/**
* Do several things here:
* 1. Compute lambda from the texcoords, if needed
* 2. Determine if we're minifying or magnifying
* 3. If minifying, choose mipmap levels
* 4. Return image filter to use within mipmap images
* \param level0 Returns first mipmap level to sample from
* \param level1 Returns second mipmap level to sample from
* \param levelBlend Returns blend factor between levels, in [0,1]
* \param imgFilter Returns either the min or mag filter, depending on lambda
*/
static void
choose_mipmap_levels(const struct pipe_texture *texture,
const struct pipe_sampler_state *sampler,
const float s[QUAD_SIZE],
const float t[QUAD_SIZE],
const float p[QUAD_SIZE],
boolean computeLambda,
float lodbias,
unsigned *level0, unsigned *level1, float *levelBlend,
unsigned *imgFilter)
{
if (sampler->min_mip_filter == PIPE_TEX_MIPFILTER_NONE) {
/* no mipmap selection needed */
*level0 = *level1 = CLAMP((int) sampler->min_lod,
0, (int) texture->last_level);
if (sampler->min_img_filter != sampler->mag_img_filter) {
/* non-mipmapped texture, but still need to determine if doing
* minification or magnification.
*/
float lambda = compute_lambda(texture, sampler, s, t, p, lodbias);
if (lambda <= 0.0) {
*imgFilter = sampler->mag_img_filter;
}
else {
*imgFilter = sampler->min_img_filter;
}
}
else {
*imgFilter = sampler->mag_img_filter;
}
}
else {
float lambda;
if (computeLambda)
/* fragment shader */
lambda = compute_lambda(texture, sampler, s, t, p, lodbias);
else
/* vertex shader */
lambda = lodbias; /* not really a bias, but absolute LOD */
if (lambda <= 0.0) { /* XXX threshold depends on the filter */
/* magnifying */
*imgFilter = sampler->mag_img_filter;
*level0 = *level1 = 0;
}
else {
/* minifying */
*imgFilter = sampler->min_img_filter;
/* choose mipmap level(s) and compute the blend factor between them */
if (sampler->min_mip_filter == PIPE_TEX_MIPFILTER_NEAREST) {
/* Nearest mipmap level */
const int lvl = (int) (lambda + 0.5);
*level0 =
*level1 = CLAMP(lvl, 0, (int) texture->last_level);
}
else {
/* Linear interpolation between mipmap levels */
const int lvl = (int) lambda;
*level0 = CLAMP(lvl, 0, (int) texture->last_level);
*level1 = CLAMP(lvl + 1, 0, (int) texture->last_level);
*levelBlend = FRAC(lambda); /* blending weight between levels */
}
}
}
}
void ICM_iteration(int N, int n, int K, int nlast, int first[], int m[], int **freq, int **ind, double **y,
double **F, double **F_new, double **cumw, double **cs, double **v, double **w,
double **nabla, double *lambda1, double *alpha1)
{
int i,j,k;
double a,lambda,alpha;
lambda=*lambda1;
for (k=1;k<=K;k++)
{
for (i=1;i<=m[k];i++)
v[k][i]=w[k][i]=0;
}
for (k=1;k<=K;k++)
{
j=0;
for (i=first[k];i<=n;i++)
{
if (freq[k][i]>0)
{
j++;
v[k][j] = freq[k][i]/(N*F[k][i]);
w[k][j] = freq[k][i]/(N*SQR(F[k][i]));
}
if (freq[0][i]>0)
