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/**********************************************************************
* File: statistc.c (Formerly stats.c)
* Description: Simple statistical package for integer values.
* Author: Ray Smith
* Created: Mon Feb 04 16:56:05 GMT 1991
*
* (C) Copyright 1991, Hewlett-Packard Ltd.
** Licensed under the Apache License, Version 2.0 (the "License");
** you may not use this file except in compliance with the License.
** You may obtain a copy of the License at
** http://www.apache.org/licenses/LICENSE-2.0
** Unless required by applicable law or agreed to in writing, software
** distributed under the License is distributed on an "AS IS" BASIS,
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
** See the License for the specific language governing permissions and
** limitations under the License.
*
**********************************************************************/
// Include automatically generated configuration file if running autoconf.
#ifdef HAVE_CONFIG_H
#include "config_auto.h"
#endif
#include "statistc.h"
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include "helpers.h"
#include "scrollview.h"
#include "tprintf.h"
using tesseract::KDPairInc;
/**********************************************************************
* STATS::STATS
*
* Construct a new stats element by allocating and zeroing the memory.
**********************************************************************/
STATS::STATS(inT32 min_bucket_value, inT32 max_bucket_value_plus_1) {
if (max_bucket_value_plus_1 <= min_bucket_value) {
min_bucket_value = 0;
max_bucket_value_plus_1 = 1;
}
rangemin_ = min_bucket_value; // setup
rangemax_ = max_bucket_value_plus_1;
buckets_ = new inT32[rangemax_ - rangemin_];
clear();
}
STATS::STATS() {
rangemax_ = 0;
rangemin_ = 0;
buckets_ = NULL;
}
/**********************************************************************
* STATS::set_range
*
* Alter the range on an existing stats element.
**********************************************************************/
bool STATS::set_range(inT32 min_bucket_value, inT32 max_bucket_value_plus_1) {
if (max_bucket_value_plus_1 <= min_bucket_value) {
return false;
}
if (rangemax_ - rangemin_ != max_bucket_value_plus_1 - min_bucket_value) {
delete [] buckets_;
buckets_ = new inT32[max_bucket_value_plus_1 - min_bucket_value];
}
rangemin_ = min_bucket_value; // setup
rangemax_ = max_bucket_value_plus_1;
clear(); // zero it
return true;
}
/**********************************************************************
* STATS::clear
*
* Clear out the STATS class by zeroing all the buckets.
**********************************************************************/
void STATS::clear() { // clear out buckets
total_count_ = 0;
if (buckets_ != NULL)
memset(buckets_, 0, (rangemax_ - rangemin_) * sizeof(buckets_[0]));
}
/**********************************************************************
* STATS::~STATS
*
* Destructor for a stats class.
**********************************************************************/
STATS::~STATS () {
delete [] buckets_;
}
/**********************************************************************
* STATS::add
*
* Add a set of samples to (or delete from) a pile.
**********************************************************************/
void STATS::add(inT32 value, inT32 count) {
if (buckets_ == NULL) {
return;
}
value = ClipToRange(value, rangemin_, rangemax_ - 1);
buckets_[value - rangemin_] += count;
total_count_ += count; // keep count of total
}
/**********************************************************************
* STATS::mode
*
* Find the mode of a stats class.
**********************************************************************/
inT32 STATS::mode() const { // get mode of samples
if (buckets_ == NULL) {
return rangemin_;
}
inT32 max = buckets_[0]; // max cell count
inT32 maxindex = 0; // index of max
for (int index = rangemax_ - rangemin_ - 1; index > 0; --index) {
if (buckets_[index] > max) {
max = buckets_[index]; // find biggest
maxindex = index;
}
}
return maxindex + rangemin_; // index of biggest
}
/**********************************************************************
* STATS::mean
*
* Find the mean of a stats class.
