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264 lines
8.3 KiB
C
264 lines
8.3 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_mat_inverse_f64.c
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* Description: Floating-point matrix inverse
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*
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* $Date: 23 April 2021
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* $Revision: V1.9.0
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*
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* Target Processor: Cortex-M and Cortex-A cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "dsp/matrix_functions.h"
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#include "dsp/matrix_utils.h"
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/**
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@ingroup groupMatrix
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*/
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/**
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@addtogroup MatrixInv
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@{
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*/
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/**
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@brief Floating-point (64 bit) matrix inverse.
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@param[in] pSrc points to input matrix structure. The source matrix is modified by the function.
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@param[out] pDst points to output matrix structure
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@return execution status
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- \ref ARM_MATH_SUCCESS : Operation successful
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- \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
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- \ref ARM_MATH_SINGULAR : Input matrix is found to be singular (non-invertible)
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*/
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arm_status arm_mat_inverse_f64(
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const arm_matrix_instance_f64 * pSrc,
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arm_matrix_instance_f64 * pDst)
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{
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float64_t *pIn = pSrc->pData; /* input data matrix pointer */
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float64_t *pOut = pDst->pData; /* output data matrix pointer */
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float64_t *pTmp;
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uint32_t numRows = pSrc->numRows; /* Number of rows in the matrix */
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uint32_t numCols = pSrc->numCols; /* Number of Cols in the matrix */
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float64_t pivot = 0.0, newPivot=0.0; /* Temporary input values */
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uint32_t selectedRow,pivotRow,i, rowNb, rowCnt, flag = 0U, j,column; /* loop counters */
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arm_status status; /* status of matrix inverse */
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#ifdef ARM_MATH_MATRIX_CHECK
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/* Check for matrix mismatch condition */
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if ((pSrc->numRows != pSrc->numCols) ||
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(pDst->numRows != pDst->numCols) ||
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(pSrc->numRows != pDst->numRows) )
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{
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/* Set status as ARM_MATH_SIZE_MISMATCH */
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status = ARM_MATH_SIZE_MISMATCH;
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}
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else
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#endif /* #ifdef ARM_MATH_MATRIX_CHECK */
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{
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/*--------------------------------------------------------------------------------------------------------------
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* Matrix Inverse can be solved using elementary row operations.
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*
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* Gauss-Jordan Method:
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*
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* 1. First combine the identity matrix and the input matrix separated by a bar to form an
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* augmented matrix as follows:
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* _ _ _ _
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* | a11 a12 | 1 0 | | X11 X12 |
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* | | | = | |
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* |_ a21 a22 | 0 1 _| |_ X21 X21 _|
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*
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* 2. In our implementation, pDst Matrix is used as identity matrix.
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*
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* 3. Begin with the first row. Let i = 1.
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*
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* 4. Check to see if the pivot for row i is zero.
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* The pivot is the element of the main diagonal that is on the current row.
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* For instance, if working with row i, then the pivot element is aii.
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* If the pivot is zero, exchange that row with a row below it that does not
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* contain a zero in column i. If this is not possible, then an inverse
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* to that matrix does not exist.
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*
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* 5. Divide every element of row i by the pivot.
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*
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* 6. For every row below and row i, replace that row with the sum of that row and
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* a multiple of row i so that each new element in column i below row i is zero.
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*
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* 7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
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* for every element below and above the main diagonal.
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*
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* 8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).
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* Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).
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*----------------------------------------------------------------------------------------------------------------*/
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/* Working pointer for destination matrix */
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pTmp = pOut;
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/* Loop over the number of rows */
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rowCnt = numRows;
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/* Making the destination matrix as identity matrix */
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while (rowCnt > 0U)
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{
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/* Writing all zeroes in lower triangle of the destination matrix */
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j = numRows - rowCnt;
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while (j > 0U)
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{
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*pTmp++ = 0.0;
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j--;
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}
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/* Writing all ones in the diagonal of the destination matrix */
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*pTmp++ = 1.0;
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/* Writing all zeroes in upper triangle of the destination matrix */
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j = rowCnt - 1U;
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while (j > 0U)
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{
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*pTmp++ = 0.0;
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j--;
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}
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/* Decrement loop counter */
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rowCnt--;
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}
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/* Loop over the number of columns of the input matrix.
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All the elements in each column are processed by the row operations */
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/* Index modifier to navigate through the columns */
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for(column = 0U; column < numCols; column++)
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{
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/* Check if the pivot element is zero..
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* If it is zero then interchange the row with non zero row below.
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* If there is no non zero element to replace in the rows below,
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* then the matrix is Singular. */
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pivotRow = column;
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/* Temporary variable to hold the pivot value */
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pTmp = ELEM(pSrc,column,column) ;
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pivot = *pTmp;
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selectedRow = column;
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/* Loop over the number rows present below */
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for (rowNb = column+1; rowNb < numRows; rowNb++)
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{
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/* Update the input and destination pointers */
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pTmp = ELEM(pSrc,rowNb,column);
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newPivot = *pTmp;
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if (fabs(newPivot) > fabs(pivot))
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{
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selectedRow = rowNb;
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pivot = newPivot;
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}
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}
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/* Check if there is a non zero pivot element to
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* replace in the rows below */
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if ((pivot != 0.0) && (selectedRow != column))
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{
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/* Loop over number of columns
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* to the right of the pilot element */
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SWAP_ROWS_F64(pSrc,column, pivotRow,selectedRow);
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SWAP_ROWS_F64(pDst,0, pivotRow,selectedRow);
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/* Flag to indicate whether exchange is done or not */
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flag = 1U;
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}
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/* Update the status if the matrix is singular */
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if ((flag != 1U) && (pivot == 0.0))
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{
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return ARM_MATH_SINGULAR;
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}
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/* Pivot element of the row */
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pivot = 1.0 / pivot;
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SCALE_ROW_F64(pSrc,column,pivot,pivotRow);
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SCALE_ROW_F64(pDst,0,pivot,pivotRow);
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/* Replace the rows with the sum of that row and a multiple of row i
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* so that each new element in column i above row i is zero.*/
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rowNb = 0;
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for (;rowNb < pivotRow; rowNb++)
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{
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pTmp = ELEM(pSrc,rowNb,column) ;
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pivot = *pTmp;
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MAS_ROW_F64(column,pSrc,rowNb,pivot,pSrc,pivotRow);
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MAS_ROW_F64(0 ,pDst,rowNb,pivot,pDst,pivotRow);
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}
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for (rowNb = pivotRow + 1; rowNb < numRows; rowNb++)
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{
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pTmp = ELEM(pSrc,rowNb,column) ;
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pivot = *pTmp;
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MAS_ROW_F64(column,pSrc,rowNb,pivot,pSrc,pivotRow);
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MAS_ROW_F64(0 ,pDst,rowNb,pivot,pDst,pivotRow);
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}
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}
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/* Set status as ARM_MATH_SUCCESS */
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status = ARM_MATH_SUCCESS;
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if ((flag != 1U) && (pivot == 0.0))
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{
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pIn = pSrc->pData;
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for (i = 0; i < numRows * numCols; i++)
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{
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if (pIn[i] != 0.0)
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break;
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}
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if (i == numRows * numCols)
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status = ARM_MATH_SINGULAR;
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}
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}
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/* Return to application */
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return (status);
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}
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/**
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@} end of MatrixInv group
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*/
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