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/*
* lu_solve_for_update.c
*
* Copyright (C) 2016-2018 ERGO-Code
*
*/
#include "lu_internal.h"
#include "lu_timer.h"
lu_int lu_solve_for_update(
struct lu *this, const lu_int nrhs, const lu_int *irhs, const double *xrhs,
lu_int *p_nlhs, lu_int *ilhs, double *xlhs, char trans)
{
const lu_int m = this->m;
const lu_int nforrest = this->nforrest;
const lu_int pivotlen = this->pivotlen;
const lu_int nz_sparse = this->sparse_thres * m;
const double droptol = this->droptol;
const lu_int *p = this->p;
const lu_int *pmap = this->pmap;
const lu_int *qmap = this->qmap;
lu_int *eta_row = this->eta_row;
const lu_int *pivotcol = this->pivotcol;
const lu_int *pivotrow = this->pivotrow;
const lu_int *Lbegin = this->Lbegin;
const lu_int *Ltbegin = this->Ltbegin;
const lu_int *Ltbegin_p = this->Ltbegin_p;
lu_int *Ubegin = this->Ubegin;
lu_int *Rbegin = this->Rbegin;
const lu_int *Wbegin = this->Wbegin;
const lu_int *Wend = this->Wend;
const double *col_pivot = this->col_pivot;
const double *row_pivot = this->row_pivot;
lu_int *Lindex = this->Lindex;
double *Lvalue = this->Lvalue;
lu_int *Uindex = this->Uindex;
double *Uvalue = this->Uvalue;
const lu_int *Windex = this->Windex;
const double *Wvalue = this->Wvalue;
lu_int *marked = this->marked;
lu_int i, j, k, n, t, top, pos, put, ipivot, jpivot, nz, nz_symb, M,
room, need, jbegin, jend;
double x, xdrop, pivot;
const lu_int want_solution = p_nlhs && ilhs && xlhs;
lu_int Lflops = 0, Uflops = 0, Rflops = 0;
double tic[2], elapsed;
lu_tic(tic);
if (trans == 't' || trans == 'T')
{
/* ----------------------- */
/* Solve transposed system */
/* ----------------------- */
lu_int *pattern_symb = this->iwork1;
lu_int *pattern = this->iwork1 + m;
double *work = this->work0;
lu_int *pstack = (void *) this->work1;
assert(sizeof(lu_int) <= sizeof(double));
jpivot = irhs[0];
ipivot = pmap[jpivot];
jbegin = Wbegin[jpivot];
jend = Wend[jpivot];
/*
* Compute row eta vector.
* Symbolic pattern in pattern_symb[top..m-1], indices of (actual)
* nonzeros in pattern[0..nz-1], values scattered into work.
* We do not drop small elements to zero, but the symbolic and the
* numeric pattern will still be different when we have exact
* cancellation.
*/
M = ++this->marker;
top = lu_solve_symbolic(m, Wbegin, Wend, Windex, jend-jbegin,
Windex+jbegin, pattern_symb, pstack, marked, M);
nz_symb = m-top;
/* reallocate if not enough memory in Li, Lx (where we store R) */
room = this->Lmem - Rbegin[nforrest];
if (room < nz_symb)
{
this->addmemL = nz_symb - room;
return BASICLU_REALLOCATE;
}
for (pos = jbegin; pos < jend; pos++)
{
work[Windex[pos]] = Wvalue[pos];
}
lu_solve_triangular(nz_symb, pattern_symb+top, Wbegin, Wend, Windex,
Wvalue, col_pivot, 0.0, work, pattern, &Uflops);
/*
* Compress row eta into L, pattern mapped from column to row indices.
* The triangularity test in lu_update requires the symbolic pattern.
*/
put = Rbegin[nforrest];
for (t = top; t < m; t++)
{
j = pattern_symb[t];
i = pmap[j];
Lindex[put] = i;
Lvalue[put++] = work[j];
work[j] = 0;
}
Rbegin[nforrest+1] = put;
eta_row[nforrest] = ipivot;
this->btran_for_update = jpivot;
if (!want_solution)
goto done;
/*
* Scatter the row eta into xlhs and scale it to become the solution
* to U^{-1}*[unit vector]. Now we can drop small entries to zero and
* recompute the numerical pattern.
*/
M = ++this->marker;
pattern[0] = ipivot;
marked[ipivot] = M;
pivot = col_pivot[jpivot];
xlhs[ipivot] = 1.0 / pivot;
xdrop = droptol * fabs(pivot);
nz = 1;
for (pos = Rbegin[nforrest]; pos < Rbegin[nforrest+1]; pos++)
{
if (fabs(Lvalue[pos]) > xdrop)
{
pattern[nz++] = i = Lindex[pos];
marked[i] = M;
xlhs[i] = -Lvalue[pos] / pivot;
}
}
/*
* Solve with update etas.
* Append fill-in to pattern.
*/
for (t = nforrest-1; t >= 0; t--)
{
ipivot = eta_row[t];
if (xlhs[ipivot])
{
x = xlhs[ipivot];
for (pos = Rbegin[t]; pos < Rbegin[t+1]; pos++)
{
i = Lindex[pos];
if (marked[i] != M)
{
marked[i] = M;
pattern[nz++] = i;
}
xlhs[i] -= x * Lvalue[pos];
Rflops++;
}
}
}
if (nz <= nz_sparse)
{
/*
* Sparse triangular solve with L'.
