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Carlos.m
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Carlos.m
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BeginPackage["Carlos`"] ;
MyAverage::usage =
"This function gives the average of more complex quantities than lists,
for example it is able to process lists of lists";
RandomUnitVector::usage = "This gives a random vector with the Haar measure. The dimension is
the argument. If no argument is suplied, it is asumed to be 3";
Seed::usage =
"This function, without any argument, gives a random integer between 0
and 1000000000-1 which can be used as a seed for an external program";
Instruction::usage =
"This instrucion creats a string that in s Linux or Unix shell will enter
some given parameters into an external program. The first argument is a list
of lists with the values to be entered and the second one is the program";
Norma::usage = "This function gives the norm of a list of numbers";
ColorCoding::usage="This recieves 2 integer inputs, and outputs a
graphic to read the number that represents each Hue";
BlockDiagonalMatrix::usage="Gives a block diagonal matrix from a list"
OffSpellErrors::usage ="Turns of spelling errors"
OnSpellErrors::usage ="Turns on spelling errors"
Log10::usage ="Calculates Log10[x_]:=Log[10,x]"
ColumnAddKeepFirst::usage="To add to matrices, keeping the first column of the first matrix untouched"
ReadListUncomment::usage="igual a ReadList[] pero quita todo lo que comienze con #"
NumberList::usage="Number a list, i.e. prepend with an intenger from 1 to the Length of the list"
HistogramListPoints::usage="Shows the points that would correspond to a Histogram. Accepts
the same options as Histogram and HistogramList. Usage HistogramListPoints[data] or
HistogramListPoints[data, bspec] or HistogramList[data,bspec,hspec]"
(* {{{ Symbols and legends *)
MySymbol::usage="Para poner simbolos. Tiene defauls. Es el recomendado ahora"
SymbolNumber::usage="Option for MySymbol"
Coordinate::usage="Option for MySymbol"
Color::usage="Option for MySymbol"
Proportion::usage="Option for MySymbol"
delta::usage="Option for MySymbol"
ThicknessBorder::usage="Option for MySymbol"
MyTriangle::usage = "Graphics almost primitive MyTriangle[{x_, y_}, Color1_, Proportion_, delta_, th_] ";
MyInvertedTriangle::usage = "Graphics almost primitive MyInvertedTriangle[{x_, y_}, Color1_, Proportion_, delta_, th_] ";
MySquare::usage = "Graphics almost primitive MySquare[{x_, y_}, Color1_, Proportion_, delta_, th_]";
MyCircle::usage = "Graphics almost primitive MyCircle[{x_, y_}, Color1_, Proportion_, delta_, th_]";
MyRhombous::usage = "Graphics almost primitive MyRhombous[{x_, y_}, Color1_, Proportion_, delta_, th_]";
My4PointStar1::usage = "Graphics almost primitive My4PointStar1[{x_, y_}, Color1_, Proportion_, delta_, th_]";
My4PointStar2::usage = "Graphics almost primitive My4PointStar2[{x_, y_}, Color1_, Proportion_, delta_, th_]";
My4PointStar3::usage = "Graphics almost primitive My4PointStar3[{x_, y_}, Color1_, Proportion_, delta_, th_]";
My5PointStar::usage = "Graphics almost primitive My5PointStar[{x_, y_}, Color1_, Proportion_, delta_, th_]";
InsetWithSymbols::usage="To create nice symbols in plots. "
MyLegend::usage="Ver LegendBox"
