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+/* ----------------------------------------------------------------------
+ * Project: CMSIS DSP Library
+ * Title: arm_mat_cholesky_f32.c
+ * Description: Floating-point Cholesky decomposition
+ *
+ * $Date: 05 October 2021
+ * $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"
+
+/**
+ @ingroup groupMatrix
+ */
+
+/**
+ @defgroup MatrixChol Cholesky and LDLT decompositions
+
+ Computes the Cholesky or LDL^t decomposition of a matrix.
+
+
+ If the input matrix does not have a decomposition, then the
+ algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE.
+ */
+
+/**
+ @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_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
+
+#include "arm_helium_utils.h"
+
+arm_status arm_mat_cholesky_f32(
+ const arm_matrix_instance_f32 * pSrc,
+ arm_matrix_instance_f32 * 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;
+ float32_t invSqrtVj;
+ float32_t *pA,*pG;
+ int kCnt;
+
+ mve_pred16_t p0;
+
+ f32x4_t acc, acc0, acc1, acc2, acc3;
+ f32x4_t vecGi;
+ f32x4_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)
+ {
+ 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];
+
+ kCnt = i;
+ acc0 = vdupq_n_f32(0.0f);
+ acc1 = vdupq_n_f32(0.0f);
+ acc2 = vdupq_n_f32(0.0f);
+ acc3 = vdupq_n_f32(0.0f);
+
+ for(k=0; k < i ; k+=4)
+ {
+ p0 = vctp32q(kCnt);
+
+ vecGi=vldrwq_z_f32(&pG[i * n + k],p0);
+
+ vecGj0=vldrwq_z_f32(&pG[(j + 0) * n + k],p0);
+ vecGj1=vldrwq_z_f32(&pG[(j + 1) * n + k],p0);
+ vecGj2=vldrwq_z_f32(&pG[(j + 2) * n + k],p0);
+ vecGj3=vldrwq_z_f32(&pG[(j + 3) * n + k],p0);
+
+ acc0 = vfmaq_m(acc0, vecGi, vecGj0, p0);
+ acc1 = vfmaq_m(acc1, vecGi, vecGj1, p0);
+ acc2 = vfmaq_m(acc2, vecGi, vecGj2, p0);
+ acc3 = vfmaq_m(acc3, vecGi, vecGj3, p0);
+
+ kCnt -= 4;
+ }
+ pG[(j + 0) * n + i] -= vecAddAcrossF32Mve(acc0);
+ pG[(j + 1) * n + i] -= vecAddAcrossF32Mve(acc1);
+ pG[(j + 2) * n + i] -= vecAddAcrossF32Mve(acc2);
+ pG[(j + 3) * n + i] -= vecAddAcrossF32Mve(acc3);
+ }
+
+ for(; j < n ; j++)
+ {
+ pG[j * n + i] = pA[j * n + i];
+
+ kCnt = i;
+ acc = vdupq_n_f32(0.0f);
+
+ for(k=0; k < i ; k+=4)
+ {
+ p0 = vctp32q(kCnt);
+
+ vecGi=vldrwq_z_f32(&pG[i * n + k],p0);
+ vecGj=vldrwq_z_f32(&pG[j * n + k],p0);
+
+ acc = vfmaq_m(acc, vecGi, vecGj,p0);
+
+ kCnt -= 4;
+ }
+ pG[j * n + i] -= vecAddAcrossF32Mve(acc);
+ }
+
+ if (pG[i * n + i] <= 0.0f)
+ {
+ return(ARM_MATH_DECOMPOSITION_FAILURE);
+ }
+
+ invSqrtVj = 1.0f/sqrtf(pG[i * n + i]);
+ for(j=i; j < n ; j++)
+ {
+ pG[j * n + i] = pG[j * n + i] * invSqrtVj ;
+ }
+ }
+
+ status = ARM_MATH_SUCCESS;
+
+ }
+
+
+ /* Return to application */
+ return (status);
+}
+
+#else
+#if defined(ARM_MATH_NEON) && !defined(ARM_MATH_AUTOVECTORIZE)
+
+arm_status arm_mat_cholesky_f32(
+ const arm_matrix_instance_f32 * pSrc,
+ arm_matrix_instance_f32 * 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;
+ float32_t invSqrtVj;
+ float32_t *pA,*pG;
+ int kCnt;
+
+
+ f32x4_t acc, acc0, acc1, acc2, acc3;
+ f32x4_t vecGi;
+ f32x4_t vecGj,vecGj0,vecGj1,vecGj2,vecGj3;
