void incomplete_qr(int m, int n, const int *Acolstart, const int *Arowindex, const double *Avalue,
double Qdroptol,
const int *Rcolstart, const int *Rrowindex, double *Rvalue, double *Rdiag)
{
// column storage for intermediate Q
std::vector<StaticSparseVector> Q(n);
// for each column of Q, how many more times it will be used in making R
// (once this gets decremented to zero, we can free the column)
std::vector<int> dependency_count(n,0);
for(int i=0; i<n; ++i){
for(int a=Rcolstart[i]; a<Rcolstart[i+1]; ++a){
int j=Rrowindex[a];
if(j<i) ++dependency_count[j];
}
}
// construct R a column at a time
for(int i=0; i<n; ++i){
DynamicSparseVector q;
copy_column(Acolstart[i], Acolstart[i+1], Arowindex, Avalue, q);
for(int a=Rcolstart[i]; a<Rcolstart[i+1]; ++a){
int j=Rrowindex[a];
if(j<i){
Rvalue[a]=dot_product(Q[j], q);
add_to_vector(-Rvalue[a], Q[j], q);
--dependency_count[j];
if(dependency_count[j]==0) Q[j].clear();
}else // j>i
Rvalue[a]=0; // ideally structure of R is upper triangular, so this waste of space won't happen
}
Rdiag[i]=vector_norm(q);
copy_large_entries(q, Qdroptol*Rdiag[i], Q[i]);
normalize(Q[i]);
}
}
void run_tests(void) {
int unsolved[HEIGHT][WIDTH] = { { 5, 3, 0, 0, 7, 0, 0, 0, 0 },
{ 6, 0, 0, 1, 9, 5, 0, 0, 0 },
{ 0, 9, 8, 0, 0, 0, 0, 6, 0 },
{ 8, 0, 0, 0, 6, 0, 0, 0, 3 },
{ 4, 0, 0, 8, 0, 3, 0, 0, 1 },
{ 7, 0, 0, 0, 2, 0, 0, 0, 6 },
{ 0, 6, 0, 0, 0, 0, 2, 8, 0 },
{ 0, 0, 0, 4, 1, 9, 0, 0, 5 },
{ 0, 0, 0, 0, 8, 0, 0, 7, 9 } };
int illegal[HEIGHT][WIDTH] = { { 5, 3, 5, 2, 7, 6, 7, 8, 9 },
{ 6, 1, 0, 1, 9, 5, 0, 0, 0 },
{ 0, 9, 8, 0, 0, 0, 0, 6, 0 },
{ 8, 2, 2, 0, 6, 0, 0, 0, 3 },
{ 4, 4, 0, 8, 0, 3, 6, 0, 1 },
{ 7, 0, 5, 0, 2, 0, 0, 0, 6 },
{ 0, 6, 0, 0, 0, 0, 2, 8, 0 },
{ 0, 0, 0, 4, 1, 9, 0, 0, 5 },
{ 4, 0, 0, 0, 8, 0, 0, 7, 9 } };
int solved[HEIGHT][WIDTH] = { { 5, 3, 4, 6, 7, 8, 9, 1, 2 },
{ 6, 7, 2, 1, 9, 5, 3, 4, 8 },
{ 1, 9, 8, 3, 4, 2, 5, 6, 7 },
{ 8, 5, 9, 7, 6, 1, 4, 2, 3 },
{ 4, 2, 6, 8, 5, 3, 7, 9, 1 },
{ 7, 1, 3, 9, 2, 4, 8, 5, 6 },
{ 9, 6, 1, 5, 3, 7, 2, 8, 4 },
{ 2, 8, 7, 4, 1, 9, 6, 3, 5 },
{ 3, 4, 5, 2, 8, 6, 1, 7, 9 } };
int row[WIDTH];
int column[HEIGHT];
int sub[SUB_HEIGHT][SUB_WIDTH];
puts("Unsolved tests");
test_rows(unsolved, 0);
test_columns(unsolved, 0);
test_subs(unsolved, 0);
test_whole(unsolved, 0);
copy_row(unsolved, 0, row);
test_row_legality(row, 1);
copy_column(unsolved, 0, column);
test_column_legality(column, 1);
copy_sub(unsolved, 0, 0, sub);
test_sub_legality(sub, 1);
test_legality(unsolved, 1);
int illegal_move[3] = {0, 2, 5};
test_legality_after_move(unsolved, illegal_move, 0);
int legal_move[3] = {0, 2, 4};
test_legality_after_move(unsolved, legal_move, 1);
puts("Illegal tests");
test_rows(illegal, 0);
test_columns(illegal, 0);
test_subs(illegal, 0);
test_whole(illegal, 0);
copy_row(illegal, 0, row);
test_row_legality(row, 0);
copy_column(illegal, 0, column);
test_column_legality(column, 0);
copy_sub(illegal, 0, 0, sub);
test_sub_legality(sub, 0);
test_legality(illegal, 0);
puts("Presolved tests");
test_rows(solved, 1);
test_columns(solved, 1);
test_subs(solved, 1);
test_whole(solved, 1);
solve(unsolved);
puts("Solved tests");
test_rows(unsolved, 1);
test_columns(unsolved, 1);
test_subs(unsolved, 1);
test_whole(unsolved, 1);
print_test_results();
}
GLOBAL Int UMF_create_element
(
NumericType *Numeric,