LegendBox::usage=" Ejemplos de uso:
{UpperHeight = 0.9, Xpos = .57, Xlength = .1,
XSepText = .1, \[CapitalDelta]Height = .15};
kk = LegendBox[{\"b1\", \"b2\",
\"b4\"}, {GrayLevel[0], Style\[Beta][#]} & /@ \[Beta]s, UpperHeight,
Xpos, Xlength, XSepText, \[CapitalDelta]Height];
LegendBox[
\"n=\" <> ToString[#] & /@ ns, {Thickness[tjh], Hue[#/Length[ns]]} & /@
Range[Length[ns]], .9, .6, .2, .05, .1]
"
Alignment::usage="Option for LegendBox and MyLegend"
(* }}} *)
(* {{{ Geometry *)
EllipseCharacteristics::usage="Get center, angle of rotation and semiaxis of an elipse. EllipseCharacteristics[poly_, vars_]
For example, EllipseCharacteristics[4 x^2 - 4 x y + 7 y^2 + 12 x + 6 y - 9, {x, y}]"
(* }}} *)
Begin["`private`"];
(* Geometry *)
EllipseCharacteristics[poly_, vars_] := (* {{{ *)
Module[{cl, center, Aq, Bq, Cq, Dq, Eq, Fq, cl2, Am},
cl = CoefficientList[poly, vars];
{Aq = cl[[3, 1]], Bq = cl[[2, 2]]/2, Cq = cl[[1, 3]],
Dq = cl[[2, 1]]/2, Eq = cl[[1, 2]]/2, Fq = cl[[1, 1]]};
center = -Inverse[{{Aq, Bq}, {Bq, Cq}}].{Dq, Eq};
cl2 = CoefficientList[poly /. {vars[[1]] -> vars[[1]] + center[[1]], vars[[2]] -> vars[[2]] + center[[2]]}, vars];
Am = {{cl2[[3, 1]], cl2[[2, 2]]/2}, {cl2[[2, 2]]/2, cl2[[1, 3]]}};
{center, ArcTan @@ (Eigenvectors[Am][[1]]),
1/Sqrt[-Eigenvalues[Am]/cl2[[1, 1]]]}
]/; PolynomialQ[poly, vars] (* }}} *)
(* *)
HistogramListPoints[data_, Options___] :=Transpose[{Drop[(#[[1]] + RotateLeft[#[[1]]])/
2, -1], #[[2]]} &[HistogramList[data, Options]]]
RandomUnitVector[n_] := Module[{v},
v = RandomReal[NormalDistribution[0, 1], n];
v/Norm[v]]
RandomUnitVector[] := RandomUnitVector[3]
BlockDiagonalMatrix[b : {__?MatrixQ}] :=
Module[{r, c, n = Length[b], i, j}, {r, c} =
Transpose[Dimensions /@ b];
ArrayFlatten[
Table[If[i == j, b[[i]], ConstantArray[0, {r[[i]], c[[j]]}]], {i,
n}, {j, n}]]]
(* From http://mathworld.wolfram.com/BlockDiagonalMatrix.html*)
NumberList[lista_]:=Flatten[Evaluate[#], 1] & /@ Transpose[{Range[Length[lista]], lista}]
OffSpellErrors[]:={Off[General::spell],Off[General::spell1]}
OnSpellErrors[]:={On[General::spell],On[General::spell1]}
MyLegend[TheStyle_List, Heigth_, Xpos_, Xlength_, TheText_, XSepText_, OptionsPattern[]] :=
{Text[TheText, Scaled[{Xpos + Xlength + XSepText, Heigth}],OptionValue[Alignment]],
Join[TheStyle, {Line[{Scaled[{Xpos, Heigth}],
Scaled[{Xpos + Xlength, Heigth}]}]}]}
LegendBox[TheLegends_, TheStyles_, UpperHeight_, Xpos_, Xlength_,
XSepText_, \[CapitalDelta]Height_, OptionsPattern[]] :=
Module[{i},
Table[MyLegend[TheStyles[[i]],
UpperHeight - (i - 1) \[CapitalDelta]Height, Xpos, Xlength,
TheLegends[[i]], XSepText, Alignment -> OptionValue[Alignment]], {i, Length[TheLegends]}]]
Options[LegendBox] = {Alignment->{0,0}};
Options[MyLegend] = {Alignment->{0,0}};
MySymbol[Coordinate_, OptionsPattern[]] :=
{MyTriangle,MySquare,MyRhombous,MyInvertedTriangle,MyCircle,My5PointStar,
My4PointStar1,My4PointStar2,MyInverted5PointStar, My4PointStar3}[[OptionValue[SymbolNumber]]][Coordinate,
OptionValue[Color], OptionValue[Proportion], OptionValue[delta], OptionValue[ThicknessBorder]]
Options[MySymbol] = {SymbolNumber -> 1, Color -> Hue[0],
Proportion -> GoldenRatio, delta -> 0.02, ThicknessBorder -> 0.001};
ReadListUncomment[file_, Options___] :=
