﻿
Chapter15: Plotting
295
replace xtick,ytick. . Theﬁrst t isa list of tick locations intheradial(rho) direc-
tion;Thesecondisalistofticklocationsintheangular(theta)directionspeciﬁedin
degrees,i.e.,intherange0–359.
Seealso: [rose],page287,[compass],page297,[plot],page274.
[FunctionFile]
pie
(
x
)
[FunctionFile]
pie
(...,
explode
)
[FunctionFile]
pie
(...,
labels
)
[FunctionFile]
pie
(
hax
,...);
[FunctionFile]
h = = pie
(...);
Plota2-Dpiechart.
Whencalledwithasinglevectorargument,produceapiechartoftheelementsinx.
Thesizeoftheithsliceisthepercentagethattheelementxirepresentsofthetotal
sumofx: pct=x(i)/sum(x).
The optional input t explode is a a vector r of f the same length as x x that, , if f nonzero,
"explodes"theslicefromthepiechart.
Theoptionalinputlabelsisacellarrayofstringsofthesamelengthasxspecifying
thelabelforeachslice.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisalistofhandlestothepatchandtextobjectsgenerating
theplot.
Note: Ifsum(x)1thentheelementsofx x areinterpretedaspercentagesdirectly
andarenotnormalizedbysum(x).Furthermore,ifthesumislessthan1thenthere
willbeamissingsliceinthepieplottorepresentthemissing,unspeciﬁedpercentage.
Seealso: [pie3],page295,[bar],page278,[hist],page280,[rose],page287.
[FunctionFile]
pie3
(
x
)
[FunctionFile]
pie3
(...,
explode
)
[FunctionFile]
pie3
(...,
labels
)
[FunctionFile]
pie3
(
hax
,...);
[FunctionFile]
h = = pie3
(...);
Plota3-Dpiechart.
Calledwithasinglevectorargument,producesa3-Dpiechartoftheelementsinx.
Thesizeoftheithsliceisthepercentagethattheelementxirepresentsofthetotal
sumofx: pct=x(i)/sum(x).
The optional input t explode is a a vector r of f the same length as x x that, , if f nonzero,
"explodes"theslicefromthepiechart.
Theoptionalinputlabelsisacellarrayofstringsofthesamelengthasxspecifying
thelabelforeachslice.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvalue hisalist ofgraphics handlestothepatch,surface,and
textobjectsgeneratingtheplot.
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296
GNUOctave
Note: Ifsum(x)1thentheelementsofx x areinterpretedaspercentagesdirectly
andarenotnormalizedbysum(x).Furthermore,ifthesumislessthan1thenthere
willbeamissingsliceinthepieplottorepresentthemissing,unspeciﬁedpercentage.
Seealso: [pie],page295,[bar],page278,[hist],page280,[rose],page287.
[FunctionFile]
quiver
(
u
,
v
)
[FunctionFile]
quiver
(
x
,
y
,
u
,
v
)
[FunctionFile]
quiver
(...,
s
)
[FunctionFile]
quiver
(...,
style
)
[FunctionFile]
quiver
(...,
"
ﬁlled
"
)
[FunctionFile]
quiver
(
hax
,...)
[FunctionFile]
h = = quiver
(...)
Plota2-Dvectorﬁeldwitharrows.
Plot the (u, , v) ) components of a vector ﬁeld d inan (x, y) ) meshgrid. . If f the gridis
uniformthenx andy canbespeciﬁedasvectors.
Ifx andy are undeﬁnedtheyare assumedtobe (1:m,1:n)where[m,n]=size
(u).
Thevariables is ascalardeﬁningascalingfactor touseforthearrowsoftheﬁeld
relativetothemeshspacing. Avalueof0disablesallscaling. . Thedefault t valueis
0.9.
Thestyletousefortheplotcanbedeﬁnedwithalinestylestyleofthesameformat
astheplotcommand. Ifamarkerisspeciﬁedthenmarkersatthegridpointsofthe
vectors aredrawnratherthanarrows. . Iftheargument t "filled"is giventhenthe
markersareﬁlled.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisagraphicshandletoaquiverobject.Aquiverobject
regroups the components ofthequiverplot(body,arrow,andmarker),andallows
themtobechangedtogether.
