Substituting and evaluating function

I have attempted to substitute the X variable into my function and evaluate it. This is the result. If it is not possible please tell me and I will find a difference method?

>> subs der(140,x);
Warning: Support of character vectors that are not valid variable names or define
a number will be removed in a future release. To create symbolic expressions,
first create symbolic variables and then use operations on them. 
> In sym>convertExpression (line 1586)
  In sym>convertChar (line 1491)
  In sym>tomupad (line 1243)
  In sym (line 199)
  In subs (line 66) 
>> eval der

der =

(13459*cos((313*x)/200 - 1689/2000))/25 + (42471*cos((1573*x)/1000 + 1153/500))/80 + (937443*cos((1849*x)/2500 + 441/250))/62500

GS.

[Stephen23]

What is der? Is it symbolic, or is it a simple function handle?

[Gavin Seddon]

Hello, der is the symbolic function that is the result of dIff fx.

Answer 1

[Star Strider]

Try this (in R2012a and later):

syms x 
X = sym(140);
der(x) = (13459*cos((313*x)/200 - 1689/2000))/25 + (42471*cos((1573*x)/1000 + 1153/500))/80 + (937443*cos((1849*x)/2500 + 441/250))/62500;
Desired_Symbolic_Result = der(X)
Desired_Numeric_Result = vpa(der(X))

Desired_Symbolic_Result = 
(937443*cos(26327/250))/62500 + (42471*cos(111263/500))/80 + (13459*cos(436511/2000))/25

Desired_Numeric_Result = 
-503.67380291547475440432522297924

Beginning in R2012a, you can create symbolic functions. You then work with them as you would any other function.

[Gavin Seddon]

Hello, AMAZING once again! This

[Star Strider]

As always, my pleasure!

Also, if you define ‘f(x)’ as the original function definition, the derivative:

der = diff(f, x)

will automatically be a function of ‘x’ as well, as ‘der(x)’.

[Gavin Seddon]

Hello again when I try to integrate this, it requires a handle. Is there a way of converting this? As always, thank you. GS.

[Star Strider]

You should be able to integrate it symbolically as written.

If you want to integrate it numerically, you need to convert it to an anonymous function to create a function handle for the numeric integration routines. [See the documentation on Anonymous Functions (link) for details.] The easiest way to convert a symbolic function to an anonymous function is to use the matlabFunction (link) function. You can then use it as an argument to integral and other functions.

As always, my pleasure.

[Gavin Seddon]

Hello Star Strider when I try with the function I get INT=integral(fx, 138.2, 306.3) Error using integral (line 82) First input argument must be a function handle. I must use your the solution, thanks. GS.

[Star Strider]

If you are using an anonymous function, this will work:

INT=integral(fx, 138.2, 306.3)

If you are using a function file, you have to precede the function name with ‘@’ to create a function handle:

INT=integral(@fx, 138.2, 306.3)

I am assuming here that ‘fx’ is a function of only one variable.

[Stephen23]

Gavin Seddon's "Answer" moved here:

Hello Star Strider, it doesn't appear to like @

>> INT=integral(@344*sin((313*x)/200 - 1689/2000) + (675*sin((1573*x)/1000 + 1153/500))/2 + (507*sin((1849*x)/2500 + 441/250))/25,(138.2000, 306.3000))
 INT=integral(@344*sin((313*x)/200 - 1689/2000) + (675*sin((1573*x)/1000 + 1153/500))/2 + (507*sin((1849*x)/2500 + 441/250))/25,(138.2000, 306.3000))
               ↑
Error: Unexpected MATLAB expression.
 GS.

[Star Strider]

To define an anonymous function, you need to specify the argument(s) to it. (See the documentation on Anonymous Functions (link) for details.)

Also, you need to remove the parentheses around the integration limits.