**********************************************************************/
double STATS::mean() const { //get mean of samples
if (buckets_ == NULL || total_count_ <= 0) {
return static_cast<double>(rangemin_);
}
inT64 sum = 0;
for (int index = rangemax_ - rangemin_ - 1; index >= 0; --index) {
sum += static_cast<inT64>(index) * buckets_[index];
}
return static_cast<double>(sum) / total_count_ + rangemin_;
}
/**********************************************************************
* STATS::sd
*
* Find the standard deviation of a stats class.
**********************************************************************/
double STATS::sd() const { //standard deviation
if (buckets_ == NULL || total_count_ <= 0) {
return 0.0;
}
inT64 sum = 0;
double sqsum = 0.0;
for (int index = rangemax_ - rangemin_ - 1; index >= 0; --index) {
sum += static_cast<inT64>(index) * buckets_[index];
sqsum += static_cast<double>(index) * index * buckets_[index];
}
double variance = static_cast<double>(sum) / total_count_;
variance = sqsum / total_count_ - variance * variance;
if (variance > 0.0)
return sqrt(variance);
return 0.0;
}
/**********************************************************************
* STATS::ile
*
* Returns the fractile value such that frac fraction (in [0,1]) of samples
* has a value less than the return value.
**********************************************************************/
double STATS::ile(double frac) const {
if (buckets_ == NULL || total_count_ == 0) {
return static_cast<double>(rangemin_);
}
#if 0
// TODO(rays) The existing code doesn't seem to be doing the right thing
// with target a double but this substitute crashes the code that uses it.
// Investigate and fix properly.
int target = IntCastRounded(frac * total_count_);
target = ClipToRange(target, 1, total_count_);
#else
double target = frac * total_count_;
target = ClipToRange(target, 1.0, static_cast<double>(total_count_));
#endif
int sum = 0;
int index = 0;
for (index = 0; index < rangemax_ - rangemin_ && sum < target;
sum += buckets_[index++]);
if (index > 0) {
ASSERT_HOST(buckets_[index - 1] > 0);
return rangemin_ + index -
static_cast<double>(sum - target) / buckets_[index - 1];
} else {
return static_cast<double>(rangemin_);
}
}
/**********************************************************************
* STATS::min_bucket
*
* Find REAL minimum bucket - ile(0.0) isn't necessarily correct
**********************************************************************/
inT32 STATS::min_bucket() const { // Find min
if (buckets_ == NULL || total_count_ == 0) {
return rangemin_;
}
inT32 min = 0;
for (min = 0; (min < rangemax_ - rangemin_) && (buckets_[min] == 0); min++);
return rangemin_ + min;
}
/**********************************************************************
* STATS::max_bucket
*
* Find REAL maximum bucket - ile(1.0) isn't necessarily correct
**********************************************************************/
inT32 STATS::max_bucket() const { // Find max
if (buckets_ == NULL || total_count_ == 0) {
return rangemin_;
}
inT32 max;
for (max = rangemax_ - rangemin_ - 1; max > 0 && buckets_[max] == 0; max--);
return rangemin_ + max;
}
/**********************************************************************
* STATS::median
*
* Finds a more useful estimate of median than ile(0.5).
*
* Overcomes a problem with ile() - if the samples are, for example,
* 6,6,13,14 ile(0.5) return 7.0 - when a more useful value would be midway
* between 6 and 13 = 9.5
**********************************************************************/
double STATS::median() const { //get median
if (buckets_ == NULL) {
return static_cast<double>(rangemin_);
}
double median = ile(0.5);
int median_pile = static_cast<int>(floor(median));
if ((total_count_ > 1) && (pile_count(median_pile) == 0)) {
inT32 min_pile;
inT32 max_pile;
/* Find preceding non zero pile */
for (min_pile = median_pile; pile_count(min_pile) == 0; min_pile--);
/* Find following non zero pile */
for (max_pile = median_pile; pile_count(max_pile) == 0; max_pile++);
median = (min_pile + max_pile) / 2.0;
}
return median;
}
/**********************************************************************
* STATS::local_min
*
* Return TRUE if this point is a local min.
