void Rasterizer::scanInterpolate(CameraDefinition *camera, ScanPoint *v1, ScanPoint *diff, double value,
ScanPoint *result) {
result->pixel.x = v1->pixel.x + diff->pixel.x * value;
result->pixel.y = v1->pixel.y + diff->pixel.y * value;
result->pixel.z = v1->pixel.z + diff->pixel.z * value;
if (perspective_correction) {
Vector3 vec1(v1->pixel.x, v1->pixel.y, v1->pixel.z);
Vector3 vecdiff(diff->pixel.x, diff->pixel.y, diff->pixel.z);
double v1depth = 1.0 / camera->getRealDepth(vec1);
double v2depth = 1.0 / camera->getRealDepth(vec1.add(vecdiff));
double factor = 1.0 / ((1.0 - value) * v1depth + value * v2depth);
result->location.x =
((1.0 - value) * (v1->location.x * v1depth) + value * (v1->location.x + diff->location.x) * v2depth) *
factor;
result->location.y =
((1.0 - value) * (v1->location.y * v1depth) + value * (v1->location.y + diff->location.y) * v2depth) *
factor;
result->location.z =
((1.0 - value) * (v1->location.z * v1depth) + value * (v1->location.z + diff->location.z) * v2depth) *
factor;
} else {
result->location.x = v1->location.x + diff->location.x * value;
result->location.y = v1->location.y + diff->location.y * value;
result->location.z = v1->location.z + diff->location.z * value;
}
result->client = v1->client;
result->front_facing = v1->front_facing;
}
// calculate a normalized vector pointint from one vector to another
void pointat(const GLfloat *from, const GLfloat *to, float *result){
int i=0;
float dist;
assert(NULL != from);
assert(NULL != to);
assert(NULL != result);
vecdiff(from,to,result);
dist = veclen(result);
assert(dist > 0);
for(;i<3;i++){
result[i] /= dist;
}
}
int localReconstruct ( lRecon * z, bCntr * bsc, int nC, int D, int * per, double * dom ) {
double E = 0.0;
int i=0,j;
bCntr * ip;
double Zi[D];
double zi;
double phi, gphi;
z->e=0.0;
for (j=0;j<D;j++) {
z->f[j]=0.0;
}
for (i=0;i<nC;i++) {
ip=&bsc[i];
vecdiff(Zi,z->r,ip->r,D,per,dom);
zi=norm(Zi,D);
kernel(zi,ip->s,&phi,&gphi);
z->e+=ip->a*phi;
for (j=0;j<D;j++) {
z->f[j]-=(zi>0)?ip->a*Zi[j]/zi*gphi:0.0;
}
}
return 0;
}
int lbfgs(
int n,
T *x,
T *ptr_fx,
typename FuncWrapper<T>::lbfgs_evaluate_t proc_evaluate,
typename FuncWrapper<T>::lbfgs_progress_t proc_progress,
void *instance,
lbfgs_parameter_t *_param
)
{
int ret;
int i, j, k, ls, end, bound;
T step;
/* Constant parameters and their default values. */
lbfgs_parameter_t param = (_param != NULL) ? (*_param) : _defparam;
const int m = param.m;
T *xp = NULL;
T *g = NULL, *gp = NULL, *pg = NULL;
T *d = NULL, *w = NULL, *pf = NULL;
iteration_data_t<T> *lm = NULL;
iteration_data_t<T>*it = NULL;
T ys, yy;
T xnorm, gnorm, beta;
T fx = 0.;
T rate = 0.;
typename LineSearchWrapper<T>::line_search_proc linesearch = line_search_morethuente;
/* Construct a callback data. */
callback_data_t<T> cd;
cd.n = n;
cd.instance = instance;
cd.proc_evaluate = proc_evaluate;
cd.proc_progress = proc_progress;
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
/* Round out the number of variables. */
n = round_out_variables(n);
#endif/*defined(USE_SSE)*/
/* Check the input parameters for errors. */
if (n <= 0) {
return LBFGSERR_INVALID_N;
}
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
if (n % 8 != 0) {
return LBFGSERR_INVALID_N_SSE;
}
if ((uintptr_t)(const void*)x % 16 != 0) {
return LBFGSERR_INVALID_X_SSE;
}
#endif/*defined(USE_SSE)*/
if (param.epsilon < 0.) {
return LBFGSERR_INVALID_EPSILON;
}
if (param.past < 0) {
return LBFGSERR_INVALID_TESTPERIOD;
}
if (param.delta < 0.) {
return LBFGSERR_INVALID_DELTA;
}
if (param.min_step < 0.) {
return LBFGSERR_INVALID_MINSTEP;
}
if (param.max_step < param.min_step) {
return LBFGSERR_INVALID_MAXSTEP;
}
if (param.ftol < 0.) {
return LBFGSERR_INVALID_FTOL;
}
if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE ||
param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {
if (param.wolfe <= param.ftol || 1. <= param.wolfe) {
return LBFGSERR_INVALID_WOLFE;
}
}
if (param.gtol < 0.) {
return LBFGSERR_INVALID_GTOL;
}
if (param.xtol < 0.) {
return LBFGSERR_INVALID_XTOL;
}
if (param.max_linesearch <= 0) {
return LBFGSERR_INVALID_MAXLINESEARCH;
}
