYT = 0;
SBTIME = 0;
LNSCHT = 0;
// c 'word' records the status of subspace solutions.
WORD = BFGSWord.aaa;
// c 'info' records the termination information.
INFO = 0;
if (IPRINT >= 1)
{
// c open a summary file 'iterate.dat'
//ERROR-ERROR OPEN (8, FILE = 'iterate.dat', STATUS = 'unknown');
ITFILE = 8;
}
// c Check the input arguments for errors.
this._errclb.Run(N, M, FACTR, L, offset_l, U, offset_u, NBD, offset_nbd
, ref TASK, ref INFO, ref K);
if (TASK == BFGSTask.ERROR)
{
this._prn3lb.Run(N, X, offset_x, F, TASK, IPRINT, INFO
, ITFILE, ITER, NFGV, NINTOL, NSKIP, NACT
, SBGNRM, ZERO, NINT, WORD, IBACK, STP
, XSTEP, K, CACHYT, SBTIME, LNSCHT);
return;
}
this._prn1lb.Run(N, M, L, offset_l, U, offset_u, X, offset_x, IPRINT
, ITFILE, EPSMCH);
// c Initialize iwhere & project x onto the feasible set.
this._active.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, ref X, offset_x, ref IWHERE, offset_iwhere
, IPRINT, ref PRJCTD, ref CNSTND, ref BOXED);
// c The end of the initialization.
}
else
{
// c restore local variables.
PRJCTD = LSAVE[1 + o_lsave];
CNSTND = LSAVE[2 + o_lsave];
BOXED = LSAVE[3 + o_lsave];
UPDATD = LSAVE[4 + o_lsave];
NINTOL = ISAVE[1 + o_isave];
ITFILE = ISAVE[3 + o_isave];
IBACK = ISAVE[4 + o_isave];
NSKIP = ISAVE[5 + o_isave];
HEAD = ISAVE[6 + o_isave];
COL = ISAVE[7 + o_isave];
ITAIL = ISAVE[8 + o_isave];
ITER = ISAVE[9 + o_isave];
IUPDAT = ISAVE[10 + o_isave];
NINT = ISAVE[12 + o_isave];
NFGV = ISAVE[13 + o_isave];
INFO = ISAVE[14 + o_isave];
IFUN = ISAVE[15 + o_isave];
IWORD = ISAVE[16 + o_isave];
NFREE = ISAVE[17 + o_isave];
NACT = ISAVE[18 + o_isave];
ILEAVE = ISAVE[19 + o_isave];
NENTER = ISAVE[20 + o_isave];
THETA = DSAVE[1 + o_dsave];
FOLD = DSAVE[2 + o_dsave];
TOL = DSAVE[3 + o_dsave];
DNORM = DSAVE[4 + o_dsave];
EPSMCH = DSAVE[5 + o_dsave];
CPU1 = DSAVE[6 + o_dsave];
CACHYT = DSAVE[7 + o_dsave];
SBTIME = DSAVE[8 + o_dsave];
LNSCHT = DSAVE[9 + o_dsave];
TIME1 = DSAVE[10 + o_dsave];
GD = DSAVE[11 + o_dsave];
STPMX = DSAVE[12 + o_dsave];
SBGNRM = DSAVE[13 + o_dsave];
STP = DSAVE[14 + o_dsave];
GDOLD = DSAVE[15 + o_dsave];
DTD = DSAVE[16 + o_dsave];
// c After returning from the driver go to the point where execution
// c is to resume.
if (TASK == BFGSTask.FG_LNSRCH) goto LABEL666;
if (TASK == BFGSTask.NEW_X) goto LABEL777;
if (TASK == BFGSTask.FG_ST || TASK == BFGSTask.FG_START) goto LABEL111;
if (TASK == BFGSTask.STOP)
{
if (TASK== BFGSTask.CPU)
{
// c restore the previous iterate.
this._dcopy.Run(N, T, offset_t, 1, ref X, offset_x, 1);
this._dcopy.Run(N, R, offset_r, 1, ref G, offset_g, 1);
F = FOLD;
}
goto LABEL999;
}
}
// c Compute f0 and g0.
TASK = BFGSTask.FG_START;
// c return to the driver to calculate f and g; reenter at 111.
goto LABEL1000;
LABEL111:;
NFGV = 1;
// c Compute the infinity norm of the (-) projected gradient.
this._projgr.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, X, offset_x, G, offset_g
, ref SBGNRM);
if (IPRINT >= 1)
{
//ERROR-ERROR WRITE (6,1002) ITER,F,SBGNRM;
//ERROR-ERROR WRITE (ITFILE,1003) ITER,NFGV,SBGNRM,F;
}
if (SBGNRM <= PGTOL)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
goto LABEL999;
}
// c ----------------- the beginning of the loop --------------------------
LABEL222:;
if (IPRINT >= 99) ;//ERROR-ERRORWRITE(6,1001)ITER+1
IWORD = - 1;
// c
if (!CNSTND && COL > 0)
{
// c skip the search for GCP.
this._dcopy.Run(N, X, offset_x, 1, ref Z, offset_z, 1);
WRK = UPDATD;
NINT = 0;
goto LABEL333;
}
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Compute the Generalized Cauchy Point (GCP).
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
this._timer.Run(ref CPU1);
this._cauchy.Run(N, X, offset_x, L, offset_l, U, offset_u, NBD, offset_nbd, G, offset_g
, ref INDX2, offset_indx2, ref IWHERE, offset_iwhere, ref T, offset_t, ref D, offset_d, ref Z, offset_z, M
, WY, offset_wy, WS, offset_ws, SY, offset_sy, WT, offset_wt, THETA, COL
, HEAD, ref WA, 1 + o_wa, ref WA, 2 * M + 1 + o_wa, ref WA, 4 * M + 1 + o_wa, ref WA, 6 * M + 1 + o_wa, ref NINT
, SG, offset_sg, YG, offset_yg, IPRINT, SBGNRM, ref INFO, EPSMCH);
if (INFO != 0)
{
// c singular triangular system detected; refresh the lbfgs memory.
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1005)
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
CACHYT += CPU2 - CPU1;
goto LABEL222;
}
this._timer.Run(ref CPU2);
CACHYT += CPU2 - CPU1;
NINTOL += NINT;
// c Count the entering and leaving variables for iter > 0;
// c find the index set of free and active variables at the GCP.
this._freev.Run(N, ref NFREE, ref INDEX, offset_index, ref NENTER, ref ILEAVE, ref INDX2, offset_indx2
, IWHERE, offset_iwhere, ref WRK, UPDATD, CNSTND, IPRINT, ITER);
NACT = N - NFREE;
LABEL333:;
// c If there are no free variables or B=theta*I, then
// c skip the subspace minimization.
if (NFREE == 0 || COL == 0) goto LABEL555;
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Subspace minimization.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
this._timer.Run(ref CPU1);
// c Form the LEL^T factorization of the indefinite
// c matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
// c [L_a -R_z theta*S'AA'S ]
// c where E = [-I 0]
// c [ 0 I]
if (WRK)
{
this._formk.Run(N, NFREE, INDEX, offset_index, NENTER, ILEAVE, INDX2, offset_indx2
, IUPDAT, UPDATD, ref WN, offset_wn, ref SND, offset_snd, M, WS, offset_ws
, WY, offset_wy, SY, offset_sy, THETA, COL, HEAD, ref INFO);
}
if (INFO != 0)
{
// c nonpositive definiteness in Cholesky factorization;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1006)
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
goto LABEL222;
}
// c compute r=-Z'B(xcp-xk)-Z'g (using wa(2m+1)=W'(xcp-x)
// c from 'cauchy').
this._cmprlb.Run(N, M, X, offset_x, G, offset_g, WS, offset_ws, WY, offset_wy
, SY, offset_sy, WT, offset_wt, Z, offset_z, ref R, offset_r, ref WA, offset_wa, INDEX, offset_index
, THETA, COL, HEAD, NFREE, CNSTND, ref INFO);
if (INFO != 0) goto LABEL444;
// c call the direct method.
this._subsm.Run(N, M, NFREE, INDEX, offset_index, L, offset_l, U, offset_u
, NBD, offset_nbd, ref Z, offset_z, ref R, offset_r, WS, offset_ws, WY, offset_wy, THETA
, COL, HEAD, ref IWORD, ref WA, offset_wa, WN, offset_wn, IPRINT
, ref INFO);
LABEL444:;
if (INFO != 0)
{
// c singular triangular system detected;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1005)
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
goto LABEL222;
}
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
LABEL555:;
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Line search and optimality tests.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c Generate the search direction d:=z-x.
for (I = 1; I <= N; I++)
{
D[I + o_d] = Z[I + o_z] - X[I + o_x];
}
this._timer.Run(ref CPU1);
LABEL666:;
this._lnsrlb.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, ref X, offset_x, F
, ref FOLD, ref GD, ref GDOLD, G, offset_g, D, offset_d, ref R, offset_r
, ref T, offset_t, Z, offset_z, ref STP, ref DNORM, ref DTD, ref XSTEP
, ref STPMX, ITER, ref IFUN, ref IBACK, ref NFGV, ref INFO
, ref TASK, BOXED, CNSTND, ref CSAVE, ref ISAVE, 22 + o_isave, ref DSAVE, 17 + o_dsave);
if (INFO != 0 || IBACK >= 20)
{
// c restore the previous iterate.
this._dcopy.Run(N, T, offset_t, 1, ref X, offset_x, 1);
this._dcopy.Run(N, R, offset_r, 1, ref G, offset_g, 1);
F = FOLD;
if (COL == 0)
{
// c abnormal termination.
if (INFO == 0)
{
INFO = - 9;
// c restore the actual number of f and g evaluations etc.
