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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) */