arm_mat_inverse_f64.c

/* ----------------------------------------------------------------------    
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
*    
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*    
* Project: 	    CMSIS DSP Library    
* Title:	    arm_mat_inverse_f64.c    
*    
* Description:	Floating-point matrix inverse.    
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* 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.    
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @ingroup groupMatrix    
 */

/**    
 * @defgroup MatrixInv Matrix Inverse    
 *    
 * Computes the inverse of a matrix.    
 *    
 * The inverse is defined only if the input matrix is square and non-singular (the determinant    
 * is non-zero). The function checks that the input and output matrices are square and of the    
 * same size.    
 *    
 * Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix    
 * inversion of floating-point matrices.    
 *    
 * \par Algorithm    
 * The Gauss-Jordan method is used to find the inverse.    
 * The algorithm performs a sequence of elementary row-operations until it    
 * reduces the input matrix to an identity matrix. Applying the same sequence    
 * of elementary row-operations to an identity matrix yields the inverse matrix.    
 * If the input matrix is singular, then the algorithm terminates and returns error status    
 * <code>ARM_MATH_SINGULAR</code>.    
 * \image html MatrixInverse.gif "Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method"    
 */

/**    
 * @addtogroup MatrixInv    
 * @{    
 */

/**    
 * @brief Floating-point matrix inverse.    
 * @param[in]       *pSrc points to input matrix structure    
 * @param[out]      *pDst points to output matrix structure    
 * @return     		The function returns    
 * <code>ARM_MATH_SIZE_MISMATCH</code> if the input matrix is not square or if the size    
 * of the output matrix does not match the size of the input matrix.    
 * If the input matrix is found to be singular (non-invertible), then the function returns    
 * <code>ARM_MATH_SINGULAR</code>.  Otherwise, the function returns <code>ARM_MATH_SUCCESS</code>.    
 */

arm_status arm_mat_inverse_f64(
  const arm_matrix_instance_f64 * pSrc,
  arm_matrix_instance_f64 * pDst)
{
  float64_t *pIn = pSrc->pData;                  /* input data matrix pointer */
  float64_t *pOut = pDst->pData;                 /* output data matrix pointer */
  float64_t *pInT1, *pInT2;                      /* Temporary input data matrix pointer */
  float64_t *pOutT1, *pOutT2;                    /* Temporary output data matrix pointer */
  float64_t *pPivotRowIn, *pPRT_in, *pPivotRowDst, *pPRT_pDst;  /* Temporary input and output data matrix pointer */
  uint32_t numRows = pSrc->numRows;              /* Number of rows in the matrix  */
  uint32_t numCols = pSrc->numCols;              /* Number of Cols in the matrix  */

#ifndef ARM_MATH_CM0_FAMILY
  float64_t maxC;                                /* maximum value in the column */

  /* Run the below code for Cortex-M4 and Cortex-M3 */

  float64_t Xchg, in = 0.0f, in1;                /* Temporary input values  */
  uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
  arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK


  /* Check for matrix mismatch condition */
  if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
     || (pSrc->numRows != pDst->numRows))
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else
#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */

