linearize
linearize returns the linearization of the polynomial \(p(x)\) at the point value(x). It is based on the command jacobian
Syntax
h = linearize(p)
Examples
The linearization is performed at the current value of x
x = sdpvar(1,1);
f = x^2;
assign(x,1);
sdisplay(linearize(f))
ans =
'-1+2*x'
assign(x,3);
sdisplay(linearize(f))
ans =
'-9+6*x'
The command is short for
sdisplay(value(f)+value(jacobian(f,x))*(x-value(x)))
ans =
'-9+6*x'
The command applies to matrices as well
p11 = sdpvar(1,1);p12 = sdpvar(1,1);
P = [p11 p12;p12 1];
assign(P,[3 2;2 1])
sdisplay(linearize(P*P))
ans =
'-13+6*p11+4*p12' '-6+2*p11+4*p12'
'-6+2*p11+4*p12' '-3+4*p12'
