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compplots_tight.m
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% compplots_tight.m
% This file runs uniform precision s-step Lanczos and mixed precision
% s-step Lanczos and creates plots of loss of
% orthogonality, normality, column error, and deviation of AV and T for the
% specified problem, using both loose and tighter upper bounds.
%
% Input:
% A : a square, symmetric coefficient matrix
% v : the starting vector for the Lanczos method
% s : the parameter s in s-step (s>0)
% basis_info : a struct containing a quantity 'type' which defines the
% polynomial basis to be used. Options are 'monomial', 'newton', or
% 'chebyshev'
% options : a struct containing a quantity 'xlim', which gives the number
% of iterations to perform, and a quantity 'name', which is used for
% naming the output file
%
% See lanczos_example_tight.m for example usage.
%
% Last edited by: Erin Carson, 2021
%
function compplots_tight(A, v, s, basis_info, options)
% Run uniform precision s-step Lanczos with the specified parameters
[results, basis_info] = ca_lanczos_bounds_tight(A, v, s, basis_info, options);
% Run mixed precision s-step Lanczos with the specified parameters
[resultsm, basis_info] = mixed_ca_lanczos_bounds_tight(A, v, s,basis_info, options);
% Set x axis limit
m = options.xlim+1;
%%%%%%%%%%%% Loss of orthogonality plot %%%%%%%%%%%
h = figure()
set(0,'DefaultAxesTitleFontWeight','normal');
axes1 = axes;
hold(axes1,'on');
semilogy(1:m-1, results.orthactual(1:m-1),'b-', 1:m-1, results.orthboundtight(1:m-1),'b--', ...
1:m-1, results.orthbound(1:m-1),'b:',...
1:m-1, resultsm.orthactual(1:m-1),'r-', 1:m-1, resultsm.orthboundtight(1:m-1),'r--', ...,
1:m-1, resultsm.orthbound(1:m-1),'r:',...
1:m-1, results.Gamma_orth(1:m-1),'k--',...
1:m-1, results.Gamval(1:m-1), 'k:', 'LineWidth',1);
tt = strcat('Loss of orthogonality, s = ', " ",num2str(s), ", ", basis_info.type, ' basis');
title(tt,'Interpreter','none','FontSize',16);
% Uncomment below to plot legend
% legend('measured, uniform', 'bound, uniform', 'measured, mixed', 'bound, mixed','$\bar{\Gamma}_k$', 'Interpreter', 'latex','FontSize',14);
xlabel('Iteration','Interpreter','none','FontSize',16)
box(axes1,'on');
hold(axes1,'off');
set(axes1,'FontSize',14,'YMinorTick','on','YScale','log');
sname = strcat('figs/',options.name,'_orthbound_s',num2str(s),'_',basis_info.type,'_tight');
saveas(h,sname,'fig')
saveas(h,sname,'pdf')
%%%%%%%%%%%% Normality plot %%%%%%%%%%%
h = figure()
axes1 = axes;
hold(axes1,'on');
semilogy(1:m-1, results.normactual(1:m-1),'b-', 1:m-1, results.normboundtight(1:m-1),'b--', ...
1:m-1, results.normbound(1:m-1),'b:',...
1:m-1, resultsm.normactual(1:m-1),'r-', 1:m-1, resultsm.normboundtight(1:m-1),'r--', ...
1:m-1, resultsm.normbound(1:m-1),'r:',...
1:m-1,results.Gamma_norm(1:m-1),'k--',...