if (param.orthantwise_c < 0.) {
return LBFGSERR_INVALID_ORTHANTWISE;
}
if (param.orthantwise_start < 0 || n < param.orthantwise_start) {
return LBFGSERR_INVALID_ORTHANTWISE_START;
}
if (param.orthantwise_end < 0) {
param.orthantwise_end = n;
}
if (n < param.orthantwise_end) {
return LBFGSERR_INVALID_ORTHANTWISE_END;
}
if (param.orthantwise_c != 0.) {
switch (param.linesearch) {
case LBFGS_LINESEARCH_BACKTRACKING:
linesearch = line_search_backtracking_owlqn;
break;
default:
/* Only the backtracking method is available. */
return LBFGSERR_INVALID_LINESEARCH;
}
} else {
switch (param.linesearch) {
case LBFGS_LINESEARCH_MORETHUENTE:
linesearch = line_search_morethuente;
break;
case LBFGS_LINESEARCH_BACKTRACKING_ARMIJO:
case LBFGS_LINESEARCH_BACKTRACKING_WOLFE:
case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE:
linesearch = line_search_backtracking;
break;
default:
return LBFGSERR_INVALID_LINESEARCH;
}
}
/* Allocate working space. */
xp = (T*)vecalloc(n * sizeof(T));
g = (T*)vecalloc(n * sizeof(T));
gp = (T*)vecalloc(n * sizeof(T));
d = (T*)vecalloc(n * sizeof(T));
w = (T*)vecalloc(n * sizeof(T));
if (xp == NULL || g == NULL || gp == NULL || d == NULL || w == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
if (param.orthantwise_c != 0.) {
/* Allocate working space for OW-LQN. */
pg = (T*)vecalloc(n * sizeof(T));
if (pg == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
}
/* Allocate limited memory storage. */
lm = (iteration_data_t<T>*)vecalloc(m * sizeof(iteration_data_t<T>));
if (lm == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
/* Initialize the limited memory. */
for (i = 0;i < m;++i) {
it = &lm[i];
it->alpha = 0;
it->ys = 0;
it->s = (T*)vecalloc(n * sizeof(T));
it->y = (T*)vecalloc(n * sizeof(T));
if (it->s == NULL || it->y == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
}
/* Allocate an array for storing previous values of the objective function. */
if (0 < param.past) {
pf = (T*)vecalloc(param.past * sizeof(T));
}
/* Evaluate the function value and its gradient. */
fx = cd.proc_evaluate(cd.instance, x, g, cd.n, 0);
if (0. != param.orthantwise_c) {
/* Compute the L1 norm of the variable and add it to the object value. */
xnorm = owlqn_x1norm(x, param.orthantwise_start, param.orthantwise_end);
fx += xnorm * param.orthantwise_c;
owlqn_pseudo_gradient(
pg, x, g, n,
T(param.orthantwise_c), param.orthantwise_start, param.orthantwise_end
);
}
/* Store the initial value of the objective function. */
if (pf != NULL) {
pf[0] = fx;
}
/*
Compute the direction;
we assume the initial hessian matrix H_0 as the identity matrix.
*/
if (param.orthantwise_c == 0.) {
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
/*
Make sure that the initial variables are not a minimizer.
*/
vec2norm(&xnorm, x, n);
if (param.orthantwise_c == 0.) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param.epsilon) {
ret = LBFGS_ALREADY_MINIMIZED;
goto lbfgs_exit;
}
/* Compute the initial step:
step = 1.0 / sqrt(vecdot(d, d, n))
*/
vec2norminv(&step, d, n);
k = 1;
end = 0;
for (;;) {
/* Store the current position and gradient vectors. */
veccpy(xp, x, n);
veccpy(gp, g, n);
/* Search for an optimal step. */
if (param.orthantwise_c == 0.) {
ls = linesearch(n, x, &fx, g, d, &step, xp, gp, w, &cd, ¶m);
} else {
ls = linesearch(n, x, &fx, g, d, &step, xp, pg, w, &cd, ¶m);
owlqn_pseudo_gradient(
pg, x, g, n,
T(param.orthantwise_c), param.orthantwise_start, param.orthantwise_end
);
}
if (ls < 0) {
/* Revert to the previous point. */
veccpy(x, xp, n);
veccpy(g, gp, n);
ret = ls;
goto lbfgs_exit;
}
/* Compute x and g norms. */
vec2norm(&xnorm, x, n);
if (param.orthantwise_c == 0.) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
/* Report the progress. */
if (cd.proc_progress) {
if ((ret = cd.proc_progress(cd.instance, x, g, fx, xnorm, gnorm, step, cd.n, k, ls))) {
goto lbfgs_exit;
}
}
/*
Convergence test.
The criterion is given by the following formula:
|g(x)| / \max(1, |x|) < \epsilon
*/
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param.epsilon) {
/* Convergence. */
ret = LBFGS_SUCCESS;
break;
}
/*
Test for stopping criterion.
