text: /* ----------------------------------------------------------------------    
  * 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 == (float64_t) 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 > (float64_t) 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 > (float64_t) 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 == (float64_t) 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 == (float64_t) 0.0f))
      {
        pIn = pSrc->pData;
        for (i = 0; i < numRows * numCols; i++)
        {
          if (pIn[i] != (float64_t) 0.0f)
              break;
        }
        
        if (i == numRows * numCols)
          status = ARM_MATH_SINGULAR;
      }
    }
    /* Return to application */
    return (status);
  }
  
  /**    
   * @} end of MatrixInv group    
   */
  