File: [local] / OpenXM_contrib2 / asir2000 / lib / sturm (download)
Revision 1.2, Mon Aug 21 08:31:43 2000 UTC (24 years, 1 month ago) by noro
Branch: MAIN
Changes since 1.1: +49 -1
lines
Added copyright notice and license agreement. It is mandatory to distribute
Risa/Asir source codes freely.
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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@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/sturm,v 1.2 2000/08/21 08:31:43 noro Exp $
*/
/* find intervals which include roots of a polynomial */
#include "defs.h"
def slice(P,XR,YR,WH) {
X = FIRST(XR); XMIN = SECOND(XR); XMAX = THIRD(XR);
Y = FIRST(YR); YMIN = SECOND(YR); YMAX = THIRD(YR);
W = FIRST(WH); H = SECOND(WH);
XS = (XMAX-XMIN)/W; YS = (YMAX-YMIN)/H;
T = ptozp(subst(P,X,X*XS+XMIN,Y,Y*YS+YMIN));
R = newvect(W+1);
for ( I = 0; I <= W; I++ ) {
S = sturm(subst(T,X,I));
R[I] = numch(S,Y,0)-numch(S,Y,H);
}
return R;
}
def slice1(P,XR,YR,WH) {
X = FIRST(XR); XMIN = SECOND(XR); XMAX = THIRD(XR);
Y = FIRST(YR); YMIN = SECOND(YR); YMAX = THIRD(YR);
W = FIRST(WH); H = SECOND(WH);
XS = (XMAX-XMIN)/W; YS = (YMAX-YMIN)/H;
T = ptozp(subst(P,X,X*XS+XMIN,Y,Y*YS+YMIN));
R = newvect(W+1);
for ( I = 0; I <= W; I++ ) {
S = sturm(subst(T,X,I));
R[I] = newvect(H+1);
seproot(S,Y,0,H,R[I]);
}
return R;
}
def seproot(S,X,MI,MA,R) {
N = car(size(S));
for ( I = MI; I <= MA; I++ )
if ( !(T = subst(S[0],X,I)) )
R[I] = -1;
else
break;
if ( I > MA )
return;
for ( J = MA; J >= MI; J-- )
if ( !(T = subst(S[0],X,J)) )
R[J] = -1;
else
break;
R[I] = numch(S,X,I); R[J] = numch(S,X,J);
if ( J <= I+1 )
return;
if ( R[I] == R[J] ) {
for ( K = I + 1; K < J; K++ )
R[K] = R[I];
return;
}
T = idiv(I+J,2);
seproot(S,X,I,T,R);
seproot(S,X,T,J,R);
}
/* compute the sturm sequence of P */
def sturm(P) {
V = var(P); N = deg(P,V); T = newvect(N+1);
G1 = T[0] = P; G2 = T[1] = ptozp(diff(P,var(P)));
for ( I = 1, H = 1, X = 1; ; ) {
if ( !deg(G2,V) )
break;
D = deg(G1,V)-deg(G2,V);
if ( (L = LCOEF(G2)) < 0 )
L = -L;
if ( !(R = -srem(L^(D+1)*G1,G2)) )
break;
if ( type(R) == 1 ) {
T[++I] = (R>0?1:-1); break;
}
M = H^D; G1 = G2;
G2 = T[++I] = sdiv(R,M*X);
if ( (X = LCOEF(G1)) < 0 )
X = -X;
H = X^D*H/M;
}
S = newvect(I+1);
for ( J = 0; J <= I; J++ )
S[J] = T[J];
return S;
}
def numch(S,V,A) {
N = car(size(S));
for ( T = subst(S[0],V,A), I = 1, C = 0; I < N; I++ ) {
T1 = subst(S[I],V,A);
if ( !T1 )
continue;
if ( (T1 > 0 && T < 0) || (T1 < 0 && T > 0) )
C++;
T = T1;
}
return C;
}
def numch0(S,V,A,T) {
N = car(size(S));
for ( I = 1, C = 0; I < N; I++ ) {
T1 = subst(S[I],V,A);
if ( !T1 )
continue;
if ( (T1 > 0 && T < 0) || (T1 < 0 && T > 0) )
C++;
T = T1;
}
return C;
}
end;