Store all iterations of a symbolic variable as double, numeric, etc. while using fmincon optimization to visualize post-run

I am using fmincon to optimize a two-reservoir system. Following the example syntax, I am using symbolic variables for reservoir storage, inflow, and releases. However, following optimization, I would like to plot and visualize the reservoir storage. I have tried cell2mat, double() and other ways of converting the symbolic variables to a format that can be used to see all iterations, but get an error each time.

What is the best way to have all iterations of each variable stored during optimization using fmincon, and what syntax should I use to convert them out of symbolic and see the values?

Thanks.

Answer 1

[Walter Roberson]

If double() fails on them, then they very likely still have symbolic variables in them, and cannot be directly plotted. To plot something that contains a symbolic variable you would need to substitute definite values for the symbolic variables. fplot() can do that for you if there is only one variable, and fsurf() can do that for 2 variables (producing a surface.)

[Sarah]

Thanks for the suggestion. It should just be a 120x1 single variable. I tried fplot, however that only returned a x=y line from -5 to 5 and did not allow me to see the values contained in the symbolic variable.

[Walter Roberson]

What does class() of the variable return? Does double() applied to the variable return an error or return an array of numeric values? Could you show some examples of the variable?

[Sarah]

The variable is monthly reservoir storage for 10 years (120 months) and thus should contain only numeric values. Variable 'S' appears as a 120x1 cell in the Matlab workspace. Class() returns 'cell', which is why I tried to use cell2mat(S) which then returns:

Error using cell2mat

CELL2MAT does not support cell arrays containing cell arrays or objects.

When I apply double(), it returns the following error:

Error using double

Conversion to double from cell is not possible.

[Walter Roberson]

What is class(storage{1}) ? What do you get for

cell2mat(cellfun(@double, storage, 'uniform', 0))

Please use

celldisp(storage)

and show us an example entry (that is not "trivial" such as being all 0)

[Sarah]

Thank you for your patience and help.

class(S{1}) returns 'sym' and cell2mat(cellfun(@double, storage, 'uniform', 0)) returns the error:

Error using symengine
DOUBLE cannot convert the input expression into a double array.
Error in sym/double (line 643)
        Xstr = mupadmex('symobj::double', S.s, 0);

Using celldisp(S), an example entry is as follows (and I've tried to attach it):

S{1} =

S0

S{2} =

S0 + c3*(QF1 - X241)

S{3} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242)

S{4} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243)

S{5} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244)

S{6} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245)

S{7} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245) + c3*(QF6 - X246)

S{8} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245) + c3*(QF6 - X246) + c3*(QF7 - X247)

S{9} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245) + c3*(QF6 - X246) + c3*(QF7 - X247) + c3*(QF8 - X248)

S{10} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245) + c3*(QF6 - X246) + c3*(QF7 - X247) + c3*(QF8 - X248) + c3*(QF9 - X249)

... 

S{120} =

S0 + c3*(QF1 - X241) + c3*(QF2 - X242) + c3*(QF3 - X243) + c3*(QF4 - X244) + c3*(QF5 - X245) + c3*(QF6 - X246) + c3*(QF7 - X247) + c3*(QF8 - X248) + c3*(QF9 - X249) + c3*(QF10 - X250) + c3*(QF11 - X251) + c3*(QF12 - X252) + c3*(QF13 - X253) + c3*(QF14 - X254) + c3*(QF15 - X255) + c3*(QF16 - X256) + c3*(QF17 - X257) + c3*(QF18 - X258) + c3*(QF19 - X259) + c3*(QF20 - X260) + c3*(QF21 - X261) + c3*(QF22 - X262) + c3*(QF23 - X263) + c3*(QF24 - X264) + c3*(QF25 - X265) + c3*(QF26 - X266) + c3*(QF27 - X267) + c3*(QF28 - X268) + c3*(QF29 - X269) + c3*(QF30 - X270) + c3*(QF31 - X271) + c3*(QF32 - X272) + c3*(QF33 - X273) + c3*(QF34 - X274) + c3*(QF35 - X275) + c3*(QF36 - X276) + c3*(QF37 - X277) + c3*(QF38 - X278) + c3*(QF39 - X279) + c3*(QF40 - X280) + c3*(QF41 - X281) + c3*(QF42 - X282) + c3*(QF43 - X283) + c3*(QF44 - X284) + c3*(QF45 - X285) + c3*(QF46 - X286) + c3*(QF47 - X287) + c3*(QF48 - X288) + c3*(QF49 - X289) + c3*(QF50 - X290) + c3*(QF51 - X291) + c3*(QF52 - X292) + c3*(QF53 - X293\\\n) + c3*(QF54 - X294) + c3*(QF55 - X295) + c3*(QF56 - X296) + c3*(QF57 - X297) + c3*(QF58 - X298) + c3*(QF59 - X299) + c3*(QF60 - X300) + c3*(QF61 - X301) + c3*(QF62 - X302) + c3*(QF63 - X303) + c3*(QF64 - X304) + c3*(QF65 - X305) + c3*(QF66 - X306) + c3*(QF67 - X307) + c3*(QF68 - X308) + c3*(QF69 - X309) + c3*(QF70 - X310) + c3*(QF71 - X311) + c3*(QF72 - X312) + c3*(QF73 - X313) + c3*(QF74 - X314) + c3*(QF75 - X315) + c3*(QF76 - X316) + c3*(QF77 - X317) + c3*(QF78 - X318) + c3*(QF79 - X319) + c3*(QF80 - X320) + c3*(QF81 - X321) + c3*(QF82 - X322) + c3*(QF83 - X323) + c3*(QF84 - X324) + c3*(QF85 - X325) + c3*(QF86 - X326) + c3*(QF87 - X327) + c3*(QF88 - X328) + c3*(QF89 - X329) + c3*(QF90 - X330) + c3*(QF91 - X331) + c3*(QF92 - X332) + c3*(QF93 - X333) + c3*(QF94 - X334) + c3*(QF95 - X335) + c3*(QF96 - X336) + c3*(QF97 - X337) + c3*(QF98 - X338) + c3*(QF99 - X339) + c3*(QF100 - X340) + c3*(QF101 - X341) + c3*(QF102 - X342) + c3*(QF103 - X343) + c3*(QF104 - X344) + c3*(QF105 - X345) + c\\\n3*(QF106 - X346) + c3*(QF107 - X347) + c3*(QF108 - X348) + c3*(QF109 - X349) + c3*(QF110 - X350) + c3*(QF111 - X351) + c3*(QF112 - X352) + c3*(QF113 - X353) + c3*(QF114 - X354) + c3*(QF115 - X355) + c3*(QF116 - X356) + c3*(QF117 - X357) + c3*(QF118 - X358) + c3*(QF119 - X359)

[Walter Roberson]

You could probably get all of those into one single symbolic vector, but you are still faced with some difficulties:

• What you are looking at there with all those equations is the value of those variables. There is no hidden numeric value
• The only way to plot those is to substitute specific numeric values for the symbolic variables. That would likely be a problem for you as it appears there are at least a few dozen symbolic variables involved and it is seldom practical to make a plot with more than 3 (at most 4) independent variables simultaneously.

When I look at those expressions, it looks to me as if you are building up an equation in a loop. I wonder if you need to store all of the iterations, or if you only need the final one?

It seems unlikely that you should be doing that computation inside an objective function. Instead likely you should be computing the equation once outside of fmincon and then using matlabFunction() to optimize over it. You would likely use the 'vars' parameter of matlabFunction to bundle a number of variables into a vector.