sm64coopdx/tools/sdk-tools/tabledesign/estimate.c

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2019-08-25 04:58:46 +00:00
#include <math.h>
#include <stdlib.h>
#include "tabledesign.h"
/**
* Computes the autocorrelation of a vector. More precisely, it computes the
* dot products of vec[i:] and vec[:-i] for i in [0, k). Unused.
*
* See https://en.wikipedia.org/wiki/Autocorrelation.
*/
void acf(double *vec, int n, double *out, int k)
{
int i, j;
double sum;
for (i = 0; i < k; i++)
{
sum = 0.0;
for (j = 0; j < n - i; j++)
{
sum += vec[j + i] * vec[j];
}
out[i] = sum;
}
}
// https://en.wikipedia.org/wiki/Durbin%E2%80%93Watson_statistic ?
// "detects the presence of autocorrelation at lag 1 in the residuals (prediction errors)"
int durbin(double *arg0, int n, double *arg2, double *arg3, double *outSomething)
{
int i, j;
double sum, div;
int ret;
arg3[0] = 1.0;
div = arg0[0];
ret = 0;
for (i = 1; i <= n; i++)
{
sum = 0.0;
for (j = 1; j <= i-1; j++)
{
sum += arg3[j] * arg0[i - j];
}
arg3[i] = (div > 0.0 ? -(arg0[i] + sum) / div : 0.0);
arg2[i] = arg3[i];
if (fabs(arg2[i]) > 1.0)
{
ret++;
}
for (j = 1; j < i; j++)
{
arg3[j] += arg3[i - j] * arg3[i];
}
div *= 1.0 - arg3[i] * arg3[i];
}
*outSomething = div;
return ret;
}
void afromk(double *in, double *out, int n)
{
int i, j;
out[0] = 1.0;
for (i = 1; i <= n; i++)
{
out[i] = in[i];
for (j = 1; j <= i - 1; j++)
{
out[j] += out[i - j] * out[i];
}
}
}
int kfroma(double *in, double *out, int n)
{
int i, j;
double div;
double temp;
double *next;
int ret;
ret = 0;
next = malloc((n + 1) * sizeof(double));
out[n] = in[n];
for (i = n - 1; i >= 1; i--)
{
for (j = 0; j <= i; j++)
{
temp = out[i + 1];
div = 1.0 - (temp * temp);
if (div == 0.0)
{
free(next);
return 1;
}
next[j] = (in[j] - in[i + 1 - j] * temp) / div;
}
for (j = 0; j <= i; j++)
{
in[j] = next[j];
}
out[i] = next[i];
if (fabs(out[i]) > 1.0)
{
ret++;
}
}
free(next);
return ret;
}
void rfroma(double *arg0, int n, double *arg2)
{
int i, j;
double **mat;
double div;
mat = malloc((n + 1) * sizeof(double*));
mat[n] = malloc((n + 1) * sizeof(double));
mat[n][0] = 1.0;
for (i = 1; i <= n; i++)
{
mat[n][i] = -arg0[i];
}
for (i = n; i >= 1; i--)
{
mat[i - 1] = malloc(i * sizeof(double));
div = 1.0 - mat[i][i] * mat[i][i];
for (j = 1; j <= i - 1; j++)
{
mat[i - 1][j] = (mat[i][i - j] * mat[i][i] + mat[i][j]) / div;
}
}
arg2[0] = 1.0;
for (i = 1; i <= n; i++)
{
arg2[i] = 0.0;
for (j = 1; j <= i; j++)
{
arg2[i] += mat[i][j] * arg2[i - j];
}
}
free(mat[n]);
for (i = n; i > 0; i--)
{
free(mat[i - 1]);
}
free(mat);
}
double model_dist(double *arg0, double *arg1, int n)
{
double *sp3C;
double *sp38;
double ret;
int i, j;
sp3C = malloc((n + 1) * sizeof(double));
sp38 = malloc((n + 1) * sizeof(double));
rfroma(arg1, n, sp3C);
for (i = 0; i <= n; i++)
{
sp38[i] = 0.0;
for (j = 0; j <= n - i; j++)
{
sp38[i] += arg0[j] * arg0[i + j];
}
}
ret = sp38[0] * sp3C[0];
for (i = 1; i <= n; i++)
{
ret += 2 * sp3C[i] * sp38[i];
}
free(sp3C);
free(sp38);
return ret;
}
// compute autocorrelation matrix?
