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/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_mat_cholesky_f16.c
* Description: Floating-point Cholesky decomposition
*
* $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 MatrixChol
@{
*/
/**
* @brief Floating-point Cholesky decomposition of positive-definite matrix.
* @param[in] pSrc points to the instance of the input floating-point matrix structure.
* @param[out] pDst points to the instance of the output floating-point matrix structure.
* @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
* @return execution status
- \ref ARM_MATH_SUCCESS : Operation successful
- \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
- \ref ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed
* @par
* If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition.
* The decomposition of A is returning a lower triangular matrix U such that A = U U^t
*/
#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
#include "arm_helium_utils.h"
arm_status arm_mat_cholesky_f16(
const arm_matrix_instance_f16 * pSrc,
arm_matrix_instance_f16 * pDst)
{
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 */
{
int i,j,k;
int n = pSrc->numRows;
_Float16 invSqrtVj;
float16_t *pA,*pG;
int kCnt;
mve_pred16_t p0;
f16x8_t acc, acc0, acc1, acc2, acc3;
f16x8_t vecGi;
f16x8_t vecGj,vecGj0,vecGj1,vecGj2,vecGj3;
pA = pSrc->pData;
pG = pDst->pData;
for(i=0 ;i < n ; i++)
{
for(j=i ; j+3 < n ; j+=4)
{
acc0 = vdupq_n_f16(0.0f16);
acc0[0]=pA[(j + 0) * n + i];
acc1 = vdupq_n_f16(0.0f16);
acc1[0]=pA[(j + 1) * n + i];
acc2 = vdupq_n_f16(0.0f16);
acc2[0]=pA[(j + 2) * n + i];
acc3 = vdupq_n_f16(0.0f16);
acc3[0]=pA[(j + 3) * n + i];
kCnt = i;
for(k=0; k < i ; k+=8)
{
p0 = vctp16q(kCnt);
vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
vecGj0=vldrhq_z_f16(&pG[(j + 0) * n + k],p0);
vecGj1=vldrhq_z_f16(&pG[(j + 1) * n + k],p0);
vecGj2=vldrhq_z_f16(&pG[(j + 2) * n + k],p0);
vecGj3=vldrhq_z_f16(&pG[(j + 3) * n + k],p0);
acc0 = vfmsq_m(acc0, vecGi, vecGj0, p0);
acc1 = vfmsq_m(acc1, vecGi, vecGj1, p0);
acc2 = vfmsq_m(acc2, vecGi, vecGj2, p0);
acc3 = vfmsq_m(acc3, vecGi, vecGj3, p0);
kCnt -= 8;
}
pG[(j + 0) * n + i] = vecAddAcrossF16Mve(acc0);
pG[(j + 1) * n + i] = vecAddAcrossF16Mve(acc1);
pG[(j + 2) * n + i] = vecAddAcrossF16Mve(acc2);
pG[(j + 3) * n + i] = vecAddAcrossF16Mve(acc3);
}
for(; j < n ; j++)
{
kCnt = i;
acc = vdupq_n_f16(0.0f16);
acc[0] = pA[j * n + i];
for(k=0; k < i ; k+=8)
{
p0 = vctp16q(kCnt);
vecGi=vldrhq_z_f16(&pG[i * n + k],p0);
vecGj=vldrhq_z_f16(&pG[j * n + k],p0);
acc = vfmsq_m(acc, vecGi, vecGj,p0);
kCnt -= 8;
}
pG[j * n + i] = vecAddAcrossF16Mve(acc);
}
if ((_Float16)pG[i * n + i] <= 0.0f16)
{
return(ARM_MATH_DECOMPOSITION_FAILURE);
}
invSqrtVj = 1.0f16/(_Float16)sqrtf((float32_t)pG[i * n + i]);
for(j=i; j < n ; j++)
{
pG[j * n + i] = (_Float16)pG[j * n + i] * (_Float16)invSqrtVj ;
}
}
status = ARM_MATH_SUCCESS;
}
/* Return to application */
return (status);
}
#else
arm_status arm_mat_cholesky_f16(
const arm_matrix_instance_f16 * pSrc,
arm_matrix_instance_f16 * pDst)
{
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 */
{
int i,j,k;
int n = pSrc->numRows;
float16_t invSqrtVj;
float16_t *pA,*pG;
pA = pSrc->pData;
pG = pDst->pData;
for(i=0 ; i < n ; i++)
{
for(j=i ; j < n ; j++)
{
pG[j * n + i] = pA[j * n + i];
for(k=0; k < i ; k++)
{
pG[j * n + i] = (_Float16)pG[j * n + i] - (_Float16)pG[i * n + k] * (_Float16)pG[j * n + k];
}
}
if ((_Float16)pG[i * n + i] <= 0.0f16)
{
return(ARM_MATH_DECOMPOSITION_FAILURE);
}
/* The division is done in float32 for accuracy reason and
because doing it in f16 would not have any impact on the performances.
*/
invSqrtVj = 1.0f/sqrtf((float32_t)pG[i * n + i]);
for(j=i ; j < n ; j++)
{
pG[j * n + i] = (_Float16)pG[j * n + i] * (_Float16)invSqrtVj ;
}
}
status = ARM_MATH_SUCCESS;
}
/* Return to application */
return (status);
}
#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
/**
@} end of MatrixChol group
*/
#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */
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