**********************************************************************/
bool STATS::local_min(inT32 x) const {
if (buckets_ == NULL) {
return false;
}
x = ClipToRange(x, rangemin_, rangemax_ - 1) - rangemin_;
if (buckets_[x] == 0)
return true;
inT32 index; // table index
for (index = x - 1; index >= 0 && buckets_[index] == buckets_[x]; --index);
if (index >= 0 && buckets_[index] < buckets_[x])
return false;
for (index = x + 1; index < rangemax_ - rangemin_ &&
buckets_[index] == buckets_[x]; ++index);
if (index < rangemax_ - rangemin_ && buckets_[index] < buckets_[x])
return false;
else
return true;
}
/**********************************************************************
* STATS::smooth
*
* Apply a triangular smoothing filter to the stats.
* This makes the modes a bit more useful.
* The factor gives the height of the triangle, i.e. the weight of the
* centre.
**********************************************************************/
void STATS::smooth(inT32 factor) {
if (buckets_ == NULL || factor < 2) {
return;
}
STATS result(rangemin_, rangemax_);
int entrycount = rangemax_ - rangemin_;
for (int entry = 0; entry < entrycount; entry++) {
//centre weight
int count = buckets_[entry] * factor;
for (int offset = 1; offset < factor; offset++) {
if (entry - offset >= 0)
count += buckets_[entry - offset] * (factor - offset);
if (entry + offset < entrycount)
count += buckets_[entry + offset] * (factor - offset);
}
result.add(entry + rangemin_, count);
}
total_count_ = result.total_count_;
memcpy(buckets_, result.buckets_, entrycount * sizeof(buckets_[0]));
}
/**********************************************************************
* STATS::cluster
*
* Cluster the samples into max_cluster clusters.
* Each call runs one iteration. The array of clusters must be
* max_clusters+1 in size as cluster 0 is used to indicate which samples
* have been used.
* The return value is the current number of clusters.
**********************************************************************/
inT32 STATS::cluster(float lower, // thresholds
float upper,
float multiple, // distance threshold
inT32 max_clusters, // max no to make
STATS *clusters) { // array of clusters
BOOL8 new_cluster; // added one
float *centres; // cluster centres
inT32 entry; // bucket index
inT32 cluster; // cluster index
inT32 best_cluster; // one to assign to
inT32 new_centre = 0; // residual mode
inT32 new_mode; // pile count of new_centre
inT32 count; // pile to place
float dist; // from cluster
float min_dist; // from best_cluster
inT32 cluster_count; // no of clusters
if (buckets_ == NULL || max_clusters < 1)
return 0;
centres = new float[max_clusters + 1];
for (cluster_count = 1; cluster_count <= max_clusters
&& clusters[cluster_count].buckets_ != NULL
&& clusters[cluster_count].total_count_ > 0;
cluster_count++) {
centres[cluster_count] =
static_cast<float>(clusters[cluster_count].ile(0.5));
new_centre = clusters[cluster_count].mode();
for (entry = new_centre - 1; centres[cluster_count] - entry < lower
&& entry >= rangemin_
&& pile_count(entry) <= pile_count(entry + 1);
entry--) {
count = pile_count(entry) - clusters[0].pile_count(entry);
if (count > 0) {
clusters[cluster_count].add(entry, count);
clusters[0].add (entry, count);
}
}
for (entry = new_centre + 1; entry - centres[cluster_count] < lower
&& entry < rangemax_
&& pile_count(entry) <= pile_count(entry - 1);
entry++) {
count = pile_count(entry) - clusters[0].pile_count(entry);
if (count > 0) {
clusters[cluster_count].add(entry, count);
clusters[0].add(entry, count);
}
}
}
cluster_count--;
if (cluster_count == 0) {
clusters[0].set_range(rangemin_, rangemax_);
}
do {
new_cluster = FALSE;
new_mode = 0;
for (entry = 0; entry < rangemax_ - rangemin_; entry++) {
count = buckets_[entry] - clusters[0].buckets_[entry];
//remaining pile
if (count > 0) { //any to handle
min_dist = static_cast<float>(MAX_INT32);
