Skip to main content

scoping - RecurrenceTable iteration variable not localized? Bug or user error?


I recently lost a lot of time on this and need to understand whether I have misunderstood MMA operations or there's a problem. I am using MMA 10.1 on Windows 7 64-bit.


The essence of the issue is this: I believed that Table, RecurrenceTable etc, per the description of Table in the documentation, localise the iterating variable, and thus that using e.g. "i" in a RecurrenceTable and elsewhere in a notebook for some other purpose should not cause a conflict.


(Related question: ParametricPlot iterator not "block"-ed)



However as the three cases below show, unless the iterating variable is not reused or explicitly shielded by e.g. a Module in a definition incorporating a RecurrenceTable, I get the error that "1", "2", etc. cannot be used as a variable.


Sample code follows (with forced clear for safety). The first two definitions of logisticMap cause no problems in subsequent use, but when the subsequent use reuses an unshielded iterating variable the error occurs.


Clear[Evaluate[Context[] <> "*"]]

1st def: OK (i as a module variable in RecurrenceTable, and i in For[])


logisticMap[x0_, μ_, n_] := 
Module[{i},
RecurrenceTable[{x[i + 1] == μ x[i] (1 - x[i]), x[1] == x0},
x, {i, 1, n}]]
pRow = {};

dataSeries := logisticMap[0.1, 3.55, 10];
For[i = 1, i <= 10, i++, AppendTo[pRow, dataSeries[[i]]]];

2nd def: OK (use b as iterator for RecurrenceTable and i in For[])


logisticMap[x0_, μ_, n_] := 
RecurrenceTable[{x[b + 1] == μ x[b] (1 - x[b]), x[1] == x0},
x, {b, 1, n}]
pRow = {};
dataSeries := logisticMap[0.1, 3.55, 10];
For[i = 1, i <= 10, i++, AppendTo[pRow, dataSeries[[i]]]];


3rd def: error (i as unshielded iterator in RecurrenceTable, and in For[])


logisticMap[x0_, μ_, n_] := 
RecurrenceTable[{x[i + 1] == μ x[i] (1 - x[i]), x[1] == x0},
x, {i, 1, n}]
pRow = {};
dataSeries := logisticMap[0.1, 3.55, 10];
For[i = 1, i <= 10, i++, AppendTo[pRow, dataSeries[[i]]]];

The error being



RecurrenceTable::dsvar: 1 cannot be used as a variable. >> etc.

a) What exactly is happening (why is "1" being used as a variable) and


b) Is this user error or a bug (that I would then report)?


[BTW Do you think Wolfram would respond +vely to a request for a free upgrade if this is a bug as this is a seriously undermining issue AND I am still suffering from an unresolved startup issue in 10.1?]


Thanks,




Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...