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readme update
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jacobwilliams committed May 30, 2023
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Expand Up @@ -33,154 +33,7 @@ a few changes to the drivers to run their applications.
The user is required to calculate the function value `f` and its gradient `g`.
In order to allow the user complete control over these computations,
reverse communication is used. The routine `setulb` must be called
repeatedly under the control of the variable task. The calling
statement of L-BFGS-B is

```fortran
call setulb(n,m,x,l,u,nbd,f,g,factr,pgtol,wa,iwa,task,iprint, csave,lsave,isave,dsave)
```

Following is a description of all the parameters used in this call.

```
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
```
repeatedly under the control of the variable task.

### License

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