692 lines
22 KiB
C
692 lines
22 KiB
C
|
/* ----------------------------------------------------------------------
|
||
|
|
* Project: CMSIS DSP Library
|
||
|
|
* Title: arm_mat_inverse_f64.c
|
||
|
|
* Description: Floating-point matrix inverse
|
||
|
|
*
|
||
|
|
* $Date: 27. January 2017
|
||
|
|
* $Revision: V.1.5.1
|
||
|
|
*
|
||
|
|
* Target Processor: Cortex-M cores
|
||
|
|
* -------------------------------------------------------------------- */
|
||
|
|
/*
|
||
|
|
* Copyright (C) 2010-2017 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 "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 until 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_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 maxC; /* maximum value in the column */
|
||
|
|
|
||
|
|
/* Run the below code for Cortex-M4 and Cortex-M3 */
|
||
|
|
|
||
|
|
float64_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 columns, 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 absolute 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 */
|
||
|
|
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++ = 0.0f;
|
||
|
|
j--;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Writing all ones in the diagonal of the destination matrix */
|
||
|
|
*pOutT1++ = 1.0f;
|
||
|
|
|
||
|
|
/* Writing all zeroes in upper triangle of the destination matrix */
|
||
|
|
j = rowCnt - 1U;
|
||
|
|
while (j > 0U)
|
||
|
|
{
|
||
|
|
*pOutT1++ = 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 */
|
||
|
|
pOutT1 = pOut + (l * numCols);
|
||
|
|
|
||
|
|
/* Temporary variable to hold the pivot value */
|
||
|
|
in = *pInT1;
|
||
|
|
|
||
|
|
/* Grab the most significant value from column l */
|
||
|
|
maxC = 0;
|
||
|
|
for (i = l; 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)
|
||
|
|
{
|
||
|
|
return ARM_MATH_SINGULAR;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Restore pInT1 */
|
||
|
|
pInT1 = pIn;
|
||
|
|
|
||
|
|
/* Destination pointer modifier */
|
||
|
|
k = 1U;
|
||
|
|
|
||
|
|
/* 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);
|
||
|
|
pOutT2 = pOutT1 + (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 = *pOutT2;
|
||
|
|
*pOutT2++ = *pOutT1;
|
||
|
|
*pOutT1++ = 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))
|
||
|
|
{
|
||
|
|
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 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 */
|
||
|
|
|
||
|
|
float64_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 */
|
||
|
|
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++ = 0.0f;
|
||
|
|
j--;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Writing all ones in the diagonal of the destination matrix */
|
||
|
|
*pOutT1++ = 1.0f;
|
||
|
|
|
||
|
|
/* Writing all zeroes in upper triangle of the destination matrix */
|
||
|
|
j = rowCnt - 1U;
|
||
|
|
while (j > 0U)
|
||
|
|
{
|
||
|
|
*pOutT1++ = 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 */
|
||
|
|
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 == 0.0f)
|
||
|
|
{
|
||
|
|
/* Loop over the number rows present below */
|
||
|
|
for (i = (l + 1U); i < numRows; i++)
|
||
|
|
{
|
||
|
|
/* Update the input and destination pointers */
|
||
|
|
pInT2 = pInT1 + (numCols * l);
|
||
|
|
pOutT2 = pOutT1 + (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 = *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 == 0.0f))
|
||
|
|
{
|
||
|
|
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 the 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 == 0.0f))
|
||
|
|
{
|
||
|
|
pIn = pSrc->pData;
|
||
|
|
for (i = 0; i < numRows * numCols; i++)
|
||
|
|
{
|
||
|
|
if (pIn[i] != 0.0f)
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (i == numRows * numCols)
|
||
|
|
status = ARM_MATH_SINGULAR;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* Return to application */
|
||
|
|
return (status);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @} end of MatrixInv group
|
||
|
|
*/
|