File: [local] / OpenXM_contrib2 / asir2000 / lib / mat (download)
Revision 1.3, Tue Aug 22 05:04:22 2000 UTC (24 years, 1 month ago) by noro
Branch: MAIN
CVS Tags: maekawa-ipv6, STABLE_1_1_3, R_1_3_1-2, RELEASE_1_3_1_13b, RELEASE_1_2_3_12, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, KNOPPIX_2006, HEAD, DEB_REL_1_2_3-9 Changes since 1.2: +2 -2
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/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
* non-exclusive and royalty-free license to use, copy, modify and
* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
* conditions of this Agreement. For the avoidance of doubt, you acquire
* only a limited right to use the SOFTWARE hereunder, and FLL or any
* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
* (1) FLL does not grant you a license in any way for commercial
* purposes. You may use the SOFTWARE only for non-commercial and
* non-profit purposes only, such as academic, research and internal
* business use.
* (2) The SOFTWARE is protected by the Copyright Law of Japan and
* international copyright treaties. If you make copies of the SOFTWARE,
* with or without modification, as permitted hereunder, you shall affix
* to all such copies of the SOFTWARE the above copyright notice.
* (3) An explicit reference to this SOFTWARE and its copyright owner
* shall be made on your publication or presentation in any form of the
* results obtained by use of the SOFTWARE.
* (4) In the event that you modify the SOFTWARE, you shall notify FLL by
* e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
* for such modification or the source code of the modified part of the
* SOFTWARE.
*
* THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
* RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
* MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
* UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
* OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
* DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
* ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
* FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
* DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
* SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
* OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
*
* $OpenXM: OpenXM_contrib2/asir2000/lib/mat,v 1.3 2000/08/22 05:04:22 noro Exp $
*/
/* fraction free gaussian elimination; detructive */
def deter(MAT)
{
S = size(MAT);
if ( car(S) != car(cdr(S)) )
return 0;
N = car(S);
for ( J = 0, D = 1; J < N; J++ ) {
for ( I = J; (I<N)&&(MAT[I][J] == 0); I++ );
if ( I != N ) {
for ( L = I; L < N; L++ )
if ( MAT[L][J] && (nmono(MAT[L][J]) < nmono(MAT[I][J])) )
I = L;
if ( J != I )
for ( K = 0; K < N; K++ ) {
B = MAT[J][K]; MAT[J][K] = MAT[I][K]; MAT[I][K] = B;
}
for ( I = J + 1, V = MAT[J][J]; I < N; I++ )
for ( K = J + 1, U = MAT[I][J]; K < N; K++ )
MAT[I][K] = sdiv(MAT[I][K]*V-MAT[J][K]*U,D);
D = V;
} else
return ( 0 );
}
return (D);
}
/* characteristic polynomial */
def cp(M)
{
tstart;
S = size(M);
if ( car(S) != car(cdr(S)) )
return 0;
N = car(S);
MAT = newmat(N,N);
for ( I = 0; I < N; I++ )
for ( J = 0; J < N; J++ )
if ( I == J )
MAT[I][J] = red(M[I][J]-x);
else
MAT[I][J] = red(M[I][J]);
D = deter(MAT);
tstop;
return (D);
}
/* calculation of charpoly by danilevskii's method */
def da(MAT)
{
tstart;
S = size(MAT);
if ( car(S) != car(cdr(S)) )
return 0;
N = car(S);
M = newmat(N,N);
for ( I = 0; I < N; I++ )
for ( J = 0; J < N; J++ )
M[I][J] = red(MAT[I][J]);
for ( W = newvect(N), J = 0, K = 0, D = 1; J < N; J++ ) {
for ( I = J + 1; (I<N) && (M[I][J] == 0); I++ );
if ( I == N ) {
for ( L = J, S = 1; L >= K; L-- )
S = S*x-M[L][J];
D *= S;
K = J + 1;
} else {
B = J + 1;
for ( L = 0; L < N; L++ ) {
T = M[I][L]; M[I][L] = M[B][L]; M[B][L] = T;
}
for ( L = 0; L < N; L++ ) {
T = M[L][B]; M[L][B] = M[L][I]; M[L][I] = T;
W[L] = M[L][J];
}
for ( L = K, T = red(1/M[B][J]); L < N; L++ )
M[B][L] *= T;
for ( L = K; L < N; L++ )
if ( W[L] && (L != J + 1) )
for ( B = K, T = W[L]; B < N; B++ )
M[L][B] -= M[J+1][B]*T;
for ( L = K; L < N; L++ ) {
for ( B = 0, T = 0; B < N ; B++ )
T += M[L][B] * W[B];
M[L][J + 1] = T;
}
}
}
tstop;
return ( D );
}
def newvmat(N) {
M = newmat(N,N);
for ( I = 0; I < N; I++ )
for ( J = 0; J < N; J++ )
M[I][J] = strtov(rtostr(x)+rtostr(I))^J;
return M;
}
def newssmat(N) {
M = newmat(N,N);
for ( I = 0; I < N; I++ )
for ( J = 0; J < N; J++ )
M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
return M;
}
def newasssmat(N) {
N *= 2;
M = newmat(N,N);
for ( I = 0; I < N; I++ )
for ( J = 0; J < I; J++ )
M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
for ( I = 0; I < N; I++ )
for ( J = I + 1; J < N; J++ )
M[I][J] = -M[J][I];
return M;
}
/* calculation of determinant by minor expansion */
def edet(M) {
S = size(M);
if ( S[0] == 1 )
return M[0][0];
else {
N = S[0];
L = newmat(N-1,N-1);
for ( I = 0, R = 0; I < N; I++ ) {
for ( J = 1; J < N; J++ ) {
for ( K = 0; K < I; K++ )
L[J-1][K] = M[J][K];
for ( K = I+1; K < N; K++ )
L[J-1][K-1] = M[J][K];
}
R += (-1)^I*edet(L)*M[0][I];
}
return R;
}
}
/* sylvester's matrix */
def syl(V,P1,P2) {
D1 = deg(P1,V); D2 = deg(P2,V);
M = newmat(D1+D2,D1+D2);
for ( J = 0; J <= D2; J++ )
M[0][J] = coef(P2,D2-J,V);
for ( I = 1; I < D1; I++ )
for ( J = 0; J <= D2; J++ )
M[I][I+J] = M[0][J];
for ( J = 0; J <= D1; J++ )
M[D1][J] = coef(P1,D1-J,V);
for ( I = 1; I < D2; I++ )
for ( J = 0; J <= D1; J++ )
M[D1+I][I+J] = M[D1][J];
return M;
}
/* calculation of resultant by edet() */
def res_minor(V,P1,P2)
{
D1 = deg(P1,V); D2 = deg(P2,V);
M = newmat(D1+D2,D1+D2);
for ( J = 0; J <= D2; J++ )
M[0][J] = coef(P2,D2-J,V);
for ( I = 1; I < D1; I++ )
for ( J = 0; J <= D2; J++ )
M[I][I+J] = M[0][J];
for ( J = 0; J <= D1; J++ )
M[D1][J] = coef(P1,D1-J,V);
for ( I = 1; I < D2; I++ )
for ( J = 0; J <= D1; J++ )
M[D1+I][I+J] = M[D1][J];
return edet(M);
}
end$