The criterion is given by the following formula:
(f(past_x) - f(x)) / f(x) < \delta
*/
if (pf != NULL) {
/* We don't test the stopping criterion while k < past. */
if (param.past <= k) {
/* Compute the relative improvement from the past. */
rate = (pf[k % param.past] - fx) / fx;
/* The stopping criterion. */
if (rate < param.delta) {
ret = LBFGS_STOP;
break;
}
}
/* Store the current value of the objective function. */
pf[k % param.past] = fx;
}
if (param.max_iterations != 0 && param.max_iterations < k+1) {
/* Maximum number of iterations. */
ret = LBFGSERR_MAXIMUMITERATION;
break;
}
/*
Update vectors s and y:
s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.
y_{k+1} = g_{k+1} - g_{k}.
*/
it = &lm[end];
vecdiff(it->s, x, xp, n);
vecdiff(it->y, g, gp, n);
/*
Compute scalars ys and yy:
ys = y^t \cdot s = 1 / \rho.
yy = y^t \cdot y.
Notice that yy is used for scaling the hessian matrix H_0 (Cholesky factor).
*/
vecdot(&ys, it->y, it->s, n);
vecdot(&yy, it->y, it->y, n);
it->ys = ys;
/*
Recursive formula to compute dir = -(H \cdot g).
This is described in page 779 of:
Jorge Nocedal.
Updating Quasi-Newton Matrices with Limited Storage.
Mathematics of Computation, Vol. 35, No. 151,
pp. 773--782, 1980.
*/
bound = (m <= k) ? m : k;
++k;
end = (end + 1) % m;
/* Compute the steepest direction. */
if (param.orthantwise_c == 0.) {
/* Compute the negative of gradients. */
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
j = end;
for (i = 0;i < bound;++i) {
j = (j + m - 1) % m; /* if (--j == -1) j = m-1; */
it = &lm[j];
/* \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}. */
vecdot(&it->alpha, it->s, d, n);
it->alpha /= it->ys;
/* q_{i} = q_{i+1} - \alpha_{i} y_{i}. */
vecadd(d, it->y, -it->alpha, n);
}
vecscale(d, ys / yy, n);
for (i = 0;i < bound;++i) {
it = &lm[j];
/* \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}. */
vecdot(&beta, it->y, d, n);
beta /= it->ys;
/* \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}. */
vecadd(d, it->s, it->alpha - beta, n);
j = (j + 1) % m; /* if (++j == m) j = 0; */
}
/*
Constrain the search direction for orthant-wise updates.
*/
if (param.orthantwise_c != 0.) {
for (i = param.orthantwise_start;i < param.orthantwise_end;++i) {
if (d[i] * pg[i] >= 0) {
d[i] = 0;
}
}
}
/*
Now the search direction d is ready. We try step = 1 first.
*/
step = 1.0;
}
lbfgs_exit:
/* Return the final value of the objective function. */
if (ptr_fx != NULL) {
*ptr_fx = fx;
}
vecfree(pf);
/* Free memory blocks used by this function. */
if (lm != NULL) {
for (i = 0;i < m;++i) {
vecfree(lm[i].s);
vecfree(lm[i].y);
}
vecfree(lm);
}
vecfree(pg);
vecfree(w);
vecfree(d);
vecfree(gp);
vecfree(g);
vecfree(xp);
return ret;
}
int lbfgs(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *ptr_fx,
lbfgs_evaluate_t proc_evaluate,
lbfgs_progress_t proc_progress,
void *instance,
lbfgs_parameter_t *_param
)
{
int ret;
int i, j, k, ls, end, bound;
lbfgsfloatval_t step;
/* Constant parameters and their default values. */
const lbfgs_parameter_t* param = (_param != NULL) ? _param : &_defparam;
const int m = param->m;
lbfgsfloatval_t *xp = NULL, *g = NULL, *gp = NULL, *d = NULL, *w = NULL;
iteration_data_t *lm = NULL, *it = NULL;
lbfgsfloatval_t ys, yy;
lbfgsfloatval_t norm, xnorm, gnorm, beta;
lbfgsfloatval_t fx = 0.;
line_search_proc linesearch = line_search_morethuente;
/* Construct a callback data. */
callback_data_t cd;
cd.n = n;
cd.instance = instance;
cd.proc_evaluate = proc_evaluate;
cd.proc_progress = proc_progress;
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
/* Round out the number of variables. */
n = round_out_variables(n);
#endif/*defined(USE_SSE)*/
/* Check the input parameters for errors. */
if (n <= 0) {
return LBFGSERR_INVALID_N;
}
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
if (n % 8 != 0) {
return LBFGSERR_INVALID_N_SSE;
}
if (((unsigned short)x & 0x000F) != 0) {
return LBFGSERR_INVALID_X_SSE;
}
#endif/*defined(USE_SSE)*/
if (param->min_step < 0.) {
return LBFGSERR_INVALID_MINSTEP;
}
if (param->max_step < param->min_step) {
return LBFGSERR_INVALID_MAXSTEP;
}
if (param->ftol < 0.) {
return LBFGSERR_INVALID_FTOL;
}
if (param->gtol < 0.) {
return LBFGSERR_INVALID_GTOL;
}
if (param->xtol < 0.) {
return LBFGSERR_INVALID_XTOL;
}
if (param->max_linesearch <= 0) {