WorkType *Work,
SymbolicType *Symbolic
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int j, col, row, *Fcols, *Frows, fnrows, fncols, *Cols, len, needunits, t1,
t2, size, e, i, *E, *Fcpos, *Frpos, *Rows, eloc, fnr_curr, f,
got_memory, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, max_mark,
*Col_degree, *Col_tlen, nn, n_row, n_col, r2, c2, do_Fcpos ;
Entry *C, *Fcol ;
Element *ep ;
Unit *p, *Memory ;
Tuple *tp, *tp1, *tp2, tuple, *tpend ;
#ifndef NDEBUG
DEBUG2 (("FRONTAL WRAPUP\n")) ;
UMF_dump_current_front (Numeric, Work, TRUE) ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
ASSERT (Work->fnpiv == 0) ;
ASSERT (Work->fnzeros == 0) ;
Row_degree = Numeric->Rperm ;
Row_tuples = Numeric->Uip ;
Row_tlen = Numeric->Uilen ;
Col_degree = Numeric->Cperm ;
Col_tuples = Numeric->Lip ;
Col_tlen = Numeric->Lilen ;
n_row = Work->n_row ;
n_col = Work->n_col ;
nn = MAX (n_row, n_col) ;
Fcols = Work->Fcols ;
Frows = Work->Frows ;
Fcpos = Work->Fcpos ;
Frpos = Work->Frpos ;
Memory = Numeric->Memory ;
fncols = Work->fncols ;
fnrows = Work->fnrows ;
tp = (Tuple *) NULL ;
tp1 = (Tuple *) NULL ;
tp2 = (Tuple *) NULL ;
/* ---------------------------------------------------------------------- */
/* add the current frontal matrix to the degrees of each column */
/* ---------------------------------------------------------------------- */
if (!Symbolic->fixQ)
{
/* but only if the column ordering is not fixed */
#pragma ivdep
for (j = 0 ; j < fncols ; j++)
{
/* add the current frontal matrix to the degree */
ASSERT (Fcols [j] >= 0 && Fcols [j] < n_col) ;
Col_degree [Fcols [j]] += fnrows ;
}
}
/* ---------------------------------------------------------------------- */
/* add the current frontal matrix to the degrees of each row */
/* ---------------------------------------------------------------------- */
#pragma ivdep
for (i = 0 ; i < fnrows ; i++)
{
/* add the current frontal matrix to the degree */
ASSERT (Frows [i] >= 0 && Frows [i] < n_row) ;
Row_degree [Frows [i]] += fncols ;
}
/* ---------------------------------------------------------------------- */
/* Reset the external degree counters */
/* ---------------------------------------------------------------------- */
E = Work->E ;
max_mark = MAX_MARK (nn) ;
if (!Work->pivcol_in_front)
{
/* clear the external column degrees. no more Usons of current front */
Work->cdeg0 += (nn + 1) ;
if (Work->cdeg0 >= max_mark)
{
/* guard against integer overflow. This is very rare */
DEBUG1 (("Integer overflow, cdeg\n")) ;
Work->cdeg0 = 1 ;
#pragma ivdep
for (e = 1 ; e <= Work->nel ; e++)
{
if (E [e])
{
ep = (Element *) (Memory + E [e]) ;
ep->cdeg = 0 ;
}
}
}
}
if (!Work->pivrow_in_front)
{
/* clear the external row degrees. no more Lsons of current front */
Work->rdeg0 += (nn + 1) ;
if (Work->rdeg0 >= max_mark)
{
/* guard against integer overflow. This is very rare */
DEBUG1 (("Integer overflow, rdeg\n")) ;
Work->rdeg0 = 1 ;
#pragma ivdep
for (e = 1 ; e <= Work->nel ; e++)
{
if (E [e])
{
ep = (Element *) (Memory + E [e]) ;
ep->rdeg = 0 ;
}
}
}
}
/* ---------------------------------------------------------------------- */
/* clear row/col offsets */
/* ---------------------------------------------------------------------- */
if (!Work->pivrow_in_front)
{
#pragma ivdep
for (j = 0 ; j < fncols ; j++)
{
