Extracting data from a loop

edited March 2011 in Science & Tech
(pseudocode)

function Sactual = Untitled( P,Cactual)

% Ccalculated = The calculated sand concentration from the loop
% Cactual = The known sand concentration from the loop

S=0:1:10;

A loop that stops looping when Ccalculated ~= Cactual
Ccalculated = S*P;
end

Extract the last value calculated to get Sactual

end

Is there a way of extracting the last calculated value. So for example if P=2 and Cactual = 6 the value of Sactual should be 3.

Also is there a loop that stops looping when Ccalculated ~= Cactual? I imagine using the while function only stops for one loop and keep iterating the rest

Comments

  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    This code makes no sense. ~= is the relational operator NOT EQUAL, so the condition Ccalculated ~= Cactual is satisfied for all S ~= Cactual/P. Beyond that, I don't understand why you're looping for what appears to be an approximation algorithm if you have a known, explicit relationship between your inputs and outputs.

    To answer your last question though, it's just a matter of changing the test of the loop. If you want the opposite behavior to NOT EQUAL, you simply invert: NOT NOT EQUAL becomes EQUAL. MATLAB uses the == relational operator for EQUAL.
  • edited March 2011
    Whoops that was a typo I did mean == Sorry looking back on this post, I really didn't explain it very well.
    For my actual problem P is an equation formed of different variables, one of which is a function of S. I thought I would need to iterate to find the value of S when Ccalculated == Cactual. There probably is a better way of doing it but im not sure how, I tried using fzero but im probably applying it wrong.
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    Post your code, input, output, and any error messages you're getting.
  • edited March 2011
    This is my code:

    function S = MyReverseEquation3(Cts,R,d,v,w,Q,W,D)
    V=Q/(W*D);
    for S0=0:0.0001:0.5;
    Us=(9.81*R*S0)^0.5;
    if ((Us*d/v)>1.2) && ((Us*d/v)<70);
    Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66);
    else
    Vcr=w*2.05;
    end
    I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w);
    J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w);
    f=@(S)(((w/(V-Vcr))*(Cts/(10^I))^(1/J))-S);
    S = fzero(f,0);
    end
    end

    It gives me an answer but not the right answer. The value of S is usual between 0 and 0.5 and can be very small which is why the values 0:0.0001:0.5 are generated.

    Sample input:
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<m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true" DefSemiHidden="true" DefQFormat="false" DefPriority="99" LatentStyleCount="267"> <w:LsdException Locked="false" Priority="0" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Normal"/> <w:LsdException Locked="false" Priority="9" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="heading 1"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/> <w:LsdException Locked="false" 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Name="Medium Shading 2 Accent 2"/> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 2"/> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 2"/> 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Name="Light List Accent 4"/> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 4"/> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 4"/> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 4"/> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 5"/> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 5"/> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 5"/> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 5"/> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 5"/> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 6"/> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 6"/> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 6"/> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 6"/> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 6"/> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/> <w:LsdException Locked="false" Priority="19" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/> <w:LsdException Locked="false" Priority="21" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/> <w:LsdException Locked="false" Priority="31" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/> <w:LsdException Locked="false" Priority="32" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/> <w:LsdException Locked="false" Priority="33" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Book Title"/> <w:LsdException Locked="false" Priority="37" Name="Bibliography"/> <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/> </w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> *******> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;} </style> <![endif]--> Cts=90;
    R=0.33333;
    d=2*10^-3;
    v=[FONT=&quot]1.6[/FONT]*10^-6;
    [FONT=&quot]w = 1.9[/FONT]*10^-1;
    Q=2;
    W=1;
    D=1;
    [FONT=&quot]S = MyReverseEquation3(Cts,R,d,v,w,Q,W,D)[/FONT][FONT=&quot][/FONT]