return LBFGSERR_INVALID_MAXLINESEARCH;
}
if (param->orthantwise_c < 0.) {
return LBFGSERR_INVALID_ORTHANTWISE;
}
if (param->orthantwise_start < 0 || n < param->orthantwise_start) {
return LBFGSERR_INVALID_ORTHANTWISE_START;
}
switch (param->linesearch) {
case LBFGS_LINESEARCH_MORETHUENTE:
linesearch = line_search_morethuente;
break;
case LBFGS_LINESEARCH_BACKTRACKING:
linesearch = line_search_backtracking;
break;
default:
return LBFGSERR_INVALID_LINESEARCH;
}
/* Allocate working space. */
xp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
g = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
gp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
d = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
w = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
if (xp == NULL || g == NULL || gp == NULL || d == NULL || w == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
/* Allocate limited memory storage. */
lm = (iteration_data_t*)vecalloc(m * sizeof(iteration_data_t));
if (lm == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
/* Initialize the limited memory. */
for (i = 0;i < m;++i) {
it = &lm[i];
it->alpha = 0;
it->ys = 0;
it->s = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
it->y = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
if (it->s == NULL || it->y == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
}
/* Evaluate the function value and its gradient. */
fx = cd.proc_evaluate(cd.instance, x, g, cd.n, 0);
if (0. < param->orthantwise_c) {
/* Compute L1-regularization factor and add it to the object value. */
norm = 0.;
for (i = param->orthantwise_start;i < n;++i) {
norm += fabs(x[i]);
}
fx += norm * param->orthantwise_c;
}
/* We assume the initial hessian matrix H_0 as the identity matrix. */
if (param->orthantwise_c == 0.) {
vecncpy(d, g, n);
} else {
/* Compute the negative of gradients. */
for (i = 0;i < param->orthantwise_start;++i) {
d[i] = -g[i];
}
/* Compute the negative of psuedo-gradients. */
for (i = param->orthantwise_start;i < n;++i) {
if (x[i] < 0.) {
/* Differentiable. */
d[i] = -g[i] + param->orthantwise_c;
} else if (0. < x[i]) {
/* Differentiable. */
d[i] = -g[i] - param->orthantwise_c;
} else {
if (g[i] < -param->orthantwise_c) {
/* Take the right partial derivative. */
d[i] = -g[i] - param->orthantwise_c;
} else if (param->orthantwise_c < g[i]) {
/* Take the left partial derivative. */
d[i] = -g[i] + param->orthantwise_c;
} else {
d[i] = 0.;
}
}
}
}
/*
Make sure that the initial variables are not a minimizer.
*/
vecnorm(&gnorm, g, n);
vecnorm(&xnorm, x, n);
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param->epsilon) {
ret = LBFGS_ALREADY_MINIMIZED;
goto lbfgs_exit;
}
/* Compute the initial step:
step = 1.0 / sqrt(vecdot(d, d, n))
*/
vecrnorm(&step, d, n);
k = 1;
end = 0;
for (;;) {
/* Store the current position and gradient vectors. */
veccpy(xp, x, n);
veccpy(gp, g, n);
/* Search for an optimal step. */
ls = linesearch(n, x, &fx, g, d, &step, w, &cd, param);
if (ls < 0) {
ret = ls;
goto lbfgs_exit;
}
/* Compute x and g norms. */
vecnorm(&gnorm, g, n);
vecnorm(&xnorm, x, n);
/* Report the progress. */
if (cd.proc_progress) {
if (ret = cd.proc_progress(cd.instance, x, g, fx, xnorm, gnorm, step, cd.n, k, ls)) {
goto lbfgs_exit;
}
}
/*
Convergence test.
The criterion is given by the following formula:
|g(x)| / \max(1, |x|) < \epsilon
*/
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param->epsilon) {
/* Convergence. */
ret = LBFGS_SUCCESS;
break;
}
if (param->max_iterations != 0 && param->max_iterations < k+1) {
/* Maximum number of iterations. */
ret = LBFGSERR_MAXIMUMITERATION;
break;
}
/*
Update vectors s and y:
s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.
y_{k+1} = g_{k+1} - g_{k}.
*/
it = &lm[end];
vecdiff(it->s, x, xp, n);
vecdiff(it->y, g, gp, n);
/*
Compute scalars ys and yy:
ys = y^t \cdot s = 1 / \rho.
yy = y^t \cdot y.
Notice that yy is used for scaling the hessian matrix H_0 (Cholesky factor).
*/
vecdot(&ys, it->y, it->s, n);
vecdot(&yy, it->y, it->y, n);
it->ys = ys;
/*
Recursive formula to compute dir = -(H \cdot g).
This is described in page 779 of:
Jorge Nocedal.
Updating Quasi-Newton Matrices with Limited Storage.
Mathematics of Computation, Vol. 35, No. 151,
pp. 773--782, 1980.