NFGV -= 1;
IFUN -= 1;
IBACK -= 1;
}
TASK = BFGSTask.ABNO;
ITER += 1;
goto LABEL999;
}
else
{
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1008)
if (INFO == 0) NFGV -= 1;
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
TASK = BFGSTask.RESTART;
this._timer.Run(ref CPU2);
LNSCHT += CPU2 - CPU1;
goto LABEL222;
}
}
else
{
if (TASK == BFGSTask.FG_LNSRCH)
{
// c return to the driver for calculating f and g; reenter at 666.
goto LABEL1000;
}
else
{
// c calculate and print out the quantities related to the new X.
this._timer.Run(ref CPU2);
LNSCHT += CPU2 - CPU1;
ITER += 1;
// c Compute the infinity norm of the projected (-)gradient.
this._projgr.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, X, offset_x, G, offset_g
, ref SBGNRM);
// c Print iteration information.
this._prn2lb.Run(N, X, offset_x, F, G, offset_g, IPRINT, ITFILE
, ITER, NFGV, NACT, SBGNRM, NINT, ref WORD
, IWORD, IBACK, STP, XSTEP);
goto LABEL1000;
}
}
LABEL777:;
// c Test for termination.
if (SBGNRM <= PGTOL)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
goto LABEL999;
}
DDUM = Math.Max(Math.Abs(FOLD), Math.Max(Math.Abs(F), ONE));
if ((FOLD - F) <= TOL * DDUM)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
if (IBACK >= 10) INFO = - 5;
// c i.e., to issue a warning if iback>10 in the line search.
goto LABEL999;
}
// c Compute d=newx-oldx, r=newg-oldg, rr=y'y and dr=y's.
for (I = 1; I <= N; I++)
{
R[I + o_r] = G[I + o_g] - R[I + o_r];
}
RR = this._ddot.Run(N, R, offset_r, 1, R, offset_r, 1);
if (STP == ONE)
{
DR = GD - GDOLD;
DDUM = - GDOLD;
}
else
{
DR = (GD - GDOLD) * STP;
this._dscal.Run(N, STP, ref D, offset_d, 1);
DDUM = - GDOLD * STP;
}
if (DR <= EPSMCH * DDUM)
{
// c skip the L-BFGS update.
NSKIP += 1;
UPDATD = false;
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1004)DR,DDUM
goto LABEL888;
}
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Update the L-BFGS matrix.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
UPDATD = true;
IUPDAT += 1;
// c Update matrices WS and WY and form the middle matrix in B.
this._matupd.Run(N, M, ref WS, offset_ws, ref WY, offset_wy, ref SY, offset_sy, ref SS, offset_ss
, D, offset_d, R, offset_r, ref ITAIL, IUPDAT, ref COL, ref HEAD
, ref THETA, RR, DR, STP, DTD);
// c Form the upper half of the pds T = theta*SS + L*D^(-1)*L';
// c Store T in the upper triangular of the array wt;
// c Cholesky factorize T to J*J' with
// c J' stored in the upper triangular of wt.
this._formt.Run(M, ref WT, offset_wt, SY, offset_sy, SS, offset_ss, COL, THETA
, ref INFO);
if (INFO != 0)
{
// c nonpositive definiteness in Cholesky factorization;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,1007)
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
goto LABEL222;
}
// c Now the inverse of the middle matrix in B is
// c [ D^(1/2) O ] [ -D^(1/2) D^(-1/2)*L' ]
// c [ -L*D^(-1/2) J ] [ 0 J' ]
LABEL888:;
// c -------------------- the end of the loop -----------------------------
goto LABEL222;
LABEL999:;
this._timer.Run(ref TIME2);
TIME = TIME2 - TIME1;
this._prn3lb.Run(N, X, offset_x, F, TASK, IPRINT, INFO
, ITFILE, ITER, NFGV, NINTOL, NSKIP, NACT
, SBGNRM, TIME, NINT, WORD, IBACK, STP
, XSTEP, K, CACHYT, SBTIME, LNSCHT);
LABEL1000:;
// c Save local variables.
LSAVE[1 + o_lsave] = PRJCTD;
LSAVE[2 + o_lsave] = CNSTND;
LSAVE[3 + o_lsave] = BOXED;
LSAVE[4 + o_lsave] = UPDATD;
ISAVE[1 + o_isave] = NINTOL;
ISAVE[3 + o_isave] = ITFILE;
ISAVE[4 + o_isave] = IBACK;
ISAVE[5 + o_isave] = NSKIP;
ISAVE[6 + o_isave] = HEAD;
ISAVE[7 + o_isave] = COL;
ISAVE[8 + o_isave] = ITAIL;
ISAVE[9 + o_isave] = ITER;
ISAVE[10 + o_isave] = IUPDAT;
ISAVE[12 + o_isave] = NINT;
ISAVE[13 + o_isave] = NFGV;
ISAVE[14 + o_isave] = INFO;
ISAVE[15 + o_isave] = IFUN;
ISAVE[16 + o_isave] = IWORD;
ISAVE[17 + o_isave] = NFREE;
ISAVE[18 + o_isave] = NACT;
ISAVE[19 + o_isave] = ILEAVE;
ISAVE[20 + o_isave] = NENTER;
DSAVE[1 + o_dsave] = THETA;
DSAVE[2 + o_dsave] = FOLD;
DSAVE[3 + o_dsave] = TOL;
DSAVE[4 + o_dsave] = DNORM;
DSAVE[5 + o_dsave] = EPSMCH;
DSAVE[6 + o_dsave] = CPU1;
DSAVE[7 + o_dsave] = CACHYT;
DSAVE[8 + o_dsave] = SBTIME;
DSAVE[9 + o_dsave] = LNSCHT;
DSAVE[10 + o_dsave] = TIME1;
DSAVE[11 + o_dsave] = GD;
DSAVE[12 + o_dsave] = STPMX;
DSAVE[13 + o_dsave] = SBGNRM;
DSAVE[14 + o_dsave] = STP;
DSAVE[15 + o_dsave] = GDOLD;
DSAVE[16 + o_dsave] = DTD;
return;
#endregion
}
/// <param name="N">
/// is an integer variable.
/// On entry n is the dimension of the problem.
/// On exit n is unchanged.
///</param>
/// <param name="M">
/// is an integer variable.
/// On entry m is the maximum number of variable metric corrections
/// used to define the limited memory matrix.
/// On exit m is unchanged.
///</param>
/// <param name="X">
/// is a double precision array of dimension n.
/// On entry x is an approximation to the solution.
/// On exit x is the current approximation.
///</param>
/// <param name="L">
/// is a double precision array of dimension n.
/// On entry l is the lower bound on x.
/// On exit l is unchanged.
///</param>
/// <param name="U">
/// is a double precision array of dimension n.
/// On entry u is the upper bound on x.
/// On exit u is unchanged.
///</param>
/// <param name="NBD">
/// is an integer array of dimension n.
/// On entry nbd represents the type of bounds imposed on the
/// variables, and must be specified as follows:
/// nbd(i)=0 if x(i) is unbounded,
/// 1 if x(i) has only a lower bound,
/// 2 if x(i) has both lower and upper bounds, and
/// 3 if x(i) has only an upper bound.
/// On exit nbd is unchanged.
///</param>
/// <param name="F">
/// is a double precision variable.
/// On first entry f is unspecified.
/// On final exit f is the value of the function at x.
///</param>
/// <param name="G">
/// is a double precision array of dimension n.
/// On first entry g is unspecified.
/// On final exit g is the value of the gradient at x.
///</param>
/// <param name="FACTR">
/// is a double precision variable.
/// On entry factr .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} .LE. factr*epsmch
///
/// where epsmch is the machine precision, which is automatically
/// generated by the code. Typical values for factr: 1.d+12 for
/// low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely
/// high accuracy.
/// On exit factr is unchanged.
///</param>
/// <param name="PGTOL">
/// is a double precision variable.
/// On entry pgtol .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// max{|proj g_i | i = 1, ..., n} .LE. pgtol
///
/// where pg_i is the ith component of the projected gradient.
/// On exit pgtol is unchanged.
///</param>
/// <param name="WA">
/// is a double precision working array of length
/// (2mmax + 4)nmax + 12mmax^2 + 12mmax.
///</param>
/// <param name="IWA">
/// is an integer working array of length 3nmax.
///</param>
/// <param name="TASK">
/// is a working string of characters of length 60 indicating
/// the current job when entering and quitting this subroutine.
///</param>
/// <param name="IPRINT">
/// is an integer variable that must be set by the user.
/// It controls the frequency and type of output generated:
/// iprint.LT.0 no output is generated;
/// iprint=0 print only one line at the last iteration;
/// 0.LT.iprint.LT.99 print also f and |proj g| every iprint iterations;
/// iprint=99 print details of every iteration except n-vectors;
/// iprint=100 print also the changes of active set and final x;
/// iprint.GT.100 print details of every iteration including x and g;
/// When iprint .GT. 0, the file iterate.dat will be created to
/// summarize the iteration.
///</param>
/// <param name="CSAVE">
/// is a working string of characters of length 60.
///</param>
/// <param name="LSAVE">
/// is a logical working array of dimension 4.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// If lsave(1) = .true. then the initial X has been replaced by
/// its projection in the feasible set;
/// If lsave(2) = .true. then the problem is constrained;
/// If lsave(3) = .true. then each variable has upper and lower
/// bounds;
///</param>
/// <param name="ISAVE">
/// is an integer working array of dimension 44.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// isave(22) = the total number of intervals explored in the
/// search of Cauchy points;
/// isave(26) = the total number of skipped BFGS updates before
/// the current iteration;
/// isave(30) = the number of current iteration;
/// isave(31) = the total number of BFGS updates prior the current
/// iteration;
/// isave(33) = the number of intervals explored in the search of
/// Cauchy point in the current iteration;
/// isave(34) = the total number of function and gradient
/// evaluations;
/// isave(36) = the number of function value or gradient
/// evaluations in the current iteration;
/// if isave(37) = 0 then the subspace argmin is within the box;
/// if isave(37) = 1 then the subspace argmin is beyond the box;
/// isave(38) = the number of free variables in the current
/// iteration;
/// isave(39) = the number of active constraints in the current
/// iteration;
/// n + 1 - isave(40) = the number of variables leaving the set of
/// active constraints in the current iteration;
/// isave(41) = the number of variables entering the set of active
/// constraints in the current iteration.
///</param>
/// <param name="DSAVE">
/// is a double precision working array of dimension 29.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// dsave(1) = current 'theta' in the BFGS matrix;
/// dsave(2) = f(x) in the previous iteration;
/// dsave(3) = factr*epsmch;
/// dsave(4) = 2-norm of the line search direction vector;
/// dsave(5) = the machine precision epsmch generated by the code;
/// dsave(7) = the accumulated time spent on searching for
/// Cauchy points;
/// dsave(8) = the accumulated time spent on
/// subspace minimization;
/// dsave(9) = the accumulated time spent on line search;
/// dsave(11) = the slope of the line search function at
/// the current point of line search;
/// dsave(12) = the maximum relative step length imposed in
/// line search;
/// dsave(13) = the infinity norm of the projected gradient;
/// dsave(14) = the relative step length in the line search;
/// dsave(15) = the slope of the line search function at
/// the starting point of the line search;
/// dsave(16) = the square of the 2-norm of the line search
/// direction vector.
