symbolic equation Empty sym: 0-by-1

here's the command line instruction I issue:-

solve('xw = xo+sin(xo)*180/pi',xo)

but I get:- ans = Empty sym: 0-by-1

I'm obviously new to Matlab...any help appreciated..Thanks

[Walter Roberson]

Are you certain that you should be multiplying the results of the sin() by 180/π ? That is the factor that you would use to convert radians to degrees, but the results of sin() are not in radians.

[george brown]

Thanks for your response. Yes that's what I need to do. The equation is correct. I just need to rewrite it to solve for xo for a given value of xw.

[Walter Roberson]

The equation cannot be correct. sin(xo) implies that xo is in radians. You can clear the factor of 180/π on the sin() term by multiplying all terms by π/180. When you do that then the xo+ term becomes xo*π/180+ which would be the conversion if xo were in degrees and you wanted to convert to radians. But if that were the case then you would not use sin(xo) because sin() is not applied to degrees.

Either you have the wrong conversion factor or else you should be using sind()

It would help if you were to indicate the expected units for your variables.

[Walter Roberson]

When I test your equation with xw arbitrarily set to sqrt(2) or 10, I find 36 or 38 real solutions: which one did you need?

[george brown]

First of all , thanks for your interest and you're absolutely correct I did want to get the sin of a value in degrees so it should indeed be sind().

Here's some info about what I'm working on.

The equation shown relates to warping (time shifting) the time locations of (angular) values along the time axis of a sine wave ...essentially warping the sine waveform. The equation calculates a time shift (angular shift) that is dependant on the instantaneous values of amplitude of the original unwarped sine wave. This amplitude instantaneous amplitude is multiplied by the 180/pi which is an offset coefficient (as you say one radian converted to degrees) because the time axis is in degrees in this version of the equation.

positive amplitudes (angles between zero and 180 degress result in time advancing and angles between 180 and 360 result in time retarding.

For example if xo is the peak (90 degree) value of the original sine wave ( xo stands for x original) the angular x value is shifted to a new "time warped" location on the x axis (xw stands for x warped)

so using the equation ....when xo is 90 degrees xw is 147.29 degrees

xw = xo+sind(xo)*180/pi

xw = 90 + sind(90) * 180/pi xw = 147.2958 degrees

or

when xo is 30 degrees xw is 58.6479 xw = 30 + sind(30) * 180/pi xw = 58.6479 degrees

Note that when xo is 0 degrees a zero time shift results and xo = xw

So the equation represents an amplitude dependant time shift of point values on a sine wave.

Here's a graph showing 10 sine waves of various amplitudes and their resulting time warped equivalents.

I'll be working in samples along the axis ultimately but for now i'm working in angles just until I get my basic math ironed out.

Without going into further detail...as I say I need to rewrite the equation to solve for xo given an xw value....because the y value that matches xw is actually the same amplitude as the y value for xo....that is the sind(xo)

This probaly sounds awfully confusing coming in cold. Anyway thanks for you help so far and I certainly understand if you leave it at that. I probbaly need to spend more than just a few hours on matlab before inflicting stupid questions on you fine folk.

Answer 1

[John D'Errico]

Being new is irrelevant. This is just a question of mathematics. Sym produces an empty result because there is no analytical solution to the problem posed. It is trivially simple to write an expression with no analytical solution. You just proved that by example.

If you have a specific value for xw, then use a tool like fzero or vpasolve, that will be able to provide a numerical root finding solution. Even there, you may need to beware, because there may be still no solution, or there may be multiple solutions, and the rootfinder will only provide a single solution. In the latter case, it will depend on the starting point for the solver.

[george brown]

thanks for your response. I'll need to read about fzero and vpasolve. I just need to rewrite the equation to solve for xo for a given value of xw and I was following an example I'd seen on solving algebraic equations symbolically.

Answer 2

[qasem qasem]

here's the command line instruction I issue:-

syms a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18...
    a19 a20

eqn0=-2*(-(e*a0)-x2*a1-x3*a2-x2*a3-x3*a4-x4*a5-x5*a6-x2*a7-x3*a8-x4*a9-...
    x5*a10-x6*a11-x7*a12-x2*a13-x3*a14-x4*a15-x5*a16-x6*a17-x7*a18-x8*a19...
    -x9*a20)==2*x1;

eqn1=-2*(-x2*a0-xx2*a1-xx3*a2-xx2*a3-xx3*a4-xx4*a5-xx5*a6-xx2*a7-xx3*a8-xx4*a9-...
    xx5*a10-xx6*a11-xx7*a12-xx2*a13-xx3*a14-xx4*a15-xx5*a16-xx6*a17-xx7*a18-xx8*a19...
    -xx9*a20)==2*xx1;