  {

    /*--------------------------------------------------------------------------------------------------------------    
	 * Matrix Inverse can be solved using elementary row operations.    
	 *    
	 *	Gauss-Jordan Method:    
	 *    
	 *	   1. First combine the identity matrix and the input matrix separated by a bar to form an    
	 *        augmented matrix as follows:    
	 *				        _ 	      	       _         _	       _    
	 *					   |  a11  a12 | 1   0  |       |  X11 X12  |    
	 *					   |           |        |   =   |           |    
	 *					   |_ a21  a22 | 0   1 _|       |_ X21 X21 _|    
	 *    
	 *		2. In our implementation, pDst Matrix is used as identity matrix.    
	 *    
	 *		3. Begin with the first row. Let i = 1.    
	 *    
	 *	    4. Check to see if the pivot for column i is the greatest of the column.    
	 *		   The pivot is the element of the main diagonal that is on the current row.    
	 *		   For instance, if working with row i, then the pivot element is aii.    
	 *		   If the pivot is not the most significant of the columns, exchange that row with a row
	 *		   below it that does contain the most significant value in column i. If the most
	 *         significant value of the column is zero, then an inverse to that matrix does not exist.
	 *		   The most significant value of the column is the absolute maximum.
	 *    
	 *	    5. Divide every element of row i by the pivot.    
	 *    
	 *	    6. For every row below and  row i, replace that row with the sum of that row and    
	 *		   a multiple of row i so that each new element in column i below row i is zero.    
	 *    
	 *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros    
	 *		   for every element below and above the main diagonal.    
	 *    
	 *		8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).    
	 *		   Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).    
	 *----------------------------------------------------------------------------------------------------------------*/

    /* Working pointer for destination matrix */
    pOutT1 = pOut;

    /* Loop over the number of rows */
    rowCnt = numRows;

    /* Making the destination matrix as identity matrix */
    while(rowCnt > 0u)
    {
      /* Writing all zeroes in lower triangle of the destination matrix */
      j = numRows - rowCnt;
      while(j > 0u)
      {
        *pOutT1++ = 0.0f;
        j--;
      }

      /* Writing all ones in the diagonal of the destination matrix */
      *pOutT1++ = 1.0f;

      /* Writing all zeroes in upper triangle of the destination matrix */
      j = rowCnt - 1u;
      while(j > 0u)
      {
        *pOutT1++ = 0.0f;
        j--;
      }

      /* Decrement the loop counter */
      rowCnt--;
    }

    /* Loop over the number of columns of the input matrix.    
       All the elements in each column are processed by the row operations */
    loopCnt = numCols;

    /* Index modifier to navigate through the columns */
    l = 0u;

    while(loopCnt > 0u)
    {
      /* Check if the pivot element is zero..    
       * If it is zero then interchange the row with non zero row below.    
       * If there is no non zero element to replace in the rows below,    
       * then the matrix is Singular. */

      /* Working pointer for the input matrix that points    
       * to the pivot element of the particular row  */
      pInT1 = pIn + (l * numCols);

      /* Working pointer for the destination matrix that points    
       * to the pivot element of the particular row  */
      pOutT1 = pOut + (l * numCols);

      /* Temporary variable to hold the pivot value */
      in = *pInT1;

      /* Grab the most significant value from column l */
      maxC = 0;
      for (i = l; i < numRows; i++)
      {
        maxC = *pInT1 > 0 ? (*pInT1 > maxC ? *pInT1 : maxC) : (-*pInT1 > maxC ? -*pInT1 : maxC);
        pInT1 += numCols;
      }

      /* Update the status if the matrix is singular */
      if(maxC == 0.0f)
      {
        return ARM_MATH_SINGULAR;
      }

      /* Restore pInT1  */
      pInT1 = pIn;

      /* Destination pointer modifier */
      k = 1u;
      
      /* Check if the pivot element is the most significant of the column */
      if( (in > 0.0f ? in : -in) != maxC)
      {
        /* Loop over the number rows present below */
        i = numRows - (l + 1u);

        while(i > 0u)
        {
          /* Update the input and destination pointers */
          pInT2 = pInT1 + (numCols * l);
          pOutT2 = pOutT1 + (numCols * k);

          /* Look for the most significant element to    
           * replace in the rows below */
          if((*pInT2 > 0.0f ? *pInT2: -*pInT2) == maxC)
          {
            /* Loop over number of columns    
             * to the right of the pilot element */
            j = numCols - l;

            while(j > 0u)
            {
              /* Exchange the row elements of the input matrix */
              Xchg = *pInT2;
              *pInT2++ = *pInT1;
              *pInT1++ = Xchg;