best_cluster = 0;
for (cluster = 1; cluster <= cluster_count; cluster++) {
dist = entry + rangemin_ - centres[cluster];
//find distance
if (dist < 0)
dist = -dist;
if (dist < min_dist) {
min_dist = dist; //find least
best_cluster = cluster;
}
}
if (min_dist > upper //far enough for new
&& (best_cluster == 0
|| entry + rangemin_ > centres[best_cluster] * multiple
|| entry + rangemin_ < centres[best_cluster] / multiple)) {
if (count > new_mode) {
new_mode = count;
new_centre = entry + rangemin_;
}
}
}
}
// need new and room
if (new_mode > 0 && cluster_count < max_clusters) {
cluster_count++;
new_cluster = TRUE;
if (!clusters[cluster_count].set_range(rangemin_, rangemax_)) {
delete [] centres;
return 0;
}
centres[cluster_count] = static_cast<float>(new_centre);
clusters[cluster_count].add(new_centre, new_mode);
clusters[0].add(new_centre, new_mode);
for (entry = new_centre - 1; centres[cluster_count] - entry < lower
&& entry >= rangemin_
&& pile_count (entry) <= pile_count(entry + 1); entry--) {
count = pile_count(entry) - clusters[0].pile_count(entry);
if (count > 0) {
clusters[cluster_count].add(entry, count);
clusters[0].add(entry, count);
}
}
for (entry = new_centre + 1; entry - centres[cluster_count] < lower
&& entry < rangemax_
&& pile_count (entry) <= pile_count(entry - 1); entry++) {
count = pile_count(entry) - clusters[0].pile_count(entry);
if (count > 0) {
clusters[cluster_count].add(entry, count);
clusters[0].add (entry, count);
}
}
centres[cluster_count] =
static_cast<float>(clusters[cluster_count].ile(0.5));
}
} while (new_cluster && cluster_count < max_clusters);
delete [] centres;
return cluster_count;
}
// Helper tests that the current index is still part of the peak and gathers
// the data into the peak, returning false when the peak is ended.
// src_buckets[index] - used_buckets[index] is the unused part of the histogram.
// prev_count is the histogram count of the previous index on entry and is
// updated to the current index on return.
// total_count and total_value are accumulating the mean of the peak.
static bool GatherPeak(int index, const int* src_buckets, int* used_buckets,
int* prev_count, int* total_count, double* total_value) {
int pile_count = src_buckets[index] - used_buckets[index];
if (pile_count <= *prev_count && pile_count > 0) {
// Accumulate count and index.count product.
*total_count += pile_count;
*total_value += index * pile_count;
// Mark this index as used
used_buckets[index] = src_buckets[index];
*prev_count = pile_count;
return true;
} else {
return false;
}
}
// Finds (at most) the top max_modes modes, well actually the whole peak around
// each mode, returning them in the given modes vector as a <mean of peak,
// total count of peak> pair in order of decreasing total count.
// Since the mean is the key and the count the data in the pair, a single call
// to sort on the output will re-sort by increasing mean of peak if that is
// more useful than decreasing total count.
// Returns the actual number of modes found.
int STATS::top_n_modes(int max_modes,
GenericVector<KDPairInc<float, int> >* modes) const {
if (max_modes <= 0) return 0;
int src_count = rangemax_ - rangemin_;
// Used copies the counts in buckets_ as they get used.
STATS used(rangemin_, rangemax_);
modes->truncate(0);
// Total count of the smallest peak found so far.
int least_count = 1;
// Mode that is used as a seed for each peak
int max_count = 0;
do {
// Find an unused mode.
max_count = 0;
int max_index = 0;
for (int src_index = 0; src_index < src_count; src_index++) {
int pile_count = buckets_[src_index] - used.buckets_[src_index];
if (pile_count > max_count) {
max_count = pile_count;
max_index = src_index;
}
}
if (max_count > 0) {
// Copy the bucket count to used so it doesn't get found again.
used.buckets_[max_index] = max_count;
// Get the entire peak.
