Manipulate piecewise functions,
in [Mathematica]
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From: Vedhas Pandit on 24 Feb 2010 06:19 That helped so far as syntax is concerned! Please note that I need to use elements of array a, a is an array is predefined with some random numbers, say a={0 7 2 1 4}. (I cannot use range, I need to use the "data" I have with me). a = {0 7 2 1 4}; Manipulate[ Plot[Evaluate[ Piecewise[{{x - p - q, x - p - q <= a}}, (x - p - q)^2]], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, 20}, {q, 0, 20}] didn't work Thanks, Vedhas On Tue, Feb 23, 2010 at 3:54 PM, Patrick Scheibe < pscheibe(a)trm.uni-leipzig.de> wrote: > Hi, > > > for plot y versus x is: > > y=x-p-q for x-p-q<a, and (x-p-q)^2 for (x-p-q)>=a i.e. 6 plots getting > > manipulated simultaneously. > > this makes absolutely no sense, because you will have no additional > information. Set k=p+q and you can do the same with only one parameter. > But your original question is easy: > > Manipulate[ > Plot[Evaluate[ > Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ > Range[6]], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, > 20}, {q, 0, 20}] > > If you give Plot a list of functions you'll have them all in the same > plot. But I'm pretty sure you expected something different from this > plot. > > Cheers > Patrick > > > > Again, Thanks for your help and I hope you will again respond to the > > query quickly! > > > > Best regards, > > > > Vedhas > > > > On Sun, Feb 21, 2010 at 8:33 AM, Bob Hanlon <hanlonr(a)cox.net> wrote: > > > > If you plot all of the curves on a single plot they will > > overlap and make it difficult to see what is happening. > > Recommend an array of plots. > > > > Manipulate[ > > Grid[ > > Partition[ > > Table[ > > Plot[ > > Piecewise[{ > > {x - p, x < a + p}, > > {(x - p)^2, x >= a + p}}], > > {x, -8, 5}, > > Frame -> True, > > Axes -> False, > > PlotRange -> {-10, 50}, > > ImageSize -> 250, > > Epilog -> > > {Style[ > > Text[ > > "a = " <> ToString[a], > > {-6, 40}], > > Blue, 16], > > Style[ > > Text[ > > "step = " <> ToString[a (a - 1)], > > {-6, 30}], > > Blue, 16]}], > > {a, 6}], > > 2]], > > {p, -6, -2, Appearance -> "Labeled"}] > > > > > > Bob Hanlon > > > > > > ---- Vedhas | sahdeV <vedhas(a)gmail.com> wrote: > > > > ============= > > a = {1 2 3 4 5 6} > > The goal is to plot a piecewise function corresponding to each > > of "a" > > values, with manipulate where control variable is p, and the > > function > > for plot y versus x is: > > y=x-p for x-p<a, and (x-p)^2 for (x-p)>=a i.e. 6 plots getting > > manipulated simultaneously. > > > > I am new to Mathematica and this might be a naive question, > > but I > > couldn't find a solution through help documentation. I will > > appreciate > > if you can help! > > > > Thanks, > > > > Vedhas > > > > > > > >
From: Patrick Scheibe on 24 Feb 2010 06:19 Hi, I thought it was clear that Range[blub] is a list which you have to substitute by whatever you want: a = {0, 7, 2, 1, 4}; Manipulate[ Plot[Evaluate[ Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ a], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, 20}, {q, 0, 20}] See where your "a" goes? You have to try to follow every step to understand and to get better! So try to understande the core which is Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ a What is the # and the &? What is /@? Why and how does it work? You only have to read the examples in the documentation and maybe the doc itself. Cheers Patrick On Tue, 2010-02-23 at 16:53 -0700, Vedhas Pandit wrote: > That helped so far as syntax is concerned! > > Please note that I need to use elements of array a, a is an array is > predefined with some random numbers, say a={0 7 2 1 4}. (I cannot use > range, I need to use the "data" I have with me). > > a = {0 7 2 1 4}; > Manipulate[ > Plot[Evaluate[ > Piecewise[{{x - p - q, x - p - q <= a}}, (x - p - q)^2]], {x, 0, > 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, 20}, {q, 0, 20}] > didn't work > > Thanks, > > Vedhas > > > On Tue, Feb 23, 2010 at 3:54 PM, Patrick Scheibe > <pscheibe(a)trm.uni-leipzig.de> wrote: > Hi, > > > for plot y versus x is: > > y=x-p-q