///</param>
public void Run(int N, int M, ref double[] X, int offset_x, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref double F, ref double[] G, int offset_g, double FACTR, double PGTOL, ref double[] WA, int offset_wa, ref int[] IWA, int offset_iwa
, ref BFGSTask TASK, int IPRINT, ref BFGSTask CSAVE, ref bool[] LSAVE, int offset_lsave, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
int L1 = 0; int L2 = 0; int L3 = 0; int LWS = 0; int LR = 0; int LZ = 0; int LT = 0; int LD = 0; int LSG = 0;
int LWA = 0;int LYG = 0; int LSGO = 0; int LWY = 0; int LSY = 0; int LSS = 0; int LYY = 0; int LWT = 0; int LWN = 0;
int LSND = 0;int LYGO = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x; int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
int o_g = -1 + offset_g; int o_wa = -1 + offset_wa; int o_iwa = -1 + offset_iwa; int o_lsave = -1 + offset_lsave;
int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c ************
// c
// c Subroutine setulb
// c
// c This subroutine partitions the working arrays wa and iwa, and
// c then uses the limited memory BFGS method to solve the bound
// c constrained optimization problem by calling mainlb.
// c (The direct method will be used in the subspace minimization.)
// c
// c n is an integer variable.
// c On entry n is the dimension of the problem.
// c On exit n is unchanged.
// c
// c m is an integer variable.
// c On entry m is the maximum number of variable metric corrections
// c used to define the limited memory matrix.
// c On exit m is unchanged.
// c
// c x is a double precision array of dimension n.
// c On entry x is an approximation to the solution.
// c On exit x is the current approximation.
// c
// c l is a double precision array of dimension n.
// c On entry l is the lower bound on x.
// c On exit l is unchanged.
// c
// c u is a double precision array of dimension n.
// c On entry u is the upper bound on x.
// c On exit u is unchanged.
// c
// c nbd is an integer array of dimension n.
// c On entry nbd represents the type of bounds imposed on the
// c variables, and must be specified as follows:
// c nbd(i)=0 if x(i) is unbounded,
// c 1 if x(i) has only a lower bound,
// c 2 if x(i) has both lower and upper bounds, and
// c 3 if x(i) has only an upper bound.
// c On exit nbd is unchanged.
// c
// c f is a double precision variable.
// c On first entry f is unspecified.
// c On final exit f is the value of the function at x.
// c
// c g is a double precision array of dimension n.
// c On first entry g is unspecified.
// c On final exit g is the value of the gradient at x.
// c
// c factr is a double precision variable.
// c On entry factr >= 0 is specified by the user. The iteration
// c will stop when
// c
// c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch
// c
// c where epsmch is the machine precision, which is automatically
// c generated by the code. Typical values for factr: 1.d+12 for
// c low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely
// c high accuracy.
// c On exit factr is unchanged.
// c
// c pgtol is a double precision variable.
// c On entry pgtol >= 0 is specified by the user. The iteration
// c will stop when
// c
// c max{|proj g_i | i = 1, ..., n} <= pgtol
// c
// c where pg_i is the ith component of the projected gradient.
// c On exit pgtol is unchanged.
// c
// c wa is a double precision working array of length
// c (2mmax + 4)nmax + 12mmax^2 + 12mmax.
// c
// c iwa is an integer working array of length 3nmax.
// c
// c task is a working string of characters of length 60 indicating
// c the current job when entering and quitting this subroutine.
// c
// c iprint is an integer variable that must be set by the user.
// c It controls the frequency and type of output generated:
// c iprint<0 no output is generated;
// c iprint=0 print only one line at the last iteration;
// c 0<iprint<99 print also f and |proj g| every iprint iterations;
// c iprint=99 print details of every iteration except n-vectors;
// c iprint=100 print also the changes of active set and final x;
// c iprint>100 print details of every iteration including x and g;
// c When iprint > 0, the file iterate.dat will be created to
// c summarize the iteration.
// c
// c csave is a working string of characters of length 60.
// c
// c lsave is a logical working array of dimension 4.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c If lsave(1) = .true. then the initial X has been replaced by
// c its projection in the feasible set;
// c If lsave(2) = .true. then the problem is constrained;
// c If lsave(3) = .true. then each variable has upper and lower
// c bounds;
// c
// c isave is an integer working array of dimension 44.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c isave(22) = the total number of intervals explored in the
// c search of Cauchy points;
// c isave(26) = the total number of skipped BFGS updates before
// c the current iteration;
// c isave(30) = the number of current iteration;
// c isave(31) = the total number of BFGS updates prior the current
// c iteration;
// c isave(33) = the number of intervals explored in the search of
// c Cauchy point in the current iteration;
// c isave(34) = the total number of function and gradient
// c evaluations;
// c isave(36) = the number of function value or gradient
// c evaluations in the current iteration;
// c if isave(37) = 0 then the subspace argmin is within the box;
// c if isave(37) = 1 then the subspace argmin is beyond the box;
// c isave(38) = the number of free variables in the current
// c iteration;
// c isave(39) = the number of active constraints in the current
// c iteration;
// c n + 1 - isave(40) = the number of variables leaving the set of
// c active constraints in the current iteration;
// c isave(41) = the number of variables entering the set of active
// c constraints in the current iteration.
// c
// c dsave is a double precision working array of dimension 29.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c dsave(1) = current 'theta' in the BFGS matrix;
// c dsave(2) = f(x) in the previous iteration;
// c dsave(3) = factr*epsmch;
// c dsave(4) = 2-norm of the line search direction vector;
// c dsave(5) = the machine precision epsmch generated by the code;
// c dsave(7) = the accumulated time spent on searching for
// c Cauchy points;
// c dsave(8) = the accumulated time spent on
// c subspace minimization;
// c dsave(9) = the accumulated time spent on line search;
// c dsave(11) = the slope of the line search function at
// c the current point of line search;
// c dsave(12) = the maximum relative step length imposed in
// c line search;
// c dsave(13) = the infinity norm of the projected gradient;
// c dsave(14) = the relative step length in the line search;
// c dsave(15) = the slope of the line search function at
// c the starting point of the line search;
// c dsave(16) = the square of the 2-norm of the line search
// c direction vector.
// c
// c Subprograms called:
// c
// c L-BFGS-B Library ... mainlb.
// c
// c
// c References:
// c
// c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited
// c memory algorithm for bound constrained optimization'',
// c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208.
// c
// c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: a
// c limited memory FORTRAN code for solving bound constrained
// c optimization problems'', Tech. Report, NAM-11, EECS Department,
// c Northwestern University, 1994.
// c
// c (Postscript files of these papers are available via anonymous
// c ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.)
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.START)
{
ISAVE[1 + o_isave] = M * N;
ISAVE[2 + o_isave] = (int)Math.Pow(M,2);
ISAVE[3 + o_isave] = 4 * (int)Math.Pow(M,2);
ISAVE[4 + o_isave] = 1;
ISAVE[5 + o_isave] = ISAVE[4 + o_isave] + ISAVE[1 + o_isave];
ISAVE[6 + o_isave] = ISAVE[5 + o_isave] + ISAVE[1 + o_isave];
ISAVE[7 + o_isave] = ISAVE[6 + o_isave] + ISAVE[2 + o_isave];
ISAVE[8 + o_isave] = ISAVE[7 + o_isave] + ISAVE[2 + o_isave];
ISAVE[9 + o_isave] = ISAVE[8 + o_isave] + ISAVE[2 + o_isave];
ISAVE[10 + o_isave] = ISAVE[9 + o_isave] + ISAVE[2 + o_isave];
ISAVE[11 + o_isave] = ISAVE[10 + o_isave] + ISAVE[3 + o_isave];
ISAVE[12 + o_isave] = ISAVE[11 + o_isave] + ISAVE[3 + o_isave];
ISAVE[13 + o_isave] = ISAVE[12 + o_isave] + N;
ISAVE[14 + o_isave] = ISAVE[13 + o_isave] + N;
ISAVE[15 + o_isave] = ISAVE[14 + o_isave] + N;
ISAVE[16 + o_isave] = ISAVE[15 + o_isave] + N;
ISAVE[17 + o_isave] = ISAVE[16 + o_isave] + 8 * M;
ISAVE[18 + o_isave] = ISAVE[17 + o_isave] + M;
ISAVE[19 + o_isave] = ISAVE[18 + o_isave] + M;
ISAVE[20 + o_isave] = ISAVE[19 + o_isave] + M;
}
L1 = ISAVE[1 + o_isave];
L2 = ISAVE[2 + o_isave];
L3 = ISAVE[3 + o_isave];
LWS = ISAVE[4 + o_isave];
LWY = ISAVE[5 + o_isave];
LSY = ISAVE[6 + o_isave];
LSS = ISAVE[7 + o_isave];
LYY = ISAVE[8 + o_isave];
LWT = ISAVE[9 + o_isave];
LWN = ISAVE[10 + o_isave];
LSND = ISAVE[11 + o_isave];
LZ = ISAVE[12 + o_isave];
LR = ISAVE[13 + o_isave];
LD = ISAVE[14 + o_isave];
LT = ISAVE[15 + o_isave];
LWA = ISAVE[16 + o_isave];
LSG = ISAVE[17 + o_isave];
LSGO = ISAVE[18 + o_isave];
LYG = ISAVE[19 + o_isave];
LYGO = ISAVE[20 + o_isave];
this._mainlb.Run(N, M, ref X, offset_x, L, offset_l, U, offset_u, NBD, offset_nbd
, ref F, ref G, offset_g, FACTR, PGTOL, ref WA, LWS + o_wa, ref WA, LWY + o_wa
, ref WA, LSY + o_wa, ref WA, LSS + o_wa, WA, LYY + o_wa, ref WA, LWT + o_wa, ref WA, LWN + o_wa, ref WA, LSND + o_wa
, ref WA, LZ + o_wa, ref WA, LR + o_wa, ref WA, LD + o_wa, ref WA, LT + o_wa, ref WA, LWA + o_wa, WA, LSG + o_wa
, WA, LSGO + o_wa, WA, LYG + o_wa, WA, LYGO + o_wa, ref IWA, 1 + o_iwa, ref IWA, N + 1 + o_iwa, ref IWA, 2 * N + 1 + o_iwa
, ref TASK, IPRINT, ref CSAVE, ref LSAVE, offset_lsave, ref ISAVE, 22 + o_isave, ref DSAVE, offset_dsave);
return;
#endregion
}
/// <param name="N">
/// is an integer variable.
/// On entry n is the dimension of the problem.
/// On exit n is unchanged.
///</param>
/// <param name="M">
/// is an integer variable.
/// On entry m is the maximum number of variable metric corrections
/// used to define the limited memory matrix.
/// On exit m is unchanged.
///</param>
/// <param name="X">
/// is a double precision array of dimension n.
/// On entry x is an approximation to the solution.
/// On exit x is the current approximation.
///</param>
/// <param name="L">
/// is a double precision array of dimension n.
/// On entry l is the lower bound on x.
/// On exit l is unchanged.
///</param>
/// <param name="U">
/// is a double precision array of dimension n.
/// On entry u is the upper bound on x.
/// On exit u is unchanged.
///</param>
/// <param name="NBD">
/// is an integer array of dimension n.
