/************************************
Given the factorization LB = U for some B, solve the problem
Bx = vec for x
Solve using LUMOD functions.
************************************/
void LU_Solve0(PT_Matrix pL, PT_Matrix pU, double *vec, double *x)
{
int mode;
ptrdiff_t n;
n = Matrix_Rows(pL);
/* solve using lumod */
/* solve for Bx = vec */
mode = 1;
/* due to 1-based indexing in Lprod, Usolve we need to shift vectors backwards */
/* Computes x = L*vec */
Lprod(mode, pL->rows_alloc, n, pL->A-1, vec-1, x-1);
/* Computes x_new s.t. U x_new = x */
Usolve(mode, pU->rows_alloc, n, pU->A-1, x-1);
/* Vector_Print_raw(x,n); */
}
void LUmod ( int mode, ptrdiff_t maxmod, ptrdiff_t n, ptrdiff_t krow, ptrdiff_t kcol,
double *L, double *U, double *y, double *z, double *w)
{
ptrdiff_t first, last, n1, i, j, lastu, lastl, ls, ll, lu, incu;
double zero = 0.0;
double one = 1.0;
double eps = MACHINEPREC; /* The machine precision -- A value slightly too large is OK. */
n1 = n - 1;
if (mode == 1) {
/* ---------------------------------------------------------------
mode = 1. Add a row y and a column z.
The LU factors will expand in dimension from n-1 to n.
The new diagonal element of C is in y[n].
--------------------------------------------------------------- */
lastu = n1*maxmod + (3 - n)*n/2;
lastl = n1*maxmod + n;
ls = n1*maxmod + 1;
L[lastl] = one;
if (n == 1) {
U[lastu] = y[n];
return;
}
/* Compute L*z and temporarily store it in w;
(changed to w from last row of L by KE). */
Lprod ( 1, maxmod, n1, L, z, w );
/* Copy L*z into the new last column of U.
Border L with zeros. */
ll = ls;
lu = n;
incu = maxmod - 1;
for (j = 1; j<=n1; j++) {
U[lu] = w[j];
L[ll] = zero;
ll++;
lu += incu;
incu--;
}
ll = n;
for (i = 1; i<=n1; i++) {
L[ll] = zero;
ll += maxmod;
}
/* Add row y to the factorization
using a forward sweep of eliminations. */
last = n;
LUforw ( 1, last, n, n, maxmod, eps, L, U, y );
}
else if (mode == 2) {
/* ---------------------------------------------------------------
mode=2. Replace the kcol-th column of C by the vector z.
---------------------------------------------------------------*/
/* Compute w = L*z. */
Lprod ( 1, maxmod, n, L, z, w );
/* Copy the top of w into column kcol of U. */
lu = kcol;
incu = maxmod - 1;
for (i = 1; i<=kcol; i++) {
U[lu] = w[i];
lu += incu;
incu--;
}
if (kcol < n) {
/* Find w[last], the last nonzero in the bottom part of w.
Eliminate elements last-1, last-2, ... kcol+1 of w[*]
using a partial backward sweep of eliminations. */
first = kcol + 1;
last = n;
LUback( first, &last, n, n, maxmod, eps, L, U, y, w );
y[kcol] = w[last];
/* Eliminate elements kcol, kcol+1, ... last-1 of y[*]
using a partial forward sweep of eliminations. */
LUforw ( kcol, last, n, n, maxmod, eps, L, U, y );
}
}
else if (mode == 3) {
/* ---------------------------------------------------------------
mode=3. Replace the krow-th row of C by the vector y.
--------------------------------------------------------------- */
if (n == 1) {
L[1] = one;
U[1] = y[1];
return;
}
/* Copy the krow-th column of L into w, and zero the column. */
ll = krow;
for (i = 1; i<=n; i++) {
w[i] = L[ll];
L[ll] = zero;
ll += maxmod;
}
/* Reduce the krow-th column of L to the unit vector e(last).
where 'last' is determined by LUback.
This is done by eliminating elements last-1, last-2, ..., 1
using a backward sweep of eliminations.
On exit, row 'last' of U is a spike stored in z, whose first
nonzero entry is in z[first]. However, z will be discarded. */
first = 1;
last = n;
LUback ( first, &last, n, n, maxmod, eps, L, U, z, w );
/* Replace the 'last' row of L by the krow-th unit vector. */
ll = (last - 1)*maxmod;
for (j = 1; j<=n; j++)
L[ll + j] = zero;
L[ll + krow] = one;
/* Eliminate the elements of the new row y,
using a forward sweep of eliminations. */
LUforw ( 1, last, n, n, maxmod, eps, L, U, y );
}
else if (mode == 4) {
/* ---------------------------------------------------------------
mode=4. Delete the krow-th row and the kcol-th column of C.
Replace them by the last row and column respectively.
--------------------------------------------------------------- */
/* First, move the last column into position kcol. */
if (kcol < n) {
/* Set w = last column of U. */
lu = n;
incu = maxmod - 1;
for (i = 1; i<=n; i++) {
w[i] = U[lu];
lu += incu;
incu--;
}
/* Copy the top of w into column kcol of U. */
lu = kcol;
incu = maxmod - 1;
for (i = 1; i<=kcol; i++) {
U[lu] = w[i];
lu += incu;
incu--;
}
/* U now has only n-1 columns.
Find w[last], the last nonzero in the bottom part of w.
Eliminate elements last-1, last-2, ... kcol+1 of w[*]
using a partial backward sweep of eliminations. */
first = kcol + 1;
last = n;
LUback ( first, &last, n, n1, maxmod, eps, L, U, y, w );
y[kcol] = w[last];
/* Eliminate elements kcol, kcol+1, ... last-1 of y[*]
using a partial forward sweep of eliminations. */
LUforw ( kcol, last, n, n1, maxmod, eps, L, U, y );
}
/* Now, move the last row into position krow. */
/* Swap columns krow and n of L, using w = krow-th column of L. */
LUdcopy ( n, &L[subvec(krow)], maxmod, w, 1 );
if (krow < n)
LUdcopy ( n, &L[subvec(n)], maxmod, &L[subvec(krow)], maxmod );
/* Reduce the last column of L (in w) to the unit vector e(n).
This is done by eliminating elements n-1, n-2, ..., 1
using a backward sweep of eliminations. */
last = - n;
LUback ( 1, &last, n, n1, maxmod, eps, L, U, z, w );
/* printvec(n, w, 0); */
/* printmatUT(maxmod, n, U, 0); */
/* printmatSQ(maxmod, n, L, 0); */
}
/* End of LUmod */
}