for x-p-q<a, and (x-p-q)^2 for (x-p-q)>=a i.e. 6 > plots getting > > manipulated simultaneously. > > > this makes absolutely no sense, because you will have no > additional > information. Set k=p+q and you can do the same with only one > parameter. > But your original question is easy: > > Manipulate[ > Plot[Evaluate[ > Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ > Range[6]], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], > {p, 0, > 20}, {q, 0, 20}] > > If you give Plot a list of functions you'll have them all in > the same > plot. But I'm pretty sure you expected something different > from this > plot. > > Cheers > Patrick > > > > > Again, Thanks for your help and I hope you will again > respond to the > > query quickly! > > > > Best regards, > > > > Vedhas > > > > On Sun, Feb 21, 2010 at 8:33 AM, Bob Hanlon > <hanlonr(a)cox.net> wrote: > > > > If you plot all of the curves on a single plot they > will > > overlap and make it difficult to see what is > happening. > > Recommend an array of plots. > > > > Manipulate[ > > Grid[ > > Partition[ > > Table[ > > Plot[ > > Piecewise[{ > > {x - p, x < a + p}, > > {(x - p)^2, x >= a + p}}], > > {x, -8, 5}, > > Frame -> True, > > Axes -> False, > > PlotRange -> {-10, 50}, > > ImageSize -> 250, > > Epilog -> > > {Style[ > > Text[ > > "a = " <> ToString[a], > > {-6, 40}], > > Blue, 16], > > Style[ > > Text[ > > "step = " <> ToString[a (a - 1)], > > {-6, 30}], > > Blue, 16]}], > > {a, 6}], > > 2]], > > {p, -6, -2, Appearance -> "Labeled"}] > > > > > > Bob Hanlon > > > > > > ---- Vedhas | sahdeV <vedhas(a)gmail.com> wrote: > > > > ============= > > a = {1 2 3 4 5 6} > > The goal is to plot a piecewise function > corresponding to each > > of "a" > > values, with manipulate where control variable is p, > and the > > function > > for plot y versus x is: > > y=x-p for x-p<a, and (x-p)^2 for (x-p)>=a i.e. 6 > plots getting > > manipulated simultaneously. > > > > I am new to Mathematica and this might be a naive > question, > > but I > > couldn't find a solution through help documentation. > I will > > appreciate > > if you can help! > > > > Thanks, > > > > Vedhas > > > > > > > > >
From: Bob Hanlon on 24 Feb 2010 06:20 You can interconnect the controls to avoid cases where everything is off the graph. Also the Exclusions option can be used if you want the vertical lines to show. a = {0, 7, 2, 1, 4}; Manipulate[ Plot[ Evaluate[ Piecewise[ {{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ a], {x, 0, 20}, PlotRange -> {Automatic, {-1, 51}}, Exclusions -> p + q], {p, 0, 20 - q, 0.1, Appearance -> "Labeled"}, {q, 0, 20 - p, 0.1, Appearance -> "Labeled"}] Bob Hanlon ---- Patrick Scheibe <pscheibe(a)trm.uni-leipzig.de> wrote: ============= Hi, I thought it was clear that Range[blub] is a list which you have to substitute by whatever you want: a = {0, 7, 2, 1, 4}; Manipulate[ Plot[Evaluate[ Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ a], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, 20}, {q, 0, 20}] See where your "a" goes? You have to try to follow every step to understand and to get better! So try to understande the core which is Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ a What is the # and the &? What is /@? Why and how does it work? You only have to read the examples in the documentation and maybe the doc itself. Cheers Patrick On Tue, 2010-02-23 at 16:53 -0700, Vedhas Pandit wrote: > That helped so far as syntax is concerned! > > Please note that I need to use elements of array a, a is an array is > predefined with some random numbers, say a={0 7 2 1 4}. (I cannot use > range, I need to use the "data" I have with me). > > a = {0 7 2 1 4}; > Manipulate[ > Plot[Evaluate[ > Piecewise[{{x - p - q, x - p - q <= a}}, (x - p - q)^2]], {x, 0, > 20}, PlotRange -> {Automatic, {0, 50}}], {p, 0, 20}, {q, 0, 20}] > didn't work > > Thanks, > > Vedhas > > > On Tue, Feb 23, 2010 at 3:54 PM, Patrick Scheibe > <pscheibe(a)trm.uni-leipzig.de> wrote: > Hi, > > > for plot y versus x is: > > y=x-p-q for x-p-q<a, and (x-p-q)^2 for (x-p-q)>=a i.e. 6 > plots getting > > manipulated simultaneously. > > > this makes absolutely no sense, because you