{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "A := RandomMatrix(2,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*%oft9-%'MATRIXG6#7$7$\"#W!#J7$\"## *\"#n%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(A); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*Wa:[\"-%'MATRIXG6#7 $7$$\"#W\"\"!$!#JF.7$$\"##*F.$\"#nF.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "U, S, V := svd(evalf(A));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>6%%\"UG%\"SG%\"VG6%-%'RTABLEG6%\"*!G@#[\"-%'MATRIXG6#7 $7$$!3#*\\&z6hIr&=!#=$!31c[%R>Sg#)*F47$$!3Sg#)*F4$\"3e^&z6hIr&=F 4%'MatrixG-F*6%\"*G$4k9-F.6#7$7$$\"33x\"\\l>iV:\"!#:\"\"!7$FG$\"3.@\"* Gg&>W-&!#;F<-F*6%\"*cB'e9-F.6#7$7$$!3$>ZkDB'**Q&)F4$!3&fSI\\KxV?&F47$F U$\"3$>ZkDB'**Q&)F4F<" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 256 655 "CondNum := proc( A :: Matrix )\n local U, S, V, m, n, k;\n\n U, S, V := svd(evalf(A)); \n m,n := LinearAlgebra:-Dimension(A);\n k := min(m,n);\n \n r eturn S[1,1]/S[k,k];\nend proc;\n\n#\n# Singular value decomposition \+ in Matlab style\n#\nsvd := proc( A :: Matrix )\n local UU, SS, VV, \+ V0, m, n, k, s;\n\n m,n := LinearAlgebra[Dimension](A);\n\n # appl y Maple SingularValues\n UU,s,V0 := LinearAlgebra[SingularValues](A, \n output=['U','S','Vt']);\n\n # rearrage output\n \+ k := min(m,n);\n SS := LinearAlgebra[DiagonalMatrix](s[1..k],m,n); # get a mxn zero matrix\n VV := LinearAlgebra[Transpose](V0);\n\n \+ return UU, SS, VV;\n\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "read \"c:/304/CondNum.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "s := CondNum(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG$\"+*e.vH#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "B := Transpose(A).A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'R TABLEG6%\"*_B?[\"-%'MATRIXG6#7$7$\"&+/\"\"%+[7$F/\"%]a%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "CondNum(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+NF_y_!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "s^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+TF_y_!\"* " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "Experiment with Francis Algorithm" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "B := RandomMatrix(5,5,g enerator=-5..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'RTABLEG6% \"*))zTY\"-%'MATRIXG6#7'7'!\"#\"\"\"\"\"&F0!\"%7'\"\"#F0!\"\"\"\"!!\"$ 7'!\"&F6F6F/F87'F.\"\"$F3F5F/7'F8F.F6F0F/%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A := evalf(B): " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 84 "for k from 1 to 200 do\n (Q,R) := QRDecomposition (A,fullspan):\n A := R.Q:\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*# *>^d\"-%'MATRIXG6#7'7'$!3WMK'o*fk8u!#<$\"3OVq=0F;OHF.$\"37l'H![A')p:F. $\"3Mzy&Rl')G\\$F.$\"3u?0CRaCCLF.7'$!3)o-!\\c-?#f'!#d$\"3+`/ul$)[grF.$ !32(fdV@2nI)!#=$\"39G7Rnre4f!#>$!3yn;h&Q@Mp&F?7'$!3J7#>'zH:75!#c$\"3L= @qy(e#4DF.$\"3#[#)eH;$)\\t%F.$\"3C#pz&*3*3ay#FZ$\"3#f:aC5ZlE$F.$! 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