Annotation of OpenXM/src/asir-contrib/packages/sample/noro_matrix-ja.txt, Revision 1.2
1.1 takayama 1: /* noro_matrix.rr $B$NMxMQNc!!(B
2: $B0J2<F~NO9T$O(B tab $B$+$i;O$^$k(B.
3: */
4:
1.2 ! noro 5: /*********************/
! 6:
! 7: $BNc(B1. $B%W%m%0%i%`$N%m!<%I(B
1.1 takayama 8:
9: load("noro_matrix.rr");
1.2 ! noro 10:
! 11: $B7k2L(B.
! 12:
! 13: $B$J$7(B
! 14:
! 15: $B7k2L$N@bL@(B.
! 16:
! 17: $B0J2<$N4X?t$rMQ$$$k:]$KI,MW(B.
! 18:
! 19: /*********************/
! 20:
! 21: $BNc(B2. $BC10L9TNs$r@8@.$9$k(B.
! 22:
! 23: E=linalg.unit_mat(3);
! 24:
! 25: $B7k2L(B.
! 26:
! 27: [ 1 0 0 0 0 ]
! 28: [ 0 1 0 0 0 ]
! 29: [ 0 0 1 0 0 ]
! 30: [ 0 0 0 1 0 ]
! 31: [ 0 0 0 0 1 ]
! 32:
! 33: $B7k2L$N@bL@(B.
! 34:
! 35: $B;XDj$5$l$?%5%$%:$NC10L9TNs$rJV$9(B.
! 36:
! 37:
! 38: /*********************/
! 39:
! 40: $BNc(B3. $B9TNs$r%i%s%@%`$K@8@.$9$k(B.
! 41:
! 42: R=linalg.random_rmat(3,4,5);
! 43:
! 44: $B7k2L(B.
! 45:
! 46: [ -4 -3 2 0 ]
! 47: [ -4 -2 -3 0 ]
! 48: [ -2 3 -3 3 ]
! 49:
! 50: $B7k2L$N@bL@(B.
! 51:
! 52: $BBh0l(B, $BBhFs0z?t$O%5%$%:(B, $B3FMWAG$O@dBPCM$,(B($BBh;00z?t(B-1)$B$N@0?t$G$"$k(B.
! 53:
! 54: /*********************/
! 55:
! 56: $BNc(B4. $B5U9TNs$r7W;;$9$k(B.
! 57:
! 58: A=linalg.random_mat(3,3,5);
! 59: Inv=invmat(A);
! 60: AI=Inv[0]/Inv[1];
! 61: M=A*AI;
! 62:
! 63: $B7k2L(B.
! 64:
! 65: A= [ 2 0 0 0 ]
! 66: [ 3 5 1 0 ]
! 67: [ -9 -9 -1 0 ]
! 68: [ -5 0 0 1 ]
! 69:
! 70: Inv=[
! 71: [ 4 0 0 0 ]
! 72: [ -6 -2 -2 0 ]
! 73: [ 18 18 10 0 ]
! 74: [ 20 0 0 8 ],8]
! 75:
! 76:
! 77: AI= [ 1/2 0 0 0 ]
! 78: [ -3/4 -1/4 -1/4 0 ]
! 79: [ 9/4 9/4 5/4 0 ]
! 80: [ 5/2 0 0 1 ]
! 81:
! 82: M= [ 1 0 0 0 ]
! 83: [ 0 1 0 0 ]
! 84: [ 0 0 1 0 ]
! 85: [ 0 0 0 1 ]
! 86:
! 87: $B7k2L$N@bL@(B.
! 88:
! 89: $B7k2L$O(B [Num,Den] $B$N7A$N%j%9%H$G(B, Num $B$O@0?t9TNs(B, Den $B$O@0?t$G$"$k(B.
! 90: Num/Den $B$,5U9TNs$rI=$9(B.
! 91:
! 92: /*********************/
! 93:
! 94: $BNc(B5. $B9TNs$N:G>.B?9`<0$r7W;;$9$k(B.
! 95:
! 96: A=linalg.random_rmat(3,3,5);
! 97: M=linalg.minipoly_mat(A);
! 98:
! 99: $B7k2L(B.
! 100:
! 101: A= [ -4 3 3 ]
! 102: [ 1 2 3 ]
! 103: [ 0 4 -3 ]
! 104:
! 105: M=x^3+5*x^2-17*x-93
! 106:
! 107: $B7k2L$N@bL@(B.
! 108:
! 109: f(A)=0 $B$H$J$k:G>.<!?t$NB?9`<0(B f(x) $B$rJV$9(B. deg(f) $B$,(B A $B$N%5%$%:(B
! 110: $B$h$j>.$5$$$3$H$b$"$jF@$k(B.
! 111:
! 112: /*********************/
! 113:
! 114: $BNc(B6. $B9TNs(BA$B$N3K$r7W;;$9$k(B.
! 115:
! 116: A=linalg.random_rmat(3,5,5);
! 117: Ker=linalg.compute_kernel(A);
! 118:
! 119: $B7k2L(B.
! 120:
! 121: A= [ 4 -3 -4 -4 -4 ]
! 122: [ 3 3 0 -1 3 ]
! 123: [ -3 -3 0 1 -3 ]
! 124:
! 125: Ker=[[[ 2 0 0 3 -1 ],0],[[ 0 16 0 3 -15 ],1],[[ 0 0 4 -3 -1 ],2]]
! 126:
! 127: $B7k2L$N@bL@(B.
