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diff --git a/driver1.f90 b/driver1.f90 new file mode 100755 index 0000000..67fa540 --- /dev/null +++ b/driver1.f90 @@ -0,0 +1,297 @@ +! +! L-BFGS-B is released under the “New BSD License” (aka “Modified BSD License” +! or “3-clause license”) +! Please read attached file License.txt +! +! +! DRIVER1 in Fortran 90 +! -------------------------------------------------------------- +! +! L-BFGS-B is a code for solving large nonlinear optimization +! problems with simple bounds on the variables. +! +! The code can also be used for unconstrained problems and is +! as efficient for these problems as the earlier limited memory +! code L-BFGS. +! +! This is the simplest driver in the package. It uses all the +! default settings of the code. +! +! +! References: +! +! [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited +! memory algorithm for bound constrained optimization'', +! SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. +! +! [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN +! Subroutines for Large Scale Bound Constrained Optimization'' +! Tech. Report, NAM-11, EECS Department, Northwestern University, +! 1994. +! +! +! (Postscript files of these papers are available via anonymous +! ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) +! +! * * * +! +! March 2011 (latest revision) +! Optimization Center at Northwestern University +! Instituto Tecnologico Autonomo de Mexico +! +! Jorge Nocedal and Jose Luis Morales +! +! -------------------------------------------------------------- +! DESCRIPTION OF THE VARIABLES IN L-BFGS-B +! -------------------------------------------------------------- +! +! n is an INTEGER variable that must be set by the user to the +! number of variables. It is not altered by the routine. +! +! m is an INTEGER variable that must be set by the user to the +! number of corrections used in the limited memory matrix. +! It is not altered by the routine. Values of m < 3 are +! not recommended, and large values of m can result in excessive +! computing time. The range 3 <= m <= 20 is recommended. +! +! x is a DOUBLE PRECISION array of length n. On initial entry +! it must be set by the user to the values of the initial +! estimate of the solution vector. Upon successful exit, it +! contains the values of the variables at the best point +! found (usually an approximate solution). +! +! l is a DOUBLE PRECISION array of length n that must be set by +! the user to the values of the lower bounds on the variables. If +! the i-th variable has no lower bound, l(i) need not be defined. +! +! u is a DOUBLE PRECISION array of length n that must be set by +! the user to the values of the upper bounds on the variables. If +! the i-th variable has no upper bound, u(i) need not be defined. +! +! nbd is an INTEGER array of dimension n that must be set by the +! user to the type of bounds imposed on the variables: +! 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. +! +! f is a DOUBLE PRECISION variable. If the routine setulb returns +! with task(1:2)= 'FG', then f must be set by the user to +! contain the value of the function at the point x. +! +! g is a DOUBLE PRECISION array of length n. If the routine setulb +! returns with taskb(1:2)= 'FG', then g must be set by the user to +! contain the components of the gradient at the point x. +! +! factr is a DOUBLE PRECISION variable that must be set by the user. +! It is a tolerance in the termination test for the algorithm. +! The iteration will stop when +! +! (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch +! +! where epsmch is the machine precision which is automatically +! generated by the code. Typical values for factr on a computer +! with 15 digits of accuracy in double precision are: +! factr=1.d+12 for low accuracy; +! 1.d+7 for moderate accuracy; +! 1.d+1 for extremely high accuracy. +! The user can suppress this termination test by setting factr=0. +! +! pgtol is a double precision variable. +! On entry pgtol >= 0 is specified by the user. The iteration +! will stop when +! +! max{|proj g_i | i = 1, ..., n} <= pgtol +! +! where pg_i is the ith component of the projected gradient. +! The user can suppress this termination test by setting pgtol=0. +! +! wa is a DOUBLE PRECISION array of length +! (2mmax + 5)nmax + 11mmax^2 + 8mmax used as workspace. +! This array must not be altered by the user. +! +! iwa is an INTEGER array of length 3nmax used as +! workspace. This array must not be altered by the user. +! +! task is a CHARACTER string of length 60. +! On first entry, it must be set to 'START'. +! On a return with task(1:2)='FG', the user must evaluate the +! function f and gradient g at the returned value of x. +! On a