Fcpos [Fcols [j]] = EMPTY ;
}
}
if (!Work->pivcol_in_front)
{
#pragma ivdep
for (i = 0 ; i < fnrows ; i++)
{
Frpos [Frows [i]] = EMPTY ;
}
}
if (fncols <= 0 || fnrows <= 0)
{
/* no element to create */
DEBUG2 (("Element evaporation\n")) ;
Work->prior_element = EMPTY ;
return (TRUE) ;
}
/* ---------------------------------------------------------------------- */
/* create element for later assembly */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
UMF_allocfail = FALSE ;
if (UMF_gprob > 0)
{
double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
UMF_allocfail = rrr < UMF_gprob ;
if (UMF_allocfail) DEBUGm2 (("Random garbage collection (create)\n"));
}
#endif
needunits = 0 ;
got_memory = FALSE ;
eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
&needunits, &ep) ;
/* if UMF_get_memory needs to be called */
if (Work->do_grow)
{
/* full compaction of current frontal matrix, since UMF_grow_front will
* be called next anyway. */
r2 = fnrows ;
c2 = fncols ;
do_Fcpos = FALSE ;
}
else
{
/* partial compaction. */
r2 = MAX (fnrows, Work->fnrows_new + 1) ;
c2 = MAX (fncols, Work->fncols_new + 1) ;
/* recompute Fcpos if pivot row is in the front */
do_Fcpos = Work->pivrow_in_front ;
}
if (!eloc)
{
/* Do garbage collection, realloc, and try again. */
/* Compact the current front if it needs to grow anyway. */
/* Note that there are no pivot rows or columns in the current front */
DEBUGm3 (("get_memory from umf_create_element, 1\n")) ;
if (!UMF_get_memory (Numeric, Work, needunits, r2, c2, do_Fcpos))
{
/* :: out of memory in umf_create_element (1) :: */
DEBUGm4 (("out of memory: create element (1)\n")) ;
return (FALSE) ; /* out of memory */
}
got_memory = TRUE ;
Memory = Numeric->Memory ;
eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
&needunits, &ep) ;
ASSERT (eloc >= 0) ;
if (!eloc)
{
/* :: out of memory in umf_create_element (2) :: */
DEBUGm4 (("out of memory: create element (2)\n")) ;
return (FALSE) ; /* out of memory */
}
}
e = ++(Work->nel) ; /* get the name of this new frontal matrix */
Work->prior_element = e ;
DEBUG8 (("wrapup e "ID" nel "ID"\n", e, Work->nel)) ;
ASSERT (e > 0 && e < Work->elen) ;
ASSERT (E [e] == 0) ;
E [e] = eloc ;
if (Work->pivcol_in_front)
{
/* the new element is a Uson of the next frontal matrix */
ep->cdeg = Work->cdeg0 ;
}
if (Work->pivrow_in_front)
{
/* the new element is an Lson of the next frontal matrix */
ep->rdeg = Work->rdeg0 ;
}
/* ---------------------------------------------------------------------- */
/* copy frontal matrix into the new element */
/* ---------------------------------------------------------------------- */
#pragma ivdep
for (i = 0 ; i < fnrows ; i++)
{
Rows [i] = Frows [i] ;
}
#pragma ivdep
for (i = 0 ; i < fncols ; i++)
{
Cols [i] = Fcols [i] ;
}
Fcol = Work->Fcblock ;
DEBUG0 (("copy front "ID" by "ID"\n", fnrows, fncols)) ;
fnr_curr = Work->fnr_curr ;
ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ;
for (j = 0 ; j < fncols ; j++)
{
copy_column (fnrows, Fcol, C) ;
Fcol += fnr_curr ;
C += fnrows ;
}
DEBUG8 (("element copied\n")) ;
/* ---------------------------------------------------------------------- */
/* add tuples for the new element */
/* ---------------------------------------------------------------------- */
tuple.e = e ;
if (got_memory)
{
/* ------------------------------------------------------------------ */