will have no > additional > information. Set k=p+q and you can do the same with only one > parameter. > But your original question is easy: > > Manipulate[ > Plot[Evaluate[ > Piecewise[{{x - p - q, x - p - q <= #}}, (x - p - q)^2] & /@ > Range[6]], {x, 0, 20}, PlotRange -> {Automatic, {0, 50}}], > {p, 0, > 20}, {q, 0, 20}] > > If you give Plot a list of functions you'll have them all in > the same > plot. But I'm pretty sure you expected something different > from this > plot. > > Cheers > Patrick > > > > > Again, Thanks for your help and I hope you will again > respond to the > > query quickly! > > > > Best regards, > > > > Vedhas > > > > On Sun, Feb 21, 2010 at 8:33 AM, Bob Hanlon > <hanlonr(a)cox.net> wrote: > > > > If you plot all of the curves on a single plot they > will > > overlap and make it difficult to see what is > happening. > > Recommend an array of plots. > > > > Manipulate[ > > Grid[ > > Partition[ > > Table[ > > Plot[ > > Piecewise[{ > > {x - p, x < a + p}, > > {(x - p)^2, x >= a + p}}], > > {x, -8, 5}, > > Frame -> True, > > Axes -> False, > > PlotRange -> {-10, 50}, > > ImageSize -> 250, > > Epilog -> > > {Style[ > > Text[ > > "a = " <> ToString[a], > > {-6, 40}], > > Blue, 16], > > Style[ > > Text[ > > "step = " <> ToString[a (a - 1)], > > {-6, 30}], > > Blue, 16]}], > > {a, 6}], > > 2]], > > {p, -6, -2, Appearance -> "Labeled"}] > > > > > > Bob Hanlon > > > > > > ---- Vedhas | sahdeV <vedhas(a)gmail.com> wrote: > > > > ============= > > a = {1 2 3 4 5 6} > > The goal is to plot a piecewise function > corresponding to each > > of "a" > > values, with manipulate where control variable is p, > and the > > function > > for plot y versus x is: > > y=x-p for x-p<a, and (x-p)^2 for (x-p)>=a i.e. 6 > plots getting > > manipulated simultaneously. > > > > I am new to Mathematica and this might be a naive > question, > > but I > > couldn't find a solution through help documentation. > I will > > appreciate > > if you can help! > > > > Thanks, > > > > Vedhas
From: Vedhas Pandit on 24 Feb 2010 06:21 Thanks Bob and Patrick! I agree with you using array of plots, but I "need" to put all the 6 curves in the same plot window. Can you help me do that? (Analyzing the curves might then be tricky, but piecewise (x-p) and (x-p)^2 is only an example function, actual piecewise function that I am trying to plot is different, having many control variables to manipulate. I only need to know the syntax so the query (adding one more control variable q if that changes anything): ) a = {1 2 3 4 5 6} The goal is to plot a piecewise function corresponding to each of "a" values, with manipulate where control variable is p,q , and the function for plot y versus x is: y=x-p-q for x-p-q<a, and (x-p-q)^2 for (x-p-q)>=a i.e. 6 plots getting manipulated simultaneously. Again, Thanks for your help and I hope you will again respond to the query quickly! Best regards, Vedhas On Sun, Feb 21, 2010 at 8:33 AM, Bob Hanlon <hanlonr(a)cox.net> wrote: > > If you plot all of the curves on a single plot they will overlap and make > it difficult to see what is happening. > Recommend an array of plots. > > Manipulate[ > Grid[ > Partition[ > Table[ > Plot[ > Piecewise[{ > {x - p, x < a + p}, > {(x - p)^2, x >= a + p}}], > {x, -8, 5}, > Frame -> True, > Axes -> False, > PlotRange -> {-10, 50}, > ImageSize -> 250, > Epilog -> > {Style[ > Text[ > "a = " <> ToString[a], > {-6, 40}], > Blue, 16], > Style[ > Text[ > "step = " <> ToString[a (a - 1)], > {-6, 30}], > Blue, 16]}], > {a, 6}], > 2]], > {p, -6, -2, Appearance -> "Labeled"}] > > > Bob Hanlon > > ---- Vedhas | sahdeV <vedhas(a)gmail.com> wrote: > > ============= > a = {1 2 3 4 5 6} > The goal is to plot a piecewise function corresponding to each of "a" > values, with manipulate where control variable is p, and the function > for plot y versus x is: > y=x-p for x-p<a, and (x-p)^2 for (x-p)>=a i.e. 6 plots getting > manipulated simultaneously. > > I am new to Mathematica and this might be a naive question, but I > couldn't find a solution through help documentation. I will appreciate > if you can help! > > Thanks, > > Vedhas > >
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