text: /* ----------------------------------------------------------------------
   * Project:      CMSIS DSP Library
   * Title:        arm_mat_inverse_f64.c
   * Description:  Floating-point matrix inverse
   *
   * $Date:        18. March 2019
   * $Revision:    V1.6.0
   *
   * Target Processor: Cortex-M cores
   * -------------------------------------------------------------------- */
  /*
   * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
   *
   * SPDX-License-Identifier: Apache-2.0
   *
   * Licensed under the Apache License, Version 2.0 (the License); you may
   * not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   *
   * www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an AS IS BASIS, WITHOUT
   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  #include "dsp/matrix_functions.h"
  
  /**
    @ingroup groupMatrix
   */
  
  
  /**
    @addtogroup MatrixInv
    @{
   */
  
  /**
    @brief         Floating-point (64 bit) matrix inverse.
    @param[in]     pSrc      points to input matrix structure. The source matrix is modified by the function.
    @param[out]    pDst      points to output matrix structure
    @return        execution status
                     - \ref ARM_MATH_SUCCESS       : Operation successful
                     - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
                     - \ref ARM_MATH_SINGULAR      : Input matrix is found to be singular (non-invertible)
   */
  
  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  */
  
  #if defined (ARM_MATH_DSP)
  
    float64_t Xchg, in = 0.0, 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 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, 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++ = 0.0;
          j--;
        }
  
        /* Writing all ones in the diagonal of the destination matrix */
        *pOutT1++ = 1.0;
  
        /* Writing all zeroes in upper triangle of the destination matrix */
        j = rowCnt - 1U;
        while (j > 0U)
        {
          *pOutT1++ = 0.0;
          j--;
        }
  
        /* Decrement 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;
  
        /* Destination pointer modifier */
        k = 1U;
  
        /* Check if the pivot element is zero */
        if (*pInT1 == 0.0)
        {
          /* Loop over the number rows present below */
          for (i = (l + 1U); i < numRows; i++)
          {
            /* Update the input and destination pointers */
            pInT2 = pInT1 + (numCols * i);
            pOutT2 = pOutT1 + (numCols * k);
  
            /* Check if there is a non zero pivot element to
             * replace in the rows below */
            if (*pInT2 != 0.0)
            {
              /* 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 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 loop counter */
            i--;
          }
        }
  
        /* Update the status if the matrix is singular */
        if ((flag != 1U) && (in == 0.0))
        {
          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 loop counter */
              j--;
            }
  
          }
  
          /* Increment temporary input pointer */
          pInT1 = pInT1 + l;
  
          /* Decrement loop counter */
          k--;
  
          /* Increment pivot index */
          i++;
        }
  
        /* Increment the input pointer */
        pIn++;
  
        /* Decrement the loop counter */
        loopCnt--;
  
        /* Increment the index modifier */
        l++;
      }
  
  
  #else
  
    float64_t Xchg, in = 0.0;                     /* 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++ = 0.0;
          j--;
        }
  
        /* Writing all ones in the diagonal of the destination matrix */
        *pOutT1++ = 1.0;
  
        /* Writing all zeroes in upper triangle of the destination matrix */
        j = rowCnt - 1U;
        while (j > 0U)
        {
          *pOutT1++ = 0.0;
          j--;
        }
  
        /* Decrement 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;
  
        /* Destination pointer modifier */
        k = 1U;
  
        /* Check if the pivot element is zero */
        if (*pInT1 == 0.0)
        {
          /* Loop over the number rows present below */
          for (i = (l + 1U); i < numRows; i++)
          {
            /* Update the input and destination pointers */
            pInT2 = pInT1 + (numCols * i);
            pOutT2 = pOutT1 + (numCols * k);
  
            /* Check if there is a non zero pivot element to
             * replace in the rows below */
            if (*pInT2 != 0.0)
            {
              /* 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 == 0.0))
        {
          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 temporary input pointer */
          pInT1 = pInT1 + l;
        }
  
        /* Increment the input pointer */
        pIn++;
  
        /* Decrement the loop counter */
        loopCnt--;
  
        /* Increment the index modifier */
        l++;
      }
  
  #endif /* #if defined (ARM_MATH_DSP) */
  
      /* Set status as ARM_MATH_SUCCESS */
      status = ARM_MATH_SUCCESS;
  
      if ((flag != 1U) && (in == 0.0))
      {
        pIn = pSrc->pData;
        for (i = 0; i < numRows * numCols; i++)
        {
          if (pIn[i] != 0.0)
              break;
        }
  
        if (i == numRows * numCols)
          status = ARM_MATH_SINGULAR;
      }
    }
  
    /* Return to application */
    return (status);
  }
  
  /**
    @} end of MatrixInv group
   */
  