/// On entry nbd represents the type of bounds imposed on the
/// variables, and must be specified as follows:
/// nbd(i)=0 if x(i) is unbounded,
/// 1 if x(i) has only a lower bound,
/// 2 if x(i) has both lower and upper bounds, and
/// 3 if x(i) has only an upper bound.
/// On exit nbd is unchanged.
///</param>
/// <param name="F">
/// is a double precision variable.
/// On first entry f is unspecified.
/// On final exit f is the value of the function at x.
///</param>
/// <param name="G">
/// is a double precision array of dimension n.
/// On first entry g is unspecified.
/// On final exit g is the value of the gradient at x.
///</param>
/// <param name="FACTR">
/// is a double precision variable.
/// On entry factr .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} .LE. factr*epsmch
///
/// where epsmch is the machine precision, which is automatically
/// generated by the code. Typical values for factr: 1.d+12 for
/// low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely
/// high accuracy.
/// On exit factr is unchanged.
///</param>
/// <param name="PGTOL">
/// is a double precision variable.
/// On entry pgtol .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// max{|proj g_i | i = 1, ..., n} .LE. pgtol
///
/// where pg_i is the ith component of the projected gradient.
/// On exit pgtol is unchanged.
///</param>
/// <param name="WA">
/// is a double precision working array of length
/// (2mmax + 4)nmax + 12mmax^2 + 12mmax.
///</param>
/// <param name="IWA">
/// is an integer working array of length 3nmax.
///</param>
/// <param name="TASK">
/// is a working string of characters of length 60 indicating
/// the current job when entering and quitting this subroutine.
///</param>
/// <param name="IPRINT">
/// is an integer variable that must be set by the user.
/// It controls the frequency and type of output generated:
/// iprint.LT.0 no output is generated;
/// iprint=0 print only one line at the last iteration;
/// 0.LT.iprint.LT.99 print also f and |proj g| every iprint iterations;
/// iprint=99 print details of every iteration except n-vectors;
/// iprint=100 print also the changes of active set and final x;
/// iprint.GT.100 print details of every iteration including x and g;
/// When iprint .GT. 0, the file iterate.dat will be created to
/// summarize the iteration.
///</param>
/// <param name="CSAVE">
/// is a working string of characters of length 60.
///</param>
/// <param name="LSAVE">
/// is a logical working array of dimension 4.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// If lsave(1) = .true. then the initial X has been replaced by
/// its projection in the feasible set;
/// If lsave(2) = .true. then the problem is constrained;
/// If lsave(3) = .true. then each variable has upper and lower
/// bounds;
///</param>
/// <param name="ISAVE">
/// is an integer working array of dimension 44.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// isave(22) = the total number of intervals explored in the
/// search of Cauchy points;
/// isave(26) = the total number of skipped BFGS updates before
/// the current iteration;
/// isave(30) = the number of current iteration;
/// isave(31) = the total number of BFGS updates prior the current
/// iteration;
/// isave(33) = the number of intervals explored in the search of
/// Cauchy point in the current iteration;
/// isave(34) = the total number of function and gradient
/// evaluations;
/// isave(36) = the number of function value or gradient
/// evaluations in the current iteration;
/// if isave(37) = 0 then the subspace argmin is within the box;
/// if isave(37) = 1 then the subspace argmin is beyond the box;
/// isave(38) = the number of free variables in the current
/// iteration;
/// isave(39) = the number of active constraints in the current
/// iteration;
/// n + 1 - isave(40) = the number of variables leaving the set of
/// active constraints in the current iteration;
/// isave(41) = the number of variables entering the set of active
/// constraints in the current iteration.
///</param>
/// <param name="DSAVE">
/// is a double precision working array of dimension 29.
/// On exit with 'task' = NEW_X, the following information is
/// available:
/// dsave(1) = current 'theta' in the BFGS matrix;
/// dsave(2) = f(x) in the previous iteration;
/// dsave(3) = factr*epsmch;
/// dsave(4) = 2-norm of the line search direction vector;
/// dsave(5) = the machine precision epsmch generated by the code;
/// dsave(7) = the accumulated time spent on searching for
/// Cauchy points;
/// dsave(8) = the accumulated time spent on
/// subspace minimization;
/// dsave(9) = the accumulated time spent on line search;
/// dsave(11) = the slope of the line search function at
/// the current point of line search;
/// dsave(12) = the maximum relative step length imposed in
/// line search;
/// dsave(13) = the infinity norm of the projected gradient;
/// dsave(14) = the relative step length in the line search;
/// dsave(15) = the slope of the line search function at
/// the starting point of the line search;
/// dsave(16) = the square of the 2-norm of the line search
/// direction vector.
///</param>
public void Run(int N, int M, ref double[] X, int offset_x, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref double F, ref double[] G, int offset_g, double FACTR, double PGTOL, ref double[] WA, int offset_wa, ref int[] IWA, int offset_iwa
, ref BFGSTask TASK, int IPRINT, ref BFGSTask CSAVE, ref bool[] LSAVE, int offset_lsave, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
int L1 = 0; int L2 = 0; int L3 = 0; int LWS = 0; int LR = 0; int LZ = 0; int LT = 0; int LD = 0; int LSG = 0;
int LWA = 0; int LYG = 0; int LSGO = 0; int LWY = 0; int LSY = 0; int LSS = 0; int LYY = 0; int LWT = 0; int LWN = 0;
int LSND = 0; int LYGO = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x; int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
int o_g = -1 + offset_g; int o_wa = -1 + offset_wa; int o_iwa = -1 + offset_iwa; int o_lsave = -1 + offset_lsave;
int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c ************
// c
// c Subroutine setulb
// c
// c This subroutine partitions the working arrays wa and iwa, and
// c then uses the limited memory BFGS method to solve the bound
// c constrained optimization problem by calling mainlb.
// c (The direct method will be used in the subspace minimization.)
// c
// c n is an integer variable.
// c On entry n is the dimension of the problem.
// c On exit n is unchanged.
// c
// c m is an integer variable.
// c On entry m is the maximum number of variable metric corrections
// c used to define the limited memory matrix.
// c On exit m is unchanged.
// c
// c x is a double precision array of dimension n.
// c On entry x is an approximation to the solution.
// c On exit x is the current approximation.
// c
// c l is a double precision array of dimension n.
// c On entry l is the lower bound on x.
// c On exit l is unchanged.
// c
// c u is a double precision array of dimension n.
// c On entry u is the upper bound on x.
// c On exit u is unchanged.
// c
// c nbd is an integer array of dimension n.
// c On entry nbd represents the type of bounds imposed on the
// c variables, and must be specified as follows:
// c nbd(i)=0 if x(i) is unbounded,
// c 1 if x(i) has only a lower bound,
// c 2 if x(i) has both lower and upper bounds, and
// c 3 if x(i) has only an upper bound.
// c On exit nbd is unchanged.
// c
// c f is a double precision variable.
// c On first entry f is unspecified.
// c On final exit f is the value of the function at x.
// c
// c g is a double precision array of dimension n.
// c On first entry g is unspecified.
// c On final exit g is the value of the gradient at x.
// c
// c factr is a double precision variable.
// c On entry factr >= 0 is specified by the user. The iteration
// c will stop when
// c
// c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch
// c
// c where epsmch is the machine precision, which is automatically
// c generated by the code. Typical values for factr: 1.d+12 for
// c low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely
// c high accuracy.
// c On exit factr is unchanged.
// c
// c pgtol is a double precision variable.
// c On entry pgtol >= 0 is specified by the user. The iteration
// c will stop when
// c
// c max{|proj g_i | i = 1, ..., n} <= pgtol
// c
// c where pg_i is the ith component of the projected gradient.
// c On exit pgtol is unchanged.
// c
// c wa is a double precision working array of length
// c (2mmax + 4)nmax + 12mmax^2 + 12mmax.
// c
// c iwa is an integer working array of length 3nmax.
// c
// c task is a working string of characters of length 60 indicating
// c the current job when entering and quitting this subroutine.
// c
// c iprint is an integer variable that must be set by the user.
// c It controls the frequency and type of output generated:
// c iprint<0 no output is generated;
// c iprint=0 print only one line at the last iteration;
// c 0<iprint<99 print also f and |proj g| every iprint iterations;
// c iprint=99 print details of every iteration except n-vectors;
// c iprint=100 print also the changes of active set and final x;
// c iprint>100 print details of every iteration including x and g;
// c When iprint > 0, the file iterate.dat will be created to
// c summarize the iteration.
// c
// c csave is a working string of characters of length 60.
// c
// c lsave is a logical working array of dimension 4.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c If lsave(1) = .true. then the initial X has been replaced by
// c its projection in the feasible set;
// c If lsave(2) = .true. then the problem is constrained;
// c If lsave(3) = .true. then each variable has upper and lower
// c bounds;
// c
// c isave is an integer working array of dimension 44.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c isave(22) = the total number of intervals explored in the
// c search of Cauchy points;
// c isave(26) = the total number of skipped BFGS updates before
// c the current iteration;
// c isave(30) = the number of current iteration;
// c isave(31) = the total number of BFGS updates prior the current
// c iteration;
// c isave(33) = the number of intervals explored in the search of
// c Cauchy point in the current iteration;
// c isave(34) = the total number of function and gradient
// c evaluations;
// c isave(36) = the number of function value or gradient
// c evaluations in the current iteration;
// c if isave(37) = 0 then the subspace argmin is within the box;
// c if isave(37) = 1 then the subspace argmin is beyond the box;
// c isave(38) = the number of free variables in the current
// c iteration;
// c isave(39) = the number of active constraints in the current
// c iteration;
// c n + 1 - isave(40) = the number of variables leaving the set of
// c active constraints in the current iteration;
// c isave(41) = the number of variables entering the set of active
// c constraints in the current iteration.
// c
// c dsave is a double precision working array of dimension 29.
// c On exit with 'task' = NEW_X, the following information is
// c available:
// c dsave(1) = current 'theta' in the BFGS matrix;
// c dsave(2) = f(x) in the previous iteration;
// c dsave(3) = factr*epsmch;
// c dsave(4) = 2-norm of the line search direction vector;
// c dsave(5) = the machine precision epsmch generated by the code;
// c dsave(7) = the accumulated time spent on searching for
// c Cauchy points;
// c dsave(8) = the accumulated time spent on
// c subspace minimization;
// c dsave(9) = the accumulated time spent on line search;
// c dsave(11) = the slope of the line search function at
// c the current point of line search;
// c dsave(12) = the maximum relative step length imposed in
// c line search;
// c dsave(13) = the infinity norm of the projected gradient;
// c dsave(14) = the relative step length in the line search;
// c dsave(15) = the slope of the line search function at
// c the starting point of the line search;
// c dsave(16) = the square of the 2-norm of the line search
// c direction vector.