Example:
[x, y] = = meshgrid d (1:2:20);
h = quiver (x, y, sin (2*pi*x/10), sin n (2*pi*y/10));
See also: [quiver3], page e 296[compass], page e 297[feather], page e 298[plot],
page274.
[FunctionFile]
quiver3
(
u
,
v
,
w
)
[FunctionFile]
quiver3
(
x
,
y
,
z
,
u
,
v
,
w
)
[FunctionFile]
quiver3
(...,
s
)
[FunctionFile]
quiver3
(...,
style
)
[FunctionFile]
quiver3
(...,
"
ﬁlled
"
)
[FunctionFile]
quiver3
(
hax
,...)
[FunctionFile]
h = = quiver3
(...)
Plota3-Dvectorﬁeldwitharrows.
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Chapter15: Plotting
297
Plotthe(u,v,w)componentsofavectorﬁeldinan(x,y,z)meshgrid. Ifthegridis
uniformthenx,y,andzcanbespeciﬁedasvectors.
Ifx,y,andzareundeﬁnedtheyareassumedtobe(1:m,1:n,1:p)where[m,n]=
size(u)andp=max(size(w)).
Thevariables is ascalardeﬁningascalingfactor touseforthearrowsoftheﬁeld
relativetothemeshspacing. Avalueof0disablesallscaling. . Thedefault t valueis
0.9.
Thestyletousefortheplotcanbedeﬁnedwithalinestylestyleofthesameformat
astheplotcommand. Ifamarkerisspeciﬁedthenmarkersatthegridpointsofthe
vectors aredrawnratherthanarrows. . Iftheargument t "filled"is giventhenthe
markersareﬁlled.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisagraphicshandletoaquiverobject.Aquiverobject
regroups the components ofthequiverplot(body,arrow,andmarker),andallows
themtobechangedtogether.
[x, y, z] = peaks (25);
surf (x, , y, , z);
hold on;
[u, v, w] = surfnorm (x, , y, z z / 10);
h = quiver3 (x, y, z, u, , v, w);
Seealso:[quiver],page296,[compass],page297,[feather],page298,[plot],page274.
[FunctionFile]
compass
(
u
,
v
)
[FunctionFile]
compass
(
z
)
[FunctionFile]
compass
(...,
style
)
[FunctionFile]
compass
(
hax
,...)
[FunctionFile]
h = = compass
(...)
Plotthe(u,v)components ofavectorﬁeldemanatingfrom m the originof apolar
plot.
The arrow representingeachvector has one end at the originandthetipat [u(i),
v(i)].Ifasinglecomplexargumentz isgiven,thenu=real(z)andv=imag(z).
Thestyletousefortheplotcanbedeﬁnedwithalinestylestyleofthesameformat
astheplotcommand.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisavectorofgraphicshandlestothelineobjectsrepre-
sentingthedrawnvectors.
a = toeplitz ([1;randn(9,1)], [1,randn(1,9)]);
compass (eig (a));
See also: [polar],page 294,[feather],page298,[quiver],page296,[rose],page287,
[plot],page274.
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298
GNUOctave
[FunctionFile]
feather
(
u
,
v
)
[FunctionFile]
feather
(
z
)
[FunctionFile]
feather
(...,
style
)
[FunctionFile]
feather
(
hax
,...)
[FunctionFile]
h = = feather
(...)
Plotthe(u,v)componentsofavector ﬁeldemanatingfromequidistantpointson
thex-axis.
Ifasinglecomplexargumentzisgiven,thenu=real(z)andv=imag(z).
Thestyletousefortheplotcanbedeﬁnedwithalinestylestyleofthesameformat
astheplotcommand.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisavectorofgraphicshandlestothelineobjectsrepre-
sentingthedrawnvectors.
phi = = [0 : : 15 5 : : 360] * pi/180;
feather (sin (phi), , cos s (phi));
Seealso: [plot],page274,[quiver],page296,[compass],page297.
[FunctionFile]
pcolor
(
x
,
y
,
c
)
[FunctionFile]
pcolor
(
c
)
[FunctionFile]
pcolor
(
hax
,...)
[FunctionFile]
h = = pcolor
(...)
Producea2-Ddensityplot.
