/*@
VecFischer - Evaluates the Fischer-Burmeister function for complementarity
problems.
Logically Collective on vectors
Input Parameters:
+ X - current point
. F - function evaluated at x
. L - lower bounds
- U - upper bounds
Output Parameters:
. FB - The Fischer-Burmeister function vector
Notes:
The Fischer-Burmeister function is defined as
$ phi(a,b) := sqrt(a*a + b*b) - a - b
and is used reformulate a complementarity problem as a semismooth
system of equations.
The result of this function is done by cases:
+ l[i] == -infinity, u[i] == infinity -- fb[i] = -f[i]
. l[i] == -infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i])
. l[i] finite, u[i] == infinity -- fb[i] = phi(x[i]-l[i], f[i])
. l[i] finite < u[i] finite -- fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u]))
- otherwise l[i] == u[i] -- fb[i] = l[i] - x[i]
Level: developer
@*/
PetscErrorCode VecFischer(Vec X, Vec F, Vec L, Vec U, Vec FB)
{
const PetscScalar *x, *f, *l, *u;
PetscScalar *fb;
PetscReal xval, fval, lval, uval;
PetscErrorCode ierr;
PetscInt low[5], high[5], n, i;
PetscFunctionBegin;
PetscValidHeaderSpecific(X, VEC_CLASSID,1);
PetscValidHeaderSpecific(F, VEC_CLASSID,2);
PetscValidHeaderSpecific(L, VEC_CLASSID,3);
PetscValidHeaderSpecific(U, VEC_CLASSID,4);
PetscValidHeaderSpecific(FB, VEC_CLASSID,4);
ierr = VecGetOwnershipRange(X, low, high);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(F, low + 1, high + 1);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(L, low + 2, high + 2);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(U, low + 3, high + 3);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(FB, low + 4, high + 4);CHKERRQ(ierr);
for (i = 1; i < 4; ++i) {
if (low[0] != low[i] || high[0] != high[i]) SETERRQ(PETSC_COMM_SELF,1,"Vectors must be identically loaded over processors");
}
ierr = VecGetArrayRead(X, &x);CHKERRQ(ierr);
ierr = VecGetArrayRead(F, &f);CHKERRQ(ierr);
ierr = VecGetArrayRead(L, &l);CHKERRQ(ierr);
ierr = VecGetArrayRead(U, &u);CHKERRQ(ierr);
ierr = VecGetArray(FB, &fb);CHKERRQ(ierr);
ierr = VecGetLocalSize(X, &n);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
xval = PetscRealPart(x[i]); fval = PetscRealPart(f[i]);
lval = PetscRealPart(l[i]); uval = PetscRealPart(u[i]);
if ((lval <= -PETSC_INFINITY) && (uval >= PETSC_INFINITY)) {
fb[i] = -fval;
} else if (lval <= -PETSC_INFINITY) {
fb[i] = -Fischer(uval - xval, -fval);
} else if (uval >= PETSC_INFINITY) {
fb[i] = Fischer(xval - lval, fval);
} else if (lval == uval) {
fb[i] = lval - xval;
} else {
fval = Fischer(uval - xval, -fval);
fb[i] = Fischer(xval - lval, fval);
}
}
ierr = VecRestoreArrayRead(X, &x);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(F, &f);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(L, &l);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(U, &u);CHKERRQ(ierr);
ierr = VecRestoreArray(FB, &fb);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
SFischer - Evaluates the Smoothed Fischer-Burmeister function for
complementarity problems.
Input Parameters:
+ xx - current point
. ff - function evaluated at x
. ll - lower bounds
. uu - upper bounds
- mu - smoothing parameter
Notes:
The Smoothed Fischer-Burmeister function is defined as
$ phi(a,b) := sqrt(a*a + b*b + 2*mu*mu) - a - b
and is used reformulate a complementarity problem as a semismooth
system of equations.
