function?[test_targets?a_star]?=?SVM（train_patterns?train_targets?test_patterns?params）

%?Classify?using?（a?very?simple?implementation?of）?the?support?vector?machine?algorithm
%?
%?Inputs:
%?	train_patterns	-?Train?patterns
%	train_targets	-?Train?targets
%???test_patterns???-?Test??patterns
%	params	????????-?[kernel?kernel?parameter?solver?type?Slack]
%?????????????????????Kernel?can?be?one?of:?Gauss?RBF?（Same?as?Gauss）?Poly?Sigmoid?or?Linear
%?????????????????????The?kernel?parameters?are:
%???????????????????????RBF?kernel??-?Gaussian?width?（One?parameter）
%???????????????????????Poly?kernel?-?Polynomial?degree
%???????????????????????Sigmoid?????-?The?slope?and?constant?of?the?sigmoid?（in?the?format?[1?2]?with?no?separating?commas）
%					????Linear		-?None?needed
%?????????????????????Solver?type?can?be?one?of:?Perceptron?Quadprog?Lagrangian
%
%?Outputs
%	test_targets	-?Predicted?targets
%	a			????-?SVM?coeficients
%
%?Note:?The?number?of?support?vectors?found?will?usually?be?larger?than?is?actually?
%?needed?because?the?two?first?solvers?are?approximate.

[Dim?Nf]???????=?size（train_patterns）;
Dim?????????????=?Dim?+?1;
train_patterns（Dim:）?=?ones（1Nf）;
test_patterns（Dim:）??=?ones（1?size（test_patterns2））;

if?（length（unique（train_targets））?==?2）
????z???=?2*（train_targets>0）?-?1;?
else
????z???=?train_targets;
end

%Get?kernel?parameters
[kernel?ker_param?solver?slack]?=?process_params（params）;

%Transform?the?input?patterns
y	=?zeros（Nf）;
switch?kernel
case?{‘Gauss‘‘RBF‘}
???for?i?=?1:Nf
??????y（:i）????=?exp（-sum（（train_patterns-train_patterns（:i）*ones（1Nf））.^2）‘/（2*ker_param^2））;
???end
case?{‘Poly‘?‘Linear‘}
???if?strcmp（kernel?‘Linear‘）
??????ker_param?=?1;
???end
???
???for?i?=?1:Nf
??????y（:i）?=?（train_patterns‘*train_patterns（:i）?+?1）.^ker_param;
???end
case?‘Sigmoid‘
????ker_param?=?str2num（ker_param）;
????
????if?（length（ker_param）?~=?2）
????????error（‘This?kernel?needs?two?parameters?to?operate!‘）
????end
????
???for?i?=?1:Nf
??????y（:i）?=?tanh（train_patterns‘*train_patterns（:i）*ker_param（1）+ker_param（2））;
???end
otherwise
???error（‘Unknown?kernel.?Can?be?Gauss?Linear?Poly?or?Sigmoid.‘）
end

%Find?the?SVM?coefficients
switch?solver
case?‘Quadprog‘
???%Quadratic?programming
???alpha_star	=?quadprog（diag（z）*y‘*y*diag（z）?-ones（1?Nf）?zeros（1?Nf）?1?z?0?zeros（1?Nf）?slack*ones（1?Nf））‘;
???a_star		=?（alpha_star.*z）*y‘;
???
???%Find?the?bias
???sv_for_bias??=?find（（alpha_star?>?0.001*slack）?&?（alpha_star????if?isempty（sv_for_bias）
???????bias?????=?0;
???else
	???B????????=?z（sv_for_bias）?-?a_star（sv_for_bias）;
???????bias?????=?mean（B）;
???end
???
???sv???????????=?find（alpha_star?>?0.001*slack）;
???
case?‘Perceptron‘
???max_iter		=?1e5;
???iter			=?0;
???rate????????=?0.0