1:m-1, results.Gamval(1:m-1),'k:','LineWidth',1);
tt = strcat('Normality, s = ', " ",num2str(s), ", ", basis_info.type, ' basis');
title(tt,'Interpreter','none','FontSize',16);
set(0,'DefaultAxesTitleFontWeight','normal');
% Uncomment below to plot legend
%legend('measured, uniform', 'tight bound, uniform', 'bound, uniform', 'measured, mixed', 'tight bound, mixed', 'bound, mixed', '$${\Gamma}^{(21)}_{sk+j}$$','$${\bar\Gamma}_{k}$$', 'Interpreter', 'none','FontSize',14);
%legend1 = legend(axes1,'show');
%set(legend1,'Interpreter','latex','FontSize',11);
xlabel('Iteration','Interpreter','none','FontSize',16)
box(axes1,'on');
hold(axes1,'off');
set(axes1,'FontSize',14,'YMinorTick','on','YScale','log');
sname = strcat('figs/',options.name,'_normbound_s',num2str(s),'_',basis_info.type,'_tight');
saveas(h,sname,'fig')
saveas(h,sname,'pdf')
%%%%%%%%%%%% Column error plot %%%%%%%%%%%
h = figure()
axes1 = axes;
hold(axes1,'on');
semilogy(1:m-1, results.colactual(1:m-1),'b-', 1:m-1, results.colboundtight(1:m-1),'b--', ...
1:m-1, results.colbound(1:m-1), 'b:',...
1:m-1, resultsm.colactual(1:m-1),'r-', 1:m-1, resultsm.colboundtight(1:m-1),'r--', ...
1:m-1, resultsm.colbound(1:m-1),'r:',...
1:m-1, results.Gamma_colbound(1:m-1),'k--', ...
1:m-1, results.Gamval(1:m-1),'k:','LineWidth',1);
tt = strcat('Error in Columns, s = ', " ",num2str(s), ", ", basis_info.type, ' basis');
title(tt,'Interpreter','none','FontSize',16);
set(0,'DefaultAxesTitleFontWeight','normal');
% Uncomment below to plot legend
% legend('col, double', 'col bound, double', 'col, double/quad', 'col s-Lanc. double/quad','$\bar{\Gamma}_k$', 'Interpreter', 'latex','FontSize',14);
xlabel('Iteration','Interpreter','none','FontSize',16)
box(axes1,'on');
hold(axes1,'off');
set(axes1,'FontSize',14,'YMinorTick','on','YScale','log');
sname = strcat('figs/',options.name,'_colbound_s',num2str(s),'_',basis_info.type,'_tight');
saveas(h,sname,'fig')
saveas(h,sname,'pdf')
%%%%%%%%%%%% Deviation of AV and T plot %%%%%%%%%%%
h = figure()
axes1 = axes;
hold(axes1,'on');
semilogy(1:m-1, results.diffactual(1:m-1),'b-', 1:m-1, results.diffboundtight(1:m-1),'b--',...
1:m-1, results.diffbound(1:m-1),'b:',...
1:m-1, resultsm.diffactual(1:m-1),'r-', 1:m-1, resultsm.diffboundtight(1:m-1),'r--', ...
1:m-1, resultsm.diffbound(1:m-1),'r:',...
1:m-1,results.Gamma_diffbound(1:m-1),'k--',...
1:m-1, results.Gamval(1:m-1), 'k:', 'LineWidth',1);
tt = strcat('Deviation of AV_m and T_m, s = '," ", num2str(s), ", ", basis_info.type, ' basis');
title(tt,'Interpreter','tex','FontSize',16);
set(0,'DefaultAxesTitleFontWeight','normal');
% Uncomment below to plot legend
% legend('diff, double', 'diff bound, double', 'diff, double/quad', 'diff s-Lanc. double/quad','$\bar{\Gamma}_k$', 'Interpreter', 'latex','FontSize',14);
xlabel('Iteration','Interpreter','none','FontSize',16)
box(axes1,'on');
hold(axes1,'off');
set(axes1,'FontSize',14,'YMinorTick','on','YScale','log');
sname = strcat('figs/',options.name,'_diffbound_s',num2str(s),'_',basis_info.type,'_tight');
saveas(h,sname,'fig')
saveas(h,sname,'pdf')