eqn2=-2*(-x3*a0-rr2*a1-rr3*a2-rr2*a3-rr3*a4-rr4*a5-rr5*a6-rr2*a7-rr3*a8-rr4*a9-...
    rr5*a10-rr6*a11-rr7*a12-rr2*a13-rr3*a14-rr4*a15-rr5*a16-rr6*a17-rr7*a18-rr8*a19...
    -rr9*a20)==2*rr1;

eqn3=-2*(-x2*a0-xx2*a1-xx3*a2-xx2*a3-xx3*a4-xx4*a5-xx5*a6-xx2*a7-xx3*a8-xx4*a9-...
    xx5*a10-xx6*a11-xx7*a12-xx2*a13-xx3*a14-xx4*a15-xx5*a16-xx6*a17-xx7*a18-xx8*a19...
    -xx9*a20)==2*xx1;

eqn4=-2*(-x3*a0-rr2*a1-rr3*a2-rr2*a3-rr3*a4-rr4*a5-rr5*a6-rr2*a7-rr3*a8-rr4*a9-...
    rr5*a10-rr6*a11-rr7*a12-rr2*a13-rr3*a14-rr4*a15-rr5*a16-rr6*a17-rr7*a18-rr8*a19...
    -rr9*a20)==2*rr1;

eqn5=-2*(-x4*a0-ww2*a1-ww3*a2-ww2*a3-ww3*a4-ww4*a5-ww5*a6-ww2*a7-ww3*a8-ww4*a9-...
    ww5*a10-ww6*a11-ww7*a12-ww2*a13-ww3*a14-ww4*a15-ww5*a16-ww6*a17-ww7*a18-ww8*a19...
    -ww9*a20)==2*ww1;

eqn6=-2*(-x5*a0-ee2*a1-ee3*a2-ee2*a3-ee3*a4-ee4*a5-ee5*a6-ee2*a7-ee3*a8-ee4*a9-...
    ee5*a10-ee6*a11-ee7*a12-ee2*a13-ee3*a14-ee4*a15-ee5*a16-ee6*a17-ee7*a18-ee8*a19...
    -ee9*a20)==2*ee1;

eqn7=-2*(-x2*a0-xx2*a1-xx3*a2-xx2*a3-xx3*a4-xx4*a5-xx5*a6-xx2*a7-xx3*a8-xx4*a9-...
    xx5*a10-xx6*a11-xx7*a12-xx2*a13-xx3*a14-xx4*a15-xx5*a16-xx6*a17-xx7*a18-xx8*a19...
    -xx9*a20)==xx1;

eqn8=-2*(-x3*a0-rr2*a1-rr3*a2-rr2*a3-rr3*a4-rr4*a5-rr5*a6-rr2*a7-rr3*a8-rr4*a9-...
    rr5*a10-rr6*a11-rr7*a12-rr2*a13-rr3*a14-rr4*a15-rr5*a16-rr6*a17-rr7*a18-rr8*a19...
    -rr9*a20)==2*rr1;

eqn9=-2*(-x4*a0-ww2*a1-ww3*a2-ww2*a3-ww3*a4-ww4*a5-ww5*a6-ww2*a7-ww3*a8-ww4*a9-...
    ww5*a10-ww6*a11-ww7*a12-ww2*a13-ww3*a14-ww4*a15-ww5*a16-ww6*a17-ww7*a18-ww8*a19...
    -ww9*a20)==2*ww1;

eqn10=-2*(-x5*a0-ee2*a1-ee3*a2-ee2*a3-ee3*a4-ee4*a5-ee5*a6-ee2*a7-ee3*a8-ee4*a9-...
    ee5*a10-ee6*a11-ee7*a12-ee2*a13-ee3*a14-ee4*a15-ee5*a16-ee6*a17-ee7*a18-ee8*a19...
    -ee9*a20)==2*ee1;

eqn11=-2*(-x6*a0-yy2*a1-yy3*a2-yy2*a3-yy3*a4-yy4*a5-yy5*a6-yy2*a7-yy3*a8-yy4*a9-...
    yy5*a10-yy6*a11-yy7*a12-yy2*a13-yy3*a14-yy4*a15-yy5*a16-yy6*a17-yy7*a18-yy8*a19...
    -yy9*a20)==2*yy1;

eqn12=-2*(-x7*a0-uu2*a1-uu3*a2-uu2*a3-uu3*a4-uu4*a5-uu5*a6-uu2*a7-uu3*a8-uu4*a9-...
    uu5*a10-uu6*a11-uu7*a12-uu2*a13-uu3*a14-uu4*a15-uu5*a16-uu6*a17-uu7*a18-uu8*a19...
    -uu9*a20)==2*uu1;