/* UMF_get_memory ensures enough space exists for each new tuple */
/* ------------------------------------------------------------------ */
/* place (e,f) in the element list of each column */
for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
{
col = Fcols [tuple.f] ;
ASSERT (col >= 0 && col < n_col) ;
ASSERT (NON_PIVOTAL_COL (col)) ;
ASSERT (Col_tuples [col]) ;
tp = ((Tuple *) (Memory + Col_tuples [col])) + Col_tlen [col]++ ;
*tp = tuple ;
}
/* ------------------------------------------------------------------ */
/* place (e,f) in the element list of each row */
for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
{
row = Frows [tuple.f] ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (NON_PIVOTAL_ROW (row)) ;
ASSERT (Row_tuples [row]) ;
tp = ((Tuple *) (Memory + Row_tuples [row])) + Row_tlen [row]++ ;
*tp = tuple ;
}
}
else
{
/* ------------------------------------------------------------------ */
/* place (e,f) in the element list of each column */
/* ------------------------------------------------------------------ */
/* might not have enough space for each tuple */
for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
{
col = Fcols [tuple.f] ;
ASSERT (col >= 0 && col < n_col) ;
ASSERT (NON_PIVOTAL_COL (col)) ;
t1 = Col_tuples [col] ;
DEBUG1 (("Placing on col:"ID" , tuples at "ID"\n",
col, Col_tuples [col])) ;
size = 0 ;
len = 0 ;
if (t1)
{
p = Memory + t1 ;
tp = (Tuple *) p ;
size = GET_BLOCK_SIZE (p) ;
len = Col_tlen [col] ;
tp2 = tp + len ;
}
needunits = UNITS (Tuple, len + 1) ;
DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
len, size, needunits));
if (needunits > size && t1)
{
/* prune the tuples */
tp1 = tp ;
tp2 = tp ;
tpend = tp + len ;
for ( ; tp < tpend ; tp++)
{
e = tp->e ;
ASSERT (e > 0 && e <= Work->nel) ;
if (!E [e]) continue ; /* element already deallocated */
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
;
if (Cols [f] == EMPTY) continue ; /* already assembled */
ASSERT (col == Cols [f]) ;
*tp2++ = *tp ; /* leave the tuple in the list */
}
len = tp2 - tp1 ;
Col_tlen [col] = len ;
needunits = UNITS (Tuple, len + 1) ;
}
if (needunits > size)
{
/* no room exists - reallocate elsewhere */
DEBUG1 (("REALLOCATE Col: "ID", size "ID" to "ID"\n",
col, size, 2*needunits)) ;
#ifndef NDEBUG
UMF_allocfail = FALSE ;
if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
{
double rrr = ((double) (rand ( ))) /
(((double) RAND_MAX) + 1) ;
DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
UMF_allocfail = rrr < UMF_gprob ;
if (UMF_allocfail) DEBUGm2 (("Random gar. (col tuple)\n")) ;
}
#endif
needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
if (!t2)
{
/* :: get memory in umf_create_element (1) :: */
/* get memory, reconstruct all tuple lists, and return */
/* Compact the current front if it needs to grow anyway. */
/* Note: no pivot rows or columns in the current front */
DEBUGm4 (("get_memory from umf_create_element, 1\n")) ;
return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
}
Col_tuples [col] = t2 ;
tp2 = (Tuple *) (Memory + t2) ;
if (t1)
{
for (i = 0 ; i < len ; i++)
{
*tp2++ = *tp1++ ;
}
UMF_mem_free_tail_block (Numeric, t1) ;
}
}
/* place the new (e,f) tuple in the element list of the column */
Col_tlen [col]++ ;
*tp2 = tuple ;
}
