//
// compute prefix sums of a grid
//
prefix_sums *compute_psums(grid *g)
{
// allocate structure
prefix_sums *p = (prefix_sums *) ALLOC(prefix_sums);
p->gridref = g;
// allocate memory for prefix sums
int size = g->width * g->height;
p->A = (cell *) ALLOCV(cell,size);
p->B = (cell *) ALLOCV(cell,size);
p->X = (cell *) ALLOCV(cell,size);
p->Y = (cell *) ALLOCV(cell,size);
// fill in computation
compute_sumA(p);
compute_sumB(p);
compute_sumX(p);
compute_sumY(p);
// check whether results are correct
assert (check_sumA(p) && "computation of prefix A failed");
assert (check_sumB(p) && "computation of prefix B failed");
assert (check_sumX(p) && "computation of prefix X failed");
assert (check_sumY(p) && "computation of prefix Y failed");
return p;
}
//
// naive implementation of LRT
//
// the complexity of the naive implementation is O(n^6) and
// hence not practical for larger grids.
//
// Steps:
// 1. allocate memory for resulting rectangles and their scores
// 2. compute grid totals
// 2. compute lrt for each rectangle
// 2.a) compute rectangle total
// 2.b) compute score
// 3. sort all rectangles according to their score
//
rectangle *naive_lrt(grid *g,int kbest)
{
int idx=0; // output index
int i,j; // index for regions in grid
// set width and height
int width=g->width;
int height=g->height;
// compute number of rectangles in the grid and allocate
// memory to store result
size_t size = (size_t)(width + 1) *
(size_t)width *
(size_t)(height + 1) *
(size_t)height / 4;
rectangle *r = (rectangle *) ALLOCV(rectangle,size);
// compute grid totals, ratio, and likelihood
int g_n = 0;
int g_k = 0;
for (i=0; i<height; i++) {
for (j=0; j<width; j++) {
g_n += g->cells[I(i,j)].n;
g_k += g->cells[I(i,j)].k;
}
}
float g_q = (float)g_k / (float)g_n;
float g_l = g_k * log(g_q);
// compute LRT for all rectangle in grid
int j1,i1,j2,i2; // coordinates of a rectangle
for (i1=0; i1<height; i1++) {
for (j1=0; j1<width; j1++) {
for (i2=i1; i2<height; i2++) {
for (j2=j1; j2<width; j2++) {
// set rectangle width and height
int r_width = j2 - j1 + 1;
int r_height = i2 - i1 + 1;
// compute rectangle totals, ratio and likelihood
int r_n=0;
int r_k=0;
cell *c = &g->cells[i1*width+j1];
for (i=0; i<r_height; i++) {
for (j=0; j<r_width; j++) {
r_n += c[I(i,j)].n;
r_k += c[I(i,j)].k;
}
}
float r_q = (float)r_k / (float)r_n;
float r_l = r_k * log(r_q) - r_k;
// compute rectangle's complement totals, ratio, and likelihood
int c_n = g_n - r_n;
int c_k = g_k - r_k;
float c_q = (float)c_k / (float)c_n;
float c_l = c_k * log(c_q) - c_k;
// compute score
float score = r_l + c_l - g_l;
// store result in array r
r[idx].score = score;
r[idx].i1 = i1;
r[idx].j1 = j1;
r[idx].i2 = i2;
r[idx].j2 = j2;
idx = idx + 1;
}
}
}
}
// sort result and return it
qsort(r,size,sizeof(rectangle),rectangle_compare);
return r;
}
//
// fast implementation of LRT using prefix sums
//
rectangle *fast_lrt(grid *g,int kbest)
{
// heap size (initialized with zero and grows up to kbest)
int heap_size=0;
// set width and height
int width = g->width;
int height = g->height;
// allocate heap with size k
rectangle *r = (rectangle *) ALLOCV(rectangle,kbest);
// compute prefix sums
prefix_sums *p = compute_psums(g);
// compute grid totals, ratio, and likelihood
int g_n = p->A[width * height - 1].n;
int g_k = p->A[width * height - 1].k;
float g_q = (float)g_k / (float)g_n;
float g_l = g_k * log(g_q);
// compute LRT for each rectangle
int j1,i1,j2,i2; // coordinates of a rectangle
for (i1=0;i1<height;i1++){
for (j1=0;j1<width;j1++){
for (i2=i1;i2<height;i2++){
for (j2=j1;j2<width;j2++){