// c
// c Subprograms called:
// c
// c L-BFGS-B Library ... mainlb.
// c
// c
// c References:
// c
// c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited
// c memory algorithm for bound constrained optimization'',
// c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208.
// c
// c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: a
// c limited memory FORTRAN code for solving bound constrained
// c optimization problems'', Tech. Report, NAM-11, EECS Department,
// c Northwestern University, 1994.
// c
// c (Postscript files of these papers are available via anonymous
// c ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.)
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.START)
{
ISAVE[1 + o_isave] = M * N;
ISAVE[2 + o_isave] = (int)Math.Pow(M, 2);
ISAVE[3 + o_isave] = 4 * (int)Math.Pow(M, 2);
ISAVE[4 + o_isave] = 1;
ISAVE[5 + o_isave] = ISAVE[4 + o_isave] + ISAVE[1 + o_isave];
ISAVE[6 + o_isave] = ISAVE[5 + o_isave] + ISAVE[1 + o_isave];
ISAVE[7 + o_isave] = ISAVE[6 + o_isave] + ISAVE[2 + o_isave];
ISAVE[8 + o_isave] = ISAVE[7 + o_isave] + ISAVE[2 + o_isave];
ISAVE[9 + o_isave] = ISAVE[8 + o_isave] + ISAVE[2 + o_isave];
ISAVE[10 + o_isave] = ISAVE[9 + o_isave] + ISAVE[2 + o_isave];
ISAVE[11 + o_isave] = ISAVE[10 + o_isave] + ISAVE[3 + o_isave];
ISAVE[12 + o_isave] = ISAVE[11 + o_isave] + ISAVE[3 + o_isave];
ISAVE[13 + o_isave] = ISAVE[12 + o_isave] + N;
ISAVE[14 + o_isave] = ISAVE[13 + o_isave] + N;
ISAVE[15 + o_isave] = ISAVE[14 + o_isave] + N;
ISAVE[16 + o_isave] = ISAVE[15 + o_isave] + N;
ISAVE[17 + o_isave] = ISAVE[16 + o_isave] + 8 * M;
ISAVE[18 + o_isave] = ISAVE[17 + o_isave] + M;
ISAVE[19 + o_isave] = ISAVE[18 + o_isave] + M;
ISAVE[20 + o_isave] = ISAVE[19 + o_isave] + M;
}
L1 = ISAVE[1 + o_isave];
L2 = ISAVE[2 + o_isave];
L3 = ISAVE[3 + o_isave];
LWS = ISAVE[4 + o_isave];
LWY = ISAVE[5 + o_isave];
LSY = ISAVE[6 + o_isave];
LSS = ISAVE[7 + o_isave];
LYY = ISAVE[8 + o_isave];
LWT = ISAVE[9 + o_isave];
LWN = ISAVE[10 + o_isave];
LSND = ISAVE[11 + o_isave];
LZ = ISAVE[12 + o_isave];
LR = ISAVE[13 + o_isave];
LD = ISAVE[14 + o_isave];
LT = ISAVE[15 + o_isave];
LWA = ISAVE[16 + o_isave];
LSG = ISAVE[17 + o_isave];
LSGO = ISAVE[18 + o_isave];
LYG = ISAVE[19 + o_isave];
LYGO = ISAVE[20 + o_isave];
this._mainlb.Run(N, M, ref X, offset_x, L, offset_l, U, offset_u, NBD, offset_nbd
, ref F, ref G, offset_g, FACTR, PGTOL, ref WA, LWS + o_wa, ref WA, LWY + o_wa
, ref WA, LSY + o_wa, ref WA, LSS + o_wa, WA, LYY + o_wa, ref WA, LWT + o_wa, ref WA, LWN + o_wa, ref WA, LSND + o_wa
, ref WA, LZ + o_wa, ref WA, LR + o_wa, ref WA, LD + o_wa, ref WA, LT + o_wa, ref WA, LWA + o_wa, WA, LSG + o_wa
, WA, LSGO + o_wa, WA, LYG + o_wa, WA, LYGO + o_wa, ref IWA, 1 + o_iwa, ref IWA, N + 1 + o_iwa, ref IWA, 2 * N + 1 + o_iwa
, ref TASK, IPRINT, ref CSAVE, ref LSAVE, offset_lsave, ref ISAVE, 22 + o_isave, ref DSAVE, offset_dsave);
return;
#endregion
}
/// <param name="N">
/// is an integer variable.
/// On entry n is the number of variables.
/// On exit n is unchanged.
///</param>
/// <param name="M">
/// is an integer variable.
/// On entry m is the maximum number of variable metric
/// corrections allowed in the limited memory matrix.
/// On exit m is unchanged.
///</param>
/// <param name="X">
/// is a double precision array of dimension n.
/// On entry x is an approximation to the solution.
/// On exit x is the current approximation.
///</param>
/// <param name="L">
/// is a double precision array of dimension n.
/// On entry l is the lower bound of x.
/// On exit l is unchanged.
///</param>
/// <param name="U">
/// is a double precision array of dimension n.
/// On entry u is the upper bound of x.
/// On exit u is unchanged.
///</param>
/// <param name="NBD">
/// is an integer array of dimension n.
/// On entry nbd represents the type of bounds imposed on the
/// variables, and must be specified as follows:
/// nbd(i)=0 if x(i) is unbounded,
/// 1 if x(i) has only a lower bound,
/// 2 if x(i) has both lower and upper bounds,
/// 3 if x(i) has only an upper bound.
/// On exit nbd is unchanged.
///</param>
/// <param name="F">
/// is a double precision variable.
/// On first entry f is unspecified.
/// On final exit f is the value of the function at x.
///</param>
/// <param name="G">
/// is a double precision array of dimension n.
/// On first entry g is unspecified.
/// On final exit g is the value of the gradient at x.
///</param>
/// <param name="FACTR">
/// is a double precision variable.
/// On entry factr .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} .LE. factr*epsmch
///
/// where epsmch is the machine precision, which is automatically
/// generated by the code.
/// On exit factr is unchanged.
///</param>
/// <param name="PGTOL">
/// is a double precision variable.
/// On entry pgtol .GE. 0 is specified by the user. The iteration
/// will stop when
///
/// max{|proj g_i | i = 1, ..., n} .LE. pgtol
///
/// where pg_i is the ith component of the projected gradient.
/// On exit pgtol is unchanged.
///</param>
/// <param name="WN">
/// is a double precision working array of dimension 2m x 2m
/// used to store the LEL^T factorization of the indefinite matrix
/// K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
/// [L_a -R_z theta*S'AA'S ]
///
/// where E = [-I 0]
/// [ 0 I]
///</param>
/// <param name="SND">
/// is a double precision working array of dimension 2m x 2m
/// used to store the lower triangular part of
/// N = [Y' ZZ'Y L_a'+R_z']
/// [L_a +R_z S'AA'S ]
///</param>
/// <param name="Z">
/// is used at different times to store the Cauchy point and
///</param>
/// <param name="INDEX">
/// is an integer working array of dimension n.
/// In subroutine freev, index is used to store the free and fixed
/// variables at the Generalized Cauchy Point (GCP).
///</param>
/// <param name="IWHERE">
/// is an integer working array of dimension n used to record
/// the status of the vector x for GCP computation.
/// iwhere(i)=0 or -3 if x(i) is free and has bounds,
/// 1 if x(i) is fixed at l(i), and l(i) .ne. u(i)
/// 2 if x(i) is fixed at u(i), and u(i) .ne. l(i)
/// 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i)
/// -1 if x(i) is always free, i.e., no bounds on it.
///</param>
/// <param name="INDX2">
/// is an integer working array of dimension n.
/// Within subroutine cauchy, indx2 corresponds to the array iorder.
/// In subroutine freev, a list of variables entering and leaving
/// the free set is stored in indx2, and it is passed on to
/// subroutine formk with this information.
///</param>
/// <param name="TASK">
/// is a working string of characters of length 60 indicating
/// the current job when entering and leaving this subroutine.
///</param>
/// <param name="IPRINT">
/// is an INTEGER variable that must be set by the user.
/// It controls the frequency and type of output generated:
/// iprint.LT.0 no output is generated;
/// iprint=0 print only one line at the last iteration;
/// 0.LT.iprint.LT.99 print also f and |proj g| every iprint iterations;
/// iprint=99 print details of every iteration except n-vectors;
/// iprint=100 print also the changes of active set and final x;
/// iprint.GT.100 print details of every iteration including x and g;
/// When iprint .GT. 0, the file iterate.dat will be created to
/// summarize the iteration.
///</param>
/// <param name="CSAVE">
/// is a working string of characters of length 60.
///</param>
/// <param name="LSAVE">
/// is a logical working array of dimension 4.
///</param>
/// <param name="ISAVE">
/// is an integer working array of dimension 23.
///</param>
/// <param name="DSAVE">
/// is a double precision working array of dimension 29.
///
///</param>
public void Run(int N, int M, ref double[] X, int offset_x, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd
, ref double F, ref double[] G, int offset_g, double FACTR, double PGTOL, ref double[] WS, int offset_ws, ref double[] WY, int offset_wy
, ref double[] SY, int offset_sy, ref double[] SS, int offset_ss, double[] YY, int offset_yy, ref double[] WT, int offset_wt, ref double[] WN, int offset_wn, ref double[] SND, int offset_snd
, ref double[] Z, int offset_z, ref double[] R, int offset_r, ref double[] D, int offset_d, ref double[] T, int offset_t, ref double[] WA, int offset_wa, double[] SG, int offset_sg
, double[] SGO, int offset_sgo, double[] YG, int offset_yg, double[] YGO, int offset_ygo, ref int[] INDEX, int offset_index, ref int[] IWHERE, int offset_iwhere, ref int[] INDX2, int offset_indx2
, ref BFGSTask TASK, int IPRINT, ref BFGSTask CSAVE, ref bool[] LSAVE, int offset_lsave, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
BFGSWord WORD = BFGSWord.aaa;
bool PRJCTD = false; bool CNSTND = false; bool BOXED = false; bool UPDATD = false; bool WRK = false;
int I = 0; int K = 0; int NINTOL = 0; int ITFILE = 0; int IBACK = 0; int NSKIP = 0;
int HEAD = 0; int COL = 0; int ITER = 0; int ITAIL = 0; int IUPDAT = 0; int NINT = 0; int NFGV = 0; int INFO = 0;
int IFUN = 0; int IWORD = 0; int NFREE = 0; int NACT = 0; int ILEAVE = 0; int NENTER = 0; double THETA = 0;
double FOLD = 0; double DDOT = 0; double DR = 0; double RR = 0; double TOL = 0; double DPMEPS = 0; double XSTEP = 0;
double SBGNRM = 0; double DDUM = 0; double DNORM = 0; double DTD = 0; double EPSMCH = 0; double CPU1 = 0;
double CPU2 = 0; double CACHYT = 0; double SBTIME = 0; double LNSCHT = 0; double TIME1 = 0; double TIME2 = 0;
double GD = 0; double GDOLD = 0; double STP = 0; double STPMX = 0; double TIME = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x; int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd;
int o_g = -1 + offset_g; int o_ws = -1 - N + offset_ws; int o_wy = -1 - N + offset_wy;
int o_sy = -1 - M + offset_sy; int o_ss = -1 - M + offset_ss; int o_yy = -1 - M + offset_yy;
int o_wt = -1 - M + offset_wt; int o_wn = -1 - (2 * M) + offset_wn; int o_snd = -1 - (2 * M) + offset_snd;
int o_z = -1 + offset_z; int o_r = -1 + offset_r; int o_d = -1 + offset_d; int o_t = -1 + offset_t;
int o_wa = -1 + offset_wa; int o_sg = -1 + offset_sg; int o_sgo = -1 + offset_sgo; int o_yg = -1 + offset_yg;
int o_ygo = -1 + offset_ygo; int o_index = -1 + offset_index; int o_iwhere = -1 + offset_iwhere;
int o_indx2 = -1 + offset_indx2; int o_lsave = -1 + offset_lsave; int o_isave = -1 + offset_isave;
int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c ************
// c
// c Subroutine mainlb
// c
// c This subroutine solves bound constrained optimization problems by
// c using the compact formula of the limited memory BFGS updates.
