Skip to main content

How many arguments does a function require, and how to use that in `Manipulate`


The goal is to vary the order parameters in wavelet transforms in the Manipulate environment. The various transformations have arguments of different rank. For example,


HaarWavelet[] has no order argument.


DaubechiesWavelet[m] has a single order argument $m$ and the desire is to present choices for $m$.


BiorthogonalSplineWavelet[m,n] has an order parameter $m$ and a dual order parameter $n$ and the desire is to let the user control $m$ and $n$.


The current state of my effort is this:


data = DiskMatrix[10]; Manipulate[ dwt = DiscreteWaveletTransform[dat32, wavelet]; gdwd = WaveletMatrixPlot[dwt] , {wavelet, {HaarWavelet[], DaubechiesWavelet[], MeyerWavelet[]}}]


enter image description here



The different transforms can be selected, but there is no capability to change the order parameters. How can order parameters be introduced?



Answer



I'm pretty sure there ought to be something cleaner. While we wait for a better answer, you may use this to return the minimum and maximum number of arguments allowed for each wavelet:


nArgs[fun_] := 
 StringCases[ToString@DownValues@fun, 
            Shortest["ArgumentCountQ"~~__~~(n1:NumberString)~~__~~ (n2:NumberString)] :> 
            ToExpression[{n1, n2}]]


{#, nArgs@#} & /@ ToExpression /@ Names["*Wavelet"]


(*
{{BattleLemarieWavelet, {{2, 2}}}, 
 {BiorthogonalSplineWavelet, {{2, 2}}}, 
 {CDFWavelet, {{1, 1}}}, 
 {CoifletWavelet, {{1, 1}}}, 
 {DaubechiesWavelet, {{1, 1}}}, 
 {DGaussianWavelet, {{1, 1}}}, 
 {GaborWavelet, {{1, 1}}}, 
 {HaarWavelet, {{0, 0}}}, 

 {MexicanHatWavelet, {{1, 1}}}, 
 {MeyerWavelet, {{2, 2}}}, 
 {MorletWavelet, {{0, 0}}}, 
 {PaulWavelet, {{1, 1}}}, 
 {ReverseBiorthogonalSplineWavelet, {{2, 2}}}, 
 {ShannonWavelet, {{1, 1}}}, 
 {SymletWavelet, {{1, 1}}}}
*)

So:



m[fun_] := nArgs[fun][[1, 2]]
d = DiskMatrix[10];
Manipulate[
 WaveletMatrixPlot@DiscreteWaveletTransform[d, wv[Sequence @@ x[[;; m@wv]]]],
 {{x, {1, 1}}, ControlType -> None},
 {wv, {HaarWavelet, DaubechiesWavelet, MeyerWavelet}}, 
 Dynamic@Panel@Grid[{Slider[Dynamic@x[[#]], {0, 10, 1}], x[[#]]} & /@ Range@m@wv]]

Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more