Try this:

INT = integral(@(x) 344*sin((313*x)/200 - 1689/2000) + (675*sin((1573*x)/1000 + 1153/500))/2 + (507*sin((1849*x)/2500 + 441/250))/25, 138.2000, 306.3000)

INT =
  -179.0603

[Gavin Seddon]

Hello I see but since the curve is positive why does it have a negative integral?

[Star Strider]

The curve is not uniformly positive. It oscillates with a median of 0 in the region of your limits of integration:

fcn = @(x) 344*sin((313*x)/200 - 1689/2000) + (675*sin((1573*x)/1000 + 1153/500))/2 + (507*sin((1849*x)/2500 + 441/250))/25;
x = linspace(138.2000, 306.3000, 10000);

figure(1)
plot(x, fcn(x))
grid

[Gavin Seddon]

Thank you I see this oscillation. Also, the curve is negative yet it lies in the upper right quadrant of a graph. This is a caveat I have never considered. This is probably obvious to a mathematician, would it be useful to investigate this further? Thank you. GS.

[Star Strider]

My pleasure.

I am not certain what you are doing, so I cannot offer specific advise. If this result seems anomalous, I certainly believe it would be useful to investigate it further.

[Gavin Seddon]

Hello again star Strider, I attempted to repeat this using V rather than der. The experiment has been modified. I received x = sym(170); >> V(x) Index exceeds matrix dimensions.

Error in sym/subsref (line 841) R_tilde = builtin('subsref',L_tilde,Idx); is the problem with my new data? My derivative is V =

- (92331455826879074318081118756173912512776418660041743993904822041876030910119699033499897171126899241725885130346424189784141742262968992408634746136851205869206855701491548798776503105475464220864413217341150170733739807706803033452925986295591352038336042192009955717827037497429499505042435549895145517335007476391376729481782080924433672184175718973072212272070882428631432519752545772508001320679085483283680177407432685533740793358744338287889355782389262329440622613778812194054590418858651122555880316120798011977434246121618976107398197182996875055142408909914155811962311415589065766422076177131304795913721217905037606990771319411*sin((5711*x)/1000 + 1311/1000))/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - (337938395605967118783451634120738357644051700575612507073379768863114967513255762797583614901123289513591827402052213060331395907562169969372033371964730098396975697478108635966708436699058012044737559749756894340141369730367633557437286745305395321673936415250385277680481135281460168325144813236682857015303680560921747257877841034623426231273488280813978055066545147906149766878637431325144908837020836874797052493218084299864947857717069041466310745423155285220128581051726929008324822350838304920263403088017826628931947265450765070760842430314065864765854552193925097073647350353333456305726858725752935749441754238330833135163923598606429196573691137345948092087*sin((8111*x)/10000 - 883/500))/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\\n0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - (2238214047960166868161666252374168002793633548200148771059904342010973189983069129042552287816045896404475905208516336659925687588964398230729666771262646881929744852332949180098520764229813389827908818003073070342095525455259306860245544499102528592805335810658944666253298566712317210412850678800593773597510804486447294828337350042527773540989757641865746337986161160684427430332725995301245617054848260084662737\\\n87587246990390362423046596214893834190927466438691935825680357272020798301699967083322502229500662422058286719988554418829338360993498526742839202506164100967762155030779279334189661438913028319732962082067372573160136054523940031056116221737040603*sin((7587*x)/10000 + 1401/1000))/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

GS.

[Star Strider]

‘V’ seems to be a (4x1) vector, so calling element 170 is certainly going to throw that error.

You probably need to create ‘V’ as a symbolic function. You can either define it directly, or by using the symfun function. (That applies to R2012a and later. In earlier versions use the subs function.)