ReadList[ StringToStream[
StringJoin[ StringInsert[#, "\n", -1] & /@ Select[ReadList[file, String], StringFreeQ[#, "#"] &]]], Options]
ColumnAddKeepFirst[MultiList_] := MapThread[Prepend, {(Plus @@ MultiList)[[All, 2 ;;]], MultiList[[1, All, 1]]}]
ColumnAddKeepFirst[FirstList_, SecondList_] := ColumnAddKeepFirst[{FirstList, SecondList}]
InsetWithSymbols[LowerLeft_List,BoxSize_List,RealtiveCoordinateLowerSymbol_, SepSymbols_,SymbolList_,TextList_, TextSpacing_]:=
Module[{i},
{Table[ SymbolList[[i]][ LowerLeft+RealtiveCoordinateLowerSymbol+{0,(i-1) SepSymbols}],{i, Length[SymbolList]}],
Graphics[ Table[Text[TextList[[i]], LowerLeft+ RealtiveCoordinateLowerSymbol+{0,(i-1) SepSymbols}+{TextSpacing, 0},{-1,0}]
,{i,Length[TextList]}]],
Graphics[{Line[{LowerLeft,LowerLeft+{0,BoxSize[[2]]},LowerLeft+BoxSize, LowerLeft+{BoxSize[[1]],0},LowerLeft}]}]}
]
MyTriangle[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Graphics[{Color1,Polygon[{Scaled[delta {-1/2, -Proportion/3}, {x, y}],
Scaled[delta {0, 2 Proportion/3}, {x, y}],Scaled[delta {1/2, -Proportion/3}, {x, y}]}], Thickness[th],
GrayLevel[0], Line[{Scaled[delta {-1/2, -Proportion/3}, {x, y}],
Scaled[delta {0, 2 Proportion/3}, {x, y}], Scaled[delta {1/2, -Proportion/3}, {x, y}],
Scaled[delta {-1/2, -Proportion/3}, {x, y}]}]}];
MyInvertedTriangle[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Graphics[{Color1,Polygon[{Scaled[delta {-1/2, Proportion/3}, {x, y}],
Scaled[delta {0, -2 Proportion/3}, {x, y}],Scaled[delta {1/2, Proportion/3}, {x, y}]}], Thickness[th],
GrayLevel[0], Line[{Scaled[delta {-1/2, Proportion/3}, {x, y}],
Scaled[delta {0, -2 Proportion/3}, {x, y}], Scaled[delta {1/2, Proportion/3}, {x, y}],
Scaled[delta {-1/2, Proportion/3}, {x, y}]}]}];
MySquare[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Graphics[{Color1, Rectangle[Scaled[delta{-1/2, -Proportion/2}, {x, y}],
Scaled[delta{1/2, Proportion/2}, {x, y}]], Thickness[th],GrayLevel[0],
Line[{Scaled[delta{-1/2, -Proportion/2}, {x, y}],Scaled[delta{-1/2, Proportion/2}, {x, y}],
Scaled[delta{1/2, Proportion/2}, {x, y}], Scaled[delta{1/2, -Proportion/2}, {x, y}],
Scaled[delta{-1/2, -Proportion/2}, {x, y}]}]}];
MyRhombous[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Graphics[{Color1,
Polygon[{Scaled[delta{0, -Proportion/2}, {x, y}],
Scaled[delta{1/2, 0}, {x, y}],
Scaled[delta{0, Proportion/2}, {x, y}],
Scaled[delta{-1/2, 0}, {x, y}]}], Thickness[th], GrayLevel[0],
Line[{Scaled[delta{0, -Proportion/2}, {x, y}],
Scaled[delta{1/2, 0}, {x, y}],
Scaled[delta{0, Proportion/2}, {x, y}],
Scaled[delta{-1/2, 0}, {x, y}],
Scaled[delta{0, -Proportion/2}, {x, y}]}]}];
My4PointStar1[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Module[{PointSet, PointSetLine, theta, alpha},
alpha = .2;
PointSet = {{1, 0}, alpha{1, 1}, {0, 1}, alpha{-1, 1}, {-1, 0},
alpha{-1, -1}, {0, -1}, alpha{1, -1}};
PointSetLine = Flatten[{PointSet, {PointSet[[1]]}}, 1];
Graphics[{Color1,
Polygon[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSet], Thickness[th], GrayLevel[0],
Line[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSetLine]}]]
My4PointStar2[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Module[{PointSet, PointSetLine, theta, alpha},
alpha = .3;