              /* Decrement the loop counter */
              j--;
            }

            /* Loop over number of columns of the destination matrix */
            j = numCols;

            while(j > 0u)
            {
              /* Exchange the row elements of the destination matrix */
              Xchg = *pOutT2;
              *pOutT2++ = *pOutT1;
              *pOutT1++ = Xchg;

              /* Decrement the loop counter */
              j--;
            }

            /* Flag to indicate whether exchange is done or not */
            flag = 1u;

            /* Break after exchange is done */
            break;
          }

          /* Update the destination pointer modifier */
          k++;

          /* Decrement the loop counter */
          i--;
        }
      }

      /* Update the status if the matrix is singular */
      if((flag != 1u) && (in == 0.0f))
      {
        return ARM_MATH_SINGULAR;
      }

      /* Points to the pivot row of input and destination matrices */
      pPivotRowIn = pIn + (l * numCols);
      pPivotRowDst = pOut + (l * numCols);

      /* Temporary pointers to the pivot row pointers */
      pInT1 = pPivotRowIn;
      pInT2 = pPivotRowDst;

      /* Pivot element of the row */
      in = *pPivotRowIn;

      /* Loop over number of columns    
       * to the right of the pilot element */
      j = (numCols - l);

      while(j > 0u)
      {
        /* Divide each element of the row of the input matrix    
         * by the pivot element */
        in1 = *pInT1;
        *pInT1++ = in1 / in;

        /* Decrement the loop counter */
        j--;
      }

      /* Loop over number of columns of the destination matrix */
      j = numCols;

      while(j > 0u)
      {
        /* Divide each element of the row of the destination matrix    
         * by the pivot element */
        in1 = *pInT2;
        *pInT2++ = in1 / in;

        /* Decrement the loop counter */
        j--;
      }

      /* Replace the rows with the sum of that row and a multiple of row i    
       * so that each new element in column i above row i is zero.*/

      /* Temporary pointers for input and destination matrices */
      pInT1 = pIn;
      pInT2 = pOut;

      /* index used to check for pivot element */
      i = 0u;

      /* Loop over number of rows */
      /*  to be replaced by the sum of that row and a multiple of row i */
      k = numRows;

      while(k > 0u)
      {
        /* Check for the pivot element */
        if(i == l)
        {
          /* If the processing element is the pivot element,    
             only the columns to the right are to be processed */
          pInT1 += numCols - l;

          pInT2 += numCols;
        }
        else
        {
          /* Element of the reference row */
          in = *pInT1;

          /* Working pointers for input and destination pivot rows */
          pPRT_in = pPivotRowIn;
          pPRT_pDst = pPivotRowDst;

          /* Loop over the number of columns to the right of the pivot element,    
             to replace the elements in the input matrix */
          j = (numCols - l);

          while(j > 0u)
          {
            /* Replace the element by the sum of that row    
               and a multiple of the reference row  */
            in1 = *pInT1;
            *pInT1++ = in1 - (in * *pPRT_in++);

            /* Decrement the loop counter */
            j--;
          }

          /* Loop over the number of columns to    
             replace the elements in the destination matrix */
          j = numCols;

          while(j > 0u)
          {
            /* Replace the element by the sum of that row    
               and a multiple of the reference row  */
            in1 = *pInT2;
            *pInT2++ = in1 - (in * *pPRT_pDst++);

            /* Decrement the loop counter */
            j--;
          }

        }

        /* Increment the temporary input pointer */
        pInT1 = pInT1 + l;

        /* Decrement the loop counter */
        k--;

        /* Increment the pivot index */
        i++;
      }

      /* Increment the input pointer */
      pIn++;

      /* Decrement the loop counter */
      loopCnt--;

      /* Increment the index modifier */
      l++;
    }


#else

  /* Run the below code for Cortex-M0 */

  float64_t Xchg, in = 0.0f;                     /* Temporary input values  */
  uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
  arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
     || (pSrc->numRows != pDst->numRows))
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else
#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
  {

