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py32f0-template/Libraries/CMSIS/DSP/Source/MatrixFunctions/arm_mat_inverse_f16.c
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/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_mat_inverse_f16.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_f16.h"
#if defined(ARM_FLOAT16_SUPPORTED)
/**
@ingroup groupMatrix
*/
/**
@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_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
arm_status arm_mat_inverse_f16(
const arm_matrix_instance_f16 * pSrc,
arm_matrix_instance_f16 * pDst)
{
float16_t *pIn = pSrc->pData; /* input data matrix pointer */
float16_t *pOut = pDst->pData; /* output data matrix pointer */
float16_t *pInT1, *pInT2; /* Temporary input data matrix pointer */
float16_t *pOutT1, *pOutT2; /* Temporary output data matrix pointer */
float16_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 */
float16_t *pTmpA, *pTmpB;
_Float16 in = 0.0f16; /* 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++ = 0.0f16;
j--;
}
/*
* Writing all ones in the diagonal of the destination matrix
*/
*pOutT1++ = 1.0f16;
/*
* Writing all zeroes in upper triangle of the destination matrix
*/
j = rowCnt - 1U;
while (j > 0U)
{
*pOutT1++ = 0.0f16;
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 ((_Float16)*pInT1 == 0.0f16)
{
/*
* 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 ((_Float16)*pInT2 != 0.0f16)
{
f16x8_t vecA, vecB;
/*
* Loop over number of columns
* * to the right of the pilot element
*/
pTmpA = pInT1;
pTmpB = pInT2;
blkCnt = (numCols - l) >> 3;
while (blkCnt > 0U)
{
vecA = vldrhq_f16(pTmpA);
vecB = vldrhq_f16(pTmpB);
vstrhq_f16(pTmpB, vecA);
vstrhq_f16(pTmpA, vecB);
pTmpA += 8;
pTmpB += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
* (will be merged thru tail predication)
*/
blkCnt = (numCols - l) & 7;
if (blkCnt > 0U)
{
mve_pred16_t p0 = vctp16q(blkCnt);
vecA = vldrhq_f16(pTmpA);
vecB = vldrhq_f16(pTmpB);
vstrhq_p_f16(pTmpB, vecA, p0);
vstrhq_p_f16(pTmpA, vecB, p0);
}
pInT1 += numCols - l;
pInT2 += numCols - l;
pTmpA = pOutT1;
pTmpB = pOutT2;
blkCnt = numCols >> 3;
while (blkCnt > 0U)
{
vecA = vldrhq_f16(pTmpA);
vecB = vldrhq_f16(pTmpB);
vstrhq_f16(pTmpB, vecA);
vstrhq_f16(pTmpA, vecB);
pTmpA += 8;
pTmpB += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
*/
blkCnt = numCols & 7;
if (blkCnt > 0U)
{
mve_pred16_t p0 = vctp16q(blkCnt);
vecA = vldrhq_f16(pTmpA);
vecB = vldrhq_f16(pTmpB);
vstrhq_p_f16(pTmpB, vecA, p0);
vstrhq_p_f16(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 == 0.0f16))
{
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;
f16x8_t invIn = vdupq_n_f16(1.0f16 / in);
blkCnt = (numCols - l) >> 3;
f16x8_t vecA;
while (blkCnt > 0U)
{
*(f16x8_t *) pTmpA = *(f16x8_t *) pTmpA * invIn;
pTmpA += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
*/
blkCnt = (numCols - l) & 7;
if (blkCnt > 0U)
{
mve_pred16_t p0 = vctp16q(blkCnt);
vecA = vldrhq_f16(pTmpA);
vecA = vecA * invIn;
vstrhq_p_f16(pTmpA, vecA, p0);
}
pInT1 += numCols - l;
/*
* Loop over number of columns
* * to the right of the pilot element
*/
pTmpA = pOutT1;
blkCnt = numCols >> 3;
while (blkCnt > 0U)
{
*(f16x8_t *) pTmpA = *(f16x8_t *) pTmpA *invIn;
pTmpA += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
* (will be merged thru tail predication)
*/
blkCnt = numCols & 7;
if (blkCnt > 0U)
{
mve_pred16_t p0 = vctp16q(blkCnt);
vecA = vldrhq_f16(pTmpA);
vecA = vecA * invIn;