    Output: S=3.5113-e006

    when S is subbed back in to the equation <!--[if gte mso 9]><xml> <o:OfficeDocumentSettings> <o:RelyOnVML/> <o:AllowPNG/> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>EN-GB</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:EnableOpenTypeKerning/> <w:DontFlipMirrorIndents/> <w:OverrideTableStyleHps/> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true" DefSemiHidden="true" DefQFormat="false" DefPriority="99" LatentStyleCount="267"> <w:LsdException Locked="false" Priority="0" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Normal"/> <w:LsdException Locked="false" Priority="9" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="heading 1"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/> <w:LsdException Locked="false" Priority="9" QFormat="true" 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Accent 6"/> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 6"/> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 6"/> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/> <w:LsdException Locked="false" Priority="19" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/> <w:LsdException Locked="false" Priority="21" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/> <w:LsdException Locked="false" Priority="31" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/> <w:LsdException Locked="false" Priority="32" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/> <w:LsdException Locked="false" Priority="33" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Book Title"/> <w:LsdException Locked="false" Priority="37" Name="Bibliography"/> <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/> </w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> *******> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;} </style> <![endif]-->[FONT=&quot]Cts should equal 90 but it doesn't so my code is wrong.
    [/FONT]
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    Your code will only ever return the solution of S for S0 = 0.5. I still can't follow what you're trying to do, but the following code is functionally identical to what you posted. That is, it removes all the extraneous bits and returns the same result.
    [php]function S = MyReverseEquationX(Cts,R,d,v,w,Q,W,D)
    V=Q/(W*D);
    S0 = 0.5;
    Us=(9.81*R*S0)^0.5;
    if ((Us*d/v)>1.2) && ((Us*d/v)<70);
    Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66);
    else
    Vcr=w*2.05;
    end
    I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w);
    J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w);
    S = w/(V-Vcr) * (Cts/10^I)^(1/J);
    end[/php]
    Also, it bears mentioning that I ran your code and didn't get the same result for S as you did. I got S = 6.3282e-006
  • edited March 2011
    Thanks for having a look at it. Do you know how I could change it so it finds the value of S so that when it is subbed back in to the equation Cts should equal oringinal Cts inputted at the beginning?
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    It's a pretty straightforward algebraic manipulation to change the form of the equation to yield Cts as a function of S. The problem I see here is that you aren't getting a unique solution because S is purely a function of S0 given all the other inputs; that is, you can pick any S0 you want and get a valid solution for S that satisfies your equation.

    Are you sure that you're not really trying to find a solution for S = S0? As in, you want S0 to converge to S?
  • edited March 2011
    Yes, I am looking for a value of S which produces the same Cts as the one inputted. I
    don't want the data displayed as a graph. Is there anyway to find the value of S which will give me the closest value of Cts to the one inputted?
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    That didn't really answer my question, but the general form for a convergence algorithm looks like this:[php]// Pseudocode
    error = 1e-6; // maximum error tolerance
    guess = 0.1; // initial solution guess
    sol_error = 0.01; // initial value for error, must be > error
    while( sol_error > error OR sol_error < -error ) // only absolute magnitude of error is important
    guess = guess - sol_error; // determine new guess
    solution = function(guess); // evaluate solution of function at guess
    sol_error = guess - solution; // determine error between solution and initial guess
    end[/php]The result is stored in the variable solution. This result exists at a point where the slope of function(guess) is nearly zero (that is, a maxima or a minima.) As such, it will only find the local maxima or minima nearest to the initial guess in higher-ordered functions.
  • edited March 2011
    I'm not really sure how to explain it differently. I am trying to find a value of S that satisfies the equation so that for the variables (Cts,R,d,v,w,Q,W,D) I have one answer S. I'm finding it tricky because Cts depends on the variable S.
    From the Pseudocode you posted above from what I can see the answer Matlab should give is the error between the guess value and the actual value?
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    Your original code feeds through each of 5000 different values of S0 inputs to your equation and finds the corresponding S value. However, only the last result for S (using the last S0 input in your input set) gets reported. That aside, you're still computing 5000 different solutions for S all of which satisfy your equation for the given S0. In this sense, in addition to all that stuff you just listed in your variable list, you have to treat S0 as an additional input.

    What I just said regarding S0 as an input isn't true if what you're trying to do is find a solution for your equation such that S is approximately equal to S0. In this case, you would want to iterate from an initial guess for S0 and revise the guess based on the error between your computed S and your guessed S0.

    What this pseudocode shows is an algorithm that performs that iteration. Once the difference between the guess value and the result from the function, in this case called sol_error, goes below a set threshold then the guess and the calculated solution are said to have converged. At this point, the guess is approximately equal to solution. The "answer" is the value of either the guess or the calculated solution since they should be approximately equal.
  • edited March 2011
    Ahh Ok so the by the sounds of it I want to use your pseudocode. I tried making a function based on it:
    function S = MyConvergance(Cts,R,d,v,w,Q,W,D)
    error = 1e-6; % maximum error tolerance
    S0 = 0.1; % initial solution guess
    sol_error = 1e-5; % initial value for error, must be > error
    while( sol_error > error || sol_error < -error ) % only absolute magnitude of error is important
    V=Q/(W*D);
    Us=(9.81*R*S0)^0.5;
    if ((Us*d/v)>1.2) && ((Us*d/v)<70);
    Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66);
    else
    Vcr=w*2.05;
    end
    I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w);
    J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w);
    S0 = S0 - sol_error; % determine new guess
    solution = @(S0)(((w/(V-Vcr))*(Cts/(10^I))^(1/J))-S0); % evaluate solution of function at guess
    S = S0 - solution; % determine error between solution and initial guess
    end
    end

    I keep getting the following error:
    ??? Undefined function or method 'minus' for input arguments of type
    'function_handle'.
    Error in ==> MyConvergance at 17
    S = S0 - solution; % determine error between solution and initial guess

    I entered the same input as before.
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    You changed the name of your earlier function from f to solution but you didn't solve it this time around. You don't really need to use fsolve or fzero for this; it's trivial to re-arrange the equation algebraically to solve explicitly. If you insist on using that solver though, you shouldn't use a variable name that's already been defined and used elsewhere as the dependent variable in your expression. Also, you're not updating sol_error after each pass of the loop.