return with task(1:5)='NEW_X', an iteration of the +! algorithm has concluded, and f and g contain f(x) and g(x) +! respectively. The user can decide whether to continue or stop +! the iteration. +! When +! task(1:4)='CONV', the termination test in L-BFGS-B has been +! satisfied; +! task(1:4)='ABNO', the routine has terminated abnormally +! without being able to satisfy the termination conditions, +! x contains the best approximation found, +! f and g contain f(x) and g(x) respectively; +! task(1:5)='ERROR', the routine has detected an error in the +! input parameters; +! On exit with task = 'CONV', 'ABNO' or 'ERROR', the variable task +! contains additional information that the user can print. +! This array should not be altered unless the user wants to +! stop the run for some reason. See driver2 or driver3 +! for a detailed explanation on how to stop the run +! by assigning task(1:4)='STOP' in the driver. +! +! iprint is an INTEGER variable that must be set by the user. +! It controls the frequency and type of output generated: +! iprint<0 no output is generated; +! iprint=0 print only one line at the last iteration; +! 0<iprint<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>100 print details of every iteration including x and g; +! When iprint > 0, the file iterate.dat will be created to +! summarize the iteration. +! +! csave is a CHARACTER working array of length 60. +! +! lsave is a LOGICAL working array of dimension 4. +! On exit with task = 'NEW_X', the following information is +! available: +! lsave(1) = .true. the initial x did not satisfy the bounds; +! lsave(2) = .true. the problem contains bounds; +! lsave(3) = .true. each variable has upper and lower bounds. +! +! isave is an INTEGER working array of dimension 44. +! On exit with task = 'NEW_X', it contains information that +! the user may want to access: +! isave(30) = the current iteration number; +! isave(34) = the total number of function and gradient +! evaluations; +! isave(36) = the number of function value or gradient +! evaluations in the current iteration; +! isave(38) = the number of free variables in the current +! iteration; +! isave(39) = the number of active constraints at the current +! iteration; +! +! see the subroutine setulb.f for a description of other +! information contained in isave +! +! dsave is a DOUBLE PRECISION working array of dimension 29. +! On exit with task = 'NEW_X', it contains information that +! the user may want to access: +! dsave(2) = the value of f at the previous iteration; +! dsave(5) = the machine precision epsmch generated by the code; +! dsave(13) = the infinity norm of the projected gradient; +! +! see the subroutine setulb.f for a description of other +! information contained in dsave +! +! -------------------------------------------------------------- +! END OF THE DESCRIPTION OF THE VARIABLES IN L-BFGS-B +! -------------------------------------------------------------- +! + program driver +! +! This simple driver demonstrates how to call the L-BFGS-B code to +! solve a sample problem (the extended Rosenbrock function +! subject to bounds on the variables). The dimension n of this +! problem is variable. + + implicit none +! +! Declare variables and parameters needed by the code. +! Note thar we wish to have output at every iteration. +! iprint=1 +! +! We also specify the tolerances in the stopping criteria. +! factr = 1.0d+7, pgtol = 1.0d-5 +! +! A description of all these variables is given at the beginning +! of the driver +! + integer, parameter :: n = 25, m = 5, iprint = 1 + integer, parameter :: dp = kind(1.0d0) + real(dp), parameter :: factr = 1.0d+7, pgtol = 1.0d-5 +! + character(len=60) :: task, csave + logical :: lsave(4) + integer :: isave(44) + real(dp) :: f + real(dp) :: dsave(29) + integer, allocatable :: nbd(:), iwa(:) + real(dp), allocatable :: x(:), l(:), u(:), g(:), wa(:) + +! Declare a few additional variables for this sample problem + + real(dp) :: t1, t2 + integer :: i + +! Allocate dynamic arrays + + allocate ( nbd(n), x(n), l(n), u(n), g(n) ) + allocate ( iwa(3*n) ) + allocate ( wa(2*m*n + 5*n + 11*m*m + 8*m) ) +! + do 10 i=1, n, 2 + nbd(i) = 2 + l(i) = 1.0d0 + u(i) = 1.0d2 + 10 continue + +! 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 + +! 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.)',/) + +! We start the iteration by initializing task. + + task = 'START' + +! The beginning of the loop + + do while(task(1:2).eq.'FG'.or.task.eq.'NEW_X'.or. & + task.eq.'START') + +! 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 + + 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 + +! 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 + + end if + end do + +! end of loop do while + + + end program driver + |