/* ----------------------------------------------------------------------
 * Copyright (C) 2010-2012 ARM Limited. All rights reserved.
 *
 * $Date:         17. January 2013
 * $Revision:     V1.4.0
 *
 * Project:       CMSIS DSP Library
 * Title:         arm_variance_example_f32.c
 *
 * Description:   Example code demonstrating variance calculation of input sequence.
 *
 * Target Processor: Cortex-M4/Cortex-M3
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
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 *     notice, this list of conditions and the following disclaimer.
 *   - Redistributions in binary form must reproduce the above copyright
 *     notice, this list of conditions and the following disclaimer in
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 *     distribution.
 *   - Neither the name of ARM LIMITED nor the names of its contributors
 *     may be used to endorse or promote products derived from this
 *     software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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 * -------------------------------------------------------------------- */

/**
 * @ingroup groupExamples
 */

/**
 * @defgroup VarianceExample Variance Example
 *
 * \par Description:
 * \par
 * Demonstrates the use of Basic Math and Support Functions to calculate the variance of an
 * input sequence with N samples. Uniformly distributed white noise is taken as input.
 *
 * \par Algorithm:
 * \par
 * The variance of a sequence is the mean of the squared deviation of the sequence from its mean.
 * \par
 * This is denoted by the following equation:
 * <pre> variance = ((x[0] - x') * (x[0] - x') + (x[1] - x') * (x[1] - x') + ... + * (x[n-1] - x') * (x[n-1] - x')) /
 * (N-1)</pre> where, <code>x[n]</code> is the input sequence, <code>N</code> is the number of input samples, and
 * <code>x'</code> is the mean value of the input sequence, <code>x[n]</code>.
 * \par
 * The mean value <code>x'</code> is defined as:
 * <pre> x' = (x[0] + x[1] + ... + x[n-1]) / N</pre>
 *
 * \par Block Diagram:
 * \par
 * \image html Variance.gif
 *
 *
 * \par Variables Description:
 * \par
 * \li \c testInput_f32 points to the input data
 * \li \c wire1, \c wir2, \c wire3 temporary buffers
 * \li \c blockSize number of samples processed at a time
 * \li \c refVarianceOut reference variance value
 *
 * \par CMSIS DSP Software Library Functions Used:
 * \par
 * - arm_dot_prod_f32()
 * - arm_mult_f32()
 * - arm_sub_f32()
 * - arm_fill_f32()
 * - arm_copy_f32()
 *
 * <b> Refer  </b>
 * \link arm_variance_example_f32.c \endlink
 *
 */

/** \example arm_variance_example_f32.c
 */
#include "arm_math.h"
#include <math.h>

/* ----------------------------------------------------------------------
 * Defines each of the tests performed
 * ------------------------------------------------------------------- */
#define MAX_BLOCKSIZE 32
#define DELTA (0.000001f)

/* ----------------------------------------------------------------------
 * Declare I/O buffers
 * ------------------------------------------------------------------- */
float32_t wire1[MAX_BLOCKSIZE];
float32_t wire2[MAX_BLOCKSIZE];
float32_t wire3[MAX_BLOCKSIZE];

/* ----------------------------------------------------------------------
 * Test input data for Floating point Variance example for 32-blockSize
 * Generated by the MATLAB randn() function
 * ------------------------------------------------------------------- */

float32_t testInput_f32[32] = {-0.432564811528221, -1.665584378238097, 0.125332306474831,  0.287676420358549,  -1.146471350681464, 1.190915465642999,
                               1.189164201652103,  -0.037633276593318, 0.327292361408654,  0.174639142820925,  -0.186708577681439, 0.725790548293303,
                               -0.588316543014189, 2.183185818197101,  -0.136395883086596, 0.113931313520810,  1.066768211359189,  0.059281460523605,
                               -0.095648405483669, -0.832349463650022, 0.294410816392640,  -1.336181857937804, 0.714324551818952,  1.623562064446271,
                               -0.691775701702287, 0.857996672828263,  1.254001421602532,  -1.593729576447477, -1.440964431901020, 0.571147623658178,
                               -0.399885577715363, 0.689997375464345

};

/* ----------------------------------------------------------------------
 * Declare Global variables
 * ------------------------------------------------------------------- */
uint32_t  blockSize      = 32;
float32_t refVarianceOut = 0.903941793931839;

/* ----------------------------------------------------------------------
 * Variance calculation test
 * ------------------------------------------------------------------- */

int32_t main(void)
{
    arm_status status;
    float32_t  mean, oneByBlockSize;
    float32_t  variance;
    float32_t  diff;

    status = ARM_MATH_SUCCESS;

    /* Calculation of mean value of input */

    /* x' = 1/blockSize * (x(0)* 1 + x(1) * 1 + ... + x(n-1) * 1) */

    /* Fill wire1 buffer with 1.0 value */
    arm_fill_f32(1.0, wire1, blockSize);

    /* Calculate the dot product of wire1 and wire2 */
    /* (x(0)* 1 + x(1) * 1 + ...+ x(n-1) * 1) */
    arm_dot_prod_f32(testInput_f32, wire1, blockSize, &mean);

    /* Calculation of 1/blockSize */
    oneByBlockSize = 1.0 / (blockSize);

    /* 1/blockSize * (x(0)* 1 + x(1) * 1 + ... + x(n-1) * 1)  */
    arm_mult_f32(&mean, &oneByBlockSize, &mean, 1);

    /* Calculation of variance value of input */

    /* (1/blockSize) * (x(0) - x') * (x(0) - x') + (x(1) - x') * (x(1) - x') + ... + (x(n-1) - x') * (x(n-1) - x') */

    /* Fill wire2 with mean value x' */
    arm_fill_f32(mean, wire2, blockSize);

    /* wire3 contains (x-x') */
    arm_sub_f32(testInput_f32, wire2, wire3, blockSize);

    /* wire2 contains (x-x') */
    arm_copy_f32(wire3, wire2, blockSize);

    /* (x(0) - x') * (x(0) - x') + (x(1) - x') * (x(1) - x') + ... + (x(n-1) - x') * (x(n-1) - x') */
    arm_dot_prod_f32(wire2, wire3, blockSize, &variance);

    /* Calculation of 1/blockSize */
    oneByBlockSize = 1.0 / (blockSize - 1);

    /* Calculation of variance */
    arm_mult_f32(&variance, &oneByBlockSize, &variance, 1);

    /* absolute value of difference between ref and test */
    diff = fabsf(refVarianceOut - variance);

    /* Comparison of variance value with reference */
    if (diff > DELTA) {
        status = ARM_MATH_TEST_FAILURE;
    }

    if (status != ARM_MATH_SUCCESS) {
        while (1)
            ;
    }

    while (1)
        ; /* main function does not return */
}

/** \endlink */
