158 lines
4.2 KiB
Text
158 lines
4.2 KiB
Text
# Single variable function minimizer
|
|
|
|
The function must be continuous unimodal,
|
|
taking a floating point argument and returning a floating point value.
|
|
|
|
The method is binary search based on the derivative at the splitting point.
|
|
Convergence is judged by the change in function value.
|
|
|
|
First, words defined elsewhere.
|
|
|
|
~~~
|
|
{{
|
|
:d:another-name (as-)
|
|
d:create &class:word reclass d:last d:xt swap d:xt fetch swap store ;
|
|
---reveal---
|
|
:d:aka (s-)_Also-Known-As,_make_alias_of_the_last_defined_word
|
|
[ d:last ] dip d:another-name ; 'aka d:aka
|
|
:d:alias (ss-)_make_alias_s2_of_s1
|
|
[ d:lookup ] dip d:another-name ; 'alias d:aka
|
|
}}
|
|
|
|
'var<n> 'var! (n-) alias
|
|
'lt? 'n:<? alias
|
|
'lteq? 'n:=<? alias
|
|
:v:put (a-) fetch n:put ;
|
|
:e:fetch (a-__-f)_fetch_as_float fetch e:to-f ; 'e:@ aka
|
|
:e:store (a-__f-)_store_as_e f:to-e swap store ; 'e:! aka
|
|
:e:call.vv (aaa-)_call_floating_point_function_variable-to-variable
|
|
rot e:@ (aa_n) call (a_n) e:! ;
|
|
|
|
:s:shout (s-) '!_%s s:format s:put ;
|
|
{{
|
|
'Depth var
|
|
:message (-)
|
|
'abort_with__trail__invoked s:shout nl
|
|
'Do__reset__to_clear_stack. s:put nl ;
|
|
:put-name (a-) fetch d:lookup-xt
|
|
dup n:-zero? [ d:name s:put nl ] [ drop ] choose ;
|
|
---reveal---
|
|
:trail repeat pop put-name again ;
|
|
:abort (-0) depth !Depth message trail ;
|
|
:s:abort (s-0) 's:abort_:_ s:prepend s:put nl abort ;
|
|
}}
|
|
|
|
:assert (q-) call [ abort ] -if ;
|
|
:assert.verbous (q-) call [ 'assert_:_fail s:abort ] -if ;
|
|
|
|
:dump-stacks (-) dump-stack
|
|
#0 f:depth lt? [ nl 'f_ s:put f:dump-stack ] if
|
|
#0 f:adepth lt? [ nl 'fa_ s:put f:dump-astack ] if ; '. aka
|
|
~~~
|
|
|
|
Program.
|
|
|
|
~~~
|
|
{{
|
|
(input_variables
|
|
'F var (Function_to_minimize_(-_n-n)_float_to_float
|
|
'L var (e:low
|
|
'H var (e:high
|
|
|
|
TRUE 'Tr var! (trace_flag
|
|
.0.000001 f:to-e 'TOL const (=173=tolerance
|
|
#30 'ITMAX const (max_#_of_iterations
|
|
|
|
(working_variables
|
|
'Ly var (e:low-value
|
|
'Hy var
|
|
'X1y var (y_at_upper_next_to_x
|
|
'Y var (function_value_at_X
|
|
'Itr var (iterations
|
|
|
|
(output_variable
|
|
'X var (candidate
|
|
|
|
:trace (-) @Tr [ ( Itr v:put sp )
|
|
( @L e:put sp ) ( @X e:put sp ) ( @H e:put sp ) nl ] if ;
|
|
:y (-) X Y @F e:call.vv ;
|
|
:x (-)_(L_H_->_X) @L @H + #2 / !X ;
|
|
:x1y (-) @X n:inc e:to-f @F call X1y e:! ;
|
|
|
|
---reveal---
|
|
:minimize (a-_nn-x)_(L_H_F_->_X)
|
|
(minimize_floating_point_function_F_over_[L,H]
|
|
(initialize ( !F f:to-e !H f:to-e !L )
|
|
( L Ly @F e:call.vv ) ( H Hy @F e:call.vv ) x y ( #0 !Itr )
|
|
[ trace x1y
|
|
( @Y @X1y n:<? ) [ @X !H @Y !Hy ] [ @X !L @Y !Ly ] choose
|
|
x y Itr v:inc [ @Itr ITMAX n:=<? ] assert.verbous
|
|
TOL @Y @X1y - n:abs n:<? ] while X e:@ ;
|
|
}}
|
|
~~~
|
|
|
|
```
|
|
:f (-_x-y)_(x-2)^2 .2. f:- f:dup f:* ;
|
|
.-3 .10 &f minimize . nl
|
|
```
|
|
|
|
```
|
|
:f (-_x-y) f:abs ;
|
|
.-5. .5 &f minimize . nl
|
|
```
|
|
|
|
Note how `x` is defined without conversios as
|
|
|
|
:x (-)_(L_H_->_X) @L @H + 2 / !X ;
|
|
|
|
rather than
|
|
|
|
:x (-)_(L_H_->_X) ( L e:@ ) ( H e:@ ) f:+ .2. f:/ X e:! ;
|
|
|
|
Doing
|
|
|
|
```
|
|
:f (-_x-y) ;
|
|
.0 .5 &f minimize . nl
|
|
```
|
|
|
|
with the first definition gives
|
|
|
|
# low mid high
|
|
0 0.000000 1.249991 5.000009
|
|
1 0.000000 0.312492 1.249991
|
|
2 0.000000 0.078120 0.312492
|
|
3 0.000000 0.019530 0.078120
|
|
4 0.000000 0.004882 0.019530
|
|
5 0.000000 0.001220 0.004882
|
|
6 0.000000 0.000305 0.001220
|
|
7 0.000000 0.000076 0.000305
|
|
8 0.000000 0.000019 0.000076
|
|
9 0.000000 0.000005 0.000019
|
|
10 0.000000 0.000001 0.000005
|
|
final x = 0.000000
|
|
|
|
whereas with the second definition gives
|
|
|
|
# low mid high
|
|
0 0.000000 2.500004 5.000009
|
|
1 0.000000 1.249991 2.500004
|
|
2 0.000000 0.625001 1.249991
|
|
3 0.000000 0.312503 0.625001
|
|
4 0.000000 0.156254 0.312503
|
|
5 0.000000 0.078126 0.156254
|
|
6 0.000000 0.039062 0.078126
|
|
7 0.000000 0.019530 0.039062
|
|
8 0.000000 0.009765 0.019530
|
|
9 0.000000 0.004883 0.009765
|
|
10 0.000000 0.002441 0.004883
|
|
11 0.000000 0.001221 0.002441
|
|
12 0.000000 0.000611 0.001221
|
|
13 0.000000 0.000305 0.000611
|
|
14 0.000000 0.000153 0.000305
|
|
15 0.000000 0.000076 0.000153
|
|
16 0.000000 0.000038 0.000076
|
|
17 0.000000 0.000019 0.000038
|
|
18 0.000000 0.000009 0.000019
|
|
final x = 0.000005
|
|
|