Diff: cmsis_dsp/MatrixFunctions/arm_mat_inverse_f32.c

Revision:

5:a912b042151f

Parent:

4:9cee975aadce

--- a/cmsis_dsp/MatrixFunctions/arm_mat_inverse_f32.c	Mon Jun 23 09:30:09 2014 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,700 +0,0 @@
-/* ----------------------------------------------------------------------    
-* Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
-*    
-* $Date:        1. March 2013 
-* $Revision: 	V1.4.1
-*    
-* Project: 	    CMSIS DSP Library    
-* Title:	    arm_mat_inverse_f32.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 till 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_f32(
-  const arm_matrix_instance_f32 * pSrc,
-  arm_matrix_instance_f32 * pDst)
-{
-  float32_t *pIn = pSrc->pData;                  /* input data matrix pointer */
-  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
-  float32_t *pInT1, *pInT2;                      /* Temporary input data matrix pointer */
-  float32_t *pInT3, *pInT4;                      /* Temporary output data matrix pointer */
-  float32_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
-  float32_t maxC;                                /* maximum value in the column */
-
-  /* Run the below code for Cortex-M4 and Cortex-M3 */
-
-  float32_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 coluimns, 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 absolut 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 */
-    pInT2 = 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)
-      {
-        *pInT2++ = 0.0f;
-        j--;
-      }
-
-      /* Writing all ones in the diagonal of the destination matrix */
-      *pInT2++ = 1.0f;
-
-      /* Writing all zeroes in upper triangle of the destination matrix */
-      j = rowCnt - 1u;
-      while(j > 0u)
-      {
-        *pInT2++ = 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  */
-      pInT3 = pOut + (l * numCols);
-
-      /* Temporary variable to hold the pivot value */
-      in = *pInT1;
-
-      /* Destination pointer modifier */
-      k = 1u;
-
-     /* Grab the most significant value from column l */
-      maxC = 0;
-      for (i = 0; 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)
-      {
-        status = ARM_MATH_SINGULAR;
-        break;
-      }
-
-      /* Restore pInT1  */
-      pInT1 -= numRows * numCols;
-      
-      /* 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);
-          pInT4 = pInT3 + (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 = *pInT4;
-              *pInT4++ = *pInT3;
-              *pInT3++ = 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))
-      {
-        status = ARM_MATH_SINGULAR;
-
-        break;
-      }
-
-      /* 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 */
-
-  float32_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 */
-    pInT2 = 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)
-      {
-        *pInT2++ = 0.0f;
-        j--;
-      }
-
-      /* Writing all ones in the diagonal of the destination matrix */
-      *pInT2++ = 1.0f;
-
-      /* Writing all zeroes in upper triangle of the destination matrix */
-      j = rowCnt - 1u;
-      while(j > 0u)
-      {
-        *pInT2++ = 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  */
-      pInT3 = 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);
-          pInT4 = pInT3 + (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 = *pInT4;
-              *pInT4++ = *pInT3;
-              *pInT3++ = 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))
-      {
-        status = ARM_MATH_SINGULAR;
-
-        break;
-      }
-
-      /* 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 = *(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 */
-        *pInT2 = *pInT2 / in;
-        pInT2++;
-      }
-
-      /* 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;
-
-      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;
-          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 */
-          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  */
-            *pInT2 = *pInT2 - (in * *pPRT_pDst++);
-            pInT2++;
-          }
-
-        }
-        /* 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))
-    {
-      status = ARM_MATH_SINGULAR;
-    }
-  }
-  /* Return to application */
-  return (status);
-}
-
-/**    
- * @} end of MatrixInv group    
- */