*/
bound = (m <= k) ? m : k;
++k;
end = (end + 1) % m;
if (param->orthantwise_c == 0.) {
/* Compute the negative of gradients. */
vecncpy(d, g, n);
} else {
/* Compute the negative of gradients. */
for (i = 0;i < param->orthantwise_start;++i) {
d[i] = -g[i];
}
/* Compute the negative of psuedo-gradients. */
for (i = param->orthantwise_start;i < n;++i) {
if (x[i] < 0.) {
/* Differentiable. */
d[i] = -g[i] + param->orthantwise_c;
} else if (0. < x[i]) {
/* Differentiable. */
d[i] = -g[i] - param->orthantwise_c;
} else {
if (g[i] < -param->orthantwise_c) {
/* Take the right partial derivative. */
d[i] = -g[i] - param->orthantwise_c;
} else if (param->orthantwise_c < g[i]) {
/* Take the left partial derivative. */
d[i] = -g[i] + param->orthantwise_c;
} else {
d[i] = 0.;
}
}
}
/* Store the steepest direction.*/
veccpy(w, d, n);
}
j = end;
for (i = 0;i < bound;++i) {
j = (j + m - 1) % m; /* if (--j == -1) j = m-1; */
it = &lm[j];
/* \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}. */
vecdot(&it->alpha, it->s, d, n);
it->alpha /= it->ys;
/* q_{i} = q_{i+1} - \alpha_{i} y_{i}. */
vecadd(d, it->y, -it->alpha, n);
}
vecscale(d, ys / yy, n);
for (i = 0;i < bound;++i) {
it = &lm[j];
/* \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}. */
vecdot(&beta, it->y, d, n);
beta /= it->ys;
/* \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}. */
vecadd(d, it->s, it->alpha - beta, n);
j = (j + 1) % m; /* if (++j == m) j = 0; */
}
/*
Constrain the search direction for orthant-wise updates.
*/
if (param->orthantwise_c != 0.) {
for (i = param->orthantwise_start;i < n;++i) {
if (d[i] * w[i] <= 0) {
d[i] = 0;
}
}
}
/*
Now the search direction d is ready. We try step = 1 first.
*/
step = 1.0;
}
lbfgs_exit:
/* Return the final value of the objective function. */
if (ptr_fx != NULL) {
*ptr_fx = fx;
}
/* Free memory blocks used by this function. */
if (lm != NULL) {
for (i = 0;i < m;++i) {
vecfree(lm[i].s);
vecfree(lm[i].y);
}
vecfree(lm);
}
vecfree(w);
vecfree(d);
vecfree(gp);
vecfree(g);
vecfree(xp);
return ret;
}
int lbfgs(
int n,
double* x,
double* pfx,
lbfgs_evaluate_t evaluate,
lbfgs_progress_t progress,
void* instance,
const lbfgs_parameter_t* _param
) {
int ret;
int i, j, k, ls, end, bound, n_evaluate = 0;
int enalbe_owlqn;
double step;
lbfgs_parameter_t param = (_param) ? (*_param) : default_param;
const int m = param.m;
double* xp;
double* g, *gp, *pg = 0;
double* d, *w, *pf = 0;
iteration_data_t* lm = 0, *it = 0;
double ys, yy;
double xnorm, gnorm, rate, beta;
double fx;
line_search_proc_t linesearch = line_search_morethuente;
callback_data_t cd;
cd.n = n;
cd.instance = instance;
cd.evaluate = evaluate;
cd.progress = (progress) ? progress : default_lbfgs_progress;
/* Check the input parameters for errors. */
if (n <= 0) {
return LBFGSERR_INVALID_N;
}
if (param.epsilon < 0.0) {
return LBFGSERR_INVALID_EPSILON;
}
if (param.past < 0) {
return LBFGSERR_INVALID_TESTPERIOD;
}
if (param.delta < 0.0) {
return LBFGSERR_INVALID_DELTA;
}
if (param.min_step < 0.0) {
return LBFGSERR_INVALID_MINSTEP;
}
if (param.max_step < param.min_step) {
return LBFGSERR_INVALID_MAXSTEP;
}
if (param.ftol < 0.0) {
return LBFGSERR_INVALID_FTOL;
}
if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE ||
param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {
if (param.wolfe <= param.ftol || 1. <= param.wolfe) {
return LBFGSERR_INVALID_WOLFE;
}
}
if (param.gtol < 0.0) {
return LBFGSERR_INVALID_GTOL;
}
if (param.xtol < 0.0) {
return LBFGSERR_INVALID_XTOL;
}
if (param.max_linesearch <= 0) {
return LBFGSERR_INVALID_MAXLINESEARCH;
}
if (param.orthantwise_c < 0.0) {
return LBFGSERR_INVALID_ORTHANTWISE;
}
if (param.orthantwise_start < 0 || param.orthantwise_start > n) {
return LBFGSERR_INVALID_ORTHANTWISE_START;
}
if (param.orthantwise_end < 0) {
param.orthantwise_end = n;
}
if (param.orthantwise_end > n) {
return LBFGSERR_INVALID_ORTHANTWISE_END;
}
enalbe_owlqn = (param.orthantwise_c != 0.0);
if (enalbe_owlqn) {
switch (param.linesearch) {
case LBFGS_LINESEARCH_BACKTRACKING_WOLFE:
linesearch = line_search_backtracking_owlqn;
break;
default:
/* Only the backtracking method is available. */
return LBFGSERR_INVALID_LINESEARCH;
}
} else {
switch (param.linesearch) {
case LBFGS_LINESEARCH_MORETHUENTE:
linesearch = line_search_morethuente;
break;
case LBFGS_LINESEARCH_BACKTRACKING_ARMIJO:
case LBFGS_LINESEARCH_BACKTRACKING_WOLFE:
case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE:
linesearch = line_search_backtracking;
break;
default:
return LBFGSERR_INVALID_LINESEARCH;
}
}
/* Allocate working space. */
xp = vecalloc(n);
g = vecalloc(n);
gp = vecalloc(n);
d = vecalloc(n);
w = vecalloc(n);
/* Allocate pseudo gradient. */
if (enalbe_owlqn) {
pg = vecalloc(n);
}
/* Allocate and initialize the limited memory storage. */
lm = (iteration_data_t*)xalloc(m * sizeof(iteration_data_t));
for (i = 0; i < m; i++) {
it = &lm[i];
it->alpha = 0.0;
it->s = vecalloc(n);
it->y = vecalloc(n);
it->ys = 0.0;
}
/* Allocate an array for storing previous values of the objective function. */
if (param.past > 0) {
pf = vecalloc((size_t)param.past);
}
fx = cd.evaluate(cd.instance, cd.n, x, g, 0);
n_evaluate++;
if (enalbe_owlqn) {
xnorm = owlqn_x1norm(x, param.orthantwise_start, param.orthantwise_end);
fx += xnorm * param.orthantwise_c;
owlqn_pseudo_gradient(
pg, x, g, n,
param.orthantwise_c, param.orthantwise_start, param.orthantwise_end);
}
/* Store the initial value of the objective function. */
if (pf) {
pf[0] = fx;
}
/**
* Compute the direction.