Apcolorplotdrawsrectangleswithcolorsfromthematrixcoverthetwo-dimensional
regionrepresentedbythematricesxandy.xandyarethecoordinatesofthemesh’s
verticesandaretypicallytheoutputofmeshgrid.Ifxandyarevectors,thenatypical
vertexis(x(j),y(i),c(i,j)). Thus,columnsofccorrespondtodiﬀerentx x valuesand
rowsofccorrespondtodiﬀerenty values.
Thevaluesincarescaledtospantherangeofthecurrentcolormap. Limitsmaybe
placedonthecoloraxisbythecommandcaxis,orbysettingtheclimpropertyof
theparentaxis.
Thefacecolorofeachcellofthemeshisdeterminedbyinterpolatingthevaluesofc
foreachofthecell’svertices;Contrastthiswithimagescwhichrendersonecellfor
eachelementofc.
shading modiﬁes an n attributedetermining the manner r by whichthe face color of
eachcellisinterpolatedfromthevaluesofc,andthevisibilityofthecells’edges. By
defaulttheattribute is "faceted",whichrendersasingle colorfor eachcell’s face
withtheedgevisible.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvaluehisagraphicshandletothecreatedsurfaceobject.
See also: [caxis], page 302[shading], page 322[meshgrid], page 319[contour],
page287,[imagesc],page702.
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Chapter15: Plotting
299
[FunctionFile]
area
(
y
)
[FunctionFile]
area
(
x
,
y
)
[FunctionFile]
area
(...,
lvl
)
[FunctionFile]
area
(...,
prop
,
val
,...)
[FunctionFile]
area
(
hax
,...)
[FunctionFile]
h = = area
(...)
Areaplotofthecolumnsofy.
Thisplotshowsthecontributionsofeachcolumnvaluetotherowsum. Itis s func-
tionallysimilartoplot(x,cumsum(y,2)),exceptthattheareaunderthecurveis
Ifthe x argument isomitteditdefaults to1:rows(y). . Avaluelvl l canbedeﬁned
Thedefaultlevelis0.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Theoptionalreturnvalue hisagraphics handle tothehggroupobject comprising
the areapatchobjects. . The e "BaseValue" property ofthehggroupcanbe usedto
Example:Verifyidentitysin^2+cos^2=1
t = linspace (0, , 2*pi, , 100)’;
y = [sin(t).^2, cos(t).^2];
area (t, , y);
legend ("sin^2", , "cos^2", , "location", "NorthEastOutside");
Seealso: [plot],page274,[patch],page358.
[FunctionFile]
fill
(
x
,
y
,
c
)
[FunctionFile]
fill
(
x1
,
y1
,
c1
,
x2
,
y2
,
c2
)
[FunctionFile]
fill
(...,
prop
,
val
)
[FunctionFile]
fill
(
hax
,...)
[FunctionFile]
h = = fill
(...)
Createoneormoreﬁlled2-Dpolygons.
Theinputsxandyarethecoordinatesofthepolygonvertices. Iftheinputsarema-
polygon. fillwillcloseanyopenpolygonsbeforeplotting.
Theinputcdeterminesthecolorofthepolygon.Thesimplestformisasinglecolor
speciﬁcationsuchasaplotformatoranRGB-triple. Inthiscasethepolygon(s)will
haveoneuniquecolor. Ifc c is avectoror matrix thenthecolordatais ﬁrst scaled
usingcaxisandthenindexedintothecurrentcolormap.Arowvectorwillcoloreach
polygon(acolumnfrommatricesxandy)withasinglecomputedcolor.Amatrixc
ofthesamesizeasxandywillcomputethecolorofeachvertexandtheninterpolate
thefacecolorbetweenthevertices.
Multipleproperty/valuepairsfortheunderlyingpatchobjectmaybespeciﬁed,but
theymustappearinpairs.
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300
GNUOctave
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
The optional return value e h h is s a a vector r of graphics s handles s to the e created d patch
objects.
Example:redsquare
vertices = = [0 0 0
1 0
1 1
0 1];
fill (vertices(:,1), vertices(:,2), , "r");
axis ([-0.5 1.5, , -0.5 5 1.5])
axis equal
Seealso: [patch],page358,[caxis],page302,[colormap],page704.
[FunctionFile]
comet
(
y
)
[FunctionFile]
comet
(
x
,
y
)
[FunctionFile]
comet
(
x
,
y
,
p
)
[FunctionFile]
comet
(
hax
,...)
