cos.m

matlab波形优化算法经常要用到的matlab toolbox工具箱:yalmip

function varargout = cos(varargin)
%COS (overloaded)

% Author Johan L鰂berg
% $Id: cos.m,v 1.14 2008/04/08 09:02:48 joloef Exp $
switch class(varargin{1})

    case 'double'
        error('Overloaded SDPVAR/COS CALLED WITH DOUBLE. Report error')

    case 'sdpvar'
        varargout{1} = InstantiateElementWise(mfilename,varargin{:});
        
    case 'char'
        
        operator = struct('convexity','none','monotonicity','none','definiteness','none','model','callback');
        operator.bounds     = @bounds;
        operator.derivative = @(x)(-sin(x));
        operator.range = [-1 1];
        operator.convexhull = @convexhull;
 
        varargout{1} = [];
        varargout{2} = operator;
        varargout{3} = varargin{3};

    otherwise
        error('SDPVAR/COS called with CHAR argument?');
end

function [L,U] = bounds(xL,xU)
if xU-xL >= 2*pi
    L = -1;
    U = 1;
else
    xL = xL + pi/2;
    xU = xU + pi/2;
    n = floor(( (xL + xU)/2/(2*pi)));
    xL = xL - n*2*pi;
    xU = xU - n*2*pi;
    yL = sin(xL);
    yU = sin(xU);
    L = min([yL yU]);
    U = max([yL yU]);
    if (xL<pi/2 & xU>pi/2) |  (xL<-3*pi/2 & xU>-3*pi/2)
        U = 1;
    end
    if (xL < 3*pi/2 & xU > 3*pi/2) | (xL < -pi/2 & xU > -pi/2)
        L = -1;
    end
end

function [Ax, Ay, b] = convexhull(xL,xU)
% Convert to sin
xL = xL + pi/2;
xU = xU + pi/2;
if sin(xL)>=0 & sin(xU)>=0 & xU-xL<pi
    fL = sin(xL);
    fU = sin(xU);
    dfL = cos(xL);
    dfU = cos(xU);
    [Ax,Ay,b] = convexhullConcave(xL,xU,fL,fU,dfL,dfU);
elseif sin(xL)<=0 & sin(xU)<=0 & xU-xL<pi
    fL = sin(xL);
    fU = sin(xU);
    dfL = cos(xL);
    dfU = cos(xU);
    [Ax,Ay,b] = convexhullConvex(xL,xU,fL,fU,dfL,dfU);
else
    [Ax,Ay,b] = convexhullGeneral(xL,xU,@sin);
end
% Back to cos
b=b-Ax*pi/2;