realtime_stats.c File Reference

Compute statistics for data entered in rreal-time. More...

#include <assert.h>
#include <math.h>
#include <stdio.h>

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Functions
void	stats_computer1 (float x, float *mean, float *variance, float *std)
	continuous mean and variance computance using first value as an approximation for the mean. More...
void	stats_computer2 (float x, float *mean, float *variance, float *std)
	continuous mean and variance computance using Welford's algorithm (very accurate) More...
void	test_function (const float *test_data, const int number_of_samples)
	Test the algorithm implementation. More...
int	main (int argc, char **argv)
	Main function. More...

Detailed Description

Compute statistics for data entered in rreal-time.

Author

Krishna Vedala

This algorithm is really beneficial to compute statistics on data read in realtime. For example, devices reading biometrics data. The algorithm is simple enough to be easily implemented in an embedded system.

Function Documentation

main()

int main	(	int	argc,
		char **	argv
	)

Main function.

{
    const float test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};
    test_function(test_data1, sizeof(test_data1) / sizeof(test_data1[0]));
 
    float s1_mean = 0.f, s1_variance = 0.f, s1_std = 0.f;
    float s2_mean = 0.f, s2_variance = 0.f, s2_std = 0.f;
 
    printf("Enter data. Any non-numeric data will terminate the data input.\n");
 
    while (1)
    {
        float val;
        printf("Enter number: ");
 
        // check for failure to read input. Happens for
        // non-numeric data
        if (!scanf("%f", &val))
            break;
 
        stats_computer1(val, &s1_mean, &s1_variance, &s1_std);
        stats_computer2(val, &s2_mean, &s2_variance, &s2_std);
 
        printf("\tMethod 1:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n",
               s1_mean, s1_variance, s1_std);
        printf("\tMethod 2:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n",
               s2_mean, s2_variance, s2_std);
    }
 
    return 0;
}

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stats_computer1()

void stats_computer1	(	float	x,
		float *	mean,
		float *	variance,
		float *	std
	)

continuous mean and variance computance using first value as an approximation for the mean.

If the first number is much far form the mean, the algorithm becomes very inaccurate to compute variance and standard deviation.

Parameters

[in]	x	new value added to data set
[out]	mean	if not NULL, mean returns mean of data set
[out]	variance	if not NULL, mean returns variance of data set
[out]	std	if not NULL, mean returns standard deviation of data set

{
    /* following variables declared static becuase they need to be remembered
     * when updating for next sample, when received.
     */
    static unsigned int n = 0;
    static float Ex = 0.f, Ex2 = 0.f;
    static float K = 0.f;
 
    if (n == 0)
        K = x;
    n++;
    float tmp = x - K;
    Ex += tmp;
    Ex2 += tmp * tmp;
 
    /* return sample mean computed till last sample */
    if (mean != NULL)
        *mean = K + Ex / n;
 
    /* return data variance computed till last sample */
    if (variance != NULL)
        *variance = (Ex2 - (Ex * Ex) / n) / (n - 1);
 
    /* return sample standard deviation computed till last sample */
    if (std != NULL)
        *std = sqrtf(*variance);
}

stats_computer2()

void stats_computer2	(	float	x,
		float *	mean,
		float *	variance,
		float *	std
	)

continuous mean and variance computance using Welford's algorithm (very accurate)

Parameters

[in]	x	new value added to data set
[out]	mean	if not NULL, mean returns mean of data set
[out]	variance	if not NULL, mean returns variance of data set
[out]	std	if not NULL, mean returns standard deviation of data set

{
    /* following variables declared static becuase they need to be remembered
     * when updating for next sample, when received.
     */
    static unsigned int n = 0;
    static float mu = 0, M = 0;
 
    n++;
    float delta = x - mu;
    mu += delta / n;
    float delta2 = x - mu;
    M += delta * delta2;
 
    /* return sample mean computed till last sample */
    if (mean != NULL)
        *mean = mu;
 
    /* return data variance computed till last sample */
    if (variance != NULL)
        *variance = M / n;
 
    /* return sample standard deviation computed till last sample */
    if (std != NULL)
        *std = sqrtf(*variance);
}

test_function()

void test_function	(	const float *	test_data,
		const int	number_of_samples
	)

Test the algorithm implementation.

Parameters

[in]	test_data	array of data to test the algorithms
[in]	number_of_samples	number of samples of data

{
    float ref_mean = 0.f, ref_variance = 0.f;
    float s1_mean = 0.f, s1_variance = 0.f, s1_std = 0.f;
    float s2_mean = 0.f, s2_variance = 0.f, s2_std = 0.f;
 
    for (int i = 0; i < number_of_samples; i++)
    {
        stats_computer1(test_data[i], &s1_mean, &s1_variance, &s1_std);
        stats_computer2(test_data[i], &s2_mean, &s2_variance, &s2_std);
        ref_mean += test_data[i];
    }
    ref_mean /= number_of_samples;
 
    for (int i = 0; i < number_of_samples; i++)
    {
        float temp = test_data[i] - ref_mean;
        ref_variance += temp * temp;
    }
    ref_variance /= number_of_samples;
 
    printf("<<<<<<<< Test Function >>>>>>>>\n");
    printf("Expected: Mean: %.4f\t Variance: %.4f\n", ref_mean, ref_variance);
    printf("\tMethod 1:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n", s1_mean,
           s1_variance, s1_std);
    printf("\tMethod 2:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n", s2_mean,
           s2_variance, s2_std);
 
    assert(fabs(s1_mean - ref_mean) < 0.01);
    assert(fabs(s2_mean - ref_mean) < 0.01);
    assert(fabs(s2_variance - ref_variance) < 0.01);
 
    printf("(Tests passed)\n\n");
}

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