double total_value = max_index * max_count;
int total_count = max_count;
int prev_pile = max_count;
for (int offset = 1; max_index + offset < src_count; ++offset) {
if (!GatherPeak(max_index + offset, buckets_, used.buckets_,
&prev_pile, &total_count, &total_value))
break;
}
prev_pile = buckets_[max_index];
for (int offset = 1; max_index - offset >= 0; ++offset) {
if (!GatherPeak(max_index - offset, buckets_, used.buckets_,
&prev_pile, &total_count, &total_value))
break;
}
if (total_count > least_count || modes->size() < max_modes) {
// We definitely want this mode, so if we have enough discard the least.
if (modes->size() == max_modes)
modes->truncate(max_modes - 1);
int target_index = 0;
// Linear search for the target insertion point.
while (target_index < modes->size() &&
(*modes)[target_index].data >= total_count)
++target_index;
float peak_mean =
static_cast<float>(total_value / total_count + rangemin_);
modes->insert(KDPairInc<float, int>(peak_mean, total_count),
target_index);
least_count = modes->back().data;
}
}
} while (max_count > 0);
return modes->size();
}
/**********************************************************************
* STATS::print
*
* Prints a summary and table of the histogram.
**********************************************************************/
void STATS::print() const {
if (buckets_ == NULL) {
return;
}
inT32 min = min_bucket() - rangemin_;
inT32 max = max_bucket() - rangemin_;
int num_printed = 0;
for (int index = min; index <= max; index++) {
if (buckets_[index] != 0) {
tprintf("%4d:%-3d ", rangemin_ + index, buckets_[index]);
if (++num_printed % 8 == 0)
tprintf ("\n");
}
}
tprintf ("\n");
print_summary();
}
/**********************************************************************
* STATS::print_summary
*
* Print a summary of the stats.
**********************************************************************/
void STATS::print_summary() const {
if (buckets_ == NULL) {
return;
}
inT32 min = min_bucket();
inT32 max = max_bucket();
tprintf("Total count=%d\n", total_count_);
tprintf("Min=%.2f Really=%d\n", ile(0.0), min);
tprintf("Lower quartile=%.2f\n", ile(0.25));
tprintf("Median=%.2f, ile(0.5)=%.2f\n", median(), ile(0.5));
tprintf("Upper quartile=%.2f\n", ile(0.75));
tprintf("Max=%.2f Really=%d\n", ile(1.0), max);
tprintf("Range=%d\n", max + 1 - min);
tprintf("Mean= %.2f\n", mean());
tprintf("SD= %.2f\n", sd());
}
/**********************************************************************
* STATS::plot
*
* Draw a histogram of the stats table.
**********************************************************************/
#ifndef GRAPHICS_DISABLED
void STATS::plot(ScrollView* window, // to draw in
float xorigin, // bottom left
float yorigin,
float xscale, // one x unit
float yscale, // one y unit
ScrollView::Color colour) const { // colour to draw in
if (buckets_ == NULL) {
return;
}
window->Pen(colour);
for (int index = 0; index < rangemax_ - rangemin_; index++) {
window->Rectangle( xorigin + xscale * index, yorigin,
xorigin + xscale * (index + 1),
yorigin + yscale * buckets_[index]);
}
}
#endif
/**********************************************************************
* STATS::plotline
*
* Draw a histogram of the stats table. (Line only)
**********************************************************************/
#ifndef GRAPHICS_DISABLED
void STATS::plotline(ScrollView* window, // to draw in
float xorigin, // bottom left
float yorigin,
float xscale, // one x unit
float yscale, // one y unit
ScrollView::Color colour) const { // colour to draw in
if (buckets_ == NULL) {
return;
}
window->Pen(colour);
window->SetCursor(xorigin, yorigin + yscale * buckets_[0]);
for (int index = 0; index < rangemax_ - rangemin_; index++) {
window->DrawTo(xorigin + xscale * index,
yorigin + yscale * buckets_[index]);
}
}
#endif
/**********************************************************************
* choose_nth_item
*
* Returns the index of what would b the nth item in the array
* if the members were sorted, without actually sorting.
