/* ----------------------------------------------------------------------
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* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
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*
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* $Date: 17. January 2013
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* $Revision: V1.4.0
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*
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* Project: CMSIS DSP Library
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* Title: arm_matrix_example_f32.c
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*
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* Description: Example code demonstrating least square fit to data
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* using matrix functions
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*
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* Target Processor: Cortex-M4/Cortex-M3
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* - Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* - Neither the name of ARM LIMITED nor the names of its contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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* -------------------------------------------------------------------- */
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/**
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* @ingroup groupExamples
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*/
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/**
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* @defgroup MatrixExample Matrix Example
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*
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* \par Description:
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* \par
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* Demonstrates the use of Matrix Transpose, Matrix Muliplication, and Matrix Inverse
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* functions to apply least squares fitting to input data. Least squares fitting is
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* the procedure for finding the best-fitting curve that minimizes the sum of the
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* squares of the offsets (least square error) from a given set of data.
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*
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* \par Algorithm:
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* \par
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* The linear combination of parameters considered is as follows:
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* \par
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* <code>A * X = B</code>, where \c X is the unknown value and can be estimated
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* from \c A & \c B.
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* \par
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* The least squares estimate \c X is given by the following equation:
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* \par
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* <code>X = Inverse(A<sup>T</sup> * A) * A<sup>T</sup> * B</code>
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*
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* \par Block Diagram:
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* \par
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* \image html matrixExample.gif
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*
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* \par Variables Description:
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* \par
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* \li \c A_f32 input matrix in the linear combination equation
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* \li \c B_f32 output matrix in the linear combination equation
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* \li \c X_f32 unknown matrix estimated using \c A_f32 & \c B_f32 matrices
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*
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* \par CMSIS DSP Software Library Functions Used:
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* \par
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* - arm_mat_init_f32()
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* - arm_mat_trans_f32()
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* - arm_mat_mult_f32()
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* - arm_mat_inverse_f32()
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*
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* <b> Refer </b>
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* \link arm_matrix_example_f32.c \endlink
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*
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*/
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/** \example arm_matrix_example_f32.c
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*/
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#include "arm_math.h"
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#include "math_helper.h"
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#define SNR_THRESHOLD 90
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/* --------------------------------------------------------------------------------
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* Test input data(Cycles) taken from FIR Q15 module for differant cases of blockSize
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* and tapSize
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* --------------------------------------------------------------------------------- */
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const float32_t B_f32[4] =
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{
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782.0, 7577.0, 470.0, 4505.0
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};
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/* --------------------------------------------------------------------------------
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* Formula to fit is C1 + C2 * numTaps + C3 * blockSize + C4 * numTaps * blockSize
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* -------------------------------------------------------------------------------- */
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const float32_t A_f32[16] =
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{
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/* Const, numTaps, blockSize, numTaps*blockSize */
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1.0, 32.0, 4.0, 128.0,
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1.0, 32.0, 64.0, 2048.0,
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1.0, 16.0, 4.0, 64.0,
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1.0, 16.0, 64.0, 1024.0,
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};
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/* ----------------------------------------------------------------------
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* Temporary buffers for storing intermediate values
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* ------------------------------------------------------------------- */
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/* Transpose of A Buffer */
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float32_t AT_f32[16];
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/* (Transpose of A * A) Buffer */
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float32_t ATMA_f32[16];
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/* Inverse(Transpose of A * A) Buffer */
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float32_t ATMAI_f32[16];
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/* Test Output Buffer */
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float32_t X_f32[4];
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/* ----------------------------------------------------------------------
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* Reference ouput buffer C1, C2, C3 and C4 taken from MATLAB
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* ------------------------------------------------------------------- */
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const float32_t xRef_f32[4] = {73.0, 8.0, 21.25, 2.875};
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float32_t snr;
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/* ----------------------------------------------------------------------
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* Max magnitude FFT Bin test
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* ------------------------------------------------------------------- */
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int32_t main(void)
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{
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arm_matrix_instance_f32 A; /* Matrix A Instance */
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arm_matrix_instance_f32 AT; /* Matrix AT(A transpose) instance */
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arm_matrix_instance_f32 ATMA; /* Matrix ATMA( AT multiply with A) instance */
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arm_matrix_instance_f32 ATMAI; /* Matrix ATMAI(Inverse of ATMA) instance */
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arm_matrix_instance_f32 B; /* Matrix B instance */
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arm_matrix_instance_f32 X; /* Matrix X(Unknown Matrix) instance */
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uint32_t srcRows, srcColumns; /* Temporary variables */
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arm_status status;
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/* Initialise A Matrix Instance with numRows, numCols and data array(A_f32) */
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srcRows = 4;
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srcColumns = 4;
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arm_mat_init_f32(&A, srcRows, srcColumns, (float32_t *)A_f32);
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/* Initialise Matrix Instance AT with numRows, numCols and data array(AT_f32) */
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srcRows = 4;
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srcColumns = 4;
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arm_mat_init_f32(&AT, srcRows, srcColumns, AT_f32);
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/* calculation of A transpose */
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status = arm_mat_trans_f32(&A, &AT);
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/* Initialise ATMA Matrix Instance with numRows, numCols and data array(ATMA_f32) */
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srcRows = 4;
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srcColumns = 4;
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arm_mat_init_f32(&ATMA, srcRows, srcColumns, ATMA_f32);
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/* calculation of AT Multiply with A */
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status = arm_mat_mult_f32(&AT, &A, &ATMA);
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/* Initialise ATMAI Matrix Instance with numRows, numCols and data array(ATMAI_f32) */
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srcRows = 4;
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srcColumns = 4;
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arm_mat_init_f32(&ATMAI, srcRows, srcColumns, ATMAI_f32);
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/* calculation of Inverse((Transpose(A) * A) */
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status = arm_mat_inverse_f32(&ATMA, &ATMAI);
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/* calculation of (Inverse((Transpose(A) * A)) * Transpose(A)) */
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status = arm_mat_mult_f32(&ATMAI, &AT, &ATMA);
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/* Initialise B Matrix Instance with numRows, numCols and data array(B_f32) */
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srcRows = 4;
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srcColumns = 1;
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arm_mat_init_f32(&B, srcRows, srcColumns, (float32_t *)B_f32);
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/* Initialise X Matrix Instance with numRows, numCols and data array(X_f32) */
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srcRows = 4;
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srcColumns = 1;
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arm_mat_init_f32(&X, srcRows, srcColumns, X_f32);
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/* calculation ((Inverse((Transpose(A) * A)) * Transpose(A)) * B) */
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status = arm_mat_mult_f32(&ATMA, &B, &X);
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/* Comparison of reference with test output */
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snr = arm_snr_f32((float32_t *)xRef_f32, X_f32, 4);
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/*------------------------------------------------------------------------------
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* Initialise status depending on SNR calculations
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*------------------------------------------------------------------------------*/
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if ( snr > SNR_THRESHOLD)
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{
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status = ARM_MATH_SUCCESS;
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}
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else
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{
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status = ARM_MATH_TEST_FAILURE;
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}
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/* ----------------------------------------------------------------------
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** Loop here if the signals fail the PASS check.
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** This denotes a test failure
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** ------------------------------------------------------------------- */
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if ( status != ARM_MATH_SUCCESS)
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{
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while (1);
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}
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while (1); /* main function does not return */
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}
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/** \endlink */
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