// c
// c n is an integer variable.
// c On entry n is the number of variables.
// c On exit n is unchanged.
// c
// c m is an integer variable.
// c On entry m is the maximum number of variable metric
// c corrections allowed in the limited memory matrix.
// c On exit m is unchanged.
// c
// c x is a double precision array of dimension n.
// c On entry x is an approximation to the solution.
// c On exit x is the current approximation.
// c
// c l is a double precision array of dimension n.
// c On entry l is the lower bound of x.
// c On exit l is unchanged.
// c
// c u is a double precision array of dimension n.
// c On entry u is the upper bound of x.
// c On exit u is unchanged.
// c
// c nbd is an integer array of dimension n.
// c On entry nbd represents the type of bounds imposed on the
// c variables, and must be specified as follows:
// c nbd(i)=0 if x(i) is unbounded,
// c 1 if x(i) has only a lower bound,
// c 2 if x(i) has both lower and upper bounds,
// c 3 if x(i) has only an upper bound.
// c On exit nbd is unchanged.
// c
// c f is a double precision variable.
// c On first entry f is unspecified.
// c On final exit f is the value of the function at x.
// c
// c g is a double precision array of dimension n.
// c On first entry g is unspecified.
// c On final exit g is the value of the gradient at x.
// c
// c factr is a double precision variable.
// c On entry factr >= 0 is specified by the user. The iteration
// c will stop when
// c
// c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch
// c
// c where epsmch is the machine precision, which is automatically
// c generated by the code.
// c On exit factr is unchanged.
// c
// c pgtol is a double precision variable.
// c On entry pgtol >= 0 is specified by the user. The iteration
// c will stop when
// c
// c max{|proj g_i | i = 1, ..., n} <= pgtol
// c
// c where pg_i is the ith component of the projected gradient.
// c On exit pgtol is unchanged.
// c
// c ws, wy, sy, and wt are double precision working arrays used to
// c store the following information defining the limited memory
// c BFGS matrix:
// c ws, of dimension n x m, stores S, the matrix of s-vectors;
// c wy, of dimension n x m, stores Y, the matrix of y-vectors;
// c sy, of dimension m x m, stores S'Y;
// c ss, of dimension m x m, stores S'S;
// c yy, of dimension m x m, stores Y'Y;
// c wt, of dimension m x m, stores the Cholesky factorization
// c of (theta*S'S+LD^(-1)L'); see eq.
// c (2.26) in [3].
// c
// c wn is a double precision working array of dimension 2m x 2m
// c used to store the LEL^T factorization of the indefinite matrix
// c K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
// c [L_a -R_z theta*S'AA'S ]
// c
// c where E = [-I 0]
// c [ 0 I]
// c
// c snd is a double precision working array of dimension 2m x 2m
// c used to store the lower triangular part of
// c N = [Y' ZZ'Y L_a'+R_z']
// c [L_a +R_z S'AA'S ]
// c
// c z(n),r(n),d(n),t(n),wa(8*m) are double precision working arrays.
// c z is used at different times to store the Cauchy point and
// c the Newton point.
// c
// c sg(m),sgo(m),yg(m),ygo(m) are double precision working arrays.
// c
// c index is an integer working array of dimension n.
// c In subroutine freev, index is used to store the free and fixed
// c variables at the Generalized Cauchy Point (GCP).
// c
// c iwhere is an integer working array of dimension n used to record
// c the status of the vector x for GCP computation.
// c iwhere(i)=0 or -3 if x(i) is free and has bounds,
// c 1 if x(i) is fixed at l(i), and l(i) .ne. u(i)
// c 2 if x(i) is fixed at u(i), and u(i) .ne. l(i)
// c 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i)
// c -1 if x(i) is always free, i.e., no bounds on it.
// c
// c indx2 is an integer working array of dimension n.
// c Within subroutine cauchy, indx2 corresponds to the array iorder.
// c In subroutine freev, a list of variables entering and leaving
// c the free set is stored in indx2, and it is passed on to
// c subroutine formk with this information.
// c
// c task is a working string of characters of length 60 indicating
// c the current job when entering and leaving this subroutine.
// c
// c iprint is an INTEGER variable that must be set by the user.
// c It controls the frequency and type of output generated:
// c iprint<0 no output is generated;
// c iprint=0 print only one line at the last iteration;
// c 0<iprint<99 print also f and |proj g| every iprint iterations;
// c iprint=99 print details of every iteration except n-vectors;
// c iprint=100 print also the changes of active set and final x;
// c iprint>100 print details of every iteration including x and g;
// c When iprint > 0, the file iterate.dat will be created to
// c summarize the iteration.
// c
// c csave is a working string of characters of length 60.
// c
// c lsave is a logical working array of dimension 4.
// c
// c isave is an integer working array of dimension 23.
// c
// c dsave is a double precision working array of dimension 29.
// c
// c
// c Subprograms called
// c
// c L-BFGS-B Library ... cauchy, subsm, lnsrlb, formk,
// c
// c errclb, prn1lb, prn2lb, prn3lb, active, projgr,
// c
// c freev, cmprlb, matupd, formt.
// c
// c Minpack2 Library ... timer, dpmeps.
// c
// c Linpack Library ... dcopy, ddot.
// c
// c
// c References:
// c
// c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited
// c memory algorithm for bound constrained optimization'',
// c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208.
// c
// c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN
// c Subroutines for Large Scale Bound Constrained Optimization''
// c Tech. Report, NAM-11, EECS Department, Northwestern University,
// c 1994.
// c
// c [3] R. Byrd, J. Nocedal and R. Schnabel "Representations of
// c Quasi-Newton Matrices and their use in Limited Memory Methods'',
// c Mathematical Programming 63 (1994), no. 4, pp. 129-156.
// c
// c (Postscript files of these papers are available via anonymous
// c ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.)
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.START)
{
this._timer.Run(ref TIME1);
// c Generate the current machine precision.
EPSMCH = this._dpmeps.Run();
// c Initialize counters and scalars when task='START'.
// c for the limited memory BFGS matrices:
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
// c for operation counts:
ITER = 0;
NFGV = 0;
NINT = 0;
NINTOL = 0;
NSKIP = 0;
NFREE = N;
// c for stopping tolerance:
TOL = FACTR * EPSMCH;
// c for measuring running time:
CACHYT = 0;
SBTIME = 0;
LNSCHT = 0;
// c 'word' records the status of subspace solutions.
WORD = BFGSWord.aaa;
// c 'info' records the termination information.
INFO = 0;
if (IPRINT >= 1)
{
// c open a summary file 'iterate.dat'
//ERROR-ERROR OPEN (8, FILE = 'iterate.dat', STATUS = 'unknown');
ITFILE = 8;
}
// c Check the input arguments for errors.
this._errclb.Run(N, M, FACTR, L, offset_l, U, offset_u, NBD, offset_nbd
, ref TASK, ref INFO, ref K);
if (TASK == BFGSTask.ERROR)
{
this._prn3lb.Run(N, X, offset_x, F, TASK, IPRINT, INFO
, ITFILE, ITER, NFGV, NINTOL, NSKIP, NACT
, SBGNRM, ZERO, NINT, WORD, IBACK, STP
, XSTEP, K, CACHYT, SBTIME, LNSCHT);
return;
}
this._prn1lb.Run(N, M, L, offset_l, U, offset_u, X, offset_x, IPRINT
, ITFILE, EPSMCH);
// c Initialize iwhere & project x onto the feasible set.
this._active.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, ref X, offset_x, ref IWHERE, offset_iwhere
, IPRINT, ref PRJCTD, ref CNSTND, ref BOXED);
// c The end of the initialization.
}
else
{
// c restore local variables.
PRJCTD = LSAVE[1 + o_lsave];
CNSTND = LSAVE[2 + o_lsave];
BOXED = LSAVE[3 + o_lsave];
UPDATD = LSAVE[4 + o_lsave];
NINTOL = ISAVE[1 + o_isave];
ITFILE = ISAVE[3 + o_isave];
IBACK = ISAVE[4 + o_isave];
NSKIP = ISAVE[5 + o_isave];
HEAD = ISAVE[6 + o_isave];
COL = ISAVE[7 + o_isave];
ITAIL = ISAVE[8 + o_isave];
ITER = ISAVE[9 + o_isave];
IUPDAT = ISAVE[10 + o_isave];
NINT = ISAVE[12 + o_isave];
NFGV = ISAVE[13 + o_isave];
INFO = ISAVE[14 + o_isave];
IFUN = ISAVE[15 + o_isave];
IWORD = ISAVE[16 + o_isave];
NFREE = ISAVE[17 + o_isave];
NACT = ISAVE[18 + o_isave];
ILEAVE = ISAVE[19 + o_isave];
NENTER = ISAVE[20 + o_isave];
THETA = DSAVE[1 + o_dsave];
FOLD = DSAVE[2 + o_dsave];
TOL = DSAVE[3 + o_dsave];
DNORM = DSAVE[4 + o_dsave];
EPSMCH = DSAVE[5 + o_dsave];
CPU1 = DSAVE[6 + o_dsave];
CACHYT = DSAVE[7 + o_dsave];
SBTIME = DSAVE[8 + o_dsave];
LNSCHT = DSAVE[9 + o_dsave];
TIME1 = DSAVE[10 + o_dsave];
GD = DSAVE[11 + o_dsave];
STPMX = DSAVE[12 + o_dsave];
SBGNRM = DSAVE[13 + o_dsave];
STP = DSAVE[14 + o_dsave];
GDOLD = DSAVE[15 + o_dsave];
DTD = DSAVE[16 + o_dsave];
// c After returning from the driver go to the point where execution
// c is to resume.
if (TASK == BFGSTask.FG_LNSRCH)
{
goto LABEL666;
}
if (TASK == BFGSTask.NEW_X)
{
goto LABEL777;
}
if (TASK == BFGSTask.FG_ST || TASK == BFGSTask.FG_START)
{
goto LABEL111;
}
if (TASK == BFGSTask.STOP)
{
if (TASK == BFGSTask.CPU)
{
// c restore the previous iterate.
this._dcopy.Run(N, T, offset_t, 1, ref X, offset_x, 1);
this._dcopy.Run(N, R, offset_r, 1, ref G, offset_g, 1);
F = FOLD;
}
goto LABEL999;
}
}
// c Compute f0 and g0.
