vector output of a symbolic vector

syms s X Y Z

l1 = X*s - 1 == 3*X + Y + Z + 2/s

l2 =Y*s == - X - Y - 1/s^2

l3 =Z*s - 2 == X - Z - (s - 1)/s^2

[Xsol,Ysol,Zsol]=solve([l1,l2,l3],[X,Y,Z])

[Xsol,Ysol,Zsol]=partfrac([Xsol,Ysol,Zsol])

Gives error: "Error using sym/partfrac

Too many output arguments."

Why?

Answer 1

[John D'Errico]

syms s X Y Z
l1 = X*s - 1 == 3*X + Y + Z + 2/s
l2 =Y*s == - X - Y - 1/s^2
l3 =Z*s - 2 == X - Z - (s - 1)/s^2
[Xsol,Ysol,Zsol]=solve([l1,l2,l3],[X,Y,Z])

Up to this point, you have done nothing wrong. Xsol, Ysol, and Zsol are all validly defined expressions of x, y, and z.

Then you tried to use partfrac, as applied to a vector, composed of [xsol,ysol,zsol].

help partfrac

--- help for sym/partfrac ---

 sym/partfrac - Partial fraction decomposition
    This MATLAB function finds the partial fraction decomposition of expr
    with respect to var.

    Syntax
      partfrac(expr,var)
      partfrac(expr,var,Name,Value)

    Input Arguments
      expr - Rational expression
        symbolic expression | symbolic function
      var - Variable of interest
        symbolic variable

    Name-Value Arguments
      FactorMode - Factorization mode
        'rational' (default) | 'real' | 'complex' | 'full'

    See also children, coeffs, collect, combine, compose, divisors, expand,
      factor, horner, numden, rewrite, simplify, simplifyFraction

    Introduced in Symbolic Math Toolbox in R2015a
    Documentation for sym/partfrac
       doc sym/partfrac

You could have applied partfrac to any one of them.

Xsolpf = partfrac(Xsol)

However, partfrac is not vectorized. And when you tried that as you did, it gave you an error. The point is, you could just have called partfrac three times. But not everything you write in MATLAB will be vectorized to work as you might hope it should work. Code is only code. As much as we wish it would do so, it cannot do more than it was written to do.

Could you have done like this?

XYZsol = partfrac([Xsol,Ysol,Zsol])

And then separated each of the three components into a separate result? Well, yes.

XYZsol(1)
XYZsol(2)
XYZsol(3)

[John D'Errico]

Sorry. The Answers bug is again present. When I wrote this post, if displays nicely. But when saved, it fails to do so.

Answer 2

[Vinay]

Hi @Lóránt Farkas,

The issue stems from the “partfrac” function, which is configured to accept only a single output argument. This function specifically performs partial fraction decomposition on:

• A single symbolic expression, or

Xsol_partfrac = partfrac(Xsol);
Ysol_partfrac = partfrac(Ysol);
Zsol_partfrac = partfrac(Zsol);

• An array of symbolic expressions

result=partfrac([Xsol,Ysol,Zsol])

To resolve this issue, decompose each expression individually using the “partfrac” function or to pass the array of symbolic expression and store result in a single argument. This approach ensures proper handling of each term and prevents the multiple output argument error.

Kindly refer to the below documentation of “partfrac” for more details:

https://www.mathworks.com/help/symbolic/sym.partfrac.html

I hope this helps!

Answer 3

[Lóránt Farkas]

I can do workaround, however it contradicts the main concepts of Matlab! The output of partfrac is 1x3 vector of symbolic variables the left side of the assigment is also a 1x3 vector of symbolic variables. Why should I do the serialization? Why works with solve (whose output is also a 1x3 symbolic vector) but not with partfrac? The non-symbolic part of matlab do this without any problem (and that is why it is so popular).

Why can I not do an assigment with symbolic vectors on the left side?