VEC *LUTsolve(const MAT *LU, PERM *pivot, const VEC *b, VEC *x)
#endif
{
if ( ! LU || ! b || ! pivot )
error(E_NULL,"LUTsolve");
if ( LU->m != LU->n || LU->n != b->dim )
error(E_SIZES,"LUTsolve");
x = v_copy(b,x);
UTsolve(LU,x,x,0.0); /* explicit diagonal */
LTsolve(LU,x,x,1.0); /* implicit diagonal = 1 */
pxinv_vec(pivot,x,x); /* x := P^T.tmp */
return (x);
}
double QRcondest(const MAT *QR)
#endif
{
STATIC VEC *y=VNULL;
Real norm1, norm2, sum, tmp1, tmp2;
int i, j, limit;
if ( QR == MNULL )
error(E_NULL,"QRcondest");
limit = min(QR->m,QR->n);
for ( i = 0; i < limit; i++ )
if ( QR->me[i][i] == 0.0 )
return HUGE_VAL;
y = v_resize(y,limit);
MEM_STAT_REG(y,TYPE_VEC);
/* use the trick for getting a unit vector y with ||R.y||_inf small
from the LU condition estimator */
for ( i = 0; i < limit; i++ )
{
sum = 0.0;
for ( j = 0; j < i; j++ )
sum -= QR->me[j][i]*y->ve[j];
sum -= (sum < 0.0) ? 1.0 : -1.0;
y->ve[i] = sum / QR->me[i][i];
}
UTmlt(QR,y,y);
/* now apply inverse power method to R^T.R */
for ( i = 0; i < 3; i++ )
{
tmp1 = v_norm2(y);
sv_mlt(1/tmp1,y,y);
UTsolve(QR,y,y,0.0);
tmp2 = v_norm2(y);
sv_mlt(1/v_norm2(y),y,y);
Usolve(QR,y,y,0.0);
}
/* now compute approximation for ||R^{-1}||_2 */
norm1 = sqrt(tmp1)*sqrt(tmp2);
/* now use complementary approach to compute approximation to ||R||_2 */
for ( i = limit-1; i >= 0; i-- )
{
sum = 0.0;
for ( j = i+1; j < limit; j++ )
sum += QR->me[i][j]*y->ve[j];
y->ve[i] = (sum >= 0.0) ? 1.0 : -1.0;
y->ve[i] = (QR->me[i][i] >= 0.0) ? y->ve[i] : - y->ve[i];
}
/* now apply power method to R^T.R */
for ( i = 0; i < 3; i++ )
{
tmp1 = v_norm2(y);
sv_mlt(1/tmp1,y,y);
Umlt(QR,y,y);
tmp2 = v_norm2(y);
sv_mlt(1/tmp2,y,y);
UTmlt(QR,y,y);
}
norm2 = sqrt(tmp1)*sqrt(tmp2);
/* printf("QRcondest: norm1 = %g, norm2 = %g\n",norm1,norm2); */
#ifdef THREADSAFE
V_FREE(y);
#endif
return norm1*norm2;
}
