Extracting data from a loop
(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
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
0
Comments
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.
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.
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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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="]1.6[/FONT]*10^-6;
[FONT="]w = 1.9[/FONT]*10^-1;
Q=2;
W=1;
D=1;
[FONT="]S = MyReverseEquation3(Cts,R,d,v,w,Q,W,D)[/FONT][FONT="][/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" Name="heading 5"/> 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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 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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="]Cts should equal 90 but it doesn't so my code is wrong.
[/FONT]
[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
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?
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?
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.
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?
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.
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.
If you haven't already, try stepping through your code one line at a time to see what each line does.
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>
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.
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.
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.