/* ------------------------------------------------------------------ */
/* place (e,f) in the element list of each row */
/* ------------------------------------------------------------------ */
for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
{
row = Frows [tuple.f] ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (NON_PIVOTAL_ROW (row)) ;
t1 = Row_tuples [row] ;
DEBUG1 (("Placing on row:"ID" , tuples at "ID"\n",
row, Row_tuples [row])) ;
size = 0 ;
len = 0 ;
if (t1)
{
p = Memory + t1 ;
tp = (Tuple *) p ;
size = GET_BLOCK_SIZE (p) ;
len = Row_tlen [row] ;
tp2 = tp + len ;
}
needunits = UNITS (Tuple, len + 1) ;
DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
len, size, needunits)) ;
if (needunits > size && t1)
{
/* prune the tuples */
tp1 = tp ;
tp2 = tp ;
tpend = tp + len ;
for ( ; tp < tpend ; tp++)
{
e = tp->e ;
ASSERT (e > 0 && e <= Work->nel) ;
if (!E [e])
{
continue ; /* element already deallocated */
}
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
Rows = Cols + (ep->ncols) ;
if (Rows [f] == EMPTY) continue ; /* already assembled */
ASSERT (row == Rows [f]) ;
*tp2++ = *tp ; /* leave the tuple in the list */
}
len = tp2 - tp1 ;
Row_tlen [row] = len ;
needunits = UNITS (Tuple, len + 1) ;
}
if (needunits > size)
{
/* no room exists - reallocate elsewhere */
DEBUG1 (("REALLOCATE Row: "ID", size "ID" to "ID"\n",
row, size, 2*needunits)) ;
#ifndef NDEBUG
UMF_allocfail = FALSE ;
if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
{
double rrr = ((double) (rand ( ))) /
(((double) RAND_MAX) + 1) ;
DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
UMF_allocfail = rrr < UMF_gprob ;
if (UMF_allocfail) DEBUGm2 (("Random gar. (row tuple)\n")) ;
}
#endif
needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
if (!t2)
{
/* :: get memory in umf_create_element (2) :: */
/* get memory, reconstruct all tuple lists, and return */
/* Compact the current front if it needs to grow anyway. */
/* Note: no pivot rows or columns in the current front */
DEBUGm4 (("get_memory from umf_create_element, 2\n")) ;
return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
}
Row_tuples [row] = t2 ;
tp2 = (Tuple *) (Memory + t2) ;
if (t1)
{
for (i = 0 ; i < len ; i++)
{
*tp2++ = *tp1++ ;
}
UMF_mem_free_tail_block (Numeric, t1) ;
}
}
/* place the new (e,f) tuple in the element list of the row */
Row_tlen [row]++ ;
*tp2 = tuple ;
}
}
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
DEBUG1 (("Done extending\nFINAL: element row pattern: len="ID"\n", fncols));
for (j = 0 ; j < fncols ; j++) DEBUG1 ((""ID"\n", Fcols [j])) ;
DEBUG1 (("FINAL: element col pattern: len="ID"\n", fnrows)) ;
for (j = 0 ; j < fnrows ; j++) DEBUG1 ((""ID"\n", Frows [j])) ;
for (j = 0 ; j < fncols ; j++)
{
col = Fcols [j] ;
ASSERT (col >= 0 && col < n_col) ;
UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
}
for (j = 0 ; j < fnrows ; j++)
{
row = Frows [j] ;
ASSERT (row >= 0 && row < n_row) ;
UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
}
if (n_row < 1000 && n_col < 1000)
{
UMF_dump_memory (Numeric) ;
}
DEBUG1 (("New element, after filling with stuff: "ID"\n", e)) ;
UMF_dump_element (Numeric, Work, e, TRUE) ;
if (nn < 1000)
{
DEBUG4 (("Matrix dump, after New element: "ID"\n", e)) ;
UMF_dump_matrix (Numeric, Work, TRUE) ;
}
DEBUG3 (("FRONTAL WRAPUP DONE\n")) ;
#endif
return (TRUE) ;
}