! 128:
! 129: [[v1,p1],[v2,p2],...] $B$N7A$N%j%9%H$,JV$k(B. vi $B$O%5%$%:$,(B A $B$NNs?t$HEy$7(B
! 130: $B$$%Y%/%H%k$G(B, [v1,v2,...] $B$,(B Ker(A) $B$N0lAH$N4pDl$G$"$k(B. pi $B$O(B vi $B$NMWAG(B
! 131: $B$r:8$+$i$_$F(B, $B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B.
! 132:
! 133: /*********************/
! 134:
! 135: $BNc(B7. $B9TNs$NA|$r7W;;$9$k(B.
! 136:
! 137: A=linalg.random_rmat(3,5,5);
! 138: Im=linalg.compute_image(A);
! 139:
! 140: $B7k2L(B.
! 141:
! 142: A= [ 1 1 1 -1 4 ]
! 143: [ -3 3 2 -4 -3 ]
! 144: [ 3 3 0 1 4 ]
! 145:
! 146: Im=[[[ 1 -3 3 ],0,(1)*<<0>>],
! 147: [[ 0 6 0 ],1,(1)*<<1>>+(-1)*<<0>>],
! 148: [[ 0 0 -18 ],2,(6)*<<2>>+(-5)*<<1>>+(-1)*<<0>>]]
! 149:
! 150: $B7k2L$N@bL@(B.
! 151:
! 152: [[v1,p1,g1],[v2,p2,g2],...] $B$N7A$N%j%9%H$rJV$9(B. vi $B$O%Y%/%H%k$G(B
! 153: [v1,v2,...] $B$,(B Im(A) $B$N0lAH$N4pDl$G$"$k(B. pi $B$O(B vi $B$NMWAG$r:8$+$i$_$F(B,
! 154: $B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B. gi $B$O(B, vi $B$,(B
! 155: $B$b$H$N9TNs$NNs$+$i$I$N$h$&$K@8@.$5$l$F$$$k$+$r<($9J,;6B?9`<0$G$"$k(B.
! 156: $BNc$($P>e$NNc$G$O(B, [0 6 0] $B$O(B ($BBh(B 1 $BNs(B-$BBh(B 0 $BNs(B) $B$KEy$7$$$3$H$,J,$+$k(B.
! 157:
! 158: /*********************/
! 159:
! 160: $BNc(B8. $B9TNs(BA$B$N(BJordan $BI8=`7A$r7W;;$9$k(B.
! 161:
! 162: A=newmat(4,4,[[2,0,0,0],[3,5,1,0],[-9,-9,-1,0],[-5,0,0,1]]);
1.1 takayama 163: B=linalg.jordan_canonical_form(A);
1.2 ! noro 164: P=B[0];
! 165: L=invmat(P); PI=L[0]/L[1];
! 166: S=PI*A*P;
1.1 takayama 167:
168: $B7k2L(B.
169:
1.2 ! noro 170: B=[
! 171: [ 0 1 1 0 ]
! 172: [ 3 0 0 0 ]
! 173: [ -9 0 -3 0 ]
! 174: [ 0 -5 -5 1 ],
! 175: [[2,2,1],[2,1,1],[1,1,1]],[]]
! 176:
! 177: S= [ 2 1 0 0 ]
! 178: [ 0 2 0 0 ]
! 179: [ 0 0 2 0 ]
! 180: [ 0 0 0 1 ]
! 181:
1.1 takayama 182: $B7k2L$N@bL@(B.
1.2 ! noro 183:
! 184: $B7k2L$O(B [P,[[e1,m1,j1],[e2,m2,j2],...],DefiningIdeal] $B$N7A$N%j%9%H$G$"$k(B.
! 185: P $B$OJQ499TNs(B, $B$9$J$o$A(B P^(-1)AP $B$,(B Jordan $BI8=`7A$K$J$k9TNs$rI=$9(B.
! 186: $B<!$NMWAG$O(B Jordan $BI8=`7A$r9=@.$9$k(B Jordan $B%V%m%C%/$N%j%9%H$G$"$k(B.
! 187: [ei,mi,ji] $B$O(B, $B8GM-CM(B ei, $B%5%$%:(B mi $B$N(B Jordan $B%V%m%C%/$,(B ji $B8D$"$k$3$H(B
! 188: $B$r<($9(B. $BF@$i$l$?(B P $B$K$h$j7W;;$9$k$H(B, $B3N$+$K$=$&$J$C$F$$$k$3$H$,>e$N(B
! 189: $BNc$GJ,$+$k(B. $B0lHL$K$O(B, $B8GM-CM$OBe?tE*?t$H$J$k(B. $B$3$N>l9g(B, $B8GM-CM$r(B
! 190: $BI=$9ITDj85$,I,MW$J$@$1@8@.$5$l(B, $B0lHL8GM-%Y%/%H%k(B (P $B$NNs%Y%/%H%k(B)
! 191: $B$O$=$l$i$GI=8=$5$l$k(B. DefiningIdeal $B$O$=$l$i$NITDj85$rDj5A$9$k(B
! 192: $B%$%G%"%k$G$"$k(B.
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