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Mathematica Graphics and Visualization

Simpler expression and Legends

Sungwoo Yang

Sungwoo Yang, MIT

Posted 10 years ago

Hi all, Here is what I wrote, but it is not beautiful. Do you think you can write it in a simpler and better way? Another question is I'd like to add Legends saying dashed line is "Receiver efficiency" and solid line is "system efficiency", but I couldn't do that. Any help will be very appreciable. Thank you. ClearAll \[Sigma] = 5.67 10^-8; "Stefan-Boltzmann Constant"; \[Epsilon] = 1; "Emissivity"; \[Alpha] = 1; "Absorbtivity"; \[Tau] = 1; "Transmittance"; g = 1 10^3; "Solar radiation 1Kw/m^2"; c = Range[10, 50, 10]; "Concentration"; receff[x_] = \[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g); syseff[x_] = (\[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g)) (1 - 293.15/x); Plot[Evaluate[{receff[x], syseff[x]}], {x, 293.15, 1073.15}, PlotStyle -> {Directive[Dashed, Black], Directive[Dashed, Red], Directive[Dashed, Blue], Directive[Dashed, Green], Directive[Dashed, Purple], Directive[Thick, Black], Directive[Thick, Red], Directive[Thick, Blue], Directive[Thick, Green], Directive[Thick, Purple]}, Frame -> True, PlotRange -> {{250, 1000}, {0, 1.05}}, FrameLabel -> {"Temperature (K)" , "Efficiency (%)"}, LabelStyle -> Directive[Black, Bold, {16, GrayLevel[0.3]}]]

Hi all,

Here is what I wrote, but it is not beautiful. Do you think you can write it in a simpler and better way? Another question is I'd like to add Legends saying dashed line is "Receiver efficiency" and solid line is "system efficiency", but I couldn't do that. Any help will be very appreciable. Thank you.

ClearAll
\[Sigma] = 5.67 10^-8; "Stefan-Boltzmann Constant";
\[Epsilon] = 1; "Emissivity";
\[Alpha] = 1; "Absorbtivity";
\[Tau] = 1; "Transmittance";
g = 1 10^3; "Solar radiation 1Kw/m^2";
c = Range[10, 50, 10]; "Concentration";
receff[x_] = \[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 
      293.15^4))/(c g);
syseff[x_] = (\[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 
        293.15^4))/(c g)) (1 - 293.15/x);
Plot[Evaluate[{receff[x], syseff[x]}], {x, 293.15, 1073.15}, 
 PlotStyle -> {Directive[Dashed, Black], Directive[Dashed, Red], 
   Directive[Dashed, Blue], Directive[Dashed, Green], 
   Directive[Dashed, Purple], Directive[Thick, Black], 
   Directive[Thick, Red], Directive[Thick, Blue], 
   Directive[Thick, Green], Directive[Thick, Purple]}, Frame -> True, 
 PlotRange -> {{250, 1000}, {0, 1.05}}, 
 FrameLabel -> {"Temperature (K)"  , "Efficiency (%)"}, 
 LabelStyle -> Directive[Black, Bold, {16, GrayLevel[0.3]}]]

enter image description here

POSTED BY: Sungwoo Yang

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Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 10 years ago

... Well, in the context of a speech bubble in comics this would mean "swearing", but here it means the same as @@@, i.e. you can write PlotStyle -> (Directive @@@ Transpose[{Join[ConstantArray[Dashed, 5], ConstantArray[Thick, 5]], Flatten[ConstantArray[{Black, Red, Blue, Green, Purple}, 2]]}]) Look for Apply in the documentation. Henrik

POSTED BY: Henrik Schachner

David Gathercole

David Gathercole, Vitol

Posted 10 years ago

On the contrary, this is nice concise code! You could pack up your plot style specification if you really wanted: PlotStyle -> (Directive @@ # & /@ Transpose[{Join[ConstantArray[Dashed, 5], ConstantArray[Thick, 5]], Flatten[ConstantArray[{Black, Red, Blue, Green, Purple}, 2]]}])

