# Simplify symbolic expression for optimized code generation

4 visualizaciones (últimos 30 días)
Ehsan Tofigh el 17 de Abr. de 2017
Comentada: Andrew Newell el 17 de Abr. de 2017
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.
##### 0 comentariosMostrar -2 comentarios más antiguosOcultar -2 comentarios más antiguos

Iniciar sesión para comentar.

### Respuestas (1)

Andrew Newell el 17 de Abr. de 2017
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));
##### 5 comentariosMostrar 3 comentarios más antiguosOcultar 3 comentarios más antiguos
Ehsan Tofigh el 17 de Abr. de 2017
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 el 17 de Abr. de 2017
X_eq = collect(2*expand(X_eq),dt)/2;

Iniciar sesión para comentar.

### Categorías

Más información sobre Symbolic Variables, Expressions, Functions, and Preferences en Help Center y File Exchange.

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by