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GSL_LP_stepsize_instant.m
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GSL_LP_stepsize_instant.m
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function [ alpha_0 ] = GSL_LP_stepsize_instant(ldp, ...
beta_0,...
FW_beta_direction,...
l_matrix,...
eig_tol,...
L_beta,...
data_label,...
n_beta,...
GD_NR)
% step 1: check first derivatives at 0 and 1
% check first derivative at 0
alpha_0=0;
lambda_FW_alpha_0=(beta_0+alpha_0*(FW_beta_direction-beta_0)).*l_matrix+eig_tol; % N x P
lambda_FW_alpha=(FW_beta_direction-beta_0).*l_matrix; % N x P
[ f_alpha_first,~ ] = ...
first_second_alpha_derivative_instant(ldp, ...
L_beta,...
data_label,...
FW_beta_direction,...
lambda_FW_alpha_0,...
lambda_FW_alpha,...
beta_0,...
l_matrix,...
n_beta);
f_alpha_first1=f_alpha_first;
% check first derivative at 1
alpha_0=1;
lambda_FW_alpha_0=(beta_0+alpha_0*(FW_beta_direction-beta_0)).*l_matrix+eig_tol; % N x P
lambda_FW_alpha=(FW_beta_direction-beta_0).*l_matrix; % N x P
[ f_alpha_first,~ ] = ...
first_second_alpha_derivative_instant(ldp, ...
L_beta,...
data_label,...
FW_beta_direction,...
lambda_FW_alpha_0,...
lambda_FW_alpha,...
beta_0,...
l_matrix,...
n_beta);
f_alpha_first2=f_alpha_first;
if f_alpha_first1>=0 && f_alpha_first2>0
alpha_0=0;
elseif f_alpha_first1<0 && f_alpha_first2<=0
alpha_0=1;
else
if GD_NR==1
gL=0;
gU=1;
nn=0;
tol_GD=1e-5;
while abs(gL-gU)>tol_GD
nn=nn+1;
alpha_0=(gL+gU)/2;
lambda_FW_alpha_0=(beta_0+alpha_0*(FW_beta_direction-beta_0)).*l_matrix+eig_tol; % N x P
[ G_gM,~ ] = ...
first_second_alpha_derivative_instant(ldp, ...
L_beta,...
data_label,...
FW_beta_direction,...
lambda_FW_alpha_0,...
lambda_FW_alpha,...
beta_0,...
l_matrix,...
n_beta);
if G_gM>0 % fmin=f(gamma\in[gL,gamma])
gU=alpha_0;
elseif G_gM<0 % fmin=f(gamma\in[gamma,gU])
gL=alpha_0;
else % G_gM=0
%gamma=gM;
break
end
end
else
alpha_0=0;
delta_alpha=Inf;
while delta_alpha>1e-5
lambda_FW_alpha_0=(beta_0+alpha_0*(FW_beta_direction-beta_0)).*l_matrix+eig_tol; % N x P
lambda_FW_alpha=(FW_beta_direction-beta_0).*l_matrix; % N x P
[ f_alpha_first,f_alpha_second ] = ...
first_second_alpha_derivative_instant(ldp, ...
L_beta,...
data_label,...
FW_beta_direction,...
lambda_FW_alpha_0,...
lambda_FW_alpha,...
beta_0,...
l_matrix,...
n_beta);
if f_alpha_second==0
gL=0;
gU=1;
nn=0;
tol_GD=1e-5;
while abs(gL-gU)>tol_GD
nn=nn+1;
alpha_0=(gL+gU)/2;
lambda_FW_alpha_0=(beta_0+alpha_0*(FW_beta_direction-beta_0)).*l_matrix+eig_tol; % N x P
[ G_gM,~ ] = ...
first_second_alpha_derivative_instant(ldp, ...
L_beta,...
data_label,...
FW_beta_direction,...
lambda_FW_alpha_0,...
lambda_FW_alpha,...
beta_0,...
l_matrix,...
n_beta);
if G_gM>0 % fmin=f(gamma\in[gL,gamma])
gU=alpha_0;
elseif G_gM<0 % fmin=f(gamma\in[gamma,gU])
gL=alpha_0;
else % G_gM=0
%gamma=gM;
break
end
end
break
end
alpha_current=alpha_0-(f_alpha_first/f_alpha_second);
if alpha_current>1
alpha_0=1;
break
elseif alpha_current<0
alpha_0=0;
break
end
delta_alpha=norm(alpha_current-alpha_0);
alpha_0=alpha_current;
end
end
end
end