* we assume the initial hessian matrix H_0 as the identity matrix.
*/
if (!enalbe_owlqn) {
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
/**
* Make sure that the initial variables are not a minimizer.
*/
vec2norm(&xnorm, x, n);
if (!enalbe_owlqn) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
if (xnorm < 1.0) {
xnorm = 1.0;
}
if (gnorm / xnorm <= param.epsilon) {
ret = LBFGS_ALREADY_MINIMIZED;
goto lbfgs_exit;
}
/**
* Compute the initial step:
* step = 1.0 / ||d||
*/
vec2norminv(&step, d, n);
k = 1;
end = 0;
for (;;) {
/* Store the current position and gradient vectors. */
veccpy(xp, x, n);
veccpy(gp, g, n);
/* Search for an optimal step. */
if (!enalbe_owlqn) {
ls = linesearch(n, x, &fx, g, d, &step, xp, gp, w, &cd, ¶m);
} else {
ls = linesearch(n, x, &fx, g, d, &step, xp, pg, w, &cd, ¶m);
owlqn_pseudo_gradient(
pg, x, g, n,
param.orthantwise_c, param.orthantwise_start, param.orthantwise_end
);
}
if (ls < 0) {
/* Revert to the previous point. */
veccpy(x, xp, n);
veccpy(g, gp, n);
ret = ls;
break;
}
n_evaluate += ls;
/* Compute x and g norms. */
vec2norm(&xnorm, x, n);
if (!enalbe_owlqn) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
/* Report the progress. */
if ((ret = cd.progress(cd.instance, cd.n, x, g, fx, xnorm, gnorm, step, k, n_evaluate)) != 0) {
ret = LBFGSERR_CANCELED;
break;
}
/* Convergence test. */
if (xnorm < 1.0) {
xnorm = 1.0;
}
if (gnorm / xnorm <= param.epsilon) {
ret = LBFGS_CONVERGENCE;
break;
}
/* Stopping criterion test. */
if (pf) {
/* We don't test the stopping criterion while k < past. */
if (param.past <= k) {
/* Compute the relative improvement from the past. */
rate = (pf[k % param.past] - fx) / fx;
/* The stopping criterion. */
if (rate < param.delta) {
ret = LBFGS_CONVERGENCE_DELTA;
break;
}
}
/* Store the current value of the objective function. */
pf[k % param.past] = fx;
}
if (param.max_iterations != 0 && param.max_iterations < k + 1) {
ret = LBFGSERR_MAXIMUMITERATION;
break;
}
/**
* Update s and y:
* s_{k+1} = x_{k+1} - x_{k} = step * d_{k}
* y_{k+1} = g_{k+1} - g_{k}
*/
it = &lm[end];
vecdiff(it->s, x, xp, n);
vecdiff(it->y, g, gp, n);
/**
* Compute scalars ys and yy:
* ys = y^t s = 1 / \rho
* yy = y^t y
* Notice that yy is used for scaling the hessian matrix H_0 (Cholesky factor).
*/
vecdot(&ys, it->y, it->s, n);
vecdot(&yy, it->y, it->y, n);
it->ys = ys;
/**
* Recursive formula to compute d = -(H g).
* This is described in page 779 of:
* Jorge Nocedal.
* Updating Quasi-Newton Matrices with Limited Storage.
* Mathematics of Computation, Vol. 35, No. 151,
* pp. 773--782, 1980.