The result of this function is done by cases:
+ l[i] == -infinity, u[i] == infinity -- fb[i] = -f[i] - 2*mu*x[i]
. l[i] == -infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i], mu)
. l[i] finite, u[i] == infinity -- fb[i] = phi(x[i]-l[i], f[i], mu)
. l[i] finite < u[i] finite -- fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u], mu), mu)
- otherwise l[i] == u[i] -- fb[i] = l[i] - x[i]
Level: advanced
.seealso TaoMat::SD_Fischer()
@*/
int TaoVec::SFischer(TaoVec* xx, TaoVec* ff, TaoVec* ll, TaoVec* uu, double mu)
{
int info;
TaoInt nn1, nn2, nn3, nn4, nn5,i;
TaoScalar *v, *x, *f, *l, *u;
TaoFunctionBegin;
if ((mu >= -TAO_EPSILON) && (mu <= TAO_EPSILON)) {
Fischer(xx, ff, ll, uu);
}
else {
info = this->GetArray(&v, &nn1); CHKERRQ(info);
info = xx->GetArray(&x, &nn2); CHKERRQ(info);
info = ff->GetArray(&f, &nn3); CHKERRQ(info);
info = ll->GetArray(&l, &nn4); CHKERRQ(info);
info = uu->GetArray(&u, &nn5); CHKERRQ(info);
if (nn1!=nn2 || nn2!=nn3 || nn3!=nn4 || nn4!=nn5) {
TaoFunctionReturn(1);
}
for (i = 0; i < nn1; ++i) {
if ((l[i] <= -TAO_INFINITY) && (u[i] >= TAO_INFINITY)) {
v[i] = -f[i] - mu*x[i];
}
else if (l[i] <= -TAO_INFINITY) {
v[i] = -sfischer(u[i] - x[i], -f[i], mu);
}
else if (u[i] >= TAO_INFINITY) {
v[i] = sfischer(x[i] - l[i], f[i], mu);
}
else if (l[i] == u[i]) {
v[i] = l[i] - x[i];
}
else {
v[i] = sfischer(u[i] - x[i], -f[i], mu);
v[i] = sfischer(x[i] - l[i], v[i], mu);
}
}
info = this->RestoreArray(&v, &nn1); CHKERRQ(info);
info = xx->RestoreArray(&x, &nn2); CHKERRQ(info);
info = ff->RestoreArray(&f, &nn3); CHKERRQ(info);
info = ll->RestoreArray(&l, &nn4); CHKERRQ(info);
info = uu->RestoreArray(&u, &nn5); CHKERRQ(info);
}
TaoFunctionReturn(0);
}
/*@
MatDFischer - Calculates an element of the B-subdifferential of the
Fischer-Burmeister function for complementarity problems.
Collective on jac
Input Parameters:
+ jac - the jacobian of f at X
. X - current point
. Con - constraints function evaluated at X
. XL - lower bounds
. XU - upper bounds
. t1 - work vector
- t2 - work vector
Output Parameters:
+ Da - diagonal perturbation component of the result
- Db - row scaling component of the result
Level: developer
.seealso: VecFischer()
@*/
PetscErrorCode MatDFischer(Mat jac, Vec X, Vec Con, Vec XL, Vec XU, Vec T1, Vec T2, Vec Da, Vec Db)
{
PetscErrorCode ierr;
PetscInt i,nn;
const PetscScalar *x,*f,*l,*u,*t2;
PetscScalar *da,*db,*t1;
PetscReal ai,bi,ci,di,ei;
PetscFunctionBegin;
ierr = VecGetLocalSize(X,&nn);CHKERRQ(ierr);
ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
ierr = VecGetArrayRead(Con,&f);CHKERRQ(ierr);
ierr = VecGetArrayRead(XL,&l);CHKERRQ(ierr);
ierr = VecGetArrayRead(XU,&u);CHKERRQ(ierr);
ierr = VecGetArray(Da,&da);CHKERRQ(ierr);
ierr = VecGetArray(Db,&db);CHKERRQ(ierr);
