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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 65 "Jak\375m zp\371sobem por
\341\236et zv\355\370ata, abychom utr\236ili ka\236d\375 rok stejn\354
?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 258 38 "\310\341st 1. Op\354t vytvo\370
\355me Leslieho matici" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "L:=diag(0,0,0,0,0,0,0,0,0,0,0,0):" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 45 "a:='a':for j from 1 to 12 do L[1,j]:=a[j] od:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "b:='b':for j from 1 to 11 do L[j+1,
j]:=b[j] od: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(L);\n" }}
{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "
Nyn\355 vytvo\370\355me matici H, kter\341 odpov\355d\341 zlomk\371m p
or\341\236ek v jednotliv\375ch v\354kov\375ch skupin\341ch. Matice (I-
H)L," }}{PARA 0 "" 0 "" {TEXT -1 119 "je op\354t Leslieho matic\355 a \+
odpov\355d\341 modelu v\375voje populace, pokud na konci ka\236d\351ho
 roku por\341\236\355me zv\355\370ata podle matice H." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "h:='h':H:=diag(h[1],h[2],h[3],h[4],
h[5],h[6],h[7],h[8],h[9],h[10],h[11],h[12]);" }{TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 45 "I12:=array(identity,1..12,1.
.12): evalm(I12):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "B:=evalm((I12-
H)&*L);\n" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 112 "Spo\350\355t\341me charakteristick\375 polynom nov\351 m
atice modelu s por\341\236kami. Podm\355nka zachov\341n\355 populace o
dpov\355d\341 tomu, \236e" }}{PARA 0 "" 0 "" {TEXT -1 71 "po\236adujem
e, aby \350\355slo 1 bylo vlastn\355m \350\355slem t\351to nov\351 Les
lieho matice." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "p(lambda):=charpol
y(B,lambda);\neval(p(lambda),lambda=1);" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "a:=array(1..12,[0
,0.045,0.391,0.472,0.484,0.546,0.543,0.502,0.468,0.459,0.433,0.421]):
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "b:=array(1..11,[0.845,0.975,0.9
65,0.950,0.926,0.895,0.850,0.786,0.691,0.561,0.370]):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 38 "for j from 1 to 12 do L[1,j]:=a[j] od:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 41 "for j from 1 to 11 do L[j+1,j]:=b[j] od: \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(L);\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'matrixG6#7.7.\"\"!$\"#X!\"$$\"$\"RF+$\"$s%F+$\"$%[
F+$\"$Y&F+$\"$V&F+$\"$-&F+$\"$o%F+$\"$f%F+$\"$L%F+$\"$@%F+7.$\"$X)F+F(
F(F(F(F(F(F(F(F(F(F(7.F($\"$v*F+F(F(F(F(F(F(F(F(F(F(7.F(F($\"$l*F+F(F(
F(F(F(F(F(F(F(7.F(F(F($\"$]*F+F(F(F(F(F(F(F(F(7.F(F(F(F($\"$E*F+F(F(F(
F(F(F(F(7.F(F(F(F(F($\"$&*)F+F(F(F(F(F(F(7.F(F(F(F(F(F($\"$])F+F(F(F(F
(F(7.F(F(F(F(F(F(F($\"$'yF+F(F(F(F(7.F(F(F(F(F(F(F(F($\"$\"pF+F(F(F(7.
F(F(F(F(F(F(F(F(F($\"$h&F+F(F(7.F(F(F(F(F(F(F(F(F(F($\"$q$F+F(" }}}
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22 "vektor:=eigenvals(L);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'vekt
orG6.$\"+B9dv6!\"*,&$\"+#H\\ih&!#5\"\"\"%\"IG$\"+>&pM\\&F,,&F*F-F.$!+>
&pM\\&F,,&$\"+gPn_BF,F-F.$\"+c4WXpF,,&F5F-F.$!+c4WXpF,,&$!+3gV,8F,F-F.
$\"+O,UZrF,,&F=F-F.$!+O,UZrF,,&$!+CC**oNF,F-F.$\"+Ga<6cF,,&FEF-F.$!+Ga
<6cF,$!+'*H\\&e'F,,&$!+R_g$o&F,F-F.$\"+Nu:JJF,,&FOF-F.$!+Nu:JJF," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lambda1:=vektor[1];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lambda1G$\"+B9dv6!\"*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 80 "Pokud por\341\236\355me z ka\236d\351 v
\354kov\351 skupiny stejn\375 zlomek zv\355\370at h, je tento d\341n j
ako:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "h:=1-1/lambda1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"hG$\"+i&)\\$\\\"!#5" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 43 "for i from 2 to 12 do h[i]:=.1493498562 od;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"#$\"+i&)\\$\\\"!#5" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"$$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"%$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"&$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"'$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"($\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\")$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"\"*$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"#5$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"#6$\"+i&)\\$\\\"!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"hG6#\"#7$\"+i&)\\$\\\"!#5" }}}
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
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