mirror of
https://github.com/IcedRooibos/py32f0-template.git
synced 2025-10-31 09:52:05 -07:00
1571 lines
49 KiB
C
1571 lines
49 KiB
C
/* ----------------------------------------------------------------------
|
|
* Project: CMSIS DSP Library
|
|
* Title: arm_mat_inverse_f32.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
|
|
*/
|
|
|
|
/**
|
|
@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. 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)
|
|
*/
|
|
#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
|
|
|
|
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 *pOutT1, *pOutT2; /* 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 */
|
|
float32_t *pTmpA, *pTmpB;
|
|
|
|
float32_t in = 0.0f; /* Temporary input values */
|
|
uint32_t i, rowCnt, flag = 0U, j, loopCnt, l; /* loop counters */
|
|
arm_status status; /* status of matrix inverse */
|
|
uint32_t blkCnt;
|
|
|
|
#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;
|
|
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 == 0.0f)
|
|
{
|
|
/*
|
|
* 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 != 0.0f)
|
|
{
|
|
f32x4_t vecA, vecB;
|
|
/*
|
|
* Loop over number of columns
|
|
* * to the right of the pilot element
|
|
*/
|
|
pTmpA = pInT1;
|
|
pTmpB = pInT2;
|
|
blkCnt = (numCols - l) >> 2;
|
|
while (blkCnt > 0U)
|
|
{
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecB = vldrwq_f32(pTmpB);
|
|
vstrwq_f32(pTmpB, vecA);
|
|
vstrwq_f32(pTmpA, vecB);
|
|
|
|
pTmpA += 4;
|
|
pTmpB += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
* (will be merged thru tail predication)
|
|
*/
|
|
blkCnt = (numCols - l) & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecB = vldrwq_f32(pTmpB);
|
|
vstrwq_p_f32(pTmpB, vecA, p0);
|
|
vstrwq_p_f32(pTmpA, vecB, p0);
|
|
}
|
|
|
|
pInT1 += numCols - l;
|
|
pInT2 += numCols - l;
|
|
pTmpA = pOutT1;
|
|
pTmpB = pOutT2;
|
|
blkCnt = numCols >> 2;
|
|
while (blkCnt > 0U)
|
|
{
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecB = vldrwq_f32(pTmpB);
|
|
vstrwq_f32(pTmpB, vecA);
|
|
vstrwq_f32(pTmpA, vecB);
|
|
pTmpA += 4;
|
|
pTmpB += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
*/
|
|
blkCnt = numCols & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecB = vldrwq_f32(pTmpB);
|
|
vstrwq_p_f32(pTmpB, vecA, p0);
|
|
vstrwq_p_f32(pTmpA, vecB, p0);
|
|
}
|
|
|
|
pOutT1 += numCols;
|
|
pOutT2 += numCols;
|
|
/*
|
|
* 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 == 0.0f))
|
|
{
|
|
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));
|
|
|
|
pTmpA = pInT1;
|
|
|
|
f32x4_t invIn = vdupq_n_f32(1.0f / in);
|
|
|
|
blkCnt = (numCols - l) >> 2;
|
|
f32x4_t vecA;
|
|
while (blkCnt > 0U)
|
|
{
|
|
*(f32x4_t *) pTmpA = *(f32x4_t *) pTmpA * invIn;
|
|
pTmpA += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
*/
|
|
blkCnt = (numCols - l) & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecA = vecA * invIn;
|
|
vstrwq_p_f32(pTmpA, vecA, p0);
|
|
}
|
|
|
|
pInT1 += numCols - l;
|
|
/*
|
|
* Loop over number of columns
|
|
* * to the right of the pilot element
|
|
*/
|
|
|
|
pTmpA = pOutT1;
|
|
blkCnt = numCols >> 2;
|
|
while (blkCnt > 0U)
|
|
{
|
|
*(f32x4_t *) pTmpA = *(f32x4_t *) pTmpA *invIn;
|
|
pTmpA += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
