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/* ----------------------------------------------------------------------
* 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:
* - Redistributions of source code must retain the above copyright
* 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
* the documentation and/or other materials provided with the
* 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
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
/**
* @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 <math.h>
#include "arm_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 */
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