[Gavin Seddon]

Hello yes I use this first but it did not evaluate the result: subs(V,x,170)

ans =

- (92331455826879074318081118756173912512776418660041743993904822041876030910119699033499897171126899241725885130346424189784141742262968992408634746136851205869206855701491548798776503105475464220864413217341150170733739807706803033452925986295591352038336042192009955717827037497429499505042435549895145517335007476391376729481782080924433672184175718973072212272070882428631432519752545772508001320679085483283680177407432685533740793358744338287889355782389262329440622613778812194054590418858651122555880316120798011977434246121618976107398197182996875055142408909914155811962311415589065766422076177131304795913721217905037606990771319411*sin((5711*x)/1000 + 1311/1000))/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - (337938395605967118783451634120738357644051700575612507073379768863114967513255762797583614901123289513591827402052213060331395907562169969372033371964730098396975697478108635966708436699058012044737559749756894340141369730367633557437286745305395321673936415250385277680481135281460168325144813236682857015303680560921747257877841034623426231273488280813978055066545147906149766878637431325144908837020836874797052493218084299864947857717069041466310745423155285220128581051726929008324822350838304920263403088017826628931947265450765070760842430314065864765854552193925097073647350353333456305726858725752935749441754238330833135163923598606429196573691137345948092087*sin((8111*x)/10000 - 883/500))/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\\n0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - (2238214047960166868161666252374168002793633548200148771059904342010973189983069129042552287816045896404475905208516336659925687588964398230729666771262646881929744852332949180098520764229813389827908818003073070342095525455259306860245544499102528592805335810658944666253298566712317210412850678800593773597510804486447294828337350042527773540989757641865746337986161160684427430332725995301245617054848260084662737\\\n87587246990390362423046596214893834190927466438691935825680357272020798301699967083322502229500662422058286719988554418829338360993498526742839202506164100967762155030779279334189661438913028319732962082067372573160136054523940031056116221737040603*sin((7587*x)/10000 + 1401/1000))/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 GS

[Star Strider]

One problem is that you have ‘\\\n’ embedded in that expression, every 1000 or so characters.

However, when I manually delete those and then execute this:

V = 
NaN

Vx = subs(V,x,170)

Vx =
NaN

Note that the arguments to trigonometric functions in the Symbolic Math Toolbox are in radians, not degrees.

For whatever reason, your function initially evaluates to NaN, possibly because of the magnitudes of the constants. I leave it to you to sort that.

[Gavin Seddon]

Hello Star Strider I am integrating the function however how do I simplify my new symbolic variable because it provides an equation rather than a number for example: INT=int(fx,160,303)

INT =

(968700*cos(12801/100))/8111 + (1094000*cos(122793/1000))/7587 - (1055*cos(216468/125))/11422 + (1055*cos(915071/1000))/11422 - (1094000*cos(2312871/10000))/7587 - (968700*cos(2439973/10000))/8111

>> eval INT

INT =

(968700*cos(12801/100))/8111 + (1094000*cos(122793/1000))/7587 - (1055*cos(216468/125))/11422 + (1055*cos(915071/1000))/11422 - (1094000*cos(2312871/10000))/7587 - (968700*cos(2439973/10000))/8111 GS.

[Steven Lord]

In general you should avoid eval. To convert that symbolic result into a numeric result you can use either double or vpa. If your result had included a symbolic variable, either vpa or subs (to substitute a value for the symbolic variable(s)) should work.

[Star Strider]

@Steven — Thank you!

[Gavin Seddon]

Yes thank you

[Gavin Seddon]

Hello again, I have shown an increase in the negative integral. However rather than repeat linespace is it possible to plot a histogram around a median? GS.

[Star Strider]

I am not following what you are doing.

You can specify the histogram edges to be symmetric about the median.

Experiment with this to define the edges:

mdn = 3;                                            % Median Of Data
N = 12;                                             % Number Of Bins Desired
edgvct = linspace(-N/2, N/2, N+1) + mdn;            % Vector Of Bin Edges

[Gavin Seddon]

Hello, this is really trivial however histogram(X) does not use my values. So how do I instruct Matlab to use my X and Y values? GS.

[Star Strider]

The documentation provides guidance:

histogram(X,edgvct)

or if you have two arrays and you want a 2-dimensional histogram, use the histogram2 function. You may have to provide a second vector of edges for the ‘Y’ data as well. See the documentation for details.