* (will be merged thru tail predication)
|
|
*/
|
|
blkCnt = numCols & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
vecA = vldrwq_f32(pTmpA);
|
|
vecA = vecA * invIn;
|
|
vstrwq_p_f32(pTmpA, vecA, p0);
|
|
}
|
|
|
|
pOutT1 += numCols;
|
|
|
|
/*
|
|
* 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
|
|
*/
|
|
|
|
/*
|
|
* 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
|
|
*/
|
|
|
|
in = *pInT1;
|
|
f32x4_t tmpV = vdupq_n_f32(in);
|
|
|
|
blkCnt = (numCols - l) >> 2;
|
|
while (blkCnt > 0U)
|
|
{
|
|
f32x4_t vec1, vec2;
|
|
/*
|
|
* Replace the element by the sum of that row
|
|
* and a multiple of the reference row
|
|
*/
|
|
vec1 = vldrwq_f32(pInT1);
|
|
vec2 = vldrwq_f32(pPRT_in);
|
|
vec1 = vfmsq_f32(vec1, tmpV, vec2);
|
|
vstrwq_f32(pInT1, vec1);
|
|
pPRT_in += 4;
|
|
pInT1 += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
* (will be merged thru tail predication)
|
|
*/
|
|
blkCnt = (numCols - l) & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
f32x4_t vec1, vec2;
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
vec1 = vldrwq_f32(pInT1);
|
|
vec2 = vldrwq_f32(pPRT_in);
|
|
vec1 = vfmsq_f32(vec1, tmpV, vec2);
|
|
vstrwq_p_f32(pInT1, vec1, p0);
|
|
pInT1 += blkCnt;
|
|
}
|
|
|
|
blkCnt = numCols >> 2;
|
|
while (blkCnt > 0U)
|
|
{
|
|
f32x4_t vec1, vec2;
|
|
|
|
/*
|
|
* Replace the element by the sum of that row
|
|
* and a multiple of the reference row
|
|
*/
|
|
vec1 = vldrwq_f32(pOutT1);
|
|
vec2 = vldrwq_f32(pPRT_pDst);
|
|
vec1 = vfmsq_f32(vec1, tmpV, vec2);
|
|
vstrwq_f32(pOutT1, vec1);
|
|
pPRT_pDst += 4;
|
|
pOutT1 += 4;
|
|
/*
|
|
* Decrement the blockSize loop counter
|
|
*/
|
|
blkCnt--;
|
|
}
|
|
/*
|
|
* tail
|
|
* (will be merged thru tail predication)
|
|
*/
|
|
blkCnt = numCols & 3;
|
|
if (blkCnt > 0U)
|
|
{
|
|
f32x4_t vec1, vec2;
|
|
mve_pred16_t p0 = vctp32q(blkCnt);
|
|
|
|
vec1 = vldrwq_f32(pOutT1);
|
|
vec2 = vldrwq_f32(pPRT_pDst);
|
|
vec1 = vfmsq_f32(vec1, tmpV, vec2);
|
|
vstrwq_p_f32(pOutT1, vec1, p0);
|
|
|
|
pInT2 += blkCnt;
|
|
pOutT1 += blkCnt;
|
|
}
|
|
}
|
|
/*
|
|
* Increment the temporary input pointer
|
|
*/
|
|
pInT1 = pInT1 + l;
|
|
}
|
|
/*
|
|
* Increment the input pointer
|
|
*/
|
|
pIn++;
|
|
/*
|
|
* Decrement the loop counter
|
|
*/
|
|
loopCnt--;
|
|
/*
|
|
* Increment the index modifier
|
|
*/
|
|
l++;
|
|
}
|
|
|
|
/*
|
|
* 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);
|
|
}
|
|
|
|
#else
|
|
#if defined(ARM_MATH_NEON)
|
|
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 *pOutT1, *pOutT2; /* 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 */
|
|
|
|
|
|
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 */
|
|
float32x4_t vec1;
|
|
float32x4_t vec2;
|
|
float32x4_t tmpV;
|
|
|
|
#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++ = 0.0f;
|
|
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;
|
|
|
|
/* Check if the pivot element is zero */
|
|
if (*pInT1 == 0.0f)
|
|
{
|
|
/* 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 != 0.0f)
|
|
{
|
|
/* 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 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;
|
|
tmpV = vdupq_n_f32(1.0f/in);
|
|
|
|
/* Loop over number of columns
|
|
* to the right of the pilot element */
