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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 840 "with(plots):\nwith(
linalg):\nf:=array(1..8, 1..8); \nF:=array(1..8, 1..8);\nc:=proc(x)\ni
f (x>0) then 1;\nelse 1/sqrt(2);\nfi\nend;\n\ncosxu:=proc(x,u)\ncos((2
*x+1)*u*Pi/16);\nend;\n\ndctf:=proc(u,v,f)\nlocal s, x, y;\ns:=0;\nfor
 x from 0 to 7 do\n   for y from 0 to 7 do\n      s:=s+f[x+1,y+1]*cosx
u(x,u)*cosxu(y,v);\n   od;\nod;\ns:=s*0.25*c(u)*c(v);\nend;\n\nidctf:=
proc(x,y,F)\nlocal s, u, v;\ns:=0;\nfor u from 0 to 7 do\n   for v fro
m 0 to 7 do\n      s:=s+c(u)*c(v)*F[u+1,v+1]*cosxu(x,u)*cosxu(y,v);\n \+
  od;\nod;\ns:=s*0.25;\nend;\n\nresetf:=proc(f)\nlocal i,j;\nfor i fro
m 1 to 8 do\nfor j from 1 to 8 do\n   f[i,j]:=0;\nod;od;\nend;\n\ngeti
dctf:=proc(f)\nlocal x,y;\nfor x from 0 to 7 do\nfor y from 0 to 7 do
\n   f[x+1,y+1]:=evalf(idctf(x,y,F));\nod; od;\nend;\n\ngetdctf:=proc(
F)\nlocal u, v;\nfor u from 0 to 7 do\nfor v from 0 to 7 do\n   F[u+1,
v+1]:=evalf(dctf(u,v,f));\nod; od;\nend;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fG-%&arrayG6%;\"\"\"\"\")F(7\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"FG-%&arrayG6%;\"\"\"\"\")F(7\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"cGR6#%\"xG6\"F(F(@%2\"\"!9$\"\"\"*&\"\"\"F/-%%sqrtG6#\"\"#!
\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&cosxuGR6$%\"xG%\"uG6
\"F)F)-%$cosG6#,$*(,&9$\"\"#\"\"\"F2F29%F2%#PiGF2#F2\"#;F)F)F)" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%dctfGR6%%\"uG%\"vG%\"fG6%%\"sG%\"xG
%\"yG6\"F.C%>8$\"\"!?(8%F2\"\"\"\"\"(%%trueG?(8&F2F5F6F7>F1,&F1F5*(&9&
6$,&F4F5F5F5,&F9F5F5F5F5-%&cosxuG6$F49$F5-FC6$F99%F5F5>F1,$*(F1F5-%\"c
G6#FEF5-FM6#FHF5$\"#D!\"#F.F.F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&
idctfGR6%%\"xG%\"yG%\"FG6%%\"sG%\"uG%\"vG6\"F.C%>8$\"\"!?(8%F2\"\"\"\"
\"(%%trueG?(8&F2F5F6F7>F1,&F1F5*,-%\"cG6#F4F5-F>6#F9F5&9&6$,&F4F5F5F5,
&F9F5F5F5F5-%&cosxuG6$9$F4F5-FH6$9%F9F5F5>F1,$F1$\"#D!\"#F.F.F." }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'resetfGR6#%\"fG6$%\"iG%\"jG6\"F+?(8
$\"\"\"F.\"\")%%trueG?(8%F.F.F/F0>&9$6$F-F2\"\"!F+F+F+" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%)getidctfGR6#%\"fG6$%\"xG%\"yG6\"F+?(8$\"\"!\"\"
\"\"\"(%%trueG?(8%F.F/F0F1>&9$6$,&F-F/F/F/,&F3F/F/F/-%&evalfG6#-%&idct
fG6%F-F3%\"FGF+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(getdctfGR6#%
\"FG6$%\"uG%\"vG6\"F+?(8$\"\"!\"\"\"\"\"(%%trueG?(8%F.F/F0F1>&9$6$,&F-
F/F/F/,&F3F/F/F/-%&evalfG6#-%%dctfG6%F-F3%\"fGF+F+F+" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 99 "setf:=proc(f) \nlocal i, j;\nfor i from 1
 to 8 do\nfor j from 1 to 8 do\n   f[i,j]:=0.125;\nod; od;\nend;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%setfGR6#%\"fG6$%\"iG%\"jG6\"F+?(8$
\"\"\"F.\"\")%%trueG?(8%F.F.F/F0>&9$6$F-F2$\"$D\"!\"$F+F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "setf(f);print(f);matrixplot(
f,axes=BOXED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$D\"!\"$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$\"$D\"!\"$F(F(F(F(F(F
(F(F'F'F'F'F'F'F'" }}{PARA 13 "" 1 "" {GLPLOT3D 399 299 299 {PLOTDATA 
3 "6%-%%GRIDG6%;\"\"\"\"\")F&7*7*$\"$D\"!\"$F+F+F+F+F+F+F+F*F*F*F*F*F*
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0 2 1 1 2 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 47 "getdctf(F); print(F);matrixplot(F, axes=BOXED);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#-%'matrixG6#7*7*$\"+++++5!\"*\"\"!F+F+F+F+F+F+7*F+F+F+F+F+F+F+F+F,F
,F,F,F,F," }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%%
GRIDG6%;\"\"\"\"\")F&7*7*$\"+++++5!\"*\"\"!F.F.F.F.F.F.7*F.F.F.F.F.F.F
