pm_optimization::isBracketMax Interface Reference

Generate and return .true. if and only if a concave quadratic curve can fit the specified input triple [xmin, xlow, xupp] and the function value at the middle pointxmin` is larger than both boundary point function values.
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Detailed Description

Generate and return .true. if and only if a concave quadratic curve can fit the specified input triple [xmin, xlow, xupp] and the function value at the middle pointxmin` is larger than both boundary point function values.

This function is useful for testing whether the initial bracket intervals to various optimization routines enclose the desired function extremum.

Specifically, this generic interface computed and returns the following criterion: bracketed = xlow <= xmax .and. xmax <= xupp .and. flow <= fmax .and. fmax >= fupp

Parameters

[in]	xmax	: The input scalar of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the abscissa corresponding to the maximum function value among the triplet [xmax, xlow, xupp].
[in]	xlow	: The input scalar of the same type and kind as the input argument xmax, containing the lower bound of the interval specified by the triplet.
[in]	xupp	: The input scalar of the same type and kind as the input argument xmax, containing the upper bound of the interval specified by the triplet.
[in]	fmax	: The input scalar of the same type and kind as the input argument xmax, containing the target function value at xmax.
[in]	flow	: The input scalar of the same type and kind as the input argument xmax, containing the target function value at xlow.
[in]	fupp	: The input scalar of the same type and kind as the input argument xmax, containing the target function value at xupp.

Possible calling interfaces ⛓

use pm_kind, only: LK
use pm_optimization, only: isBracketMax
logical(LK) :: bracketed
 
bracketed = isBracketMax(xmax, xlow, xupp, fmax, flow, fupp)

Remarks

The procedures under discussion are pure.

The procedures under discussion are elemental.

See also

isBracketMax
isBracketMin
setBracketMax
setBracketMin
getMinBrent
setMinBrent

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: setBracketMax, isBracketMax
    use pm_err, only: setAsserted
    use pm_val2str, only: getStr
 
    implicit none
 
    integer(IK) :: niter, minniter = 1000
    real(RKG) :: xlow, xmax, xupp, flow, fmax, fupp
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("getSqNeg(x) = (x - 1)**2")
    call disp%show("xlow = -3; xupp = -1; niter = minniter")
                    xlow = -3; xupp = -1; niter = minniter
    call disp%show("call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax)")
                    call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax)
    call disp%show("if (niter > minniter) error stop 'Bracketing failed.'")
                    if (niter > minniter) error stop 'Bracketing failed.'
    call disp%show("[xlow, xmax, xupp, getSqNeg(xlow), fmax, getSqNeg(xupp)]")
    call disp%show( [xlow, xmax, xupp, getSqNeg(xlow), fmax, getSqNeg(xupp)] )
    call disp%show("niter")
    call disp%show( niter )
    call disp%show("call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, getSqNeg(xlow), getSqNeg(xupp)))")
                    call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, getSqNeg(xlow), getSqNeg(xupp)))
    call disp%skip()
 
    call disp%skip()
    call disp%show("getSqNeg(x) = (x - 1)**2")
    call disp%show("xlow = -3; xupp = -1; niter = minniter")
                    xlow = -3; xupp = -1; niter = minniter
    call disp%show("call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)")
                    call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
    call disp%show("if (niter > minniter) error stop 'Bracketing failed.'")
                    if (niter > minniter) error stop 'Bracketing failed.'
    call disp%show("[xlow, xmax, xupp, flow, fmax, fupp]")
    call disp%show( [xlow, xmax, xupp, flow, fmax, fupp] )
    call disp%show("niter")
    call disp%show( niter )
    call disp%show("call setAsserted(isBracketMax(xmax, xlow, xupp, flow, fmax, fupp))")
                    call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))
    call disp%skip()
 
    call disp%skip()
    call disp%show("getSqNeg(x) = (x - 1)**2")
    call disp%show("xlow = 3; xupp = 9; niter = minniter")
                    xlow = 3; xupp = 9; niter = minniter
    call disp%show("call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)")
                    call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
    call disp%show("if (niter > minniter) error stop 'Bracketing failed.'")
                    if (niter > minniter) error stop 'Bracketing failed.'
    call disp%show("[xlow, xmax, xupp, flow, fmax, fupp]")
    call disp%show( [xlow, xmax, xupp, flow, fmax, fupp] )
    call disp%show("niter")
    call disp%show( niter )
    call disp%show("call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))")
                    call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))
    call disp%skip()
 
    call disp%skip()
    call disp%show("getSqNeg(x) = (x - 1)**2")
    call disp%show("xlow = -5; xupp = 4; niter = minniter")
                    xlow = -5; xupp = 4; niter = minniter
    call disp%show("call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)")
                    call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
    call disp%show("if (niter > minniter) error stop 'Bracketing failed.'")
                    if (niter > minniter) error stop 'Bracketing failed.'
    call disp%show("[xlow, xmax, xupp, flow, fmax, fupp]")
    call disp%show( [xlow, xmax, xupp, flow, fmax, fupp] )
    call disp%show("niter")
    call disp%show( niter )
    call disp%show("call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))")
                    call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))
    call disp%skip()
 
contains
 
    function getSqNeg(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 ⛓

 
getSqNeg(x) = (x - 1)**2
xlow = -3; xupp = -1; niter = minniter
call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax)
if (niter > minniter) error stop 'Bracketing failed.'
[xlow, xmax, xupp, getSqNeg(xlow), fmax, getSqNeg(xupp)]
-1.00000000000000000000000000000000000, +1.00000000000000000000000000000000000, +2.23606797749978969640917366873127632, -4.00000000000000000000000000000000000, -0.00000000000000000000000000000000000, -1.52786404500042060718165266253744775
niter
+1
call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, getSqNeg(xlow), getSqNeg(xupp)))
 
 
getSqNeg(x) = (x - 1)**2
xlow = -3; xupp = -1; niter = minniter
call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
if (niter > minniter) error stop 'Bracketing failed.'
[xlow, xmax, xupp, flow, fmax, fupp]
-1.00000000000000000000000000000000000, +1.00000000000000000000000000000000000, +2.23606797749978969640917366873127632, -4.00000000000000000000000000000000000, -0.00000000000000000000000000000000000, -1.52786404500042060718165266253744775
niter
+1
call setAsserted(isBracketMax(xmax, xlow, xupp, flow, fmax, fupp))
 
 
getSqNeg(x) = (x - 1)**2
xlow = 3; xupp = 9; niter = minniter
call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
if (niter > minniter) error stop 'Bracketing failed.'
[xlow, xmax, xupp, flow, fmax, fupp]
-6.70820393249936908922752100619382819, +3.00000000000000000000000000000000000, +9.00000000000000000000000000000000000, -64.0000000000000000000000000000000000, -4.00000000000000000000000000000000000, -59.4164078649987381784550420123876502
niter
+1
call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))
 
 
getSqNeg(x) = (x - 1)**2
xlow = -5; xupp = 4; niter = minniter
call setBracketMax(getSqNeg, niter, xmax, xlow, xupp, fmax, flow, fupp)
if (niter > minniter) error stop 'Bracketing failed.'
[xlow, xmax, xupp, flow, fmax, fupp]
-5.00000000000000000000000000000000000, +4.00000000000000000000000000000000000, +18.5623058987490536338412815092907438, -36.0000000000000000000000000000000000, -9.00000000000000000000000000000000000, -308.434588481235804507619222639361176
niter
+1
call setAsserted(isBracketMax(xmax, xlow, xupp, fmax, flow, fupp))
 
 

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 151 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