ierr = VecGetArray(T1,&t1);CHKERRQ(ierr);
ierr = VecGetArrayRead(T2,&t2);CHKERRQ(ierr);
for (i = 0; i < nn; i++) {
da[i] = 0.0;
db[i] = 0.0;
t1[i] = 0.0;
if (PetscAbsScalar(f[i]) <= PETSC_MACHINE_EPSILON) {
if (PetscRealPart(l[i]) > PETSC_NINFINITY && PetscAbsScalar(x[i] - l[i]) <= PETSC_MACHINE_EPSILON) {
t1[i] = 1.0;
da[i] = 1.0;
}
if (PetscRealPart(u[i]) < PETSC_INFINITY && PetscAbsScalar(u[i] - x[i]) <= PETSC_MACHINE_EPSILON) {
t1[i] = 1.0;
db[i] = 1.0;
}
}
}
ierr = VecRestoreArray(T1,&t1);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(T2,&t2);CHKERRQ(ierr);
ierr = MatMult(jac,T1,T2);CHKERRQ(ierr);
ierr = VecGetArrayRead(T2,&t2);CHKERRQ(ierr);
for (i = 0; i < nn; i++) {
if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) {
da[i] = 0.0;
db[i] = -1.0;
} else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {
if (PetscRealPart(db[i]) >= 1) {
ai = fischnorm(1.0, PetscRealPart(t2[i]));
da[i] = -1.0 / ai - 1.0;
db[i] = -t2[i] / ai - 1.0;
} else {
bi = PetscRealPart(u[i]) - PetscRealPart(x[i]);
ai = fischnorm(bi, PetscRealPart(f[i]));
ai = PetscMax(PETSC_MACHINE_EPSILON, ai);
da[i] = bi / ai - 1.0;
db[i] = -f[i] / ai - 1.0;
}
} else if (PetscRealPart(u[i]) >= PETSC_INFINITY) {
if (PetscRealPart(da[i]) >= 1) {
ai = fischnorm(1.0, PetscRealPart(t2[i]));
da[i] = 1.0 / ai - 1.0;
db[i] = t2[i] / ai - 1.0;
} else {
bi = PetscRealPart(x[i]) - PetscRealPart(l[i]);
ai = fischnorm(bi, PetscRealPart(f[i]));
ai = PetscMax(PETSC_MACHINE_EPSILON, ai);
da[i] = bi / ai - 1.0;
db[i] = f[i] / ai - 1.0;
}
} else if (PetscRealPart(l[i]) == PetscRealPart(u[i])) {
da[i] = -1.0;
db[i] = 0.0;
} else {
if (PetscRealPart(db[i]) >= 1) {
ai = fischnorm(1.0, PetscRealPart(t2[i]));
ci = 1.0 / ai + 1.0;
di = PetscRealPart(t2[i]) / ai + 1.0;
} else {
bi = PetscRealPart(x[i]) - PetscRealPart(u[i]);
ai = fischnorm(bi, PetscRealPart(f[i]));
ai = PetscMax(PETSC_MACHINE_EPSILON, ai);
ci = bi / ai + 1.0;
di = PetscRealPart(f[i]) / ai + 1.0;
}
if (PetscRealPart(da[i]) >= 1) {
bi = ci + di*PetscRealPart(t2[i]);
ai = fischnorm(1.0, bi);
bi = bi / ai - 1.0;
ai = 1.0 / ai - 1.0;
} else {
ei = Fischer(PetscRealPart(u[i]) - PetscRealPart(x[i]), -PetscRealPart(f[i]));
ai = fischnorm(PetscRealPart(x[i]) - PetscRealPart(l[i]), ei);
ai = PetscMax(PETSC_MACHINE_EPSILON, ai);
bi = ei / ai - 1.0;
ai = (PetscRealPart(x[i]) - PetscRealPart(l[i])) / ai - 1.0;
}
da[i] = ai + bi*ci;
db[i] = bi*di;
}
}
ierr = VecRestoreArray(Da,&da);CHKERRQ(ierr);
ierr = VecRestoreArray(Db,&db);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Con,&f);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(XL,&l);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(XU,&u);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(T2,&t2);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
