DSP/Source/MatrixFunctions/arm_mat_solve_upper_triangular_f32.c

/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_mat_solve_upper_triangular_f32.c
 * Description:  Solve linear system UT X = A with UT upper triangular matrix
 *
 * $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.h"


/**
  @ingroup groupMatrix
 */


/**
  @addtogroup MatrixInv
  @{
 */

/**
   * @brief Solve UT . X = A where UT is an upper triangular matrix
   * @param[in]  ut  The upper triangular matrix
   * @param[in]  a  The matrix a
   * @param[out] dst The solution X of UT . X = A
   * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved.
  */

#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)

#include "arm_helium_utils.h"

  arm_status arm_mat_solve_upper_triangular_f32(
  const arm_matrix_instance_f32 * ut,
  const arm_matrix_instance_f32 * a,
  arm_matrix_instance_f32 * dst)
  {
arm_status status;                             /* status of matrix inverse */


#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((ut->numRows != ut->numCols) ||
      (ut->numRows != a->numRows)   )
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

  {

    int i,j,k,n,cols;

    n = dst->numRows;
    cols = dst->numCols;

    float32_t *pX = dst->pData;
    float32_t *pUT = ut->pData;
    float32_t *pA = a->pData;

    float32_t *ut_row;
    float32_t *a_col;

    float32_t invUT;

    f32x4_t vecA;
    f32x4_t vecX;
    
    for(i=n-1; i >= 0 ; i--)
    {
      for(j=0; j+3 < cols; j +=4)
      {
            vecA = vld1q_f32(&pA[i * cols + j]);
            
            for(k=n-1; k > i; k--)
            {
                vecX = vld1q_f32(&pX[cols*k+j]);          
                vecA = vfmsq(vecA,vdupq_n_f32(pUT[n*i + k]),vecX);
            }

            if (pUT[n*i + i]==0.0f)
            {
              return(ARM_MATH_SINGULAR);
            }

            invUT = 1.0f / pUT[n*i + i];
            vecA = vmulq(vecA,vdupq_n_f32(invUT));
           

            vst1q(&pX[i*cols+j],vecA);
      }

      for(; j < cols; j ++)
      {
            a_col = &pA[j];

            ut_row = &pUT[n*i];

            float32_t tmp=a_col[i * cols];
            
            for(k=n-1; k > i; k--)
            {
                tmp -= ut_row[k] * pX[cols*k+j];
            }

            if (ut_row[i]==0.0f)
            {
              return(ARM_MATH_SINGULAR);
            }
            tmp = tmp / ut_row[i];
            pX[i*cols+j] = tmp;
       }

    }
    status = ARM_MATH_SUCCESS;

  }

  
  /* Return to application */
  return (status);
}

#else
#if defined(ARM_MATH_NEON) && !defined(ARM_MATH_AUTOVECTORIZE)
  arm_status arm_mat_solve_upper_triangular_f32(
  const arm_matrix_instance_f32 * ut,
  const arm_matrix_instance_f32 * a,
  arm_matrix_instance_f32 * dst)
  {
arm_status status;                             /* status of matrix inverse */


#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((ut->numRows != ut->numCols) ||
      (ut->numRows != a->numRows)   )
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

  {

    int i,j,k,n,cols;

    n = dst->numRows;
    cols = dst->numCols;

    float32_t *pX = dst->pData;
    float32_t *pUT = ut->pData;
    float32_t *pA = a->pData;

    float32_t *ut_row;
    float32_t *a_col;

    float32_t invUT;

    f32x4_t vecA;
    f32x4_t vecX;
    
    for(i=n-1; i >= 0 ; i--)
    {
      for(j=0; j+3 < cols; j +=4)
      {
            vecA = vld1q_f32(&pA[i * cols + j]);
            
            for(k=n-1; k > i; k--)
            {
                vecX = vld1q_f32(&pX[cols*k+j]);          
                vecA = vfmsq_f32(vecA,vdupq_n_f32(pUT[n*i + k]),vecX);
            }

            if (pUT[n*i + i]==0.0f)
            {
              return(ARM_MATH_SINGULAR);
            }

            invUT = 1.0f / pUT[n*i + i];
            vecA = vmulq_f32(vecA,vdupq_n_f32(invUT));
           

            vst1q_f32(&pX[i*cols+j],vecA);
      }

      for(; j < cols; j ++)
      {
            a_col = &pA[j];

            ut_row = &pUT[n*i];

            float32_t tmp=a_col[i * cols];
            
            for(k=n-1; k > i; k--)
            {
                tmp -= ut_row[k] * pX[cols*k+j];
            }

            if (ut_row[i]==0.0f)
            {
              return(ARM_MATH_SINGULAR);
            }
            tmp = tmp / ut_row[i];
            pX[i*cols+j] = tmp;
       }

    }
    status = ARM_MATH_SUCCESS;

  }

  
  /* Return to application */
  return (status);
}

#else
  arm_status arm_mat_solve_upper_triangular_f32(
  const arm_matrix_instance_f32 * ut,
  const arm_matrix_instance_f32 * a,
  arm_matrix_instance_f32 * dst)
  {
arm_status status;                             /* status of matrix inverse */


#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((ut->numRows != ut->numCols) ||
      (ut->numRows != a->numRows)   )
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

  {

    int i,j,k,n,cols;

    float32_t *pX = dst->pData;
    float32_t *pUT = ut->pData;
    float32_t *pA = a->pData;

    float32_t *ut_row;
    float32_t *a_col;

    n = dst->numRows;
    cols = dst->numCols;

    for(j=0; j < cols; j ++)
    {
       a_col = &pA[j];

       for(i=n-1; i >= 0 ; i--)
       {
            float32_t tmp=a_col[i * cols];

            ut_row = &pUT[n*i];

            for(k=n-1; k > i; k--)
            {
                tmp -= ut_row[k] * pX[cols*k+j];
            }

            if (ut_row[i]==0.0f)
            {
              return(ARM_MATH_SINGULAR);
            }
            tmp = tmp / ut_row[i];
            pX[i*cols+j] = tmp;
       }

    }
    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 MatrixInv group
 */