*/
bound = (m <= k) ? m : k;
k++;
end = (end + 1) % m;
/* Compute the steepest direction. */
/* Compute the negative of (pseudo) gradient. */
if (!enalbe_owlqn) {
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
j = end;
for (i = 0; i < bound; i++) {
j = (j + m - 1) % m; /* if (--j == -1) j = m-1; */
it = &lm[j];
/* \alpha_{j} = \rho_{j} s^{t}_{j} q_{k+1} */
vecdot(&it->alpha, it->s, d, n);
it->alpha /= it->ys;
/* q_{i} = q_{i+1} - \alpha_{i} y_{i} */
vecadd(d, it->y, -it->alpha, n);
}
vecscale(d, ys / yy, n);
for (i = 0; i < bound; i++) {
it = &lm[j];
/* \beta_{j} = \rho_{j} y^t_{j} \gamma_{i} */
vecdot(&beta, it->y, d, n);
beta /= it->ys;
/* \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j} */
vecadd(d, it->s, it->alpha - beta, n);
j = (j + 1) % m; /* if (++j == m) j = 0; */
}
/* Constrain the search direction for orthant-wise updates. */
if (enalbe_owlqn) {
owlqn_contrain_line_search(d, pg, param.orthantwise_start, param.orthantwise_end);
}
/* Now the search direction d is ready. We try step = 1 first. */
step = 1.0;
}
lbfgs_exit:
/* Return the final value of the objective function. */
if (pfx) {
*pfx = fx;
}
vecfree(pf);
if (lm != 0) {
for (i = 0; i < m; i++) {
vecfree(lm[i].s);
vecfree(lm[i].y);
}
xfree(lm);
}
vecfree(pg);
vecfree(w);
vecfree(d);
vecfree(gp);
vecfree(g);
vecfree(xp);
return ret;
}
int
main(
int argc, /* arg count */
char * argv[] /* arg vector */
){
static char * context = "main(chain)";
char * stem = NULL; /* dump filename stem */
char * suffix = NULL; /* dump filename suffix */
char * suff2 = NULL; /* last half of suffix */
int nr, nc; /* integer matrix sizes */
int n; /* square matrix/vector size */
real base_x, base_y; /* base of Mandelbrot */
real ext_x, ext_y; /* extent of Mandelbrot */
int limit, seed; /* randmat controls */
real fraction; /* invperc/thresh filling */
int itersLife; /* life iterations */
int itersElastic, relax; /* elastic controls */
int2D i2D; /* integer matrix */
bool2D b2D; /* boolean matrix */
pt1D cities; /* cities point vector */
int n_cities; /* number of cities */
pt1D net; /* net point vector */
int n_net; /* number of net points */
real2D r2D_gauss; /* real matrix for Gaussian */
real2D r2D_sor; /* real matrix for SOR */
real1D r1D_gauss_v; /* real vector input for Gaussian */
real1D r1D_sor_v; /* real vector input for SOR */
real1D r1D_gauss_a; /* real vector answer for Gaussian */
real1D r1D_sor_a; /* real vector answer for SOR */
real1D r1D_gauss_c; /* real vector check for Gaussian */
real1D r1D_sor_c; /* real vector check for SOR */
real tol; /* SOR tolerance */
real realDiff; /* vector difference */
bool choicesSet = FALSE; /* path choices set? */
bool doMandel = TRUE; /* mandel vs. randmat */
bool doInvperc = TRUE; /* invperc vs. thresholding */
bool doDump = FALSE; /* dump intermediate results? */
int argd = 1; /* argument index */
/* arguments */
#if NUMA
MAIN_INITENV(,32000000)
#endif
while (argd < argc){
CHECK(argv[argd][0] == '-',
fail(context, "bad argument", "index", "%d", argd, NULL));
switch(argv[argd][1]){
case 'E' : /* elastic */
itersElastic = arg_int(context, argc, argv, argd+1, argv[argd]);
relax = arg_int(context, argc, argv, argd+2, argv[argd]);
argd += 3;
break;
case 'F' : /* fraction (invperc/thresh) */
fraction = arg_real(context, argc, argv, argd+1, argv[argd]);
argd += 2;
break;
case 'L' : /* life */
itersLife = arg_int(context, argc, argv, argd+1, argv[argd]);
argd += 2;
break;
case 'M' : /* mandel */
base_x = arg_real(context, argc, argv, argd+1, argv[argd]);
base_y = arg_real(context, argc, argv, argd+2, argv[argd]);
ext_x = arg_real(context, argc, argv, argd+3, argv[argd]);
ext_y = arg_real(context, argc, argv, argd+4, argv[argd]);
argd += 5;
break;
case 'N' : /* winnow */
n_cities = arg_int(context, argc, argv, argd+1, argv[argd]);
argd += 2;
break;
case 'R' : /* randmat */
limit = arg_int(context, argc, argv, argd+1, argv[argd]);
seed = arg_int(context, argc, argv, argd+2, argv[argd]);
argd += 3;
break;
case 'S' : /* matrix size */
