void
TensorProductBasis<BASIS0,BASIS1>::reconstruct_1(const Index& lambda,
const int j,
InfiniteVector<double, Index>& c) const {
if (lambda.j() >= j) {
// then we can just copy \psi_\lambda
c.add_coefficient(lambda, 1.0);
} else {
// reconstruct by recursion
typedef typename BASIS0::Index Index0;
typedef typename BASIS1::Index Index1;
InfiniteVector<double,Index0> c1;
InfiniteVector<double,Index1> c2;
basis0().reconstruct_1(lambda.index0(), lambda.j()+1, c1);
basis1().reconstruct_1(lambda.index1(), lambda.j()+1, c2);
for (typename InfiniteVector<double,Index0>::const_iterator it1(c1.begin()), it1end(c1.end());
it1 != it1end; ++it1)
for (typename InfiniteVector<double,Index1>::const_iterator it2(c2.begin()), it2end(c2.end());
it2 != it2end; ++it2) {
InfiniteVector<double,Index> d;
reconstruct_1(Index(it1.index(), it2.index()), j, d);
c.add(*it1 * *it2, d);
}
}
}
void
TensorProductBasis<BASIS0,BASIS1>::decompose_1(const Index& lambda,
const int j0,
InfiniteVector<double, Index>& c) const {
assert(lambda.j() >= j0);
c.clear();
if (lambda.index0().e() != 0 || lambda.index1().e() != 0) {
// the true wavelet coefficients don't have to be modified
c.set_coefficient(lambda, 1.0);
} else {
// a generator on a (possibly) fine level
if (lambda.j() == j0) {
// generators from the coarsest level can be copied
c.set_coefficient(lambda, 1.0);
} else {
// j>j0, perform multiscale decomposition
typedef typename BASIS0::Index Index0;
typedef typename BASIS1::Index Index1;
InfiniteVector<double,Index0> c1;
InfiniteVector<double,Index1> c2;
basis0().decompose_1(lambda.index0(), lambda.j()-1, c1);
basis1().decompose_1(lambda.index1(), lambda.j()-1, c2);
for (typename InfiniteVector<double,Index0>::const_iterator it1(c1.begin()), it1end(c1.end());
it1 != it1end; ++it1)
for (typename InfiniteVector<double,Index1>::const_iterator it2(c2.begin()), it2end(c2.end());
it2 != it2end; ++it2) {
// if (it1.index().e() == 0 && it2.index().e() == 0) { // generators have to be refined further
InfiniteVector<double,Index> d;
decompose_1(Index(it1.index(), it2.index()), j0, d);
c.add(*it1 * *it2, d);
// } else
// c.set_coefficient(Index(this, it1.index(), it2.index()), *it1 * *it2);
}
}
}
}
int Rsimp(int m, int n, double **A, double *b, double *c,
double *x, int *basis, int *nonbasis,
double **R, double **Q, double *t1, double *t2){
int i,j,k,l,q,qv;
int max_steps=20;
double r,a,at;
void GQR(int,int,double**,double**);
max_steps=4*n;
for(k=0; k<=max_steps;k++){
/*
++ Step 0) load new basis matrix and factor it
*/
for(i=0;i<m;i++)for(j=0;j<m;j++)R0(i,j)=AB0(i,j);
GQR(m,m,Q,R);
/*
++ Step 1) solving system B'*w=c(basis)
++ a) forward solve R'*y=c(basis)
*/
for(i=0;i<m;i++){
Y0(i)=0.0;
for(j=0;j<i;j++)Y0(i)+=R0(j,i)*Y0(j);
if (R0(i,i)!=0.0) Y0(i)=(CB0(i)-Y0(i))/R0(i,i);
else {
printf("Warning Singular Matrix Found\n");
return LP_FAIL;
}
}
/*
++ b) find w=Q*y
++ note: B'*w=(Q*R)'*Q*y= R'*(Q'*Q)*y=R'*y=c(basis)
*/
for(i=0;i<m;i++){
W0(i)=0.0;
for(j=0;j<m;j++)W0(i)+=Q0(i,j)*Y0(j);
}
/*
++ Step 2)find entering variable,
++ (use lexicographically first variable with negative reduced cost)
*/
q=n;
for(i=0;i<n-m;i++){
/* calculate reduced cost */
r=CN0(i);
for(j=0;j<m;j++) r-=W0(j)*AN0(j,i);
if (r<-zero_tol && (q==n || nonbasis0(i)<nonbasis0(q))) q=i;
}
/*
++ if ratios were all nonnegative current solution is optimal
*/
if (q==n){
if (verbose>0) printf("optimal solution found in %d iterations\n",k);
return LP_OPT;
}
/*
++ Step 3)Calculate translation direction for q entering
++ by solving system B*d=-A(:,nonbasis(q));
++ a) let y=-Q'*A(:,nonbasis(q));
*/
for(i=0;i<m;i++){
Y0(i)=0.0;
for(j=0;j<m;j++) Y0(i)-=Q0(j,i)*AN0(j,q);
}
/*
++ b) back solve Rd=y (d=R\y)
++ note B*d= Q*R*d=Q*y=Q*-Q'*A(:nonbasis(q))=-A(:,nonbasis(q))
*/
for(i=m-1;i>=0;i--){
D0(i)=0.0;
for(j=m-1;j>=i+1;j--)D0(i)+=R0(i,j)*D0(j);
if (R0(i,i)!=0.0) D0(i)=(Y0(i)-D0(i))/R0(i,i);
else {
printf("Warning Singular Matrix Found\n");
return LP_FAIL;
}
}
/*
++ Step 4 Choose leaving variable
++ (first variable to become negative, by moving in direction D)
++ (if none become negative, then objective function unbounded)
*/
a=0;
l=-1;
for(i=0;i<m;i++){
if (D0(i)<-zero_tol){
at=-1*XB0(i)/D0(i);
if (l==-1 || at<a){ a=at; l=i;}
}
}
if (l==-1){
if (verbose>0){
printf("Objective function Unbounded (%d iterations)\n",k);
}
return LP_UNBD;
}
/*
++ Step 5) Update solution and basis data
*/
XN0(q)=a;
for(j=0;j<m;j++) XB0(j)+=a*D0(j);
XB0(l)=0.0; /* enforce strict zeroness of nonbasis variables */
qv=nonbasis0(q);
nonbasis0(q)=basis0(l);
basis0(l)=qv;
}
if (verbose>=0){
printf("Simplex Algorithm did not Terminate in %d iterations\n",k);
}
return LP_FAIL;
}