{
v[k][j] -= freq[0][i]/(N*(1-F[K+1][i]));
w[k][j] += freq[0][i]/(N*SQR(1-F[K+1][i]));
}
}
if (nlast<n)
v[k][m[k]] -=lambda;
for (i=1;i<=m[k];i++)
v[k][i] += w[k][i]*F[k][ind[k][i]];
}
cumsum(K,m,v,cs);
convexmin(K,m,cumw,cs,w,y);
Compute_F(K,n,freq,first,y,F_new);
if (F_new[K+1][nlast]>=1)
{
a=(1-F[K+1][nlast])/(F_new[K+1][nlast]-F[K+1][nlast]);
for (k=1;k<=K;k++)
{
for (i=first[k];i<=n;i++)
F_new[k][i]=F[k][i]+a*(F_new[k][i]-F[k][i]);
}
compute_Fplus(n,K,F_new);
for (k=1;k<=K;k++)
{
j=0;
for (i=first[k];i<=n;i++)
{
if (freq[k][i]>0)
{
j++;
y[k][j]=F_new[k][i];
}
}
}
}
if (f_alpha_prime(N,n,K,freq,1.0,F,F_new,lambda)<=0) alpha=1;
else
alpha=golden(N,n,K,freq,F,F_new,0.1,1,f_alpha,lambda);
for (k=1;k<=K;k++)
{
for (i=first[k];i<=n;i++)
F[k][i] += alpha*(F_new[k][i]-F[k][i]);
}
compute_Fplus(n,K,F);
if (nlast<n)
lambda=compute_lambda(N,n,K,freq,F);
else
lambda=0;
compute_nabla(N,n,K,first,m,freq,F,lambda,nabla);
*lambda1=lambda;
*alpha1=alpha;
}
void CG::solve_lp(double epsilon){
bool no_delete = valid_solution();
if (no_delete) { // if there is no need to delete nodes
cout << "CG::solve_lp() no need to delete nodes" << endl;
return;
}
cout << "problem size: " << n_vertex_ << endl;
double max_weight = 0;
for (int ii = 0; ii < n_vertex_; ii++) {
if (g_[ii].weight > max_weight) {
max_weight = g_[ii].weight;
}
}
// find the initial solution, which is the longest path in terms of the weights assigned
for (int ii = 0; ii < n_vertex_; ii++) {
g_[ii].dual_val = 1 + max_weight - g_[ii].weight;
}
double dummy1;
vector<int> initial_path;
find_shortest_path(dummy1, initial_path);
for (vector<int>::iterator iter1 = initial_path.begin(); iter1 != initial_path.end(); ++iter1) {
g_[*iter1].total_flow = 1;
}
double lambda = compute_lambda();
double alpha = (4 / (lambda * epsilon)) * log(2 * n_vertex_ / epsilon);
double delta = epsilon / (4 * alpha);
double crt_left = 0.0;
double crt_lambda = lambda;
int iteration = -1;
while (true) {
iteration++;
compute_dual_vals(alpha);
double middle = 0; // middle corresponds to \vec{z}^tA\vec{y}
for (int ii = 0; ii < n_vertex_; ii++) {
middle = middle + g_[ii].dual_val * g_[ii].total_flow;
}
double right = 0; // right corresponds to \lambda\vec{z}^t\vec{b}
for (int ii = 0; ii < n_vertex_; ii++) {
right = right + crt_lambda * g_[ii].dual_val * g_[ii].weight;
}
vector<int> opt_path;
double left; // left corresponds to \vec{z}^tA\vec{y}
find_shortest_path(left, opt_path);
crt_left = left;
if (iteration % 1000 == 0) {
cout << "iteration " << iteration
<< " left:" << left
<< " middle:" << middle
<< " right:" << right
<< " sol:" << 1 / crt_lambda
<< endl;
}
// check if the following condition is met or not
// \vec{z}^tA\vec{y} - C(\vec{z}) \le \epsilon(\vec{z}^tA\vec{y} + \lambda\vec{z}^t\vec{b})
if ((middle - left) < epsilon * (middle + right) ) {
