how can a symbolic derivative be vectorized automatically?

Hello,

here is the simplified problem.

I have a symblic function with three arguments. And the derivative of f wrt. b

syms a b c
f = a*sin(b)*exp(c)
df = diff(f,b)

The solution is:

df = a*exp(c)*cos(b)

Now i will use this derivatve in a numeric script. And the argumetns a,b,c are vectors:

a=rand(10,1);
b=rand(10,1);
c=rand(10,1);

My current approach is to modify the derivative manualy: (adding "dots")

df = a.*exp(c).*cos(b)

Is there a way how i can change a symblic expression automatically?

My equations are has 80 or more characters and the derivatives has 2x to 3x the amount of characters.

So an automatic transform into an vectorized version would help me a lot.

Best regards,

MJ

Answer 1

[Stephen23]

Use MATLABFUNCTION:

syms a b c
f = a*sin(b)*exp(c)

f = 

df = diff(f,b)

df = 

mf = matlabFunction(df)

mf = function_handle with value:
    @(a,b,c)a.*exp(c).*cos(b)

a=rand(10,1);
b=rand(10,1);
c=rand(10,1);
mf(a,b,c)

ans = 10×1

0.8287 0.4912 0.5251 2.2295 1.7548 0.0752 1.3973 0.6642 0.1812 0.5342

Answer 2

[Dyuman Joshi]

Convert it to a function handle -

syms a b c
f = a*sin(b)*exp(c)

f = 

df = diff(f,b)

df = 

%Convert the symbolic function to an anonymous function
fun = matlabFunction(df)

fun = function_handle with value:
    @(a,b,c)a.*exp(c).*cos(b)

a=rand(10,1);
b=rand(10,1);
c=rand(10,1);

fun(a,b,c)

ans = 10×1

1.6337 0.7283 1.9453 1.1977 0.0795 1.0797 0.8060 0.3090 2.5127 0.9578

Answer 3

[Walter Roberson]

format long g
syms a b c
f(a,b,c) = a*sin(b)*exp(c)

f(a, b, c) = 

df = diff(f,b)

df(a, b, c) = 

A = rand(10,1);
B = rand(10,1);
C = rand(10,1);

D = df(A, B, C)

D = 

vpa(D)

ans = 

double(D)

ans = 10×1

0.472553502790635 1.26659066678776 0.609162623765823 0.642273629496948 0.893411797110293 0.88743081840584 0.39637226337217 0.303468357868928 0.198740877661276 1.09526181869221