/* ---------------------------------------------------------------------- * Project: CMSIS DSP Library * Title: arm_mat_cholesky_f64.c * Description: Floating-point Cholesky decomposition * * $Date: 10 August 2022 * $Revision: V1.9.1 * * 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" #include "dsp/matrix_utils.h" /** @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 L such that A = L L^t * * @par * The destination matrix should be set to 0 before calling the functions because * the function may not overwrite all output elements. */ #if defined(ARM_MATH_NEON) && !defined(ARM_MATH_AUTOVECTORIZE) && defined(__aarch64__) ARM_DSP_ATTRIBUTE arm_status arm_mat_cholesky_f64( const arm_matrix_instance_f64 * pSrc, arm_matrix_instance_f64 * 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; float64_t invSqrtVj; float64_t *pA,*pG; int kCnt; float64x2_t acc, acc0, acc1, acc2, acc3; float64x2_t vecGi; float64x2_t vecGj,vecGj0,vecGj1,vecGj2,vecGj3; float64_t sum=0.0; float64_t sum0=0.0,sum1=0.0,sum2=0.0,sum3=0.0; pA = pSrc->pData; pG = pDst->pData; for(i=0 ;i < n ; i++) { for(j=i ; j+3 < n ; j+=4) { pG[(j + 0) * n + i] = pA[(j + 0) * n + i]; pG[(j + 1) * n + i] = pA[(j + 1) * n + i]; pG[(j + 2) * n + i] = pA[(j + 2) * n + i]; pG[(j + 3) * n + i] = pA[(j + 3) * n + i]; acc0 = vdupq_n_f64(0.0); acc1 = vdupq_n_f64(0.0); acc2 = vdupq_n_f64(0.0); acc3 = vdupq_n_f64(0.0); kCnt = i >> 1U; k=0; while(kCnt > 0) { vecGi=vld1q_f64(&pG[i * n + k]); vecGj0=vld1q_f64(&pG[(j + 0) * n + k]); vecGj1=vld1q_f64(&pG[(j + 1) * n + k]); vecGj2=vld1q_f64(&pG[(j + 2) * n + k]); vecGj3=vld1q_f64(&pG[(j + 3) * n + k]); acc0 = vfmaq_f64(acc0, vecGi, vecGj0); acc1 = vfmaq_f64(acc1, vecGi, vecGj1); acc2 = vfmaq_f64(acc2, vecGi, vecGj2); acc3 = vfmaq_f64(acc3, vecGi, vecGj3); kCnt--; k+=2; } sum0 = vaddvq_f64(acc0); sum1 = vaddvq_f64(acc1); sum2 = vaddvq_f64(acc2); sum3 = vaddvq_f64(acc3); kCnt = i & 1; while(kCnt > 0) { sum0 = sum0 + pG[i * n + k] * pG[(j + 0) * n + k]; sum1 = sum1 + pG[i * n + k] * pG[(j + 1) * n + k]; sum2 = sum2 + pG[i * n + k] * pG[(j + 2) * n + k]; sum3 = sum3 + pG[i * n + k] * pG[(j + 3) * n + k]; kCnt--; k++; } pG[(j + 0) * n + i] -= sum0; pG[(j + 1) * n + i] -= sum1; pG[(j + 2) * n + i] -= sum2; pG[(j + 3) * n + i] -= sum3; } for(; j < n ; j++) { pG[j * n + i] = pA[j * n + i]; acc = vdupq_n_f64(0.0); kCnt = i >> 1U; k=0; while(kCnt > 0) { vecGi=vld1q_f64(&pG[i * n + k]); vecGj=vld1q_f64(&pG[j * n + k]); acc = vfmaq_f64(acc, vecGi, vecGj); kCnt--; k+=2; } sum = vaddvq_f64(acc); kCnt = i & 1; while(kCnt > 0) { sum = sum + pG[i * n + k] * pG[(j + 0) * n + k]; kCnt--; k++; } pG[j * n + i] -= sum; } if (pG[i * n + i] <= 0.0) { return(ARM_MATH_DECOMPOSITION_FAILURE); } invSqrtVj = 1.0/sqrt(pG[i * n + i]); SCALE_COL_F64(pDst,i,invSqrtVj,i); } status = ARM_MATH_SUCCESS; } /* Return to application */ return (status); } #else ARM_DSP_ATTRIBUTE arm_status arm_mat_cholesky_f64( const arm_matrix_instance_f64 * pSrc, arm_matrix_instance_f64 * 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; float64_t invSqrtVj; float64_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] = pG[j * n + i] - pG[i * n + k] * pG[j * n + k]; } } if (pG[i * n + i] <= 0.0) { return(ARM_MATH_DECOMPOSITION_FAILURE); } invSqrtVj = 1.0/sqrt(pG[i * n + i]); SCALE_COL_F64(pDst,i,invSqrtVj,i); } status = ARM_MATH_SUCCESS; } /* Return to application */ return (status); } #endif /** @} end of MatrixChol group */