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// Copyright 2006 Google Inc.
// All Rights Reserved.
// Author: <renn@google.com> (Marius Renn)
// Local includes
#include "debugging.h"
#include "mathfunctions.h"
// C includes
#include <math.h>
#include <stdlib.h>
unsigned helium::SquaredRoot(unsigned x) {
unsigned k = 0, c = 0;
for(unsigned o = 1; o <= x; o += k) {
k += 2;
c++;
}
return c;
}
unsigned helium::Binomi(unsigned n, int k) {
return ((n == k) || (k <= 1)) ? 1 : Binomi(n-1, k-1) + Binomi(n-1, k);
}
// This comparison function is required for qsort(...), which is used in
// the Median(...) function below.
int float_compare(const void* a, const void* b) {
const float* f_a = reinterpret_cast<const float*>(a);
const float* f_b = reinterpret_cast<const float*>(b);
return (*f_a > *f_b) ? 1 : ((*f_a < *f_b) ? -1 : 0);
}
float helium::Median(float* values, unsigned size) {
qsort(values, size, sizeof(float), float_compare);
return values[size / 2];
}
// I feel the need to defend the rare case of using macros here:
// To avoid having to actually swap a row value-by-value in memory, an internal
// list of n values is stored that map each index to the position of the row.
// To access an element in the matrix, a look-up must be made to access the
// correct row. These macros should simplify this access, and make the code
// more readable.
#define ELEM_A(ROW, COL) A[rows[ROW] * n + COL]
#define ELEM_B(ROW) b[rows[ROW]]
bool helium::Gauss(float* A, float* b, float* x, unsigned n) {
float tmp_x[n];
unsigned rows[n];
for (unsigned i = 0; i < n; i++) rows[i] = i;
// Diagonalization
for (unsigned i = 0; i < n; i++) {
// Find pivot
float max_val = fabs(ELEM_A(i, i));
float cur_val = 0.0;
unsigned r = i;
for (unsigned k = i + 1; k < n; k++) {
cur_val = fabs(ELEM_A(k, i));
if (cur_val > max_val) {
max_val = cur_val;
r = k;
}
}
// Swap rows to make pivot the current row
unsigned tmp = rows[r];
rows[r] = rows[i];
rows[i] = tmp;
if (max_val == 0.0) return false;
// Scale row and subtract
for (unsigned k = i + 1; k < n; k++) {
float cur_factor = ELEM_A(k, i) / max_val;
for (unsigned j = i; j < n; j++)
ELEM_A(k, j) = ELEM_A(k, j) - ELEM_A(i, j) * cur_factor;
ELEM_B(k) = ELEM_B(k) - ELEM_B(i) * cur_factor;
}
}
// Back substitution
for (int i = n - 1; i >= 0; i--) {
tmp_x[rows[i]] = ELEM_B(i);
for (unsigned j = n - 1; j > i; j--)
tmp_x[rows[i]] -= tmp_x[rows[j]] * ELEM_A(i, j);
tmp_x[rows[i]] /= ELEM_A(i, i);
}
// Swap back values
for (int i = 0; i < n; i++) x[i] = tmp_x[rows[i]];
return true;
}
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