Energy landscape objective function Color coding Warm high Cold low To find a minimum approximately along this line Steps To bracket a minimum To shrink the bracket 0 Search step ID: 529117
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Slide1
Line Search
Energy landscape / objective function
Color coding:Warm—high Cold—low
To find a minimum (approximately) along this line
Steps:
To bracket a minimum
To shrink the bracket
0
Search step
EnergySlide2
Bracketing
If downhill, keep shifting and increasing the bracket,
untill it hits uphill.
a
b
c
a
b
c
a
bcخلاصKhalas!Slide3
Bracketing
If uphill, keep backtracking the bracket,
untill the middle point is the lowest.
a
b
خلاص
Khalas
!
a
bcSlide4
Shrinking the Bracket
c
a
b
minimum at 4minimum at 5
Shrinked
bracket: [ ]Slide5
Fortran-MPI implementation
Rank of the MPI process
For bracketing:
Step lengths
energies
0 1 2 3
MPI processes:
Bifurcate
t
ogether!Rather than each process compares floating-point numbers to pick a conditional branch,let the root process do this job alone and then tell everyone else its decision as an INTEGER!!!returns the data misfit for a trial step length x Slide6
Fortran-MPI implementation
Root:
Non-roots:Slide7
References
Numerical Recipe in C, second edition, Chapter 10.1, 10.2http://www.fizyka.umk.pl/~jacek/docs/nrc/c10-1.pdf
http://www.fizyka.umk.pl/~jacek/docs/nrc/c10-2.pdfWikipedia: Brent’s methodhttp://en.wikipedia.org/wiki/Brent%27s_method