vstrhq_p_f16(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;
f16x8_t tmpV = vdupq_n_f16(in);
blkCnt = (numCols - l) >> 3;
while (blkCnt > 0U)
{
f16x8_t vec1, vec2;
/*
* Replace the element by the sum of that row
* and a multiple of the reference row
*/
vec1 = vldrhq_f16(pInT1);
vec2 = vldrhq_f16(pPRT_in);
vec1 = vfmsq_f16(vec1, tmpV, vec2);
vstrhq_f16(pInT1, vec1);
pPRT_in += 8;
pInT1 += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
* (will be merged thru tail predication)
*/
blkCnt = (numCols - l) & 7;
if (blkCnt > 0U)
{
f16x8_t vec1, vec2;
mve_pred16_t p0 = vctp16q(blkCnt);
vec1 = vldrhq_f16(pInT1);
vec2 = vldrhq_f16(pPRT_in);
vec1 = vfmsq_f16(vec1, tmpV, vec2);
vstrhq_p_f16(pInT1, vec1, p0);
pInT1 += blkCnt;
}
blkCnt = numCols >> 3;
while (blkCnt > 0U)
{
f16x8_t vec1, vec2;
/*
* Replace the element by the sum of that row
* and a multiple of the reference row
*/
vec1 = vldrhq_f16(pOutT1);
vec2 = vldrhq_f16(pPRT_pDst);
vec1 = vfmsq_f16(vec1, tmpV, vec2);
vstrhq_f16(pOutT1, vec1);
pPRT_pDst += 8;
pOutT1 += 8;
/*
* Decrement the blockSize loop counter
*/
blkCnt--;
}
/*
* tail
* (will be merged thru tail predication)
*/
blkCnt = numCols & 7;
if (blkCnt > 0U)
{
f16x8_t vec1, vec2;
mve_pred16_t p0 = vctp16q(blkCnt);
vec1 = vldrhq_f16(pOutT1);
vec2 = vldrhq_f16(pPRT_pDst);
vec1 = vfmsq_f16(vec1, tmpV, vec2);
vstrhq_p_f16(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 == 0.0f16))
{
pIn = pSrc->pData;
for (i = 0; i < numRows * numCols; i++)
{
if ((_Float16)pIn[i] != 0.0f16)
break;
}
if (i == numRows * numCols)
status = ARM_MATH_SINGULAR;
}
}
/* Return to application */
return (status);
}
#else
arm_status arm_mat_inverse_f16(
const arm_matrix_instance_f16 * pSrc,
arm_matrix_instance_f16 * pDst)
{
float16_t *pIn = pSrc->pData; /* input data matrix pointer */
float16_t *pOut = pDst->pData; /* output data matrix pointer */
float16_t *pInT1, *pInT2; /* Temporary input data matrix pointer */
float16_t *pOutT1, *pOutT2; /* Temporary output data matrix pointer */
float16_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 */
_Float16 Xchg, in = 0.0f16, 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++ = 0.0f16;
j--;
}
/* Writing all ones in the diagonal of the destination matrix */
*pOutT1++ = 1.0f16;
/* Writing all zeroes in upper triangle of the destination matrix */
j = rowCnt - 1U;
while (j > 0U)
{
*pOutT1++ = 0.0f16;
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 ((_Float16)*pInT1 == 0.0f16)
{
/* 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 ((_Float16)*pInT2 != 0.0f16)
{
/* 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;
}
}
}
/* Update the status if the matrix is singular */
if ((flag != 1U) && (in == 0.0f16))
{
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++ = (_Float16)in1 - ((_Float16)in * (_Float16)*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++ = (_Float16)in1 - ((_Float16)in * (_Float16)*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++;
}
/* Set status as ARM_MATH_SUCCESS */
status = ARM_MATH_SUCCESS;
if ((flag != 1U) && ((_Float16)in == 0.0f16))
{
pIn = pSrc->pData;
for (i = 0; i < numRows * numCols; i++)
{
if ((_Float16)pIn[i] != 0.0f16)
break;
}
if (i == numRows * numCols)
status = ARM_MATH_SINGULAR;
}
}
/* Return to application */
return (status);
}
#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
/**
@} end of MatrixInv group
*/
#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */
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