cout << "converged!" << endl;
cout << "iteration " << iteration
<< " left:" << left
<< " middle:" << middle
<< " right:" << right
<< " sol:" << 1 / crt_lambda
<< endl;
break;
} else {
update_solution(delta, opt_path);
crt_lambda = compute_lambda();
if (crt_lambda < 0.5 * lambda) {
lambda = crt_lambda;
alpha = 4 / (lambda * epsilon) * log(2 * n_vertex_ / epsilon);
delta = epsilon / (4 * alpha);
}
}
}
// compute the normalized dual solution
for (int ii = 0; ii < n_vertex_; ii++) {
g_[ii].nor_dual_val = g_[ii].dual_val / crt_left;
if (g_[ii].nor_dual_val > 1) {
g_[ii].nor_dual_val = 1;
}
}
// as the last step, round the fractional solution to integral solutions
round_lp();
}
void ICM(int N, int n, int **freq, int K, int **ind, double **F,
int n_It, double *phi1, int *iteration)
{
int *first,nlast,i,j,k,iteration1,*m,*n1,m_total;
double **cumw,**cs,**v,**w,**nabla,**F_new;
double **y;
double sum,alpha,lambda,inprod,partialsum,eta=1.0e-10;
y= new double *[K+2];
F_new=new double *[K+2];
cumw=new double *[K+2];
cs=new double *[K+2];
v=new double *[K+2];
w=new double *[K+2];
nabla=new double *[K+2];
first= new int[K+2];
m = new int[K+2];
n1 = new int[K+2];
for (i=0;i<K+2;i++)
{
y[i]= new double[N+1];
F_new[i]= new double[N+1];
cumw[i]= new double[N+1];
cs[i]= new double[N+1];
v[i]= new double[N+1];
w[i]= new double[N+1];
nabla[i]= new double[N+1];
}
j=n;
while (freq[0][j]==0)
j--;
nlast=j;
for (k=1;k<=K;k++)
{
j=1;
while (freq[k][j]==0)
j++;
first[k]=j;
}
for (k=0;k<=K;k++)
m[k]=n1[k]=0;
for (k=1;k<=K;k++)
{
j=0;
for (i=first[k];i<=n;i++)
{
if (freq[k][i]>0)
{
j++;
ind[k][j]=i;
n1[k] += freq[k][i];
}
}
m[k]=j;
}
for (k=1;k<=K;k++)
{
for (i=0;i<first[k];i++)
F[k][i]=F_new[k][i]=0;
}
m_total=0;
for (k=1;k<=K;k++)
m_total += n1[k];
for (k=1;k<=K;k++)
{
for (i=first[k];i<=n;i++)
{
if (freq[k][i]>0)
F[k][i]=F[k][i-1]+freq[k][i]*1.0/(m_total+K);
else
F[k][i]=F[k][i-1];
}
}
for (i=1;i<=n;i++)
{
sum=0;
for (k=1;k<=K;k++)
sum += F[k][i];
F[K+1][i]=sum;
}
for (k=1;k<=K;k++)
{
j=0;
for (i=first[k];i<=n;i++)
{
if (freq[k][i]>0)
{
j++;
y[k][j]=F[k][i];
}
}
}
if (nlast<n)
lambda=compute_lambda(N,n,K,freq,F);
else
lambda=0;
for (k=1;k<=K;k++)
{
for (i=first[k];i<=n;i++)
F_new[k][i]=F[k][i];
}
compute_Fplus(n,K,F_new);
compute_nabla(N,n,K,first,m,freq,F,lambda,nabla);
iteration1=0;
while (iteration1<=n_It && fenchelviol(K,m,ind,y,nabla,eta,&partialsum,&inprod))
{
iteration1++;
ICM_iteration(N,n,K,nlast,first,m,freq,ind,y,F,F_new,cumw,cs,v,w,nabla,&lambda,&alpha);
}
*phi1=phi_ICM(n,K,nlast,freq,F);
*iteration=iteration1;
for (i=0;i<K+2;i++){
delete[] y[i], delete[] F_new[i], delete[] cumw[i], delete[] cs[i], delete[] v[i], delete[] w[i], delete[] nabla[i];
}
delete[] y, delete[] cumw, delete[] cs, delete[] v, delete[] w, delete[] nabla;
delete[] m, delete[] n1, delete[] first;
}