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avutil/tests/lfg.c: added proper normality test

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The Chen-Shapiro(CS) test was used to test normality for
Lagged Fibonacci PRNG.

Normality Hypothesis Test:

The null hypothesis formally tests if the population
the sample represents is normally-distributed. For
CS, when the normality hypothesis is True, the
distribution of QH will have a mean close to 1.

Information on CS can be found here:

http://www.stata-journal.com/sjpdf.html?articlenum=st0264
http://www.originlab.com/doc/Origin-Help/NormalityTest-Algorithm

Signed-off-by: Thomas Turner <thomastdt@googlemail.com>
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>
pull/230/merge
Thomas Turner 8 years ago committed by Michael Niedermayer
parent 61926b6c3e
commit a50ccbd240
3 changed files with 1153 additions and 22 deletions
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  1. 164
      libavutil/tests/lfg.c
  2. 4
      tests/fate/libavutil.mak
  3. 1007
      tests/ref/fate/lfg

164
libavutil/tests/lfg.c
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@ -20,6 +20,85 @@
#include "libavutil/timer.h"
#include "libavutil/lfg.h"
static const double Z_TABLE[31][10] = {
{0.5000, 0.5040, 0.5080, 0.5120, 0.5160, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359},
{0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753},
{0.5793, 0.5832, 0.5871, 0.5910, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141},
{0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.6480, 0.6517},
{0.6554, 0.6591, 0.6628, 0.6664, 0.6700, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879},
{0.6915, 0.6950, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.7190, 0.7224},
{0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549},
{0.7580, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852},
{0.7881, 0.7910, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133},
{0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.8340, 0.8365, 0.8389},
{0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621},
{0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.8770, 0.8790, 0.8810, 0.8830},
{0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.8980, 0.8997, 0.9015},
{0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177},
{0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319},
{0.9332, 0.9345, 0.9357, 0.9370, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441},
{0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545},
{0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633},
{0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706},
{0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.9750, 0.9756, 0.9761, 0.9767},
{0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817},
{0.9821, 0.9826, 0.9830, 0.9834, 0.9838, 0.9842, 0.9846, 0.9850, 0.9854, 0.9857},
{0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.9890},
{0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916},
{0.9918, 0.9920, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936},
{0.9938, 0.9940, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952},
{0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.9960, 0.9961, 0.9962, 0.9963, 0.9964},
{0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.9970, 0.9971, 0.9972, 0.9973, 0.9974},
{0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.9980, 0.9981},
{0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986},
{0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.9990, 0.9990} };
// Inverse cumulative distribution function
static double inv_cdf(double u)
{
const double a[4] = { 2.50662823884,
