问题

In MatLab, you can declare symbols pretty easily:

syms a,b
mat = [a,b]

I'm getting an error, however, when I try to replicate this in Octave. This is the code I'm using:

> symbols
> a = sym("a")
a =

a
> b = sym("b")
b =

b
> mat = [a,b]
error: octave_base_value::resize (): wrong type argument `ex'
error: octave_base_value::resize (): wrong type argument `<unknown type>'
octave-3.2.3.exe:4:C:\Octave\3.2.3_gcc-4.4.0\bin

How do you declare a symbolic matrix in octave?

回答1:

Would this help ?

It looks like you might need the symbolic toolbox package, reference here.

回答2:

If you don't already have the symbolic package, download it. From Octave command line, or gui command line. e.g.

octave> pkg install -forge symbolic

If you have python and sympy installed, that will install the package for you from octave forge. I used google to figure out how to get sympy installed, hit me up if you need help.

With symbolic package installed, use "pkg load" to import the package functions, and then use syms function to declare symbols.

octave> pkg load symbolic

octave> syms a b

This defined symbols a and b.

octave> syms
Symbolic variables in current scope:
  a
  b

"syms" by itself will print all the symbols you have defined.

octave> mat = [a,b]
mat = (sym) [a  b]  (1×2 matrix)

octave:34> mat * 2
ans = (sym) [2⋅a  2⋅b]  (1×2 matrix)

I found this package very helpful in computing Rotation matrices for my Robotic Manipulators class. Hope this helps.

Here's part of my script for more examples:

pkg load symbolic
syms psi phi theta psidot phidot thetadot

RzPsi = [[cos(psi), -sin(psi), 0]; [sin(psi), cos(psi), 0]; [0,0,1]]
RyTheta = [[cos(theta), 0, sin(theta)];[0,1,0];[-sin(theta), 0, cos(theta)]]
RzPhi = [[cos(phi), -sin(phi), 0]; [sin(phi), cos(phi), 0]; [0,0,1]]

RzPsi = (sym 3×3 matrix)

  ⎡cos(ψ)  -sin(ψ)  0⎤
  ⎢                  ⎥
  ⎢sin(ψ)  cos(ψ)   0⎥
  ⎢                  ⎥
  ⎣  0        0     1⎦

RyTheta = (sym 3×3 matrix)

  ⎡cos(θ)   0  sin(θ)⎤
  ⎢                  ⎥
  ⎢   0     1    0   ⎥
  ⎢                  ⎥
  ⎣-sin(θ)  0  cos(θ)⎦

RzPhi = (sym 3×3 matrix)

  ⎡cos(φ)  -sin(φ)  0⎤
  ⎢                  ⎥
  ⎢sin(φ)  cos(φ)   0⎥
  ⎢                  ⎥
  ⎣  0        0     1⎦

octave> RzPhi * RyTheta
ans = (sym 3×3 matrix)

  ⎡cos(φ)⋅cos(θ)   -sin(φ)  sin(θ)⋅cos(φ)⎤
  ⎢                                     ⎥
  ⎢sin(φ)⋅cos(θ)   cos(φ)   sin(φ)⋅sin(θ)⎥
  ⎢                                     ⎥
  ⎣   -sin(θ)        0        cos(θ)    ⎦

回答3:

After installing the symbolic toolbox (you can do this on some environments by issuing sudo apt-get install octave-symbolic), you have to do the following:

symbols
x = sym('x')

but beware that Octave's functions for manipulating symbolic expressions are much worse than MATLAB's.

回答4:

Symbolic Toolbox for Octave is more or less useless. You cannot resize a matrix as in your case, you cannot use the "-" operator. For example, you can differentiate a simple symbolic operation:

octave:1> symbols
octave:2> q1 = sym("q1");
octave:3> differentiate(Sin(q1)*Cos(q1),q1)
ans =

-sin(q1)^2+cos(q1)^2

but if you try to do this:

octave:6> -Sin(q1)
error: unary operator `-' not implemented for `ex' operands
octave:6> -q1
error: unary operator `-' not implemented for `ex' operands

Same happens in your case, i.e. resizing a matrix containing symbolic values

回答5:

Another example for posterity.

I used http://octave-online.net/ to develop and run this octave script.

NB: I included output as comments to show results.

disp("2-state markov chain symbolic analysis");

syms lambda mu

L = [lambda,0]
# L = (sym) [λ  0]  (1×2 matrix)

U = [1;0]
#U =
#   1
#   0

C = [ [1,1]; [lambda,-mu]]
#C = (sym 2×2 matrix)
#  ⎡1  1 ⎤
#  ⎢     ⎥
#  ⎣λ  -μ⎦

C^-1
#ans = (sym 2×2 matrix)
#  ⎡  λ          -1   ⎤
#  ⎢────── + 1  ──────⎥
#  ⎢-λ - μ      -λ - μ⎥
#  ⎢                  ⎥
#  ⎢   -λ         1   ⎥
#  ⎢  ──────    ──────⎥
#  ⎣  -λ - μ    -λ - μ⎦

P = C^-1 * U
#P = (sym 2×1 matrix)
#
#  ⎡  λ       ⎤
#  ⎢────── + 1⎥
#  ⎢-λ - μ    ⎥
#  ⎢          ⎥
#  ⎢   -λ     ⎥
#  ⎢  ──────  ⎥
#  ⎣  -λ - μ  ⎦

lambda_sys = L * C^-1 * U
#lambda_sys = (sym)
#
#    ⎛  λ       ⎞
#  λ⋅⎜────── + 1⎟
#    ⎝-λ - μ    ⎠

回答6:

Array of Handles

You can use the Octave Struct Array to create a symbolic matrix like this:

b(1,1).vector = @sin;
b(1,2).vector = @cos;
b(2,1).vector = @sec;
b(2,2).vector = @csc;

b
b.vector

printf( "\n\nCalling each element:\n" )
b(1,1).vector
b(1,2).vector
b(2,1).vector
b(2,2).vector

printf( "\nCalculatin the sin of 1:\n" )
b(1,1).vector(1)

Running this above returns:

b =

  2x2 struct array containing the fields:

    vector

ans = @sin
ans = @sec
ans = @cos
ans = @csc


Calling each element:
ans = @sin
ans = @cos
ans = @sec
ans = @csc

Calculatin the sin of 1:
ans =  0.841470984807897

Array of Symbols

You could replace the @sin, @cos, etc by sym("a"), sym("b"), sym("c"), etc.

pkg load symbolic;

b(1,1).vector = sym("a");
b(1,2).vector = sym("b");
b(2,1).vector = sym("c");
b(2,2).vector = sym("d");

b
b.vector

printf( "\n\nCalling each element:\n" )
b(1,1).vector
b(1,2).vector
b(2,1).vector
b(2,2).vector

Running this above returns:

b =

  2x2 struct array containing the fields:

    vector

ans = (sym) a
ans = (sym) c
ans = (sym) b
ans = (sym) d


Calling each element:
ans = (sym) a
ans = (sym) b
ans = (sym) c
ans = (sym) d

References:

https://www.gnu.org/software/octave/doc/v4.0.0/Structure-Arrays.html
http://mattpap.github.io/scipy-2011-tutorial/html/installing.html
https://github.com/cbm755/octsympy
https://askubuntu.com/questions/737746/installing-symbolic-package-in-octave
https://github.com/sympy/sympy

来源：https://stackoverflow.com/questions/2472486/how-do-i-declare-a-symbolic-matrix-in-octave

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How do I declare a symbolic matrix in Octave?

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