    /*--------------------------------------------------------------------------------------------------------------       
	 * Matrix Inverse can be solved using elementary row operations.        
	 *        
	 *	Gauss-Jordan Method:       
	 *	 	       
	 *	   1. First combine the identity matrix and the input matrix separated by a bar to form an        
	 *        augmented matrix as follows:        
	 *				        _  _	      _	    _	   _   _         _	       _       
	 *					   |  |  a11  a12  | | | 1   0  |   |       |  X11 X12  |         
	 *					   |  |            | | |        |   |   =   |           |        
	 *					   |_ |_ a21  a22 _| | |_0   1 _|  _|       |_ X21 X21 _|       
	 *					          
	 *		2. In our implementation, pDst Matrix is used as identity matrix.    
	 *       
	 *		3. Begin with the first row. Let i = 1.       
	 *       
	 *	    4. Check to see if the pivot for row i is zero.       
	 *		   The pivot is the element of the main diagonal that is on the current row.       
	 *		   For instance, if working with row i, then the pivot element is aii.       
	 *		   If the pivot is zero, exchange that row with a row below it that does not        
	 *		   contain a zero in column i. If this is not possible, then an inverse        
	 *		   to that matrix does not exist.       
	 *	       
	 *	    5. Divide every element of row i by the pivot.       
	 *	       
	 *	    6. For every row below and  row i, replace that row with the sum of that row and        
	 *		   a multiple of row i so that each new element in column i below row i is zero.       
	 *	       
	 *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros       
	 *		   for every element below and above the main diagonal.        
	 *		   		          
	 *		8. Now an identical matrix is formed to the left of the bar(input matrix, src).       
	 *		   Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).         
	 *----------------------------------------------------------------------------------------------------------------*/

    /* Working pointer for destination matrix */
    pOutT1 = pOut;

    /* Loop over the number of rows */
    rowCnt = numRows;

    /* Making the destination matrix as identity matrix */
    while(rowCnt > 0u)
    {
      /* Writing all zeroes in lower triangle of the destination matrix */
      j = numRows - rowCnt;
      while(j > 0u)
      {
        *pOutT1++ = 0.0f;
        j--;
      }

      /* Writing all ones in the diagonal of the destination matrix */
      *pOutT1++ = 1.0f;

      /* Writing all zeroes in upper triangle of the destination matrix */
      j = rowCnt - 1u;
      while(j > 0u)
      {
        *pOutT1++ = 0.0f;
        j--;
      }

      /* Decrement the loop counter */
      rowCnt--;
    }

    /* Loop over the number of columns of the input matrix.     
       All the elements in each column are processed by the row operations */
    loopCnt = numCols;

    /* Index modifier to navigate through the columns */
    l = 0u;
    //for(loopCnt = 0u; loopCnt < numCols; loopCnt++)   
    while(loopCnt > 0u)
    {
      /* Check if the pivot element is zero..    
       * If it is zero then interchange the row with non zero row below.   
       * If there is no non zero element to replace in the rows below,   
       * then the matrix is Singular. */

      /* Working pointer for the input matrix that points     
       * to the pivot element of the particular row  */
      pInT1 = pIn + (l * numCols);

      /* Working pointer for the destination matrix that points     
       * to the pivot element of the particular row  */
      pOutT1 = pOut + (l * numCols);

      /* Temporary variable to hold the pivot value */
      in = *pInT1;

      /* Destination pointer modifier */
      k = 1u;

      /* Check if the pivot element is zero */
      if(*pInT1 == 0.0f)
      {
        /* Loop over the number rows present below */
        for (i = (l + 1u); i < numRows; i++)
        {
          /* Update the input and destination pointers */
          pInT2 = pInT1 + (numCols * l);
          pOutT2 = pOutT1 + (numCols * k);