nr = arg_int(context, argc, argv, argd+1, argv[argd]);
nc = arg_int(context, argc, argv, argd+2, argv[argd]);
argd += 3;
break;
case 'T' : /* SOR tolerance */
tol = arg_real(context, argc, argv, argd+1, argv[argd]);
argd += 2;
break;
case 'c' : /* choice */
CHECK(!choicesSet,
fail(context, "choices already set", NULL));
suffix = arg_str(context, argc, argv, argd+1, argv[argd]);
argd += 2;
switch(suffix[0]){
case 'i' : doInvperc = TRUE; break;
case 't' : doInvperc = FALSE; break;
default :
fail(context, "unknown choice(s)", "choice", "%s", suffix, NULL);
}
switch(suffix[1]){
case 'm' : doMandel = TRUE; break;
case 'r' : doMandel = FALSE; break;
default :
fail(context, "unknown choice(s)", "choice", "%s", suffix, NULL);
}
suff2 = suffix+1;
choicesSet = TRUE;
break;
case 'd' : /* dump */
doDump = TRUE;
argd += 1;
if ((argd < argc) && (argv[argd][0] != '-')){
stem = arg_str(context, argc, argv, argd, argv[argd-1]);
argd += 1;
}
break;
#if GRAPHICS
case 'g' :
gfx_open(app_chain, arg_gfxCtrl(context, argc, argv, argd+1, argv[argd]));
argd += 2;
break;
#endif
#if MIMD
case 'p' :
DataDist = arg_dataDist(context, argc, argv, argd+1, argv[argd]);
ParWidth = arg_int(context, argc, argv, argd+2, argv[argd]);
argd += 3;
break;
#endif
case 'u' :
io_init(FALSE);
argd += 1;
break;
default :
fail(context, "unknown flag", "flag", "%s", argv[argd], NULL);
break;
}
}
CHECK(choicesSet,
fail("context", "choices not set using -c flag", NULL));
/* initialize */
#if MIMD
sch_init(DataDist);
#endif
/* mandel vs. randmat */
if (doMandel){
mandel(i2D, nr, nc, base_x, base_y, ext_x, ext_y);
if (doDump) io_wrInt2D(context, mkfname(stem, NULL, suff2, "i2"), i2D, nr, nc);
} else {
randmat(i2D, nr, nc, limit, seed);
if (doDump) io_wrInt2D(context, mkfname(stem, NULL, suff2, "i2"), i2D, nr, nc);
}
/* half */
half(i2D, nr, nc);
if (doDump) io_wrInt2D(context, mkfname(stem, "h", suff2, "i2"), i2D, nr, nc);
/* invperc vs. thresh */
if (doInvperc){
invperc(i2D, b2D, nr, nc, fraction);
if (doDump) io_wrBool2D(context, mkfname(stem, NULL, suffix, "b2"), b2D, nr, nc);
} else {
thresh(i2D, b2D, nr, nc, fraction);
if (doDump) io_wrBool2D(context, mkfname(stem, NULL, suffix, "b2"), b2D, nr, nc);
}
/* life */
life(b2D, nr, nc, itersLife);
if (doDump) io_wrBool2D(context, mkfname(stem, "l", suffix, "b2"), b2D, nr, nc);
/* winnow */
winnow(i2D, b2D, nr, nc, cities, n_cities);
if (doDump) io_wrPt1D(context, mkfname(stem, "w", suffix, "p1"), cities, n_cities);
/* norm */
norm(cities, n_cities);
if (doDump) io_wrPt1D(context, mkfname(stem, "n", suffix, "p1"), cities, n_cities);
/* elastic */
n_net = (int)(ELASTIC_RATIO * n_cities);
CHECK(n_net <= MAXEXT,
fail(context, "too many net points required",
"number of net points", "%d", n_net, NULL));
elastic(cities, n_cities, net, n_net, itersElastic, relax);
if (doDump) io_wrPt1D(context, mkfname(stem, "e", suffix, "p1"), net, n_net);
/* outer */
n = n_net;
outer(net, r2D_gauss, r1D_gauss_v, n);
if (doDump){
io_wrReal2D(context, mkfname(stem, "o", suffix, "r2"), r2D_gauss, n, n);
io_wrReal1D(context, mkfname(stem, "o", suffix, "r1"), r1D_gauss_v, n);
}
cpReal2D(r2D_gauss, r2D_sor, n, n);
cpReal1D(r1D_gauss_v, r1D_sor_v, n);
/* gauss */
gauss(r2D_gauss, r1D_gauss_v, r1D_gauss_a, n);
if (doDump) io_wrReal1D(context, mkfname(stem, "g", suffix, "r1"), r1D_gauss_a, n);
/* product (gauss) */
product(r2D_gauss, r1D_gauss_a, r1D_gauss_c, n, n);
if (doDump) io_wrReal1D(context, mkfname(stem, "pg", suffix, "r1"), r1D_gauss_c, n);
/* sor */
sor(r2D_sor, r1D_sor_v, r1D_sor_a, n, tol);
if (doDump) io_wrReal1D(context, mkfname(stem, "s", suffix, "r1"), r1D_gauss_a, n);
/* product (sor) */
product(r2D_sor, r1D_sor_a, r1D_sor_c, n, n);
if (doDump) io_wrReal1D(context, mkfname(stem, "ps", suffix, "r1"), r1D_gauss_c, n);
/* difference */
vecdiff(r1D_gauss_a, r1D_sor_a, n, &realDiff);
if (doDump) io_wrReal0D(context, mkfname(stem, "v", suffix, "r0"), realDiff);
#if IEEE
ieee_retrospective(stderr);
#endif
#if NUMA
MAIN_END;
#endif
return 0;
}
