# Class: Minimization::GoldenSection

Inherits:
Unidimensional
show all
Defined in:
lib/minimization.rb

# Golden Section Minimizer.

Basic minimization algorithm. Slow, but robust. See Unidimensional for methods.

## Usage.

``````require 'minimization'
min=Minimization::GoldenSection.new(-1000,20000  , proc {|x| (x+1)**2}
min.expected=1.5  # Expected value
min.iterate
min.x_minimum
min.f_minimum
min.log
``````

## Instance Method Summary collapse

• Start the iteration.

## Constructor Details

This class inherits a constructor from Minimization::Unidimensional

## Instance Method Details

### #iterate ⇒ Object

Start the iteration

 ``` 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201``` ```# File 'lib/minimization.rb', line 151 def iterate ax=@lower bx=@expected cx=@upper c = (3-Math::sqrt(5)).quo(2); r = 1-c; x0 = ax; x3 = cx; if ((cx-bx).abs > (bx-ax).abs) x1 = bx; x2 = bx + c*(cx-bx); else x2 = bx; x1 = bx - c*(bx-ax); end f1 = f(x1); f2 = f(x2); k = 1; while (x3-x0).abs > @epsilon and k<@max_iteration if f2 < f1 x0 = x1; x1 = x2; x2 = r*x1 + c*x3; # x2 = x1+c*(x3-x1) f1 = f2; f2 = f(x2); else x3 = x2; x2 = x1; x1 = r*x2 + c*x0; # x1 = x2+c*(x0-x2) f2 = f1; f1 = f(x1); end @log << [k, x3,x0, f1,f2,(x3-x0).abs, (f1-f2).abs] k +=1; end if f1 < f2 @x_minimum = x1; @f_minimum = f1; else @x_minimum = x2; @f_minimum = f2; end true end```