.F.F/F/F/F/F/F/-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%%$rowG%'columnG%\"
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "getidctf(f); print(f); matrixplot(f
, axes=BOXED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++]7!#5" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$\"++++]7!#5F(F(F(F(F(
F(F(F'F'F'F'F'F'F'" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 
{PLOTDATA 3 "6%-%%GRIDG6%;\"\"\"\"\")F&7*7*$\"++++]7!#5F+F+F+F+F+F+F+F
*F*F*F*F*F*F*-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%%$rowG%'columnG%\"AG
" 1 2 0 1 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 149 "bwstrip:=proc(f)\nlocal i,j;\nfor i from
 1 to 8 do\nfor j from 1 to 8 do\n   if (i mod 4 > 1) then  f[i,j]:=0;
\n   else  f[i,j]:=100;\n   fi;\nod; \nod;\nend;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(bwstripGR6#%\"fG6$%\"iG%\"jG6\"F+?(8$\"\"\"F.\"\")%%
trueG?(8%F.F.F/F0@%2F.-%$modG6$F-\"\"%>&9$6$F-F2\"\"!>F:\"$+\"F+F+F+" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "bwstrip(f);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "print(f); matrixplot(f, axes=BOXED);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7*7*\"$+\"F(F(F(F(F(F(F(7*\"\"!F*F*F*F*F*F*
F*F)F'F'F)F)F'" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "
6%-%%GRIDG6%;\"\"\"\"\")F&7*7*\"$+\"F+F+F+F+F+F+F+7*\"\"!F-F-F-F-F-F-F
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" 1 2 0 1 0 2 5 1 2 2 1.000000 5.000000 61.000000 0 }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 48 "getdctf(F); print(F); matrixplot(F, axes=
BOXED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7*7*$\"&++%!\"#\"\"!F+F+F+F+F+F+7*F+F+F+F+F
+F+F+F+F,F,F'F,F,F," }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 
{PLOTDATA 3 "6%-%%GRIDG6%;\"\"\"\"\")F&7*7*$\"&++%!\"#\"\"!F.F.F.F.F.F
.7*F.F.F.F.F.F.F.F.F/F/F*F/F/F/-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%%$
rowG%'columnG%\"AG" 1 2 0 1 0 2 1 1 2 2 1.000000 45.000000 45.000000 
0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "resetf(F);F[1,1]:=128;
 F[8,8]:=-128; print(F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"FG6$\"\"\"F'\"$G\"" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%\"FG6$\"\")F'!$G\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7*7*\"$G\"\"\"!F)F)F)F)F)F)7*F)F)F)F)F)F)F)
F)F*F*F*F*F*7*F)F)F)F)F)F)F)!$G\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "getidctf(f); print(f); matrixplot(f, axes=BOXED);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+_s?y9!\")" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7*7*$\"+_s?y9!\")$\"+-k$o%>F*$\"+UE#43\"F*$
\"+#\\$H7AF*$\"+#3lq()*!\"*$\"+et2>@F*$\"+)fjJD\"F*$\"+[Fz@<F*7*F+$\"+
A\\$H7'F3$\"+_s?yIF*$!*TVmV\"F*$\"+TVmVLF*$\"*[Fz@\"F*$\"+3lq(e#F*F67*
F-F=$!*#\\$H7'F*$\"+-\"y&4UF*$!+-\"y&45F*$\"+#\\$H7QF*FCF47*F/F?FJ$!+_
s?y9F*$\"+_s?yYF*FLFAF17*F1FAFLFSFQFJF?F/7*F4FCFNFLFJFHF=F-7*F6FEFCFAF
?F=F;F+7*F8F6F4F1F/F-F+F(" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 
{PLOTDATA 3 "6%-%%GRIDG6%;\"\"\"\"\")F&7*7*$\"+_s?y9!\")$\"+-k$o%>F-$
\"+UE#43\"F-$\"+#\\$H7AF-$\"+#3lq()*!\"*$\"+et2>@F-$\"+)fjJD\"F-$\"+[F
z@<F-7*F.$\"+A\\$H7'F6$\"+_s?yIF-$!*TVmV\"F-$\"+TVmVLF-$\"*[Fz@\"F-$\"
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77*F2FBFM$!+_s?y9F-$\"+_s?yYF-FOFDF47*F4FDFOFVFTFMFBF27*F7FFFQFOFMFKF@
F07*F9FHFFFDFBF@F>F.7*F;F9F7F4F2F0F.F+-%*AXESSTYLEG6#%$BOXG-%+AXESLABE
LSG6%%$rowG%'columnG%\"AG" 1 2 0 1 0 2 5 1 2 2 1.000000 59.000000 
-38.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK 
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