CMSIS_5/CMSIS/DSP/Source/MatrixFunctions/arm_mat_inverse_f64.c

/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_mat_inverse_f64.c
 * Description:  Floating-point matrix inverse
 *
 * $Date:        23 April 2021
 * $Revision:    V1.9.0
 *
 * Target Processor: Cortex-M and Cortex-A cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2021 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;

    

      /* Check if the pivot element is zero */
      if (*pInT1 == 0.0)
      {
        /* Loop over the number rows present below */

        for (i = 1U; i < numRows - l; i++)
        {
          /* Update the input and destination pointers */
          pInT2 = pInT1 + (numCols * i);
          pOutT2 = pOutT1 + (numCols * i);

          /* 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;
          }


          /* Decrement loop counter */
        }
      }

      /* 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, 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;

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

          /* 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 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
 */