pm_optimization::getMinBrent Interface Reference

Generate and return the minimum value and the corresponding abscissa xmin of the input 1-dimensional function isolated to a fractional precision of about tol using the Brent method.
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Detailed Description

Generate and return the minimum value and the corresponding abscissa xmin of the input 1-dimensional function isolated to a fractional precision of about tol using the Brent method.

Parameters

[in]	getFunc	: The scalar function be minimized. On input, it must take a scalar of the same type and kind as the output argument xmin. On output, it must return a scalar of the same type and kind as the output argument xmin, containing the function value at the specified input scalar point. The following demonstrates the interface of getFunc, function getFunc(x) result(func) real(RKG), intent(in) :: x real(RKG) :: func end function where RKG can refer to any real type kind parameter any supported by the processor (e.g., RK, RK32, RK64, or RK128) supported by the library.
[in]	xlow	: The input scalar of the same type and kind as the output argument xmin, containing the lower bound of the search interval for the function minimum abscissa. The condition xlow < xmin .and. getFunc(xmin) < getFunc(xlow) must hold for the corresponding input arguments. (optional, default = 0.1. This requires 0.1 to be within the support of getFunc())
[in]	xupp	: The input scalar of the same type and kind as the output argument xmin, containing the upper bound of the search interval for the function minimum abscissa. The condition xmin < xupp .and. getFunc(xmin) < getFunc(xupp) must hold for the corresponding input arguments. (optional, default = 0.9. This requires 0.9 to be within the support of getFunc())
[out]	fmin	: The output scalar of the same type and kind as the output argument xmin. On output, it contains the function value at the identified minimum xmin. (optional. If missing, the function value at the minimum will not be returned.)
[in]	tol	: The input positive scalar of the same type and kind as the output argument xmin, containing the fractional minimum distance that a new function evaluation point xmin can have from any previously evaluated point. Values smaller than the suggestion below might lead to algorithm failure due to roundoff error accumulation. (optional. default = sqrt(epsilon(xmin)).)
[in,out]	niter	: The input/output positive scalar of type integer of default kind IK containing the maximum number of allowed iterations in the algorithm in search of the minimum. On output, If the algorithm succeeds, niter will be set to the actual number of iterations taken to find the minimum which is by definition, less than or equal to the input value. If the algorithm fails to converge, it will be a number larger than the input value (by only 1 unit). The value of niter is effectively the number of calls to the user-specified input function. (optional. default = int(100 * precision(xmin) / 53.).)

Returns

xmin : The output scalar of,

1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the inferred abscissa at the function minimum, if the algorithm succeeds.

Possible calling interfaces ⛓

use pm_optimization, only: getMinBrent
 
xmin = getMinBrent(getFunc, xlow = xlow, xupp = xupp, fmin = fmin, tol = tol, niter = niter)

Warning

The condition 0 < niter must hold for the corresponding input arguments.
The condition 0 < tol must hold for the corresponding input arguments.

Remarks

The procedures under discussion are impure.

The procedures under discussion are recursive.

See also

getMinBrent

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RKG => RKH ! all processor kinds are supported.
    use pm_io, only: display_type
    use pm_optimization, only: getMinBrent
 
    implicit none
 
    integer(IK) :: niter
    real(RKG) :: xmin, fmin
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("getSq(x) = (x - 1)**2")
    call disp%show("xmin = getMinBrent(getSq)")
                    xmin = getMinBrent(getSq)
    call disp%show("xmin")
    call disp%show( xmin )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getSq(x) = (x - 1)**2")
    call disp%show("niter = 10")
                    niter = 10
    call disp%show("xmin = getMinBrent(getSq, fmin = fmin, tol = epsilon(xmin)**.8, niter = niter)")
                    xmin = getMinBrent(getSq, fmin = fmin, tol = epsilon(xmin)**.8, niter = niter)
    call disp%show("niter")
    call disp%show( niter )
    call disp%show("if (niter > 10) error stop 'minimization failed.'")
                    if (niter > 10) error stop 'minimization failed.'
    call disp%show("[xmin, fmin]")
    call disp%show( [xmin, fmin] )
    call disp%skip()
 
contains
 
    function getSq(x) result(func)
        real(RKG), intent(in) :: x
        real(RKG) :: func
        func = (x - 1)**2
    end function
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
getSq(x) = (x - 1)**2
xmin = getMinBrent(getSq)
xmin
+1.00000000000000000000000000000000000
 
 
getSq(x) = (x - 1)**2
niter = 10
xmin = getMinBrent(getSq, fmin = fmin, tol = epsilon(xmin)**.8, niter = niter)
niter
+10
if (niter > 10) error stop 'minimization failed.'
[xmin, fmin]
+1.00000000000000000000000000000000000, +0.00000000000000000000000000000000000
 
 

Test:

test_pm_optimization

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Tuesday March 7, 2017, 3:50 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin

Definition at line 768 of file pm_optimization.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_optimization.F90