File: [local] / OpenXM_contrib2 / asir2000 / lib / mat (download)
Revision 1.1.1.1 (vendor branch), Fri Dec 3 07:39:11 1999 UTC (24 years, 10 months ago) by noro
Branch: NORO
CVS Tags: RELEASE_20000124, RELEASE_1_1_2, ASIR2000 Changes since 1.1: +0 -0
lines
Imported asir2000 as OpenXM_contrib2/asir2000.
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/* $OpenXM: OpenXM_contrib2/asir2000/lib/mat,v 1.1.1.1 1999/12/03 07:39:11 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$