    If you haven't already, try stepping through your code one line at a time to see what each line does.
  • edited March 2011
    Thank you for your help but I'm failing to understand what you mean. When you say re-arrange what value am I re-arranging to become the subject of the formula?
    I don't mind how I get to it a long as I can get to the right solution.
    I'm not really sure how the convergance alogorithm works, for instance <code style="white-space: nowrap;"><code>"sol_error" </code></code>I'm not sure what value to set it as and what it does.<code style="white-space: nowrap;"><code>
    </code></code>
  • edited March 2011
    I have the following code and it runs fine but it doesn't give me the answer I'm looking for. If I change the value of S0 it gives me a different answer which it shouldn't as far as I'm aware. So I'm not sure what is wrong with it.
    function S = MyReverseEquation3(Cts,R,d,v,w,Q,W,D,S0)
    V=Q/(W*D);
    Us=(9.81*R*S0)^0.5;
    if ((Us*d/v)>1.2) && ((Us*d/v)<70);
    Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66);
    else
    Vcr=w*2.05;
    I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w);
    J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w);
    f=@(S)(((w/(V-Vcr))*(Cts/(10^I))^(1/J))-S);
    S = fsolve(f,S0);
    end
    end
    My input is: Cts=90; R=0.33333; d=2*10^-3; v=1.6*10^-6; w = 1.9*10^-1; Q=2; W=1; D=1; S0 = 0.1 S = MyReverseEquation3(Cts,R,d,v,w,Q,W,D,S0)
    S0 is my inital guess. I am trying to find a value of S which satisfies the equation. So I am using fsolve to find S. S is a function of (Cts,R,d,v,w,Q,W,D,S0) however Cts is a function of S.
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    Ok, so in your original code you implemented the expression:
    f(S): w/(V-Vcr) * (Cts/10^I)^(1/J) - S
    and then you used fzero(f,0) to find the zeros of the expression f(S). This can be written as:
    0 = f(S)
    substituting for f(S):
    0 = w/(V-Vcr) * (Cts/10^I)^(1/J) - S
    which can be further simplified to:
    S = w/(V-Vcr) * (Cts/10^I)^(1/J)
    which is what I wrote earlier. Trivial, right? So instead of using the code:
    [php]f = @(Schk)(((w/(V-Vcr))*(Cts/(10^I))^(1/J))-Schk); % f(Schk)
    S = fzero(f,0); % 0 = f(Schk), solved for Schk[/php]You could instead use:[php]S = w/(V-Vcr) * (Cts/10^I)^(1/J);[/php]Because they are equivalent as proven above. The difference is that the second implementation is a LOT faster.

    Regarding convergence, "sol_error" is the difference between the solution "S" evaluated using either of the algorithms above and your initial guess "S0". The purpose of the convergence algorithm is to find an initial guess "S0" that when used with all your other code causes the solution "S" to be approximately equal to "S0". For that to happen, the value of "sol_error" as defined as the difference between "S" and "S0" needs to be approximately zero. The convergence algorithm starts from an initial guess for "S0" and adjusts the guess by the size of the error ("sol_error") between iterations. The idea is that with each pass (each time the while loop executes) the error between the guess and the solution diminishes to approximately zero. The variable "error" is the largest number you would consider approximately zero. Depending on the accuracy and precision of your inputs "error" should be a few to several orders of magnitude smaller than your expected result. Once "sol_error" is smaller than "error" in magnitude the loop exits and you can use either "S" or "S0" as your answer.
  • edited March 2011
    Okay I think I understand it now. I tried this code:
    function S = MyConvergance(Cts,R,d,v,w,Q,W,D)
    error = 1e-6; % maximum error tolerance
    S0 = 0.1; % initial solution guess
    sol_error = 0.01; % initial value for error, must be > error
    while( sol_error > error || sol_error < -error ) % only absolute magnitude of error is important
    V=Q/(W*D);
    Us=(9.81*R*S0)^0.5;
    if ((Us*d/v)>1.2) && ((Us*d/v)<70);
    Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66);
    else
    Vcr=w*2.05;
    end
    I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w);
    J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w);
    solution = (w/(V-Vcr))*(Cts/(10^I))^(1/J); % evaluate solution of function at guess
    S = S0 - solution; % determine error between solution and initial guess
    S0 = S0 - sol_error; % determine new guess
    end
    end
    However it doesn't give me an answer, Matlab says it's busy but nothing happens and you can still type in the command window.
  • drasnordrasnor Starship Operator Hawthorne, CA Icrontian
    edited March 2011
    You're still not changing the value of sol_error between loop iterations which causes the loop to run infinitely. Try changing the line S = S0 - solution to sol_error = S0 - solution. You might also consider changing the variable name of solution to S since that's what you're solving for.
  • edited March 2011
    Success!! Thank you so much for your help. You've played an instrumental part in helping me with my project :)
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