Annotation of OpenXM_contrib2/asir2018/lib/mat, Revision 1.1
1.1 ! 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
! 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
! 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'
! 34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
! 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: *
! 48: * $OpenXM$
! 49: */
! 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$
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to mat CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM_contrib2 / asir2018 / lib