void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
int n1, int n2, int r, int nskip)
{
int i;
dAASSERT(A && p && L && d && n1 > 0 && n2 > 0 && r >= 0 && r < n2 &&
n1 >= n2 && nskip >= n1);
#ifndef dNODEBUG
for (i=0; i<n2; i++) dIASSERT(p[i] >= 0 && p[i] < n1);
#endif
if (r==n2-1) {
return; // deleting last row/col is easy
}
else if (r==0) {
dReal *a = (dReal*) ALLOCA (n2 * sizeof(dReal));
for (i=0; i<n2; i++) a[i] = -GETA(p[i],p[0]);
a[0] += REAL(1.0);
dLDLTAddTL (L,d,a,n2,nskip);
}
else {
dReal *t = (dReal*) ALLOCA (r * sizeof(dReal));
dReal *a = (dReal*) ALLOCA ((n2-r) * sizeof(dReal));
for (i=0; i<r; i++) t[i] = L[r*nskip+i] / d[i];
for (i=0; i<(n2-r); i++)
a[i] = dDot(L+(r+i)*nskip,t,r) - GETA(p[r+i],p[r]);
a[0] += REAL(1.0);
dLDLTAddTL (L + r*nskip+r, d+r, a, n2-r, nskip);
}
// snip out row/column r from L and d
dRemoveRowCol (L,n2,nskip,r);
if (r < (n2-1)) memmove (d+r,d+r+1,(n2-r-1)*sizeof(dReal));
}
void _dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
int n1, int n2, int r, int nskip, void *tmpbuf/*n2 + 2*nskip*/)
{
dAASSERT(A && p && L && d && n1 > 0 && n2 > 0 && r >= 0 && r < n2 &&
n1 >= n2 && nskip >= n1);
#ifndef dNODEBUG
for (int i=0; i<n2; ++i) dIASSERT(p[i] >= 0 && p[i] < n1);
#endif
if (r==n2-1) {
return; // deleting last row/col is easy
}
else {
size_t LDLTAddTL_size = _dEstimateLDLTAddTLTmpbufSize(nskip);
dIASSERT(LDLTAddTL_size % sizeof(dReal) == 0);
dReal *tmp = tmpbuf ? (dReal *)tmpbuf : (dReal*) ALLOCA (LDLTAddTL_size + n2 * sizeof(dReal));
if (r==0) {
dReal *a = (dReal *)((char *)tmp + LDLTAddTL_size);
const int p_0 = p[0];
for (int i=0; i<n2; ++i) {
a[i] = -GETA(p[i],p_0);
}
a[0] += REAL(1.0);
dLDLTAddTL (L,d,a,n2,nskip,tmp);
}
else {
dReal *t = (dReal *)((char *)tmp + LDLTAddTL_size);
{
dReal *Lcurr = L + r*nskip;
for (int i=0; i<r; ++Lcurr, ++i) {
dIASSERT(d[i] != dReal(0.0));
t[i] = *Lcurr / d[i];
}
}
dReal *a = t + r;
{
dReal *Lcurr = L + r*nskip;
const int *pp_r = p + r, p_r = *pp_r;
const int n2_minus_r = n2-r;
for (int i=0; i<n2_minus_r; Lcurr+=nskip,++i) {
a[i] = dDot(Lcurr,t,r) - GETA(pp_r[i],p_r);
}
}
a[0] += REAL(1.0);
dLDLTAddTL (L + r*nskip+r, d+r, a, n2-r, nskip, tmp);
}
}
// snip out row/column r from L and d
dRemoveRowCol (L,n2,nskip,r);
if (r < (n2-1)) memmove (d+r,d+r+1,(n2-r-1)*sizeof(dReal));
}
void testLDLTRemove()
{
int i,j,r,p[MSIZE];
dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], d[MSIZE],
L2[MSIZE4*MSIZE], d2[MSIZE], DL2[MSIZE4*MSIZE],
Atest1[MSIZE4*MSIZE], Atest2[MSIZE4*MSIZE], diff, maxdiff;
HEADER;
// make array of A row pointers
dReal *Arows[MSIZE];
for (i=0; i<MSIZE; i++) Arows[i] = A+i*MSIZE4;
// fill permutation vector
for (i=0; i<MSIZE; i++) p[i]=i;
dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));
dFactorLDLT (L,d,MSIZE,MSIZE4);
maxdiff = 1e10;
for (r=0; r<MSIZE; r++) {
// get Atest1 = A with row/column r removed
memcpy (Atest1,A,MSIZE4*MSIZE*sizeof(dReal));
dRemoveRowCol (Atest1,MSIZE,MSIZE4,r);
// test that the row/column removal worked
int bad = 0;
for (i=0; i<MSIZE; i++) {
for (j=0; j<MSIZE; j++) {
if (i != r && j != r) {
int ii = i;
int jj = j;
if (ii >= r) ii--;
if (jj >= r) jj--;
if (A[i*MSIZE4+j] != Atest1[ii*MSIZE4+jj]) bad = 1;
}
}
}
if (bad) printf ("\trow/col removal FAILED for row %d\n",r);
// zero out last row/column of Atest1
for (i=0; i<MSIZE; i++) {
Atest1[(MSIZE-1)*MSIZE4+i] = 0;
Atest1[i*MSIZE4+MSIZE-1] = 0;
}
// get L2*D2*L2' = adjusted factorization to remove that row
memcpy (L2,L,MSIZE4*MSIZE*sizeof(dReal));
memcpy (d2,d,MSIZE*sizeof(dReal));
dLDLTRemove (/*A*/ Arows,p,L2,d2,MSIZE,MSIZE,r,MSIZE4);
// get Atest2 = L2*D2*L2'
dClearUpperTriangle (L2,MSIZE);
for (i=0; i<(MSIZE-1); i++) L2[i*MSIZE4+i] = 1.0;
for (i=0; i<MSIZE; i++) L2[(MSIZE-1)*MSIZE4+i] = 0;
d2[MSIZE-1] = 1;
dSetZero (DL2,MSIZE4*MSIZE);
for (i=0; i<(MSIZE-1); i++) {
for (j=0; j<MSIZE-1; j++) DL2[i*MSIZE4+j] = L2[i*MSIZE4+j] / d2[j];
}
dMultiply2 (Atest2,L2,DL2,MSIZE,MSIZE,MSIZE);
diff = dMaxDifference(Atest1,Atest2,MSIZE,MSIZE);
if (diff < maxdiff) maxdiff = diff;
/*
dPrintMatrix (Atest1,MSIZE,MSIZE);
printf ("\n");
dPrintMatrix (Atest2,MSIZE,MSIZE);
printf ("\n");
*/
}
printf ("\tmaximum difference = %.6e - %s\n",maxdiff,
maxdiff > tol ? "FAILED" : "passed");
}