TASK = BFGSTask.FG_START;
// c return to the driver to calculate f and g; reenter at 111.
goto LABEL1000;
LABEL111 :;
NFGV = 1;
// c Compute the infinity norm of the (-) projected gradient.
this._projgr.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, X, offset_x, G, offset_g
, ref SBGNRM);
if (IPRINT >= 1)
{
//ERROR-ERROR WRITE (6,1002) ITER,F,SBGNRM;
//ERROR-ERROR WRITE (ITFILE,1003) ITER,NFGV,SBGNRM,F;
}
if (SBGNRM <= PGTOL)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
goto LABEL999;
}
// c ----------------- the beginning of the loop --------------------------
LABEL222 :;
if (IPRINT >= 99)
{
; //ERROR-ERRORWRITE(6,1001)ITER+1
}
IWORD = -1;
// c
if (!CNSTND && COL > 0)
{
// c skip the search for GCP.
this._dcopy.Run(N, X, offset_x, 1, ref Z, offset_z, 1);
WRK = UPDATD;
NINT = 0;
goto LABEL333;
}
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Compute the Generalized Cauchy Point (GCP).
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
this._timer.Run(ref CPU1);
this._cauchy.Run(N, X, offset_x, L, offset_l, U, offset_u, NBD, offset_nbd, G, offset_g
, ref INDX2, offset_indx2, ref IWHERE, offset_iwhere, ref T, offset_t, ref D, offset_d, ref Z, offset_z, M
, WY, offset_wy, WS, offset_ws, SY, offset_sy, WT, offset_wt, THETA, COL
, HEAD, ref WA, 1 + o_wa, ref WA, 2 * M + 1 + o_wa, ref WA, 4 * M + 1 + o_wa, ref WA, 6 * M + 1 + o_wa, ref NINT
, SG, offset_sg, YG, offset_yg, IPRINT, SBGNRM, ref INFO, EPSMCH);
if (INFO != 0)
{
// c singular triangular system detected; refresh the lbfgs memory.
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1005)
}
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
CACHYT += CPU2 - CPU1;
goto LABEL222;
}
this._timer.Run(ref CPU2);
CACHYT += CPU2 - CPU1;
NINTOL += NINT;
// c Count the entering and leaving variables for iter > 0;
// c find the index set of free and active variables at the GCP.
this._freev.Run(N, ref NFREE, ref INDEX, offset_index, ref NENTER, ref ILEAVE, ref INDX2, offset_indx2
, IWHERE, offset_iwhere, ref WRK, UPDATD, CNSTND, IPRINT, ITER);
NACT = N - NFREE;
LABEL333 :;
// c If there are no free variables or B=theta*I, then
// c skip the subspace minimization.
if (NFREE == 0 || COL == 0)
{
goto LABEL555;
}
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Subspace minimization.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
this._timer.Run(ref CPU1);
// c Form the LEL^T factorization of the indefinite
// c matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ]
// c [L_a -R_z theta*S'AA'S ]
// c where E = [-I 0]
// c [ 0 I]
if (WRK)
{
this._formk.Run(N, NFREE, INDEX, offset_index, NENTER, ILEAVE, INDX2, offset_indx2
, IUPDAT, UPDATD, ref WN, offset_wn, ref SND, offset_snd, M, WS, offset_ws
, WY, offset_wy, SY, offset_sy, THETA, COL, HEAD, ref INFO);
}
if (INFO != 0)
{
// c nonpositive definiteness in Cholesky factorization;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1006)
}
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
goto LABEL222;
}
// c compute r=-Z'B(xcp-xk)-Z'g (using wa(2m+1)=W'(xcp-x)
// c from 'cauchy').
this._cmprlb.Run(N, M, X, offset_x, G, offset_g, WS, offset_ws, WY, offset_wy
, SY, offset_sy, WT, offset_wt, Z, offset_z, ref R, offset_r, ref WA, offset_wa, INDEX, offset_index
, THETA, COL, HEAD, NFREE, CNSTND, ref INFO);
if (INFO != 0)
{
goto LABEL444;
}
// c call the direct method.
this._subsm.Run(N, M, NFREE, INDEX, offset_index, L, offset_l, U, offset_u
, NBD, offset_nbd, ref Z, offset_z, ref R, offset_r, WS, offset_ws, WY, offset_wy, THETA
, COL, HEAD, ref IWORD, ref WA, offset_wa, WN, offset_wn, IPRINT
, ref INFO);
LABEL444 :;
if (INFO != 0)
{
// c singular triangular system detected;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1005)
}
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
goto LABEL222;
}
this._timer.Run(ref CPU2);
SBTIME += CPU2 - CPU1;
LABEL555 :;
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Line search and optimality tests.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c Generate the search direction d:=z-x.
for (I = 1; I <= N; I++)
{
D[I + o_d] = Z[I + o_z] - X[I + o_x];
}
this._timer.Run(ref CPU1);
LABEL666 :;
this._lnsrlb.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, ref X, offset_x, F
, ref FOLD, ref GD, ref GDOLD, G, offset_g, D, offset_d, ref R, offset_r
, ref T, offset_t, Z, offset_z, ref STP, ref DNORM, ref DTD, ref XSTEP
, ref STPMX, ITER, ref IFUN, ref IBACK, ref NFGV, ref INFO
, ref TASK, BOXED, CNSTND, ref CSAVE, ref ISAVE, 22 + o_isave, ref DSAVE, 17 + o_dsave);
if (INFO != 0 || IBACK >= 20)
{
// c restore the previous iterate.
this._dcopy.Run(N, T, offset_t, 1, ref X, offset_x, 1);
this._dcopy.Run(N, R, offset_r, 1, ref G, offset_g, 1);
F = FOLD;
if (COL == 0)
{
// c abnormal termination.
if (INFO == 0)
{
INFO = -9;
// c restore the actual number of f and g evaluations etc.
NFGV -= 1;
IFUN -= 1;
IBACK -= 1;
}
TASK = BFGSTask.ABNO;
ITER += 1;
goto LABEL999;
}
else
{
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1008)
}
if (INFO == 0)
{
NFGV -= 1;
}
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
TASK = BFGSTask.RESTART;
this._timer.Run(ref CPU2);
LNSCHT += CPU2 - CPU1;
goto LABEL222;
}
}
else
{
if (TASK == BFGSTask.FG_LNSRCH)
{
// c return to the driver for calculating f and g; reenter at 666.
goto LABEL1000;
}
else
{
// c calculate and print out the quantities related to the new X.
this._timer.Run(ref CPU2);
LNSCHT += CPU2 - CPU1;
ITER += 1;
// c Compute the infinity norm of the projected (-)gradient.
this._projgr.Run(N, L, offset_l, U, offset_u, NBD, offset_nbd, X, offset_x, G, offset_g
, ref SBGNRM);
// c Print iteration information.
this._prn2lb.Run(N, X, offset_x, F, G, offset_g, IPRINT, ITFILE
, ITER, NFGV, NACT, SBGNRM, NINT, ref WORD
, IWORD, IBACK, STP, XSTEP);
goto LABEL1000;
}
}
LABEL777 :;
// c Test for termination.
if (SBGNRM <= PGTOL)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
goto LABEL999;
}
DDUM = Math.Max(Math.Abs(FOLD), Math.Max(Math.Abs(F), ONE));
if ((FOLD - F) <= TOL * DDUM)
{
// c terminate the algorithm.
TASK = BFGSTask.CONV;
if (IBACK >= 10)
{
INFO = -5;
}
// c i.e., to issue a warning if iback>10 in the line search.
goto LABEL999;
}
// c Compute d=newx-oldx, r=newg-oldg, rr=y'y and dr=y's.
for (I = 1; I <= N; I++)
{
R[I + o_r] = G[I + o_g] - R[I + o_r];
}
RR = this._ddot.Run(N, R, offset_r, 1, R, offset_r, 1);
if (STP == ONE)
{
DR = GD - GDOLD;
DDUM = -GDOLD;
}
else
{
DR = (GD - GDOLD) * STP;
this._dscal.Run(N, STP, ref D, offset_d, 1);
DDUM = -GDOLD * STP;
}
if (DR <= EPSMCH * DDUM)
{
// c skip the L-BFGS update.
NSKIP += 1;
UPDATD = false;
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1004)DR,DDUM
}
goto LABEL888;
}
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
// c
// c Update the L-BFGS matrix.
// c
// cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
UPDATD = true;
IUPDAT += 1;
// c Update matrices WS and WY and form the middle matrix in B.
this._matupd.Run(N, M, ref WS, offset_ws, ref WY, offset_wy, ref SY, offset_sy, ref SS, offset_ss
, D, offset_d, R, offset_r, ref ITAIL, IUPDAT, ref COL, ref HEAD
, ref THETA, RR, DR, STP, DTD);
// c Form the upper half of the pds T = theta*SS + L*D^(-1)*L';
// c Store T in the upper triangular of the array wt;
// c Cholesky factorize T to J*J' with
// c J' stored in the upper triangular of wt.
this._formt.Run(M, ref WT, offset_wt, SY, offset_sy, SS, offset_ss, COL, THETA
, ref INFO);
if (INFO != 0)
{
// c nonpositive definiteness in Cholesky factorization;
// c refresh the lbfgs memory and restart the iteration.
if (IPRINT >= 1)
{
; //ERROR-ERRORWRITE(6,1007)
}
INFO = 0;
COL = 0;
HEAD = 1;
THETA = ONE;
IUPDAT = 0;
UPDATD = false;
goto LABEL222;
}
// c Now the inverse of the middle matrix in B is
// c [ D^(1/2) O ] [ -D^(1/2) D^(-1/2)*L' ]
// c [ -L*D^(-1/2) J ] [ 0 J' ]
LABEL888 :;
// c -------------------- the end of the loop -----------------------------
goto LABEL222;
LABEL999 :;
this._timer.Run(ref TIME2);
TIME = TIME2 - TIME1;
this._prn3lb.Run(N, X, offset_x, F, TASK, IPRINT, INFO
, ITFILE, ITER, NFGV, NINTOL, NSKIP, NACT
, SBGNRM, TIME, NINT, WORD, IBACK, STP
, XSTEP, K, CACHYT, SBTIME, LNSCHT);
LABEL1000 :;
// c Save local variables.