**********************************************************************/
inT32 choose_nth_item(inT32 index, float *array, inT32 count) {
inT32 next_sample; // next one to do
inT32 next_lesser; // space for new
inT32 prev_greater; // last one saved
inT32 equal_count; // no of equal ones
float pivot; // proposed median
float sample; // current sample
if (count <= 1)
return 0;
if (count == 2) {
if (array[0] < array[1]) {
return index >= 1 ? 1 : 0;
}
else {
return index >= 1 ? 0 : 1;
}
}
else {
if (index < 0)
index = 0; // ensure legal
else if (index >= count)
index = count - 1;
equal_count = (inT32) (rand() % count);
pivot = array[equal_count];
// fill gap
array[equal_count] = array[0];
next_lesser = 0;
prev_greater = count;
equal_count = 1;
for (next_sample = 1; next_sample < prev_greater;) {
sample = array[next_sample];
if (sample < pivot) {
// shuffle
array[next_lesser++] = sample;
next_sample++;
}
else if (sample > pivot) {
prev_greater--;
// juggle
array[next_sample] = array[prev_greater];
array[prev_greater] = sample;
}
else {
equal_count++;
next_sample++;
}
}
for (next_sample = next_lesser; next_sample < prev_greater;)
array[next_sample++] = pivot;
if (index < next_lesser)
return choose_nth_item (index, array, next_lesser);
else if (index < prev_greater)
return next_lesser; // in equal bracket
else
return choose_nth_item (index - prev_greater,
array + prev_greater,
count - prev_greater) + prev_greater;
}
}
/**********************************************************************
* choose_nth_item
*
* Returns the index of what would be the nth item in the array
* if the members were sorted, without actually sorting.
**********************************************************************/
inT32 choose_nth_item(inT32 index, void *array, inT32 count, size_t size,
int (*compar)(const void*, const void*)) {
int result; // of compar
inT32 next_sample; // next one to do
inT32 next_lesser; // space for new
inT32 prev_greater; // last one saved
inT32 equal_count; // no of equal ones
inT32 pivot; // proposed median
if (count <= 1)
return 0;
if (count == 2) {
if (compar (array, (char *) array + size) < 0) {
return index >= 1 ? 1 : 0;
}
else {
return index >= 1 ? 0 : 1;
}
}
if (index < 0)
index = 0; // ensure legal
else if (index >= count)
index = count - 1;
pivot = (inT32) (rand () % count);
swap_entries (array, size, pivot, 0);
next_lesser = 0;
prev_greater = count;
equal_count = 1;
for (next_sample = 1; next_sample < prev_greater;) {
result =
compar ((char *) array + size * next_sample,
(char *) array + size * next_lesser);
if (result < 0) {
swap_entries (array, size, next_lesser++, next_sample++);
// shuffle
}
else if (result > 0) {
prev_greater--;
swap_entries(array, size, prev_greater, next_sample);
}
else {
equal_count++;
next_sample++;
}
}
if (index < next_lesser)
return choose_nth_item (index, array, next_lesser, size, compar);
else if (index < prev_greater)
return next_lesser; // in equal bracket
else
return choose_nth_item (index - prev_greater,
(char *) array + size * prev_greater,
count - prev_greater, size,
compar) + prev_greater;
}
/**********************************************************************
* swap_entries
*
* Swap 2 entries of arbitrary size in-place in a table.
**********************************************************************/
void swap_entries(void *array, // array of entries
size_t size, // size of entry
inT32 index1, // entries to swap
inT32 index2) {
char tmp;
char *ptr1; // to entries
char *ptr2;
size_t count; // of bytes
ptr1 = reinterpret_cast<char*>(array) + index1 * size;
ptr2 = reinterpret_cast<char*>(array) + index2 * size;
for (count = 0; count < size; count++) {
tmp = *ptr1;
*ptr1++ = *ptr2;
*ptr2++ = tmp; // tedious!
}
}
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