eqn13=-2*(-x2*a0-xx2*a1-xx3*a2-xx2*a3-xx3*a4-xx4*a5-xx5*a6-xx2*a7-xx3*a8-xx4*a9-...
    xx5*a10-xx6*a11-xx7*a12-xx2*a13-xx3*a14-xx4*a15-xx5*a16-xx6*a17-xx7*a18-xx8*a19...
    -xx9*a20)==2*xx1;

eqn14=-2*(-x3*a0-rr2*a1-rr3*a2-rr2*a3-rr3*a4-rr4*a5-rr5*a6-rr2*a7-rr3*a8-rr4*a9-...
    rr5*a10-rr6*a11-rr7*a12-rr2*a13-rr3*a14-rr4*a15-rr5*a16-rr6*a17-rr7*a18-rr8*a19...
    -rr9*a20)==2*rr1;

eqn15=-2*(-x4*a0-ww2*a1-ww3*a2-ww2*a3-ww3*a4-ww4*a5-ww5*a6-ww2*a7-ww3*a8-ww4*a9-...
    ww5*a10-ww6*a11-ww7*a12-ww2*a13-ww3*a14-ww4*a15-ww5*a16-ww6*a17-ww7*a18-ww8*a19...
   -ww9*a20)==2*ww1;

eqn16=-2*(-x5*a0-ee2*a1-ee3*a2-ee2*a3-ee3*a4-ee4*a5-ee5*a6-ee2*a7-ee3*a8-ee4*a9-...
    ee5*a10-ee6*a11-ee7*a12-ee2*a13-ee3*a14-ee4*a15-ee5*a16-ee6*a17-ee7*a18-ee8*a19...
    -ee9*a20)==2*ee1;

eqn17=-2*(-x6*a0-yy2*a1-yy3*a2-yy2*a3-yy3*a4-yy4*a5-yy5*a6-yy2*a7-yy3*a8-yy4*a9-...
    yy5*a10-yy6*a11-yy7*a12-yy2*a13-yy3*a14-yy4*a15-yy5*a16-yy6*a17-yy7*a18-yy8*a19...
    -yy9*a20)==2*yy1;

eqn18=-2*(-x7*a0-uu2*a1-uu3*a2-uu2*a3-uu3*a4-uu4*a5-uu5*a6-uu2*a7-uu3*a8-uu4*a9-...
    uu5*a10-uu6*a11-uu7*a12-uu2*a13-uu3*a14-uu4*a15-uu5*a16-uu6*a17-uu7*a18-uu8*a19...
    -uu9*a20)==2*uu1;

eqn19=-2*(-x8*a0-ii2*a1-ii3*a2-ii2*a3-ii3*a4-ii4*a5-ii5*a6-ii2*a7-ii3*a8-ii4*a9-...
    ii5*a10-ii6*a11-ii7*a12-ii2*a13-ii3*a14-ii4*a15-ii5*a16-ii6*a17-ii7*a18-ii8*a19...
    -ii9*a20)==2*ii1;

eqn20=-2*(-x9*a0-oo2*a1-oo3*a2-oo2*a3-oo3*a4-oo4*a5-oo5*a6-oo2*a7-oo3*a8-oo4*a9-...
    oo5*a10-oo6*a11-oo7*a12-oo2*a13-oo3*a14-oo4*a15-oo5*a16-oo6*a17-oo7*a18-oo8*a19...
    -oo9*a20)==2*oo1;

sol = solve(eqn0, eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7, eqn8,...
    eqn9, eqn10, eqn11, eqn12, eqn13, eqn14, eqn15, eqn16, eqn17, eqn18, eqn19, eqn20)


a0sol=double(sol.a0)
a1sol=double(sol.a1) 
a2sol=double(sol.a2 )
a3sol=double(sol.a3 )
a4sol=double(sol.a4) 
a5sol=double(sol.a5) 
a6sol=double(sol.a6) 
a7sol=double(sol.a7) 
a8sol=double(sol.a8) 
a9sol=double(sol.a9 )
a10sol=double(sol.a10 )
a11sol=double(sol.a11) 
a12sol=double(sol.a12) 
a13sol=double(sol.a13 )
a14sol=double(sol.a14 )
a15sol=double(sol.a15 )
a16sol=double(sol.a16) 
a17sol=double(sol.a17) 
a18sol=double(sol.a18) 
a19sol=double(sol.a19) 
a20sol=double(sol.a20)

but I get:- ans = Empty sym: 0-by-1

I'm obviously new to Matlab...any help appreciated..Thanks

[Rik]

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