Strange output using symbols in a matrix

Question

Jason Gauthier 2018-10-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/423805-strange-output-using-symbols-in-a-matrix

评论： Jason Gauthier 2018-10-13

I always seem to have some weird results when using symbols in matrices. I wrote a simple function that generates a transformation matrix based on arguments.

    function rot = dh_t (a,alpha, d, theta)
       rot = [cos(theta)            -sin(theta)           0           a;...
              sin(theta)*cos(alpha) cos(theta)*cos(alpha) -sin(alpha) -d*sin(alpha);...
              sin(theta)*sin(alpha) cos(theta)*sin(alpha) cos(alpha)  d*cos(alpha);...
              0                     0                     0           1]
    end

When I call this function:

dh_t(0,pi/2,L1,t2)

I get an ugly output.

   [                                                     cos(t2),                                                    -sin(t2),                                                 0,                                                      0]
   [ (4967757600021511*sin(t2))/81129638414606681695789005144064, (4967757600021511*cos(t2))/81129638414606681695789005144064,                                                -1,                                                    -L1]
   [                                                     sin(t2),                                                     cos(t2), 4967757600021511/81129638414606681695789005144064, (4967757600021511*L1)/81129638414606681695789005144064]
   [                                                           0,                                                           0,                                                 0,                                                      1]

I stick this in my calculator where I wrote an equivalent function:

    [cos(t2)   −sin(t2)   0  0]
    [sin(t2)   cos(t2)    0  0]
    [0         0          1 l1]
    [0         0          0  1]

Suggestions are welcome on how to handle this. Thanks!

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madhan ravi 2018-10-13

I stick this in my calculator where I wrote an equivalent function:

What do you mean by this? can you elaborate more?

Jason Gauthier 2018-10-13

Yes. It doesn't happen with my Ti-Inspire calculator.

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Answer 1

Walter Roberson 2018-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/423805-strange-output-using-symbols-in-a-matrix#answer_341244

在 MATLAB Online 中打开

dh_t(0,sym(pi)/2,L1,t2)

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Jason Gauthier 2018-10-13

oh, that's very nice.

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Answer 2

Star Strider 2018-10-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/423805-strange-output-using-symbols-in-a-matrix#answer_341222

在 MATLAB Online 中打开

Use the vpa (link) function.

Result = vpa(dh_t(0,pi/2,L1,t2), 3)

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Jason Gauthier 2018-10-13

although that appears more to be an issue with cos/sin inaccuracies.

Star Strider 2018-10-13

I suspect that the TI-inspire is not using the extended-precision representation that the Symbolic Math Toolbox does. It may instead be using the IEEE 754 standard, and considers 6.12e-17 as essentially 0.

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