* Solution scattered into xlhs, indices in ilhs[0..nz-1].
*/
M = ++this->marker;
top = lu_solve_symbolic(m, Ltbegin, NULL, Lindex, nz, pattern,
pattern_symb, pstack, marked, M);
nz_symb = m-top;
nz = lu_solve_triangular(nz_symb, pattern_symb+top, Ltbegin, NULL,
Lindex, Lvalue, NULL, droptol, xlhs, ilhs,
&Lflops);
*p_nlhs = nz;
}
else
{
/*
* Sequential triangular solve with L'.
* Solution scattered into xlhs, indices in ilhs[0..nz-1].
*/
nz = 0;
for (k = m-1; k >= 0; k--)
{
ipivot = p[k];
if (xlhs[ipivot])
{
x = xlhs[ipivot];
for (pos = Ltbegin_p[k]; (i = Lindex[pos]) >= 0; pos++)
{
xlhs[i] -= x * Lvalue[pos];
Lflops++;
}
if (fabs(x) > droptol)
ilhs[nz++] = ipivot;
else
xlhs[ipivot] = 0.0;
}
}
*p_nlhs = nz;
}
}
else
{
/* -------------------- */
/* Solve forward system */
/* -------------------- */
lu_int *pattern_symb = this->iwork1;
lu_int *pattern = this->iwork1 + m;
double *work = this->work0;
lu_int *pstack = (void *) this->work1;
assert(sizeof(lu_int) <= sizeof(double));
/*
* Sparse triangular solve with L.
* Solution scattered into work, indices in pattern[0..nz-1].
*/
M = ++this->marker;
top = lu_solve_symbolic(m, Lbegin, NULL, Lindex, nrhs, irhs,
pattern_symb, pstack, marked, M);
nz_symb = m-top;
for (n = 0; n < nrhs; n++)
work[irhs[n]] = xrhs[n];
nz = lu_solve_triangular(nz_symb, pattern_symb+top, Lbegin, NULL,
Lindex, Lvalue, NULL, droptol, work, pattern,
&Lflops);
/* unmark cancellation */
if (nz < nz_symb)
{
for (t = top, n = 0; n < nz; t++)
{
i = pattern_symb[t];
if (i == pattern[n])
n++;
else
marked[i]--;
}
for ( ; t < m; t++)
marked[pattern_symb[t]]--;
}
/*
* Solve with update etas.
* Append fill-in to pattern.
*/
pos = Rbegin[0];
for (t = 0; t < nforrest; t++)
{
ipivot = eta_row[t];
x = 0.0;
for ( ; pos < Rbegin[t+1]; pos++)
{
x += work[Lindex[pos]] * Lvalue[pos];
}
work[ipivot] -= x;
if (x && marked[ipivot] != M)
{
marked[ipivot] = M;
pattern[nz++] = ipivot;
}
}
Rflops += Rbegin[nforrest] - Rbegin[0];
/* reallocate if not enough memory in U */
room = this->Umem - Ubegin[m];
need = nz+1;
if (room < need)
{
for (n = 0; n < nz; n++)
work[pattern[n]] = 0.0;
this->addmemU = need - room;
return BASICLU_REALLOCATE;
}
/* Compress spike into U. */
put = Ubegin[m];
for (n = 0; n < nz; n++)
{
i = pattern[n];
Uindex[put] = i;
Uvalue[put++] = work[i];
if (!want_solution)
work[i] = 0.0;
}
Uindex[put++] = -1; /* terminate column */
this->ftran_for_update = 0;
if (!want_solution)
goto done;
if (nz <= nz_sparse)
{
/*
* Sparse triangular solve with U.
* Solution scattered into work, indices in ilhs[0..nz-1].
*/
M = ++this->marker;
top = lu_solve_symbolic(m, Ubegin, NULL, Uindex, nz, pattern,
pattern_symb, pstack, marked, M);
nz_symb = m-top;
nz = lu_solve_triangular(nz_symb, pattern_symb+top, Ubegin, NULL,
Uindex, Uvalue, row_pivot, droptol, work,
ilhs, &Uflops);
/*
* Permute solution into xlhs.
* Map pattern from row indices to column indices.
*/
for (n = 0; n < nz; n++)
{
i = ilhs[n];
j = qmap[i];
ilhs[n] = j;
xlhs[j] = work[i];
work[i] = 0;
}
}
else
{
/*
* Sequential triangular solve with U.
* Solution computed in work and permuted into xlhs.
* Pattern (in column indices) stored in ilhs[0..nz-1].
*/
nz = 0;
for (k = pivotlen-1; k >= 0; k--)
{
ipivot = pivotrow[k];
jpivot = pivotcol[k];
if (work[ipivot])
{
x = work[ipivot] / row_pivot[ipivot];
work[ipivot] = 0.0;
for (pos = Ubegin[ipivot]; (i = Uindex[pos]) >= 0; pos++)
{
work[i] -= x * Uvalue[pos];
Uflops++;
}
if (fabs(x) > droptol)
{
ilhs[nz++] = jpivot;
xlhs[jpivot] = x;
}
}
}
}
*p_nlhs = nz;
}
done:
elapsed = lu_toc(tic);
this->time_solve += elapsed;
this->time_solve_total += elapsed;
this->Lflops += Lflops;
this->Uflops += Uflops;
this->Rflops += Rflops;
this->update_cost_numer += Rflops;
return BASICLU_OK;
}