Annotation of OpenXM_contrib2/asir2000/lib/mat, Revision 1.3
1.2 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3 ! noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.3 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/lib/mat,v 1.2 2000/08/21 08:31:41 noro Exp $
1.2 noro 49: */
1.1 noro 50: /* fraction free gaussian elimination; detructive */
51:
52: def deter(MAT)
53: {
54: S = size(MAT);
55: if ( car(S) != car(cdr(S)) )
56: return 0;
57: N = car(S);
58: for ( J = 0, D = 1; J < N; J++ ) {
59: for ( I = J; (I<N)&&(MAT[I][J] == 0); I++ );
60: if ( I != N ) {
61: for ( L = I; L < N; L++ )
62: if ( MAT[L][J] && (nmono(MAT[L][J]) < nmono(MAT[I][J])) )
63: I = L;
64: if ( J != I )
65: for ( K = 0; K < N; K++ ) {
66: B = MAT[J][K]; MAT[J][K] = MAT[I][K]; MAT[I][K] = B;
67: }
68:
69: for ( I = J + 1, V = MAT[J][J]; I < N; I++ )
70: for ( K = J + 1, U = MAT[I][J]; K < N; K++ )
71: MAT[I][K] = sdiv(MAT[I][K]*V-MAT[J][K]*U,D);
72: D = V;
73: } else
74: return ( 0 );
75: }
76: return (D);
77: }
78:
79: /* characteristic polynomial */
80:
81: def cp(M)
82: {
83: tstart;
84: S = size(M);
85: if ( car(S) != car(cdr(S)) )
86: return 0;
87: N = car(S);
88: MAT = newmat(N,N);
89: for ( I = 0; I < N; I++ )
90: for ( J = 0; J < N; J++ )
91: if ( I == J )
92: MAT[I][J] = red(M[I][J]-x);
93: else
94: MAT[I][J] = red(M[I][J]);
95: D = deter(MAT);
96: tstop;
97: return (D);
98: }
99:
100: /* calculation of charpoly by danilevskii's method */
101:
102: def da(MAT)
103: {
104: tstart;
105: S = size(MAT);
106: if ( car(S) != car(cdr(S)) )
107: return 0;
108: N = car(S);
109: M = newmat(N,N);
110: for ( I = 0; I < N; I++ )
111: for ( J = 0; J < N; J++ )
112: M[I][J] = red(MAT[I][J]);
113:
114: for ( W = newvect(N), J = 0, K = 0, D = 1; J < N; J++ ) {
115: for ( I = J + 1; (I<N) && (M[I][J] == 0); I++ );
116: if ( I == N ) {
117: for ( L = J, S = 1; L >= K; L-- )
118: S = S*x-M[L][J];
119: D *= S;
120: K = J + 1;
121: } else {
122: B = J + 1;
123: for ( L = 0; L < N; L++ ) {
124: T = M[I][L]; M[I][L] = M[B][L]; M[B][L] = T;
125: }
126: for ( L = 0; L < N; L++ ) {
127: T = M[L][B]; M[L][B] = M[L][I]; M[L][I] = T;
128: W[L] = M[L][J];
129: }
130: for ( L = K, T = red(1/M[B][J]); L < N; L++ )
131: M[B][L] *= T;
132: for ( L = K; L < N; L++ )
133: if ( W[L] && (L != J + 1) )
134: for ( B = K, T = W[L]; B < N; B++ )
135: M[L][B] -= M[J+1][B]*T;
136: for ( L = K; L < N; L++ ) {
137: for ( B = 0, T = 0; B < N ; B++ )
138: T += M[L][B] * W[B];
139: M[L][J + 1] = T;
140: }
141: }
142: }
143: tstop;
144: return ( D );
145: }
146:
147: def newvmat(N) {
148: M = newmat(N,N);
149: for ( I = 0; I < N; I++ )
150: for ( J = 0; J < N; J++ )
151: M[I][J] = strtov(rtostr(x)+rtostr(I))^J;
152: return M;
153: }
154:
155: def newssmat(N) {
156: M = newmat(N,N);
157: for ( I = 0; I < N; I++ )
158: for ( J = 0; J < N; J++ )
159: M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
160: return M;
161: }
162:
163: def newasssmat(N) {
164: N *= 2;
165: M = newmat(N,N);
166: for ( I = 0; I < N; I++ )
167: for ( J = 0; J < I; J++ )
168: M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
169: for ( I = 0; I < N; I++ )
170: for ( J = I + 1; J < N; J++ )
171: M[I][J] = -M[J][I];
172: return M;
173: }
174:
175: /* calculation of determinant by minor expansion */
176:
177: def edet(M) {
178: S = size(M);
179: if ( S[0] == 1 )
180: return M[0][0];
181: else {
182: N = S[0];
183: L = newmat(N-1,N-1);
184: for ( I = 0, R = 0; I < N; I++ ) {
185: for ( J = 1; J < N; J++ ) {
186: for ( K = 0; K < I; K++ )
187: L[J-1][K] = M[J][K];
188: for ( K = I+1; K < N; K++ )
189: L[J-1][K-1] = M[J][K];
190: }
191: R += (-1)^I*edet(L)*M[0][I];
192: }
193: return R;
194: }
195: }
196:
197: /* sylvester's matrix */
198:
199: def syl(V,P1,P2) {
200: D1 = deg(P1,V); D2 = deg(P2,V);
201: M = newmat(D1+D2,D1+D2);
202: for ( J = 0; J <= D2; J++ )
203: M[0][J] = coef(P2,D2-J,V);
204: for ( I = 1; I < D1; I++ )
205: for ( J = 0; J <= D2; J++ )
206: M[I][I+J] = M[0][J];
207: for ( J = 0; J <= D1; J++ )
208: M[D1][J] = coef(P1,D1-J,V);
209: for ( I = 1; I < D2; I++ )
210: for ( J = 0; J <= D1; J++ )
211: M[D1+I][I+J] = M[D1][J];
212: return M;
213: }
214:
215: /* calculation of resultant by edet() */
216:
217: def res_minor(V,P1,P2)
218: {
219: D1 = deg(P1,V); D2 = deg(P2,V);
220: M = newmat(D1+D2,D1+D2);
221: for ( J = 0; J <= D2; J++ )
222: M[0][J] = coef(P2,D2-J,V);
223: for ( I = 1; I < D1; I++ )
224: for ( J = 0; J <= D2; J++ )
225: M[I][I+J] = M[0][J];
226: for ( J = 0; J <= D1; J++ )
227: M[D1][J] = coef(P1,D1-J,V);
228: for ( I = 1; I < D2; I++ )
229: for ( J = 0; J <= D1; J++ )
230: M[D1+I][I+J] = M[D1][J];
231: return edet(M);
232: }
233: end$
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