PointSet = {alpha{1, 0}, {1, 1}, alpha{0, 1}, {-1, 1},
alpha{-1, 0}, {-1, -1}, alpha{0, -1}, {1, -1}};
PointSetLine = Flatten[{PointSet, {PointSet[[1]]}}, 1];
Graphics[{Color1,
Polygon[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSet], Thickness[th], GrayLevel[0],
Line[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSetLine]}]]
My5PointStar[{x_, y_}, Color1_, Proportion_, delta_, th_] := Module[{PointSet, PointSetLine, theta,theta2},
PointSet = Flatten[Table[
{{Cos[theta + Pi/2], Sin[theta + Pi/2]},
1/2 (3 - Sqrt[5]) {Cos[theta + Pi/5 + Pi/2],
Sin[theta + Pi/5 + Pi/2]}}, {theta, 0, 2 Pi - 2 Pi/5, 2 Pi/5}], 1];
PointSetLine = Flatten[{PointSet, {PointSet[[1]]}}, 1];
Graphics[{Color1, Polygon[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@ PointSet],
Thickness[th], GrayLevel[0],
Line[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] &/@ PointSetLine]}]]
MyInverted5PointStar[{x_, y_}, Color1_, Proportion_, delta_, th_] := Module[{PointSet, PointSetLine, theta,theta2},
PointSet = Flatten[Table[
theta=theta2+Pi;
{{Cos[theta + Pi/2], Sin[theta + Pi/2]},
1/2 (3 - Sqrt[5]) {Cos[theta + Pi/5 + Pi/2],
Sin[theta + Pi/5 + Pi/2]}}, {theta2, 0, 2 Pi - 2 Pi/5, 2 Pi/5}], 1];
PointSetLine = Flatten[{PointSet, {PointSet[[1]]}}, 1];
Graphics[{Color1, Polygon[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@ PointSet],
Thickness[th], GrayLevel[0],
Line[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] &/@ PointSetLine]}]]
MyCircle[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Graphics[{Color1, Disk[{x, y}, Scaled[delta{1/2, Proportion/2}]],
Thickness[th], GrayLevel[0], Circle[{x, y}, Scaled[delta{1/2, Proportion/2}]]}]
My4PointStar3[{x_, y_}, Color1_, Proportion_, delta_, th_] :=
Module[{PointSet, PointSetLine, theta, alpha}, alpha = .3;
PointSet = {{0, 0}, {Cos[\[Pi]/4 - alpha],
Sin[\[Pi]/4 - alpha]}, {Cos[\[Pi]/4 + alpha],
Sin[\[Pi]/4 + alpha]}, {0, 0}, {Cos[3 \[Pi]/4 - alpha],
Sin[3 \[Pi]/4 - alpha]}, {Cos[3 \[Pi]/4 + alpha],
Sin[3 \[Pi]/4 + alpha]}, {0, 0}, {Cos[5 \[Pi]/4 - alpha],
Sin[5 \[Pi]/4 - alpha]}, {Cos[5 \[Pi]/4 + alpha],
Sin[5 \[Pi]/4 + alpha]}, {0, 0}, {Cos[7 \[Pi]/4 - alpha],
Sin[7 \[Pi]/4 - alpha]}, {Cos[7 \[Pi]/4 + alpha],
Sin[7 \[Pi]/4 + alpha]}};
PointSetLine = Flatten[{PointSet, {PointSet[[1]]}}, 1];
Graphics[{Color1,
Polygon[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSet], Thickness[th], GrayLevel[0],
Line[Scaled[delta {#[[1]], Proportion #[[2]]}, {x, y}] & /@
PointSetLine]}]]
MyAverage[x_] := Plus @@ x/Length[x]
Seed[] := Floor[Random[] 1000000000]
Instruction[jodas_List, Executable_String] := Module[{tmpins},
tmpins = "printf \"";
Do[Do[tmpins = tmpins <> ToString[jodas[[i, j]]] <> " ";, {j,
Length[ jodas[[i]] ]}];
tmpins = tmpins <> "\\n";, {i, Length[jodas]}];
tmpins <> "\" | " <> Executable];
Norma[x_List] := Sqrt[Plus @@( (Abs[x])^2)]
ColorCoding[NumberOfNumbers_Integer,NumberOfColors_Integer]:=
Module[{n1,n2},n1=2 Pi/NumberOfNumbers;
n2=2 Pi/NumberOfColors;
Show[{Graphics[({Hue[#1/(2 Pi-n1)],
Text[ToString[N[#1/(2. Pi),2]],1.2 {Cos[#1],Sin[#1]}]}&)/@
Range[0,2 Pi-n1,n1]],
Graphics[({Hue[#1/(2 Pi-n2)],Disk[{0,0},1,{#1,#1+n2}]}&)/@
Range[0,2 Pi-n2,n2]]},DisplayFunction\[Rule]Identity,
AspectRatio\[Rule]Automatic]]
End[];
EndPackage[]