/* ---------------------------------------------------------------------- * 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) */