// compute rectangle totals, ratio and likelihood
int a_n = p->A[I(i2,j2)].n;
int a_k = p->A[I(i2,j2)].k;
int b_n = p->B[I(i1,j1)].n;
int b_k = p->B[I(i1,j1)].k;
int y_n = p->Y[I(i1,j2)].n;
int y_k = p->Y[I(i1,j2)].k;
int x_n = p->X[I(i2,j1)].n;
int x_k = p->X[I(i2,j1)].k;
int r_n = a_n + b_n + x_n + y_n - g_n;
int r_k = a_k + b_k + x_k + y_k - g_k;
float r_q = (float)r_k / (float)r_n;
float r_l = r_k * log(r_q) - r_k;
// check whether prefix sums are correct
#if DEBUG_LEVEL > 0
int t_n=0;
int t_k=0;
int i,j;
int r_width = j2 - j1 + 1;
int r_height = i2 - i1 + 1;
cell *c = &g->cells[i1*width+j1];
for (i=0;i<r_height;i++) {
for (j=0;j<r_width;j++) {
t_n += c[I(i,j)].n;
t_k += c[I(i,j)].k;
}
}
assert((t_n == r_n && t_k == r_k) && "problems with prefix");
#endif
// compute rectangle's complement totals, ratio, and likelihood
int c_n = g_n - r_n;
int c_k = g_k - r_k;
float c_q = (float)c_k / (float)c_n;
float c_l = c_k * log(c_q) - c_k;
// compute score
float score = r_l + c_l - g_l;
// populate current rectangle
rectangle current;
current.score = score;
current.i1 = i1;
current.j1 = j1;
current.i2 = i2;
current.j2 = j2;
// store result in heap
// if the heap size is still smaller than kbest, add rectangle to the end of the heap
// and rise the last element until the heap condition holds
if (heap_size < kbest) {
r[heap_size].score = score;
r[heap_size].j1 = j1;
r[heap_size].i1 = i1;
r[heap_size].j2 = j2;
r[heap_size].i2 = i2;
heap_size = heap_size + 1;
minheap_rise(r,heap_size,sizeof(rectangle),heap_rcmp);
// otherwise check whether the current score is greater than the smallest element (=first element)
// if so, replace the first element with current rectangle and sink the current element until
// the heap condition holds.
} else if (heap_rcmp(¤t,r) > 0) {
r[0] = current;
minheap_sink(r,kbest,sizeof(rectangle),heap_rcmp);
}
}
}
}
}
// sort result and return it
qsort(r,kbest,sizeof(rectangle),rectangle_compare);
return r;
}
static VALUE
function_call(int argc, VALUE argv[], VALUE self)
{
struct nogvl_ffi_call_args args = { 0 };
fiddle_generic *generic_args;
VALUE cfunc, types, cPointer;
int i;
VALUE alloc_buffer = 0;
cfunc = rb_iv_get(self, "@ptr");
types = rb_iv_get(self, "@args");
cPointer = rb_const_get(mFiddle, rb_intern("Pointer"));
Check_Max_Args("number of arguments", argc);
if (argc != (i = RARRAY_LENINT(types))) {
rb_error_arity(argc, i, i);
}
TypedData_Get_Struct(self, ffi_cif, &function_data_type, args.cif);
if (rb_safe_level() >= 1) {
for (i = 0; i < argc; i++) {
VALUE src = argv[i];
if (OBJ_TAINTED(src)) {
rb_raise(rb_eSecurityError, "tainted parameter not allowed");
}
}
}
generic_args = ALLOCV(alloc_buffer,
(size_t)(argc + 1) * sizeof(void *) + (size_t)argc * sizeof(fiddle_generic));
args.values = (void **)((char *)generic_args +
(size_t)argc * sizeof(fiddle_generic));
for (i = 0; i < argc; i++) {
VALUE type = RARRAY_AREF(types, i);
VALUE src = argv[i];
int argtype = FIX2INT(type);
if (argtype == TYPE_VOIDP) {
if(NIL_P(src)) {
src = INT2FIX(0);
} else if(cPointer != CLASS_OF(src)) {
src = rb_funcall(cPointer, rb_intern("[]"), 1, src);
}
src = rb_Integer(src);
}
VALUE2GENERIC(argtype, src, &generic_args[i]);
args.values[i] = (void *)&generic_args[i];
}
args.values[argc] = NULL;
args.fn = NUM2PTR(cfunc);
(void)rb_thread_call_without_gvl(nogvl_ffi_call, &args, 0, 0);
rb_funcall(mFiddle, rb_intern("last_error="), 1, INT2NUM(errno));
#if defined(_WIN32)
rb_funcall(mFiddle, rb_intern("win32_last_error="), 1, INT2NUM(errno));
#endif
ALLOCV_END(alloc_buffer);
return GENERIC2VALUE(rb_iv_get(self, "@return_type"), args.retval);
}