LSAVE[1 + o_lsave] = PRJCTD;
LSAVE[2 + o_lsave] = CNSTND;
LSAVE[3 + o_lsave] = BOXED;
LSAVE[4 + o_lsave] = UPDATD;
ISAVE[1 + o_isave] = NINTOL;
ISAVE[3 + o_isave] = ITFILE;
ISAVE[4 + o_isave] = IBACK;
ISAVE[5 + o_isave] = NSKIP;
ISAVE[6 + o_isave] = HEAD;
ISAVE[7 + o_isave] = COL;
ISAVE[8 + o_isave] = ITAIL;
ISAVE[9 + o_isave] = ITER;
ISAVE[10 + o_isave] = IUPDAT;
ISAVE[12 + o_isave] = NINT;
ISAVE[13 + o_isave] = NFGV;
ISAVE[14 + o_isave] = INFO;
ISAVE[15 + o_isave] = IFUN;
ISAVE[16 + o_isave] = IWORD;
ISAVE[17 + o_isave] = NFREE;
ISAVE[18 + o_isave] = NACT;
ISAVE[19 + o_isave] = ILEAVE;
ISAVE[20 + o_isave] = NENTER;
DSAVE[1 + o_dsave] = THETA;
DSAVE[2 + o_dsave] = FOLD;
DSAVE[3 + o_dsave] = TOL;
DSAVE[4 + o_dsave] = DNORM;
DSAVE[5 + o_dsave] = EPSMCH;
DSAVE[6 + o_dsave] = CPU1;
DSAVE[7 + o_dsave] = CACHYT;
DSAVE[8 + o_dsave] = SBTIME;
DSAVE[9 + o_dsave] = LNSCHT;
DSAVE[10 + o_dsave] = TIME1;
DSAVE[11 + o_dsave] = GD;
DSAVE[12 + o_dsave] = STPMX;
DSAVE[13 + o_dsave] = SBGNRM;
DSAVE[14 + o_dsave] = STP;
DSAVE[15 + o_dsave] = GDOLD;
DSAVE[16 + o_dsave] = DTD;
return;
#endregion
}
public void Run(int N, double[] X, int offset_x, double F, BFGSTask TASK, int IPRINT, int INFO
, int ITFILE, int ITER, int NFGV, int NINTOL, int NSKIP, int NACT
, double SBGNRM, double TIME, int NINT, BFGSWord WORD, int IBACK, double STP
, double XSTEP, int K, double CACHYT, double SBTIME, double LNSCHT)
{
#region Variables
int I = 0;
#endregion
#region Array Index Correction
int o_x = -1 + offset_x;
#endregion
#region Prolog
// c ************
// c
// c Subroutine prn3lb
// c
// c This subroutine prints out information when either a built-in
// c convergence test is satisfied or when an error message is
// c generated.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c ************
#endregion
#region Body
if (TASK == BFGSTask.ERROR) goto LABEL999;
if (IPRINT >= 0)
{
//ERROR-ERROR WRITE (6,3003);
//ERROR-ERROR WRITE (6,3004);
//ERROR-ERROR WRITE(6,3005) N,ITER,NFGV,NINTOL,NSKIP,NACT,SBGNRM,F;
if (IPRINT >= 100)
{
//ERROR-ERROR WRITE (6,1004) 'X =',(X(I),I = 1,N);
}
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,*)' F =',F
}
LABEL999:;
if (IPRINT >= 0)
{
//ERROR-ERROR WRITE (6,3009) TASK;
if (INFO != 0)
{
if (INFO == - 1) ;//ERROR-ERRORWRITE(6,9011)
if (INFO == - 2) ;//ERROR-ERRORWRITE(6,9012)
if (INFO == - 3) ;//ERROR-ERRORWRITE(6,9013)
if (INFO == - 4) ;//ERROR-ERRORWRITE(6,9014)
if (INFO == - 5) ;//ERROR-ERRORWRITE(6,9015)
if (INFO == - 6) ;//ERROR-ERRORWRITE(6,*)' Input nbd(',K,') is invalid.'
if (INFO == - 7) ;//ERROR-ERRORWRITE(6,*)' l(',K,') > u(',K,'). No feasible solution.'
if (INFO == - 8) ;//ERROR-ERRORWRITE(6,9018)
if (INFO == - 9) ;//ERROR-ERRORWRITE(6,9019)
}
if (IPRINT >= 1) ;//ERROR-ERRORWRITE(6,3007)CACHYT,SBTIME,LNSCHT
//ERROR-ERROR WRITE (6,3008) TIME;
if (IPRINT >= 1)
{
if (INFO == - 4 || INFO == - 9)
{
//ERROR-ERROR WRITE (ITFILE,3002)ITER,NFGV,NINT,NACT,WORD,IBACK,STP,XSTEP;
}
//ERROR-ERROR WRITE (ITFILE,3009) TASK;
if (INFO != 0)
{
if (INFO == - 1) ;//ERROR-ERRORWRITE(ITFILE,9011)
if (INFO == - 2) ;//ERROR-ERRORWRITE(ITFILE,9012)
if (INFO == - 3) ;//ERROR-ERRORWRITE(ITFILE,9013)
if (INFO == - 4) ;//ERROR-ERRORWRITE(ITFILE,9014)
if (INFO == - 5) ;//ERROR-ERRORWRITE(ITFILE,9015)
if (INFO == - 8) ;//ERROR-ERRORWRITE(ITFILE,9018)
if (INFO == - 9) ;//ERROR-ERRORWRITE(ITFILE,9019)
}
//ERROR-ERROR WRITE (ITFILE,3008) TIME;
}
}
return;
#endregion
}
public void Run(int N, double[] L, int offset_l, double[] U, int offset_u, int[] NBD, int offset_nbd, ref double[] X, int offset_x, double F
, ref double FOLD, ref double GD, ref double GDOLD, double[] G, int offset_g, double[] D, int offset_d, ref double[] R, int offset_r
, ref double[] T, int offset_t, double[] Z, int offset_z, ref double STP, ref double DNORM, ref double DTD, ref double XSTEP
, ref double STPMX, int ITER, ref int IFUN, ref int IBACK, ref int NFGV, ref int INFO
, ref BFGSTask TASK, bool BOXED, bool CNSTND, ref BFGSTask CSAVE, ref int[] ISAVE, int offset_isave, ref double[] DSAVE, int offset_dsave)
{
#region Variables
int I = 0; double DDOT = 0; double A1 = 0; double A2 = 0;
#endregion
#region Array Index Correction
int o_l = -1 + offset_l; int o_u = -1 + offset_u; int o_nbd = -1 + offset_nbd; int o_x = -1 + offset_x;
int o_g = -1 + offset_g; int o_d = -1 + offset_d; int o_r = -1 + offset_r; int o_t = -1 + offset_t;
int o_z = -1 + offset_z; int o_isave = -1 + offset_isave; int o_dsave = -1 + offset_dsave;
#endregion
#region Prolog
// c **********
// c
// c Subroutine lnsrlb
// c
// c This subroutine calls subroutine dcsrch from the Minpack2 library
// c to perform the line search. Subroutine dscrch is safeguarded so
// c that all trial points lie within the feasible region.
// c
// c Subprograms called:
// c
// c Minpack2 Library ... dcsrch.
// c
// c Linpack ... dtrsl, ddot.
// c
// c
// c * * *
// c
// c NEOS, November 1994. (Latest revision June 1996.)
// c Optimization Technology Center.
// c Argonne National Laboratory and Northwestern University.
// c Written by
// c Ciyou Zhu
// c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal.
// c
// c
// c **********
#endregion
#region Body
if (TASK == BFGSTask.FG_LNSRCH)
{
goto LABEL556;
}
DTD = this._ddot.Run(N, D, offset_d, 1, D, offset_d, 1);
DNORM = Math.Sqrt(DTD);
// c Determine the maximum step length.
STPMX = BIG;
if (CNSTND)
{
if (ITER == 0)
{
STPMX = ONE;
}
else
{
for (I = 1; I <= N; I++)
{
A1 = D[I + o_d];
if (NBD[I + o_nbd] != 0)
{
if (A1 < ZERO && NBD[I + o_nbd] <= 2)
{
A2 = L[I + o_l] - X[I + o_x];
if (A2 >= ZERO)
{
STPMX = ZERO;
}
else
{
if (A1 * STPMX < A2)
{
STPMX = A2 / A1;
}
}
}
else
{
if (A1 > ZERO && NBD[I + o_nbd] >= 2)
{
A2 = U[I + o_u] - X[I + o_x];
if (A2 <= ZERO)
{
STPMX = ZERO;
}
else
{
if (A1 * STPMX > A2)
{
STPMX = A2 / A1;
}
}
}
}
}
}
}
}
if (ITER == 0 && !BOXED)
{
STP = Math.Min(ONE / DNORM, STPMX);
}
else
{
STP = ONE;
}
this._dcopy.Run(N, X, offset_x, 1, ref T, offset_t, 1);
this._dcopy.Run(N, G, offset_g, 1, ref R, offset_r, 1);
FOLD = F;
IFUN = 0;
IBACK = 0;
CSAVE = BFGSTask.START;
LABEL556 :;
GD = this._ddot.Run(N, G, offset_g, 1, D, offset_d, 1);
if (IFUN == 0)
{
GDOLD = GD;
if (GD >= ZERO)
{
// c the directional derivative >=0.
// c Line search is impossible.
INFO = -4;
return;
}
}
this._dcsrch.Run(F, GD, ref STP, FTOL, GTOL, XTOL
, ZERO, STPMX, ref CSAVE, ref ISAVE, offset_isave, ref DSAVE, offset_dsave);
XSTEP = STP * DNORM;
if (CSAVE != BFGSTask.CONV && CSAVE != BFGSTask.WARNING)
{
TASK = BFGSTask.FG_LNSRCH;
IFUN += 1;
NFGV += 1;
IBACK = IFUN - 1;
if (STP == ONE)
{
this._dcopy.Run(N, Z, offset_z, 1, ref X, offset_x, 1);
}
else
{
for (I = 1; I <= N; I++)
{
X[I + o_x] = STP * D[I + o_d] + T[I + o_t];
}
}
}
else
{
TASK = BFGSTask.NEW_X;
}
return;
#endregion
}
