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CMSIS/DSP/Source/MatrixFunctions/arm_mat_inverse_f64.c Normal file
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/* ----------------------------------------------------------------------
* 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"
#include "dsp/matrix_utils.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 *pTmp;
uint32_t numRows = pSrc->numRows; /* Number of rows in the matrix */
uint32_t numCols = pSrc->numCols; /* Number of Cols in the matrix */
float64_t pivot = 0.0, newPivot=0.0; /* Temporary input values */
uint32_t selectedRow,pivotRow,i, rowNb, rowCnt, flag = 0U, j,column; /* 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 */
pTmp = 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)
{
*pTmp++ = 0.0;
j--;
}
/* Writing all ones in the diagonal of the destination matrix */
*pTmp++ = 1.0;
/* Writing all zeroes in upper triangle of the destination matrix */
j = rowCnt - 1U;
while (j > 0U)
{
*pTmp++ = 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 */
/* Index modifier to navigate through the columns */
for(column = 0U; column < numCols; column++)
{
/* 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. */
pivotRow = column;
/* Temporary variable to hold the pivot value */
pTmp = ELEM(pSrc,column,column) ;
pivot = *pTmp;
selectedRow = column;
/* Loop over the number rows present below */
for (rowNb = column+1; rowNb < numRows; rowNb++)
{
/* Update the input and destination pointers */
pTmp = ELEM(pSrc,rowNb,column);
newPivot = *pTmp;
if (fabs(newPivot) > fabs(pivot))
{
selectedRow = rowNb;
pivot = newPivot;
}
}
/* Check if there is a non zero pivot element to
* replace in the rows below */
if ((pivot != 0.0) && (selectedRow != column))
{
/* Loop over number of columns
* to the right of the pilot element */
SWAP_ROWS_F64(pSrc,column, pivotRow,selectedRow);
SWAP_ROWS_F64(pDst,0, pivotRow,selectedRow);
/* Flag to indicate whether exchange is done or not */
flag = 1U;
}
/* Update the status if the matrix is singular */
if ((flag != 1U) && (pivot == 0.0))
{
return ARM_MATH_SINGULAR;
}
/* Pivot element of the row */
pivot = 1.0 / pivot;
SCALE_ROW_F64(pSrc,column,pivot,pivotRow);
SCALE_ROW_F64(pDst,0,pivot,pivotRow);
/* 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.*/
rowNb = 0;
for (;rowNb < pivotRow; rowNb++)
{
pTmp = ELEM(pSrc,rowNb,column) ;
pivot = *pTmp;
MAS_ROW_F64(column,pSrc,rowNb,pivot,pSrc,pivotRow);
MAS_ROW_F64(0 ,pDst,rowNb,pivot,pDst,pivotRow);
}
for (rowNb = pivotRow + 1; rowNb < numRows; rowNb++)
{
pTmp = ELEM(pSrc,rowNb,column) ;
pivot = *pTmp;
MAS_ROW_F64(column,pSrc,rowNb,pivot,pSrc,pivotRow);
MAS_ROW_F64(0 ,pDst,rowNb,pivot,pDst,pivotRow);
}
}
/* Set status as ARM_MATH_SUCCESS */
status = ARM_MATH_SUCCESS;
if ((flag != 1U) && (pivot == 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
*/