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diff --git a/driver1.f b/driver1.f new file mode 100644 index 0000000..b898e5d --- /dev/null +++ b/driver1.f @@ -0,0 +1,321 @@ +c +c L-BFGS-B is released under the “New BSD License” (aka “Modified BSD License” +c or “3-clause license”) +c Please read attached file License.txt +c +c DRIVER 1 in Fortran 77 +c -------------------------------------------------------------- +c SIMPLE DRIVER FOR L-BFGS-B (version 3.0) +c -------------------------------------------------------------- +c +c L-BFGS-B is a code for solving large nonlinear optimization +c problems with simple bounds on the variables. +c +c The code can also be used for unconstrained problems and is +c as efficient for these problems as the earlier limited memory +c code L-BFGS. +c +c This is the simplest driver in the package. It uses all the +c default settings of the code. +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 +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 March 2011 (latest revision) +c Optimization Center at Northwestern University +c Instituto Tecnologico Autonomo de Mexico +c +c Jorge Nocedal and Jose Luis Morales, Remark on "Algorithm 778: +c L-BFGS-B: Fortran Subroutines for Large-Scale Bound Constrained +c Optimization" (2011). To appear in ACM Transactions on +c Mathematical Software, + +c -------------------------------------------------------------- +c DESCRIPTION OF THE VARIABLES IN L-BFGS-B +c -------------------------------------------------------------- +c +c n is an INTEGER variable that must be set by the user to the +c number of variables. It is not altered by the routine. +c +c m is an INTEGER variable that must be set by the user to the +c number of corrections used in the limited memory matrix. +c It is not altered by the routine. Values of m < 3 are +c not recommended, and large values of m can result in excessive +c computing time. The range 3 <= m <= 20 is recommended. +c +c x is a DOUBLE PRECISION array of length n. On initial entry +c it must be set by the user to the values of the initial +c estimate of the solution vector. Upon successful exit, it +c contains the values of the variables at the best point +c found (usually an approximate solution). +c +c l is a DOUBLE PRECISION array of length n that must be set by +c the user to the values of the lower bounds on the variables. If +c the i-th variable has no lower bound, l(i) need not be defined. +c +c u is a DOUBLE PRECISION array of length n that must be set by +c the user to the values of the upper bounds on the variables. If +c the i-th variable has no upper bound, u(i) need not be defined. +c +c nbd is an INTEGER array of dimension n that must be set by the +c user to the type of bounds imposed on the variables: +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 +c f is a DOUBLE PRECISION variable. If the routine setulb returns +c with task(1:2)= 'FG', then f must be set by the user to +c contain the value of the function at the point x. +c +c g is a DOUBLE PRECISION array of length n. If the routine setulb +c returns with taskb(1:2)= 'FG', then g must be set by the user to +c contain the components of the gradient at the point x. +c +c factr is a DOUBLE PRECISION variable that must be set by the user. +c It is a tolerance in the termination test for the algorithm. +c The iteration 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 on a computer +c with 15 digits of accuracy in double precision are: +c factr=1.d+12 for low accuracy; +c 1.d+7 for moderate accuracy; +c 1.d+1 for extremely high accuracy. +c The user can suppress this termination test by setting factr=0. +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 The user can suppress this termination test by setting pgtol=0. +c +c wa is a DOUBLE PRECISION array of length +c (2mmax + 5)nmax + 11mmax^2 + 8mmax used as workspace. +c This array must not be altered by the user. +c +c iwa is an INTEGER array of length 3nmax used as +c workspace. This array must not be altered by the user. +c +c task is a CHARACTER string of length 60. +c On first entry, it must be set to 'START'. +c On a return with task(1:2)='FG', the user must evaluate the +c function f and gradient g at the returned value of x. +c On a return with task(1:5)='NEW_X', an iteration of the +c algorithm has concluded, and f and g contain f(x) and g(x) +c respectively. The user can decide whether to continue or stop +c the iteration. +c When +c task(1:4)='CONV', the termination test in L-BFGS-B has been +c satisfied; +c task(1:4)='ABNO', the routine has terminated abnormally +c without being able to satisfy the termination conditions, +c x contains the best approximation found, +c f and g contain f(x) and g(x) respectively; +c