          /* Check if there is a non zero pivot element to     
           * replace in the rows below */
          if(*pInT2 != 0.0f)
          {
            /* Loop over number of columns     
             * to the right of the pilot element */
            for (j = 0u; j < (numCols - l); j++)
            {
              /* Exchange the row elements of the input matrix */
              Xchg = *pInT2;
              *pInT2++ = *pInT1;
              *pInT1++ = Xchg;
            }

            for (j = 0u; j < numCols; j++)
            {
              Xchg = *pOutT2;
              *pOutT2++ = *pOutT1;
              *pOutT1++ = Xchg;
            }

            /* Flag to indicate whether exchange is done or not */
            flag = 1u;

            /* Break after exchange is done */
            break;
          }

          /* Update the destination pointer modifier */
          k++;
        }
      }

      /* Update the status if the matrix is singular */
      if((flag != 1u) && (in == 0.0f))
      {
        return ARM_MATH_SINGULAR;
      }

      /* Points to the pivot row of input and destination matrices */
      pPivotRowIn = pIn + (l * numCols);
      pPivotRowDst = pOut + (l * numCols);

      /* Temporary pointers to the pivot row pointers */
      pInT1 = pPivotRowIn;
      pOutT1 = pPivotRowDst;

      /* Pivot element of the row */
      in = *(pIn + (l * numCols));

      /* Loop over number of columns     
       * to the right of the pilot element */
      for (j = 0u; j < (numCols - l); j++)
      {
        /* Divide each element of the row of the input matrix     
         * by the pivot element */
        *pInT1 = *pInT1 / in;
        pInT1++;
      }
      for (j = 0u; j < numCols; j++)
      {
        /* Divide each element of the row of the destination matrix     
         * by the pivot element */
        *pOutT1 = *pOutT1 / in;
        pOutT1++;
      }

      /* Replace the rows with the sum of that row and a multiple of row i     
       * so that each new element in column i above row i is zero.*/

      /* Temporary pointers for input and destination matrices */
      pInT1 = pIn;
      pOutT1 = pOut;

      for (i = 0u; i < numRows; i++)
      {
        /* Check for the pivot element */
        if(i == l)
        {
          /* If the processing element is the pivot element,     
             only the columns to the right are to be processed */
          pInT1 += numCols - l;
          pOutT1 += numCols;
        }
        else
        {
          /* Element of the reference row */
          in = *pInT1;

          /* Working pointers for input and destination pivot rows */
          pPRT_in = pPivotRowIn;
          pPRT_pDst = pPivotRowDst;

          /* Loop over the number of columns to the right of the pivot element,     
             to replace the elements in the input matrix */
          for (j = 0u; j < (numCols - l); j++)
          {
            /* Replace the element by the sum of that row     
               and a multiple of the reference row  */
            *pInT1 = *pInT1 - (in * *pPRT_in++);
            pInT1++;
          }
          /* Loop over the number of columns to     
             replace the elements in the destination matrix */
          for (j = 0u; j < numCols; j++)
          {
            /* Replace the element by the sum of that row     
               and a multiple of the reference row  */
            *pOutT1 = *pOutT1 - (in * *pPRT_pDst++);
            pOutT1++;
          }

        }
        /* Increment the temporary input pointer */
        pInT1 = pInT1 + l;
      }
      /* Increment the input pointer */
      pIn++;

      /* Decrement the loop counter */
      loopCnt--;
      /* Increment the index modifier */
      l++;
    }


#endif /* #ifndef ARM_MATH_CM0_FAMILY */

    /* Set status as ARM_MATH_SUCCESS */
    status = ARM_MATH_SUCCESS;

    if((flag != 1u) && (in == 0.0f))
    {
      pIn = pSrc->pData;
      for (i = 0; i < numRows * numCols; i++)
      {
        if (pIn[i] != 0.0f)
            break;
      }
      
      if (i == numRows * numCols)
        status = ARM_MATH_SINGULAR;
    }
  }
  /* Return to application */
  return (status);
}

/**    
 * @} end of MatrixInv group    
 */