-18.61500062529,
41.39119773534,
-25.44106049637};
const double b[4] = {-8.47351093090,
23.08336743743,
-21.06224101826,
3.13082909833};
const double c[9] = {0.3374754822726147,
0.9761690190917186,
0.1607979714918209,
0.0276438810333863,
0.0038405729373609,
0.0003951896511919,
0.0000321767881768,
0.0000002888167364,
0.0000003960315187};
double r;
double x = u - 0.5;
// Beasley-Springer
if (fabs(x) < 0.42) {
double y = x * x;
r = x * (((a[3]*y+a[2])*y+a[1])*y+a[0]) /
((((b[3]*y+b[2])*y+b[1])*y+b[0])*y+1.0);
}
else {// Moro
r = u;
if (x > 0.0)
r = 1.0 - u;
r = log(-log(r));
r = c[0] + r*(c[1]+r*(c[2]+r*(c[3]+r*(c[4]+r*(c[5]+r*(c[6]+
r*(c[7]+r*c[8])))))));
if (x < 0.0)
r = -r;
}
return r;
}
int main(void)
{
int x = 0;
@ -41,34 +120,75 @@ int main(void)
{
double mean = 1000;
double stddev = 53;
double samp_mean = 0.0, samp_stddev = 0.0;
double samp0, samp1;
double samp_mean = 0.0, samp_stddev = 0.0, QH = 0;
double Z, p_value = -1, tot_samp = 1000;
double *PRN_arr = av_malloc_array(tot_samp, sizeof(double));
av_lfg_init(&state, 42);
if (!PRN_arr) {
fprintf(stderr, "failed to allocate memory!\n");
return 1;
}
for (i = 0; i < 1000; i += 2) {
av_lfg_init(&state, 42);
for (i = 0; i < tot_samp; i += 2) {
double bmg_out[2];
av_bmg_get(&state, bmg_out);
samp0 = bmg_out[0] * stddev + mean;
samp1 = bmg_out[1] * stddev + mean;
samp_mean += samp0 + samp1;
samp_stddev += samp0 * samp0 + samp1 * samp1;
av_log(NULL, AV_LOG_INFO,
"%f\n%f\n",
samp0,
samp1);
PRN_arr[i ] = bmg_out[0] * stddev + mean;
PRN_arr[i+1] = bmg_out[1] * stddev + mean;
samp_mean += PRN_arr[i] + PRN_arr[i+1];
samp_stddev += PRN_arr[i] * PRN_arr[i] + PRN_arr[i+1] * PRN_arr[i+1];
printf("PRN%d : %f\n"
"PRN%d : %f\n",
i, PRN_arr[i], i+1, PRN_arr[i+1]);
}
/* TODO: add proper normality test */
samp_mean /= 1000;
samp_stddev /= 999;
samp_stddev -= (1000.0/999.0)*samp_mean*samp_mean;
samp_mean /= tot_samp;
samp_stddev /= (tot_samp - 1);
samp_stddev -= (tot_samp * 1.0 / (tot_samp - 1))*samp_mean*samp_mean;
samp_stddev = sqrt(samp_stddev);
av_log(NULL, AV_LOG_INFO, "sample mean : %f\n"
"true mean : %f\n"
"sample stddev: %f\n"
"true stddev : %f\n",
samp_mean, mean, samp_stddev, stddev);
}
Z = (mean - samp_mean) / (stddev / sqrt(tot_samp));
{
int x, y, a, b, flag = 0;
if (Z < 0.0) {
flag = !flag;
Z = Z * -1.0;
}
a = (int)(Z * 100);
b = ((int)Z * 100);
x = Z * 10;
y = (b > 0) ? a % b : a;
y = y % 10;
if (x > 30 || y > 9) {
av_log(NULL, AV_LOG_INFO, "error: out of bounds! tried to access"
"Z_TABLE[%d][%d]\n", x, y);
goto SKIP;
}
p_value = flag ? 1 - Z_TABLE[x][y] : Z_TABLE[x][y];
}
SKIP: for (i = 0; i < tot_samp; ++i) {
if ( i < (tot_samp - 1)) {
double H_diff;
H_diff = inv_cdf((i + 2.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
H_diff -= inv_cdf((i + 1.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
QH += ((PRN_arr[i + 1] - PRN_arr[i]) / H_diff);
}
}
QH = 1.0 - QH / ((tot_samp - 1.0) * samp_stddev);
printf("sample mean : %f\n"
"true mean : %f\n"
"sample stddev: %f\n"
"true stddev : %f\n"
"z-score : %f\n"
"p-value : %f\n"
"QH[normality]: %f\n",
samp_mean, mean, samp_stddev, stddev, Z, p_value, QH);
av_freep(&PRN_arr);
}
return 0;
}

4
tests/fate/libavutil.mak
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@ -101,6 +101,10 @@ FATE_LIBAVUTIL += fate-imgutils
fate-imgutils: libavutil/tests/imgutils$(EXESUF)
fate-imgutils: CMD = run libavutil/tests/imgutils
FATE_LIBAVUTIL += fate-lfg
fate-lfg: libavutil/tests/lfg$(EXESUF)
fate-lfg: CMD = run libavutil/tests/lfg
FATE_LIBAVUTIL += fate-md5
fate-md5: libavutil/tests/md5$(EXESUF)
fate-md5: CMD = run libavutil/tests/md5

1007
tests/ref/fate/lfg
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