|
|
j = (numCols - l) >> 2;
|
|
|
|
while (j > 0U)
|
|
{
|
|
/* Divide each element of the row of the input matrix
|
|
* by the pivot element */
|
|
vec1 = vld1q_f32(pInT1);
|
|
|
|
vec1 = vmulq_f32(vec1, tmpV);
|
|
vst1q_f32(pInT1, vec1);
|
|
pInT1 += 4;
|
|
|
|
/* Decrement the loop counter */
|
|
j--;
|
|
}
|
|
|
|
/* Tail */
|
|
j = (numCols - l) & 3;
|
|
|
|
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 >> 2;
|
|
|
|
while (j > 0U)
|
|
{
|
|
/* Divide each element of the row of the destination matrix
|
|
* by the pivot element */
|
|
vec1 = vld1q_f32(pInT2);
|
|
|
|
vec1 = vmulq_f32(vec1, tmpV);
|
|
vst1q_f32(pInT2, vec1);
|
|
pInT2 += 4;
|
|
|
|
/* Decrement the loop counter */
|
|
j--;
|
|
}
|
|
|
|
/* Tail */
|
|
j = numCols & 3;
|
|
|
|
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;
|
|
tmpV = vdupq_n_f32(in);
|
|
|
|
/* 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) >> 2;
|
|
|
|
while (j > 0U)
|
|
{
|
|
/* Replace the element by the sum of that row
|
|
and a multiple of the reference row */
|
|
vec1 = vld1q_f32(pInT1);
|
|
vec2 = vld1q_f32(pPRT_in);
|
|
vec1 = vmlsq_f32(vec1, tmpV, vec2);
|
|
vst1q_f32(pInT1, vec1);
|
|
pPRT_in += 4;
|
|
pInT1 += 4;
|
|
|
|
/* Decrement the loop counter */
|
|
j--;
|
|
}
|
|
|
|
/* Tail */
|
|
j = (numCols - l) & 3;
|
|
|
|
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 >> 2;
|
|
|
|
while (j > 0U)
|
|
{
|
|
/* Replace the element by the sum of that row
|
|
and a multiple of the reference row */
|
|
vec1 = vld1q_f32(pInT2);
|
|
vec2 = vld1q_f32(pPRT_pDst);
|
|
vec1 = vmlsq_f32(vec1, tmpV, vec2);
|
|
vst1q_f32(pInT2, vec1);
|
|
pPRT_pDst += 4;
|
|
pInT2 += 4;
|
|
|
|
/* Decrement the loop counter */
|
|
j--;
|
|
}
|
|
|
|
/* Tail */
|
|
j = numCols & 3;
|
|
|
|
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++;
|
|
}
|
|
|
|
/* 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);
|
|
}
|
|
#else
|
|
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 *pOutT1, *pOutT2; /* 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 */
|
|
|
|
#if defined (ARM_MATH_DSP)
|
|
|
|
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 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++ = 0.0f;
|
|
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 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 == 0.0f)
|
|
{
|
|
/* 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 != 0.0f)
|
|
{
|
|
/* 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 == 0.0f))
|
|
{
|
|
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 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
|
|
|
|
float32_t Xchg, in = 0.0f; /* 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++ = 0.0f;
|
|
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 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 == 0.0f)
|
|
{
|
|
/* 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 != 0.0f)
|
|
{
|
|
/* 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 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 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);
|
|
}
|
|
#endif /* #if defined(ARM_MATH_NEON) */
|
|
#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
|
|
|
|
/**
|
|
@} end of MatrixInv group
|
|
*/
|