task(1:5)='ERROR', the routine has detected an error in the +c input parameters; +c On exit with task = 'CONV', 'ABNO' or 'ERROR', the variable task +c contains additional information that the user can print. +c This array should not be altered unless the user wants to +c stop the run for some reason. See driver2 or driver3 +c for a detailed explanation on how to stop the run +c by assigning task(1:4)='STOP' in the driver. +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 CHARACTER working array 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 lsave(1) = .true. the initial x did not satisfy the bounds; +c lsave(2) = .true. the problem contains bounds; +c lsave(3) = .true. each variable has upper and lower bounds. +c +c isave is an INTEGER working array of dimension 44. +c On exit with task = 'NEW_X', it contains information that +c the user may want to access: +c isave(30) = the current iteration number; +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 isave(38) = the number of free variables in the current +c iteration; +c isave(39) = the number of active constraints at the current +c iteration; +c +c see the subroutine setulb.f for a description of other +c information contained in isave +c +c dsave is a DOUBLE PRECISION working array of dimension 29. +c On exit with task = 'NEW_X', it contains information that +c the user may want to access: +c dsave(2) = the value of f at the previous iteration; +c dsave(5) = the machine precision epsmch generated by the code; +c dsave(13) = the infinity norm of the projected gradient; +c +c see the subroutine setulb.f for a description of other +c information contained in dsave +c +c -------------------------------------------------------------- +c END OF THE DESCRIPTION OF THE VARIABLES IN L-BFGS-B +c -------------------------------------------------------------- + + program driver + +c This simple driver demonstrates how to call the L-BFGS-B code to +c solve a sample problem (the extended Rosenbrock function +c subject to bounds on the variables). The dimension n of this +c problem is variable. + + integer nmax, mmax + parameter (nmax=1024, mmax=17) +c nmax is the dimension of the largest problem to be solved. +c mmax is the maximum number of limited memory corrections. + +c Declare the variables needed by the code. +c A description of all these variables is given at the end of +c the driver. + + character*60 task, csave + logical lsave(4) + integer n, m, iprint, + + nbd(nmax), iwa(3*nmax), isave(44) + double precision f, factr, pgtol, + + x(nmax), l(nmax), u(nmax), g(nmax), dsave(29), + + wa(2*mmax*nmax + 5*nmax + 11*mmax*mmax + 8*mmax) + +c Declare a few additional variables for this sample problem. + + double precision t1, t2 + integer i + +c We wish to have output at every iteration. + + iprint = 1 + +c We specify the tolerances in the stopping criteria. + + factr=1.0d+7 + pgtol=1.0d-5 + +c We specify the dimension n of the sample problem and the number +c m of limited memory corrections stored. (n and m should not +c exceed the limits nmax and mmax respectively.) + + n=25 + m=5 + +c We now provide nbd which defines the bounds on the variables: +c l specifies the lower bounds, +c u specifies the upper bounds. + +c First set bounds on the odd-numbered variables. + + do 10 i=1,n,2 + nbd(i)=2 + l(i)=1.0d0 + u(i)=1.0d2 + 10 continue + +c Next set bounds on the even-numbered variables. + + do 12 i=2,n,2 + nbd(i)=2 + l(i)=-1.0d2 + u(i)=1.0d2 + 12 continue + +c We now define the starting point. + + do 14 i=1,n + x(i)=3.0d0 + 14 continue + + write (6,16) + 16 format(/,5x, 'Solving sample problem.', + + /,5x, ' (f = 0.0 at the optimal solution.)',/) + +c We start the iteration by initializing task. +c + task = 'START' + +c ------- the beginning of the loop ---------- + + 111 continue + +c This is the call to the L-BFGS-B code. + + call setulb(n,m,x,l,u,nbd,f,g,factr,pgtol,wa,iwa,task,iprint, + + csave,lsave,isave,dsave) + + if (task(1:2) .eq. 'FG') then +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. + + f=.25d0*(x(1)-1.d0)**2 + do 20 i=2,n + f=f+(x(i)-x(i-1)**2)**2 + 20 continue + f=4.d0*f + +c Compute gradient g for the sample problem. + + t1=x(2)-x(1)**2 + g(1)=2.d0*(x(1)-1.d0)-1.6d1*x(1)*t1 + do 22 i=2,n-1 + t2=t1 + t1=x(i+1)-x(i)**2 + g(i)=8.d0*t2-1.6d1*x(i)*t1 + 22 continue + g(n)=8.d0*t1 + +c go back to the minimization routine. + goto 111 + endif +c + if (task(1:5) .eq. 'NEW_X') goto 111 +c the minimization routine has returned with a new iterate, +c and we have opted to continue the iteration. + +c ---------- the end of the loop ------------- + +c If task is neither FG nor NEW_X we terminate execution. + + stop + + end + +c======================= The end of driver1 ============================ |