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193 lines
3.9 KiB
C
193 lines
3.9 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_householder_f32.c
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* Description: Floating-point Householder transform
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*
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* $Date: 15 June 2022
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* $Revision: V1.11.0
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*
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* Target Processor: Cortex-M and Cortex-A cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "dsp/matrix_functions.h"
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#include "dsp/basic_math_functions.h"
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#include "dsp/fast_math_functions.h"
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#include "dsp/matrix_utils.h"
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#include <math.h>
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/**
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@ingroup groupMatrix
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*/
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/**
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@defgroup MatrixHouseholder Householder transform of a vector
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Computes the Householder transform of a vector x.
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The Householder transform of x is a vector v with
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\f[
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v_0 = 1
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\f]
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and a scalar \f$\beta\f$ such that:
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\f[
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P = I - \beta v v^T
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\f]
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is an orthogonal matrix and
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\f[
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P x = ||x||_2 e_1
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\f]
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So P is an hyperplane reflection such that the image of x
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is proportional to \f$e_1\f$.
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\f$e_1\f$ is the vector of coordinates:
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\f[
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\begin{pmatrix}
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1 \\
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0 \\
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\vdots \\
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\end{pmatrix}
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\f]
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If x is already proportional to \f$e_1\f$ then
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the matrix P should be the identity.
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Thus, \f$\beta\f$ should be 0 and in this case the vector v
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can also be null.
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But how do we detect that x is already proportional to
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\f$e_1\f$.
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If x
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\f[
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x =
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\begin{pmatrix}
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x_0 \\
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xr \\
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\end{pmatrix}
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\f]
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where \f$xr\f$ is a vector.
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The algorithm is computing the norm squared of this vector:
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\f[
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||xr||^2
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\f]
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and this value is compared to a `threshold`. If the value
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is smaller than the `threshold`, the algorithm is
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returning 0 for \f$\beta\f$ and the householder vector.
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This `threshold` is an argument of the function.
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Default values are provided in the header
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`dsp/matrix_functions.h` like for instance
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`DEFAULT_HOUSEHOLDER_THRESHOLD_F32`
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*/
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/**
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@addtogroup MatrixHouseholder
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@{
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*/
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/**
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@brief Householder transform of a floating point vector.
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@param[in] pSrc points to the input vector.
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@param[in] threshold norm2 threshold.
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@param[in] blockSize dimension of the vector space.
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@param[out] pOut points to the output vector.
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@return beta return the scaling factor beta
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*/
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float32_t arm_householder_f32(
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const float32_t * pSrc,
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const float32_t threshold,
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uint32_t blockSize,
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float32_t * pOut
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)
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{
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uint32_t i;
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float32_t epsilon;
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float32_t x1norm2,alpha;
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float32_t beta,tau,r;
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epsilon = threshold;
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alpha = pSrc[0];
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for(i=1; i < blockSize; i++)
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{
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pOut[i] = pSrc[i];
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}
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pOut[0] = 1.0f;
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arm_dot_prod_f32(pSrc+1,pSrc+1,blockSize-1,&x1norm2);
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if (x1norm2<=epsilon)
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{
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tau = 0.0f;
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memset(pOut,0,blockSize * sizeof(float32_t));
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}
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else
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{
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beta = alpha * alpha + x1norm2;
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(void)arm_sqrt_f32(beta,&beta);
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if (alpha > 0.0f)
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{
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beta = -beta;
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}
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r = 1.0f / (alpha -beta);
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arm_scale_f32(pOut,r,pOut,blockSize);
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pOut[0] = 1.0f;
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tau = (beta - alpha) / beta;
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}
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return(tau);
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}
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/**
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@} end of MatrixHouseholder group
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*/
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