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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_matrix_example_f32.c
*
* Description: Example code demonstrating least square fit to data
* using matrix functions
*
* 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 MatrixExample Matrix Example
*
* \par Description:
* \par
* Demonstrates the use of Matrix Transpose, Matrix Muliplication, and Matrix Inverse
* functions to apply least squares fitting to input data. Least squares fitting is
* the procedure for finding the best-fitting curve that minimizes the sum of the
* squares of the offsets (least square error) from a given set of data.
*
* \par Algorithm:
* \par
* The linear combination of parameters considered is as follows:
* \par
* <code>A * X = B</code>, where \c X is the unknown value and can be estimated
* from \c A & \c B.
* \par
* The least squares estimate \c X is given by the following equation:
* \par
* <code>X = Inverse(A<sup>T</sup> * A) * A<sup>T</sup> * B</code>
*
* \par Block Diagram:
* \par
* \image html matrixExample.gif
*
* \par Variables Description:
* \par
* \li \c A_f32 input matrix in the linear combination equation
* \li \c B_f32 output matrix in the linear combination equation
* \li \c X_f32 unknown matrix estimated using \c A_f32 & \c B_f32 matrices
*
* \par CMSIS DSP Software Library Functions Used:
* \par
* - arm_mat_init_f32()
* - arm_mat_trans_f32()
* - arm_mat_mult_f32()
* - arm_mat_inverse_f32()
*
* <b> Refer </b>
* \link arm_matrix_example_f32.c \endlink
*
*/
/** \example arm_matrix_example_f32.c
*/
#include "arm_math.h"
#include "math_helper.h"
#define SNR_THRESHOLD 90
/* --------------------------------------------------------------------------------
* Test input data(Cycles) taken from FIR Q15 module for differant cases of blockSize
* and tapSize
* --------------------------------------------------------------------------------- */
const float32_t B_f32[4] =
{
782.0, 7577.0, 470.0, 4505.0
};
/* --------------------------------------------------------------------------------
* Formula to fit is C1 + C2 * numTaps + C3 * blockSize + C4 * numTaps * blockSize
* -------------------------------------------------------------------------------- */
const float32_t A_f32[16] =
{
/* Const, numTaps, blockSize, numTaps*blockSize */
1.0, 32.0, 4.0, 128.0,
1.0, 32.0, 64.0, 2048.0,
1.0, 16.0, 4.0, 64.0,
1.0, 16.0, 64.0, 1024.0,
};
/* ----------------------------------------------------------------------
* Temporary buffers for storing intermediate values
* ------------------------------------------------------------------- */
/* Transpose of A Buffer */
float32_t AT_f32[16];
/* (Transpose of A * A) Buffer */
float32_t ATMA_f32[16];
/* Inverse(Transpose of A * A) Buffer */
float32_t ATMAI_f32[16];
/* Test Output Buffer */
float32_t X_f32[4];
/* ----------------------------------------------------------------------
* Reference ouput buffer C1, C2, C3 and C4 taken from MATLAB
* ------------------------------------------------------------------- */
const float32_t xRef_f32[4] = {73.0, 8.0, 21.25, 2.875};
float32_t snr;
/* ----------------------------------------------------------------------
* Max magnitude FFT Bin test
* ------------------------------------------------------------------- */
int32_t main(void)
{
arm_matrix_instance_f32 A; /* Matrix A Instance */
arm_matrix_instance_f32 AT; /* Matrix AT(A transpose) instance */
arm_matrix_instance_f32 ATMA; /* Matrix ATMA( AT multiply with A) instance */
arm_matrix_instance_f32 ATMAI; /* Matrix ATMAI(Inverse of ATMA) instance */
arm_matrix_instance_f32 B; /* Matrix B instance */
arm_matrix_instance_f32 X; /* Matrix X(Unknown Matrix) instance */
uint32_t srcRows, srcColumns; /* Temporary variables */
arm_status status;
/* Initialise A Matrix Instance with numRows, numCols and data array(A_f32) */
srcRows = 4;
srcColumns = 4;
arm_mat_init_f32(&A, srcRows, srcColumns, (float32_t *)A_f32);
/* Initialise Matrix Instance AT with numRows, numCols and data array(AT_f32) */
srcRows = 4;
srcColumns = 4;
arm_mat_init_f32(&AT, srcRows, srcColumns, AT_f32);
/* calculation of A transpose */
status = arm_mat_trans_f32(&A, &AT);
/* Initialise ATMA Matrix Instance with numRows, numCols and data array(ATMA_f32) */
srcRows = 4;
srcColumns = 4;
arm_mat_init_f32(&ATMA, srcRows, srcColumns, ATMA_f32);
/* calculation of AT Multiply with A */
status = arm_mat_mult_f32(&AT, &A, &ATMA);
/* Initialise ATMAI Matrix Instance with numRows, numCols and data array(ATMAI_f32) */
srcRows = 4;
srcColumns = 4;
arm_mat_init_f32(&ATMAI, srcRows, srcColumns, ATMAI_f32);
/* calculation of Inverse((Transpose(A) * A) */
status = arm_mat_inverse_f32(&ATMA, &ATMAI);
/* calculation of (Inverse((Transpose(A) * A)) * Transpose(A)) */
status = arm_mat_mult_f32(&ATMAI, &AT, &ATMA);
/* Initialise B Matrix Instance with numRows, numCols and data array(B_f32) */
srcRows = 4;
srcColumns = 1;
arm_mat_init_f32(&B, srcRows, srcColumns, (float32_t *)B_f32);
/* Initialise X Matrix Instance with numRows, numCols and data array(X_f32) */
srcRows = 4;
srcColumns = 1;
arm_mat_init_f32(&X, srcRows, srcColumns, X_f32);
/* calculation ((Inverse((Transpose(A) * A)) * Transpose(A)) * B) */
status = arm_mat_mult_f32(&ATMA, &B, &X);
/* Comparison of reference with test output */
snr = arm_snr_f32((float32_t *)xRef_f32, X_f32, 4);
/*------------------------------------------------------------------------------
* Initialise status depending on SNR calculations
*------------------------------------------------------------------------------*/
if ( snr > SNR_THRESHOLD)
{
status = ARM_MATH_SUCCESS;
}
else
{
status = ARM_MATH_TEST_FAILURE;
}
/* ----------------------------------------------------------------------
** Loop here if the signals fail the PASS check.
** This denotes a test failure
** ------------------------------------------------------------------- */
if ( status != ARM_MATH_SUCCESS)
{
while (1);
}
while (1); /* main function does not return */
}
/** \endlink */
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