POSTED BY: David Gathercole

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 10 years ago

Dear Sungwoo Yang, I cannot verify any error. I would like to propose some further changes. In particular below I replaced in your definition of the functions receff and syseff "=" with ":=", which might be important. So your already nice code together with Davids improvements and my minor remarks now looks like: ClearAll["Global`"] \[Sigma] = 5.67^-8; (* Stefan-Boltzmann Constant) \[Epsilon] = 1; ( Emissivity ) \[Alpha] = 1; ( Absorbtivity ) \[Tau] = 1; ( Transmittance ) g = 1^3; (* Solar radiation 1Kw/m^2" ) c = Range[10, 50, 10]; ( Concentration *) receff[x_] := \[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g); syseff[x_] := (\[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g)) (1 - 293.15/x); Plot[Evaluate[{receff[x], syseff[x]}], {x, 293.15, 1073.15}, PlotStyle -> (Directive @@@ Transpose[{Join[ConstantArray[Dashed, 5], ConstantArray[Thick, 5]], Flatten[ConstantArray[{Black, Red, Blue, Green, Purple}, 2]]}]), Frame -> True, PlotRange -> {{250, 1000}, {0, 1.05}}, FrameLabel -> {"Temperature (K)", "Efficiency (%)"}, LabelStyle -> Directive[Black, Bold, {16, GrayLevel[0.3]}]] Henrik

Dear Sungwoo Yang,

I cannot verify any error. I would like to propose some further changes. In particular below I replaced in your definition of the functions receff and syseff "=" with ":=", which might be important. So your already nice code together with Davids improvements and my minor remarks now looks like:

ClearAll["Global`*"]
\[Sigma] = 5.67*^-8;            (* Stefan-Boltzmann Constant*)
\[Epsilon] = 1;                 (* Emissivity *)
\[Alpha] = 1;                   (* Absorbtivity *)
\[Tau] = 1;                     (* Transmittance *)
g = 1*^3;                       (* Solar radiation 1Kw/m^2" *)
c = Range[10, 50, 10];          (* Concentration *)

receff[x_] := \[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g);
syseff[x_] := (\[Alpha] \[Tau] - (\[Sigma] \[Epsilon] (x^4 - 293.15^4))/(c g)) (1 - 293.15/x);
Plot[Evaluate[{receff[x], syseff[x]}], {x, 293.15, 1073.15}, 
 PlotStyle -> (Directive @@@ Transpose[{Join[ConstantArray[Dashed, 5], ConstantArray[Thick, 5]], 
      Flatten[ConstantArray[{Black, Red, Blue, Green, Purple}, 2]]}]),
  Frame -> True, PlotRange -> {{250, 1000}, {0, 1.05}}, 
 FrameLabel -> {"Temperature (K)", "Efficiency (%)"}, 
 LabelStyle -> Directive[Black, Bold, {16, GrayLevel[0.3]}]]

Henrik

POSTED BY: Henrik Schachner

Sungwoo Yang

Sungwoo Yang, MIT

Posted 10 years ago

Hi David, Yes, this is what I was looking for. It looks simpler and better. I don't fully understand "@@ # & /@", but I guess it takes time. Thank you so much for your help.

POSTED BY: Sungwoo Yang

Sungwoo Yang

Sungwoo Yang, MIT

Posted 10 years ago

It actually gives me an error saying "An improperly formatted option was encountered. The left-hand side of the option was not a symbol or string." I will take a look at the documentation about "Apply @@@" Thank you for your help.

POSTED BY: Sungwoo Yang

Sungwoo Yang

Sungwoo Yang, MIT

Posted 10 years ago

You're right. I just try again by replacing @@ # & /@ with @@@, now, it does not give me any error. I don't understand why there was the error before. But I had similar issue before. There was several codes I wrote and they worked fine initially and at some point stopped working because they generated errors. I think I need more learning to eventually understand this issue. In addition, I also replace = with :=, which also works well. I'm still not good enough to see the difference between = and := in real usage. Your suggested code definitely looks better. Thank you so much for your help. I really appreciate it.

POSTED BY: Sungwoo Yang

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