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70 lines
3.0 KiB
70 lines
3.0 KiB
function [LTE,LTE2,LTE3] = Cal_locl_er(x_ori,k,h)
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% Calculation of local error
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%
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% FUNCTION Cal_locl_er
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%
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% Author: Kaiyang Huang <khuang@anl.gov>
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%
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% Copyright (C) 2023, 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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% INPUT
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% x_ori - Initial system state
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% xNew - Updated system state (algebraic variables to be solved)
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% SysDataNew - (optional) updated system data
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%
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% OUTPUT
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% Vx, Wx, Qx, fx - Last HE coefficients of algebraic variables
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% xx - Solved updated system state
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% finalAlpha - The ending length of this segment of simulation
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% alphas - Record of alphas
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% diffRec - A list of errors
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%
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x = x_ori(:,k-3:k);
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Xh = x.*h.^(k-4:k-1);
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x_new = polyvalVec(x_ori,h);
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eta = 0.001;
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infcof = max(abs(Xh(:,end))./(abs(x_new)+eta));
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trc = infcof^(1/k);
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LTE = infcof/(1-trc);
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LTE3 = max(abs(Xh(:,end-1)./(x_new+eta)));
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% relative error used to change order
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e1 = abs(Xh(:,end-1)./Xh(:,end));
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e2 = abs(Xh(:,end-2)./Xh(:,end));
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e3 = abs(Xh(:,end-3)./Xh(:,end-1));
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% delete nan induced by zero/zero
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f1 = find(Xh(:,end)==0);
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f2 = find(Xh(:,end-1)==0);
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f2 = f2(:);
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e1(f1) = 0;
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e2(f1) = 0;
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e3(f2) = 0;
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LTE2 = infcof/min([norm(e1,Inf), sqrt(norm(e2,Inf)), sqrt(norm(e3,Inf))]);
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end
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