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{MPLTEXT 1 0 584 "findMin:= proc(f,firstguess)\n  local i, len, h, gue
ss, oldht, ht;\n  guess := evalf(firstguess);  # we want to use approx
imations.\n  oldht := f(op(guess));\n  for i from 1 to 100 do\n     le
n := leng(Df(f,guess));\n  #   if ( len > 1) then\n        h:=1/len;\n
  #  else\n  #      h:=.5;\n  #   fi;\n     guess := gradstep2(f,guess
,h);\n     ht := f(op(guess));\n# print(i,guess,ht);\n   #  if ( abs(o
ldht - ht) < .00001) then\n   #     print(\"took\",i,\"steps.  value i
s\",ht);\n   #     RETURN(guess);\n   #  fi;\n     oldht := ht;\n  od;
\n  print(\"took\",i,\"steps.  value is\",ht);\n  RETURN(guess);\n end
:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "gradstep2:= proc(f,p
t,h)\n  local v;\n  v := Df(f,pt);\n  [ pt[1] - h*v[1], pt[2] - h*v[2]
];\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*gradstep2GR6%%\"fG%#ptG
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 698 "findMin:= proc(f,firstguess)\n  lo
cal i, len, h, guess, oldht, ht;\n  global finderpath;\n \n  guess := \+
evalf(firstguess);  # we want to use approximations.\n  oldht := f(op(
guess));\n\n  finderpath := [ [op(guess), oldht] ];\n  for i from 1 to
 100 do\n     len := leng(Df(f,guess));\n  #   if ( len > 1) then\n   \+
     h:=1/len;\n  #  else\n  #      h:=.5;\n  #   fi;\n     guess := g
radstep2(f,guess,h);\n     ht := f(op(guess));\n     finderpath := [ o
p(finderpath) , [op(guess), ht] ];\n# print(i,guess,ht);\n    if ( abs
(oldht - ht) < .00001) then\n        print(\"took\",i,\"steps.  value \+
is\",ht);\n        RETURN(guess);\n    fi;\n     oldht := ht;\n  od;\n
  print(\"took\",i,\"steps.  value is\",ht);\n  RETURN(guess);\n end:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(f,[1,2]);" }}
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{MPLTEXT 1 0 690 "findMin:= proc(f,firstguess)\n  local i, len, h, gue
ss, oldht, ht;\n  global finderpath;\n \n  guess := evalf(firstguess);
  # we want to use approximations.\n  oldht := f(op(guess));\n\n  find
erpath := [ [op(guess), oldht] ];\n  for i from 1 to 100 do\n     len \+
:= leng(Df(f,guess));\n     if ( len > 1) then\n        h:=1/len;\n   \+
 else\n       h:=1;\n     fi;\n     guess := gradstep2(f,guess,h);\n  \+
   ht := f(op(guess));\n     finderpath := [ op(finderpath) , [op(gues
s), ht] ];\n\n    if ( abs(oldht - ht) < .00001) then\n        print(
\"took\",i,\"steps.  value is\",ht);\n        RETURN(guess);\n    fi;
\n     oldht := ht;\n  od;\n  print(\"took\",i,\"steps.  value is\",ht
);\n  RETURN(guess);\n end:findMin(f,[1,2]);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6&Q%took6\"\"\"$Q1steps.~~value~isF$$\"+up;x!*!#:" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+9=8qH!#5$\"+![^c'GF&" }}}{EXCHG 
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ep3:= proc(f,pt)\n  local v, L, h, guess, ht, newht;\n  v := evalf(Df(
f,pt));\n  L := 1/leng(v);  # so v*L is a unit vector in the grad dir.
\n  h := 1;\n  ht:= f(op(pt));\n  newht := ht+1;\n  while ( ht < newht
 and h > .000001 ) do\n    guess:=[ pt[1] - h*L*v[1], pt[2] - h*L*v[2]
];\n    newht := f(op(guess));\n    h := .5*h;\n  od;\n  RETURN(guess)
;\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*gradstep3GR6$%\"fG%#ptG6
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{MPLTEXT 1 0 617 "findMin:= proc(f,firstguess)\n  local i, len, h, gue
ss, oldht, ht, nguess;\n  global finderpath;\n \n  guess := evalf(firs
tguess);  # we want to use approximations.\n  oldht := f(op(guess));\n
\n  finderpath := [ [op(guess), oldht] ];\n  for i from 1 to 100 do\n \+
 \n     nguess := gradstep3(f,guess);\n     ht := f(op(nguess));\n    \+
 finderpath := [ op(finderpath) , [op(nguess), ht] ];\n\n    if ( abs(
nguess[1] - guess[1]) + abs(nguess[2] - guess[2]) < .00001) then\n    \+
    print(\"took\",i,\"steps.  value is\",ht);\n        RETURN(guess);
\n    fi;\n     oldht := ht;\n  od;\n  print(\"took\",i,\"steps.  valu
e is\",ht);\n  RETURN(guess);\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
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