1  /* ----------------------------------------------------------------------
  2   * Project:      CMSIS DSP Library
  3   * Title:        arm_mat_solve_upper_triangular_f16.c
  4   * Description:  Solve linear system UT X = A with UT upper triangular matrix
  5   *
  6   * $Date:        23 April 2021
  7   * $Revision:    V1.9.0
  8   *
  9   * Target Processor: Cortex-M and Cortex-A cores
 10   * -------------------------------------------------------------------- */
 11  /*
 12   * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
 13   *
 14   * SPDX-License-Identifier: Apache-2.0
 15   *
 16   * Licensed under the Apache License, Version 2.0 (the License); you may
 17   * not use this file except in compliance with the License.
 18   * You may obtain a copy of the License at
 19   *
 20   * www.apache.org/licenses/LICENSE-2.0
 21   *
 22   * Unless required by applicable law or agreed to in writing, software
 23   * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 24   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 25   * See the License for the specific language governing permissions and
 26   * limitations under the License.
 27   */
 28  
 29  
 30  #include "dsp/matrix_functions_f16.h"
 31  
 32  #if defined(ARM_FLOAT16_SUPPORTED)
 33  
 34  
 35  /**
 36    @ingroup groupMatrix
 37   */
 38  
 39  
 40  /**
 41    @addtogroup MatrixInv
 42    @{
 43   */
 44  
 45  /**
 46     * @brief Solve UT . X = A where UT is an upper triangular matrix
 47     * @param[in]  ut  The upper triangular matrix
 48     * @param[in]  a  The matrix a
 49     * @param[out] dst The solution X of UT . X = A
 50     * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved.
 51    */
 52  
 53  #if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
 54  
 55  #include "arm_helium_utils.h"
 56  
 57    arm_status arm_mat_solve_upper_triangular_f16(
 58    const arm_matrix_instance_f16 * ut,
 59    const arm_matrix_instance_f16 * a,
 60    arm_matrix_instance_f16 * dst)
 61    {
 62  arm_status status;                             /* status of matrix inverse */
 63  
 64  
 65  #ifdef ARM_MATH_MATRIX_CHECK
 66  
 67    /* Check for matrix mismatch condition */
 68    if ((ut->numRows != ut->numCols) ||
 69        (ut->numRows != a->numRows)   )
 70    {
 71      /* Set status as ARM_MATH_SIZE_MISMATCH */
 72      status = ARM_MATH_SIZE_MISMATCH;
 73    }
 74    else
 75  
 76  #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
 77  
 78    {
 79  
 80      int i,j,k,n,cols;
 81  
 82      n = dst->numRows;
 83      cols = dst->numCols;
 84  
 85      float16_t *pX = dst->pData;
 86      float16_t *pUT = ut->pData;
 87      float16_t *pA = a->pData;
 88  
 89      float16_t *ut_row;
 90      float16_t *a_col;
 91  
 92      _Float16 invUT;
 93  
 94      f16x8_t vecA;
 95      f16x8_t vecX;
 96      
 97      for(i=n-1; i >= 0 ; i--)
 98      {
 99        for(j=0; j+7 < cols; j +=8)
100        {
101              vecA = vld1q_f16(&pA[i * cols + j]);
102              
103              for(k=n-1; k > i; k--)
104              {
105                  vecX = vld1q_f16(&pX[cols*k+j]);          
106                  vecA = vfmsq(vecA,vdupq_n_f16(pUT[n*i + k]),vecX);
107              }
108  
109              if ((_Float16)pUT[n*i + i]==0.0f16)
110              {
111                return(ARM_MATH_SINGULAR);
112              }
113  
114              invUT = 1.0f16 / (_Float16)pUT[n*i + i];
115              vecA = vmulq(vecA,vdupq_n_f16(invUT));
116             
117  
118              vst1q(&pX[i*cols+j],vecA);
119        }
120  
121        for(; j < cols; j ++)
122        {
123              a_col = &pA[j];
124  
125              ut_row = &pUT[n*i];
126  
127              _Float16 tmp=a_col[i * cols];
128              
129              for(k=n-1; k > i; k--)
130              {
131                  tmp -= (_Float16)ut_row[k] * (_Float16)pX[cols*k+j];
132              }
133  
134              if ((_Float16)ut_row[i]==0.0f16)
135              {
136                return(ARM_MATH_SINGULAR);
137              }
138              tmp = tmp / (_Float16)ut_row[i];
139              pX[i*cols+j] = tmp;
140         }
141  
142      }
143      status = ARM_MATH_SUCCESS;
144  
145    }
146  
147    
148    /* Return to application */
149    return (status);
150  }
151  
152  #else
153    arm_status arm_mat_solve_upper_triangular_f16(
154    const arm_matrix_instance_f16 * ut,
155    const arm_matrix_instance_f16 * a,
156    arm_matrix_instance_f16 * dst)
157    {
158  arm_status status;                             /* status of matrix inverse */
159  
160  
161  #ifdef ARM_MATH_MATRIX_CHECK
162  
163    /* Check for matrix mismatch condition */
164    if ((ut->numRows != ut->numCols) ||
165        (ut->numRows != a->numRows)   )
166    {
167      /* Set status as ARM_MATH_SIZE_MISMATCH */
168      status = ARM_MATH_SIZE_MISMATCH;
169    }
170    else
171  
172  #endif /* #ifdef ARM_MATH_MATRIX_CHECK */
173  
174    {
175  
176      int i,j,k,n,cols;
177  
178      n = dst->numRows;
179      cols = dst->numCols;
180  
181      float16_t *pX = dst->pData;
182      float16_t *pUT = ut->pData;
183      float16_t *pA = a->pData;
184  
185      float16_t *ut_row;
186      float16_t *a_col;
187  
188      for(j=0; j < cols; j ++)
189      {
190         a_col = &pA[j];
191  
192         for(i=n-1; i >= 0 ; i--)
193         {
194              ut_row = &pUT[n*i];
195  
196              float16_t tmp=a_col[i * cols];
197              
198              for(k=n-1; k > i; k--)
199              {
200                  tmp -= (_Float16)ut_row[k] * (_Float16)pX[cols*k+j];
201              }
202  
203              if ((_Float16)ut_row[i]==0.0f16)
204              {
205                return(ARM_MATH_SINGULAR);
206              }
207              tmp = (_Float16)tmp / (_Float16)ut_row[i];
208              pX[i*cols+j] = tmp;
209         }
210  
211      }
212      status = ARM_MATH_SUCCESS;
213  
214    }
215  
216    
217    /* Return to application */
218    return (status);
219  }
220  
221  #endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
222  
223  /**
224    @} end of MatrixInv group
225   */
226  #endif /* #if defined(ARM_FLOAT16_SUPPORTED) */