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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,

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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

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* 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 */