+#if !defined(__aarch64__)
+ f32x2_t tmp = vdup_n_f32(0);
+#endif
+ float32_t sum=0.0f;
+ float32_t sum0=0.0f,sum1=0.0f,sum2=0.0f,sum3=0.0f;
+
+
+ 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_f32(0.0f);
+ acc1 = vdupq_n_f32(0.0f);
+ acc2 = vdupq_n_f32(0.0f);
+ acc3 = vdupq_n_f32(0.0f);
+
+ kCnt = i >> 2;
+ k=0;
+ while(kCnt > 0)
+ {
+
+ vecGi=vld1q_f32(&pG[i * n + k]);
+
+ vecGj0=vld1q_f32(&pG[(j + 0) * n + k]);
+ vecGj1=vld1q_f32(&pG[(j + 1) * n + k]);
+ vecGj2=vld1q_f32(&pG[(j + 2) * n + k]);
+ vecGj3=vld1q_f32(&pG[(j + 3) * n + k]);
+
+ acc0 = vfmaq_f32(acc0, vecGi, vecGj0);
+ acc1 = vfmaq_f32(acc1, vecGi, vecGj1);
+ acc2 = vfmaq_f32(acc2, vecGi, vecGj2);
+ acc3 = vfmaq_f32(acc3, vecGi, vecGj3);
+
+ kCnt--;
+ k+=4;
+ }
+
+#if defined(__aarch64__)
+ sum0 = vpadds_f32(vpadd_f32(vget_low_f32(acc0), vget_high_f32(acc0)));
+ sum1 = vpadds_f32(vpadd_f32(vget_low_f32(acc1), vget_high_f32(acc1)));
+ sum2 = vpadds_f32(vpadd_f32(vget_low_f32(acc2), vget_high_f32(acc2)));
+ sum3 = vpadds_f32(vpadd_f32(vget_low_f32(acc3), vget_high_f32(acc3)));
+
+#else
+ tmp = vpadd_f32(vget_low_f32(acc0), vget_high_f32(acc0));
+ sum0 = vget_lane_f32(tmp, 0) + vget_lane_f32(tmp, 1);
+
+ tmp = vpadd_f32(vget_low_f32(acc1), vget_high_f32(acc1));
+ sum1 = vget_lane_f32(tmp, 0) + vget_lane_f32(tmp, 1);
+
+ tmp = vpadd_f32(vget_low_f32(acc2), vget_high_f32(acc2));
+ sum2 = vget_lane_f32(tmp, 0) + vget_lane_f32(tmp, 1);
+
+ tmp = vpadd_f32(vget_low_f32(acc3), vget_high_f32(acc3));
+ sum3 = vget_lane_f32(tmp, 0) + vget_lane_f32(tmp, 1);
+#endif
+
+ kCnt = i & 3;
+ 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_f32(0.0f);
+
+ kCnt = i >> 2;
+ k=0;
+ while(kCnt > 0)
+ {
+
+ vecGi=vld1q_f32(&pG[i * n + k]);
+ vecGj=vld1q_f32(&pG[j * n + k]);
+
+ acc = vfmaq_f32(acc, vecGi, vecGj);
+
+ kCnt--;
+ k+=4;
+ }
+
+#if defined(__aarch64__)
+ sum = vpadds_f32(vpadd_f32(vget_low_f32(acc), vget_high_f32(acc)));
+#else
+ tmp = vpadd_f32(vget_low_f32(acc), vget_high_f32(acc));
+ sum = vget_lane_f32(tmp, 0) + vget_lane_f32(tmp, 1);
+#endif
+
+ kCnt = i & 3;
+ 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] <= 0.0f)
+ {
+ return(ARM_MATH_DECOMPOSITION_FAILURE);
+ }
+
+ invSqrtVj = 1.0f/sqrtf(pG[i * n + i]);
+ for(j=i; j < n ; j++)
+ {
+ pG[j * n + i] = pG[j * n + i] * invSqrtVj ;
+ }
+ }
+
+ status = ARM_MATH_SUCCESS;
+
+ }
+
+
+ /* Return to application */
+ return (status);
+}
+
+#else
+arm_status arm_mat_cholesky_f32(
+ const arm_matrix_instance_f32 * pSrc,
+ arm_matrix_instance_f32 * 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;
+ float32_t invSqrtVj;
+ float32_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] <= 0.0f)
+ {
+ return(ARM_MATH_DECOMPOSITION_FAILURE);
+ }
+
+ invSqrtVj = 1.0f/sqrtf(pG[i * n + i]);
+ for(j=i ; j < n ; j++)
+ {
+ pG[j * n + i] = pG[j * n + i] * invSqrtVj ;
+ }
+ }
+
+ status = ARM_MATH_SUCCESS;
+
+ }
+
+
+ /* Return to application */
+ return (status);
+}
+#endif /* #if defined(ARM_MATH_NEON) */
+#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
+
+/**
+ @} end of MatrixChol group
+ */