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65 lines
2.8 KiB
65 lines
2.8 KiB
function [cosp,sinp,n]=getTaylorPolynomials(d0,n)
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% Use Taylor expansion to approximate trigonometric functions
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%
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% FUNCTION getTaylorPolynomials
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%
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% Author: Rui Yao <ruiyao@ieee.org>
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%
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% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
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%
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% OPEN SOURCE LICENSE
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%
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% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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%
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% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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% 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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% 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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%
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%
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% ******************************************************************************************************
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% DISCLAIMER
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
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% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
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% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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% ***************************************************************************************************
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%
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if n>4
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n=4;
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end
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if n<0
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n=0;
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end
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cosd0=cos(d0);
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sind0=sin(d0);
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cosp=zeros(size(d0,1),n+1);
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sinp=zeros(size(d0,1),n+1);
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if n>=0
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cosp(:,1)=cosd0;
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sinp(:,1)=sind0;
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end
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if n>=1
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cosp(:,1:2)=cosp(:,1:2)+[d0.*sind0,-sind0];
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sinp(:,1:2)=sinp(:,1:2)+[-d0.*cosd0,cosd0];
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end
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if n>=2
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cosp(:,1:3)=cosp(:,1:3)+[-cosd0.*d0.*d0,2*cosd0.*d0,-cosd0]/2;
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sinp(:,1:3)=sinp(:,1:3)+[-sind0.*d0.*d0,2*sind0.*d0,-sind0]/2;
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end
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if n>=3
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cosp(:,1:4)=cosp(:,1:4)+[-sind0.*d0.*d0.*d0,3*sind0.*d0.*d0,-3*sind0.*d0,sind0]/6;
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sinp(:,1:4)=sinp(:,1:4)+[cosd0.*d0.*d0.*d0,-3*cosd0.*d0.*d0,3*cosd0.*d0,-cosd0]/6;
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end
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if n>=4
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cosp(:,1:5)=cosp(:,1:5)+[cosd0.*d0.*d0.*d0.*d0,-4*cosd0.*d0.*d0.*d0,6*cosd0.*d0.*d0,-4*cosd0.*d0,cosd0]/24;
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sinp(:,1:5)=sinp(:,1:5)+[sind0.*d0.*d0.*d0.*d0,-4*sind0.*d0.*d0.*d0,6*sind0.*d0.*d0,-4*sind0.*d0,sind0]/24;
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end
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end |