Simplify symbolic expression for optimized code generation

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Ehsan Tofigh
Ehsan Tofigh 2017-4-17
评论： Andrew Newell 2017-4-17
I'm trying to generate optimized c code (reduce the number of operations) from symbolic MATLAB expressions. However I MATLAB doesn't seem to want to simplify even the simplest equations.
lets take the following expression as an example:
X_eq = [
q0 + (dt*q1*(gyrobx - omegax))/2 + (dt*q2*(gyroby - omegay))/2 + (dt*q3*(gyrobz - omegaz))/2;
q1 - (dt*q0*(gyrobx - omegax))/2 + (dt*q3*(gyroby - omegay))/2 - (dt*q2*(gyrobz - omegaz))/2;
q2 - (dt*q0*(gyroby - omegay))/2 - (dt*q3*(gyrobx - omegax))/2 + (dt*q1*(gyrobz - omegaz))/2;
q3 + (dt*q2*(gyrobx - omegax))/2 - (dt*q1*(gyroby - omegay))/2 - (dt*q0*(gyrobz - omegaz))/2];
What i'm looking for is (basically factor out dt and (1/2)):
X_eq = [
q0 + (((q1*(gyrobx - omegax)) + (q2*(gyroby - omegay)) + (q3*(gyrobz - omegaz)))*dt)/2;
q1 - (((q0*(gyrobx - omegax)) + (q3*(gyroby - omegay)) - (q2*(gyrobz - omegaz)))*dt)/2;
q2 - (((q0*(gyroby - omegay)) - (q3*(gyrobx - omegax)) + (q1*(gyrobz - omegaz)))*dt)/2;
q3 + (((q2*(gyrobx - omegax)) - (q1*(gyroby - omegay)) - (q0*(gyrobz - omegaz)))*dt)/2];
simplify(X_eq, 'steps', 100) returns the original expression so it's useless:
ans =
q0 + (dt*q1*(gyrobx - omegax))/2 + (dt*q2*(gyroby - omegay))/2 + (dt*q3*(gyrobz - omegaz))/2
q1 - (dt*q0*(gyrobx - omegax))/2 + (dt*q3*(gyroby - omegay))/2 - (dt*q2*(gyrobz - omegaz))/2
q2 - (dt*q0*(gyroby - omegay))/2 - (dt*q3*(gyrobx - omegax))/2 + (dt*q1*(gyrobz - omegaz))/2
q3 + (dt*q2*(gyrobx - omegax))/2 - (dt*q1*(gyroby - omegay))/2 - (dt*q0*(gyrobz - omegaz))/2
collect(X_eq, [dt]) returns the following which is a step forward but doesn't factorize (1/2):
ans =
((q1*(gyrobx - omegax))/2 + (q2*(gyroby - omegay))/2 + (q3*(gyrobz - omegaz))/2)*dt + q0
((q3*(gyroby - omegay))/2 - (q0*(gyrobx - omegax))/2 - (q2*(gyrobz - omegaz))/2)*dt + q1
((q1*(gyrobz - omegaz))/2 - (q3*(gyrobx - omegax))/2 - (q0*(gyroby - omegay))/2)*dt + q2
((q2*(gyrobx - omegax))/2 - (q1*(gyroby - omegay))/2 - (q0*(gyrobz - omegaz))/2)*dt + q3
Finally, collect(X_eq, [1/2, -1/2, dt, -dt]) does the following which comes close but is still not what I expect:
ans =
((q1*(gyrobx - omegax) + q2*(gyroby - omegay) + q3*(gyrobz - omegaz))*dt)/2 + q0
((q3*(gyroby - omegay))*dt)/2 - ((q0*(gyrobx - omegax) + q2*(gyrobz - omegaz))*dt)/2 + q1
((q1*(gyrobz - omegaz))*dt)/2 - ((q0*(gyroby - omegay) + q3*(gyrobx - omegax))*dt)/2 + q2
((q2*(gyrobx - omegax))*dt)/2 - ((q1*(gyroby - omegay) + q0*(gyrobz - omegaz))*dt)/2 + q3
I've tried subexpr() as well which has it's used by doesn't help me in this situation. The number of equations is high so finding an automated way of reducing the number of calculations is important.

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回答（1 个）

Andrew Newell
Andrew Newell 2017-4-17
I don't know how particular you are about the exact form of the simplified expression, but this certainly produces a simpler expression:
Q = [q0; q1; q2; q3];
X_eq = Q + simplify(expand(X_eq-Q));
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Ehsan Tofigh
Ehsan Tofigh 2017-4-17
I was afraid of that. Thanks for the response none the less! can you tell me why collect() doesn't want to factor out all of the (1/2) factors? it does it for some terms but not all of them.
Andrew Newell
Andrew Newell 2017-4-17
Maybe because 1/2 is not a variable. How about this?
X_eq = collect(2*expand(X_eq),dt)/2;

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