void acmat(short *in, int n, int m, double **out)
{
int i, j, k;
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
out[i][j] = 0.0;
for (k = 0; k < m; k++)
{
out[i][j] += in[k - i] * in[k - j];
}
}
}
}
// compute autocorrelation vector?
void acvect(short *in, int n, int m, double *out)
{
int i, j;
for (i = 0; i <= n; i++)
{
out[i] = 0.0;
for (j = 0; j < m; j++)
{
out[i] -= in[j - i] * in[j];
}
}
}
/**
* Replaces a real n-by-n matrix "a" with the LU decomposition of a row-wise
* permutation of itself.
*
* Input parameters:
* a: The matrix which is operated on. 1-indexed; it should be of size
* (n+1) x (n+1), and row/column index 0 is not used.
* n: The size of the matrix.
*
* Output parameters:
* indx: The row permutation performed. 1-indexed; it should be of size n+1,
* and index 0 is not used.
* d: the determinant of the permutation matrix.
*
* Returns 1 to indicate failure if the matrix is singular or has zeroes on the
* diagonal, 0 on success.
*
* Derived from ludcmp in "Numerical Recipes in C: The Art of Scientific Computing",
* with modified error handling.
*/
int lud(double **a, int n, int *indx, int *d)
{
int i,imax,j,k;
double big,dum,sum,temp;
double min,max;
double *vv;
vv = malloc((n + 1) * sizeof(double));
*d=1;
for (i=1;i<=n;i++) {
big=0.0;
for (j=1;j<=n;j++)
if ((temp=fabs(a[i][j])) > big) big=temp;
if (big == 0.0) return 1;
vv[i]=1.0/big;
}
for (j=1;j<=n;j++) {
for (i=1;i<j;i++) {
sum=a[i][j];
for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];
a[i][j]=sum;
}
big=0.0;
for (i=j;i<=n;i++) {
sum=a[i][j];
for (k=1;k<j;k++)
sum -= a[i][k]*a[k][j];
a[i][j]=sum;
if ( (dum=vv[i]*fabs(sum)) >= big) {
big=dum;
imax=i;
}
}
if (j != imax) {
for (k=1;k<=n;k++) {
dum=a[imax][k];
a[imax][k]=a[j][k];
a[j][k]=dum;
}
*d = -(*d);
vv[imax]=vv[j];
}
indx[j]=imax;
if (a[j][j] == 0.0) return 1;
if (j != n) {
dum=1.0/(a[j][j]);
for (i=j+1;i<=n;i++) a[i][j] *= dum;
}
}
free(vv);
min = 1e10;
max = 0.0;
for (i = 1; i <= n; i++)
{
temp = fabs(a[i][i]);
if (temp < min) min = temp;
if (temp > max) max = temp;
}
return min / max < 1e-10 ? 1 : 0;
}
/**
* Solves the set of n linear equations Ax = b, using LU decomposition
* back-substitution.
*
* Input parameters:
* a: The LU decomposition of a matrix, created by "lud".
* n: The size of the matrix.
* indx: Row permutation vector, created by "lud".
* b: The vector b in the equation. 1-indexed; is should be of size n+1, and
* index 0 is not used.
*
* Output parameters:
* b: The output vector x. 1-indexed.
*
* From "Numerical Recipes in C: The Art of Scientific Computing".
*/
void lubksb(double **a, int n, int *indx, double *b)
{
int i,ii=0,ip,j;
double sum;
for (i=1;i<=n;i++) {
ip=indx[i];
sum=b[ip];
b[ip]=b[i];
if (ii)
for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];
else if (sum) ii=i;
b[i]=sum;
}
for (i=n;i>=1;i--) {
sum=b[i];
for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];
b[i]=sum/a[i][i];
}
}