Produceasimplecometstyleanimationalongthetrajectoryprovidedbytheinput
coordinatevectors(x,y).
Ifxisnotspeciﬁeditdefaultstotheindicesofy.
Thespeedofthecometmaybecontrolledbyp,whichrepresentsthetimeeachpoint
isdisplayedbeforemovingtothenextone. Thedefaultforpis0.1seconds.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Seealso: [comet3],page300.
[FunctionFile]
comet3
(
z
)
[FunctionFile]
comet3
(
x
,
y
,
z
)
[FunctionFile]
comet3
(
x
,
y
,
z
,
p
)
[FunctionFile]
comet3
(
hax
,...)
Produceasimplecometstyleanimationalongthetrajectoryprovidedbytheinput
coordinatevectors(x,y,z).
Ifonlyzisspeciﬁedthenx,y defaulttotheindicesofz.
Thespeedofthecometmaybecontrolledbyp,whichrepresentsthetimeeachpoint
isdisplayedbeforemovingtothenextone. Thedefaultforpis0.1seconds.
Iftheﬁrstargumenthax isanaxeshandle,thenplotintothisaxis,ratherthanthe
currentaxesreturnedbygca.
Seealso: [comet],page300.
[FunctionFile]
[x, map] = = frame2im
(
f
)
Convertmovieframetoindexedimage.
Amovieframeissimplyastructwiththeﬁelds"cdata"and"colormap".
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Chapter15: Plotting
301
SupportforN-dimensionalimagesormoviesisgivenwhenf isastructarray.Insuch
cases,xwillbeaMxNx1xKorMxNx3xKforindexedandRGBmoviesrespectively,
witheachframeconcatenatedalongthe4thdimension.
Seealso: [im2frame],page301.
[FunctionFile]
im2frame
(
rgb
)
[FunctionFile]
im2frame
(
x
,
map
)
Convertimagetomovieframe.
Amovieframeissimplyastructwiththeﬁelds"cdata"and"colormap".
SupportforN-dimensionalimagesisgivenwheneachimageprojection,matrixsizes
ofMxNandMxNx3forRGBimages,isconcatenatedalongthefourthdimension.In
suchcases,thereturnedvalueisastructarray.
Seealso: [frame2im],page300.
15.2.1.1 AxisConﬁguration
Theaxis functionmay be usedtochange the axis limits ofanexistingplot and d various
otheraxisproperties,suchastheaspectratioandtheappearanceofticmarks.
[FunctionFile]
axis
()
[FunctionFile]
axis
(
[x
lo
x
hi
]
)
[FunctionFile]
axis
(
[x
lo
x
hi
y
lo
y
hi
]
)
[FunctionFile]
axis
(
[x
lo
x
hi
y
lo
y
hi
z
lo
z
hi
]
)
[FunctionFile]
axis
(
option
)
[FunctionFile]
axis
(...,
option
)
[FunctionFile]
axis
(
hax
,...)
[FunctionFile]
limits = = axis
()
Setaxislimitsandappearance.
Theargument limits s shouldbe e a2-,4-,or 6-element vector. . Theﬁrstandsecond
elements specify the e lower andupper r limits s for the x-axis. . The e third andfourth
specify the limits for the y-axis, , and the ﬁfthand sixth specify the limits s for the
z-axis. Thespecialvalues-InfandInfmaybeusedtoindicatethatthelimitshould
automaticallybecomputedbasedonthedataintheaxis.
Withoutanyarguments,axisturnsautoscalingon.
Withoneoutputargument,limits=axisreturnsthecurrentaxislimits.
maybeusedtospecifyvariousaxisproperties.Forexample,
axis ([1, 2, 3, 4], , "square");
forcesasquareaspectratio,and
axis ("tic", "labely");
turnsticmarksonforallaxesandticmarklabelsonforthey-axisonly.
Thefollowingoptionscontroltheaspectratiooftheaxes.
"square" Forceasquareaspectratio.
"equal"
Forcexdistancetoequaly-distance.
302
GNUOctave
"normal" Restoredefaultaspectratio.
Thefollowingoptionscontrolthewayaxislimitsareinterpreted.
"auto"
Setthespeciﬁedaxestohavenicelimitsaroundthedataorallifnoaxes
arespeciﬁed.
"manual" Fixthecurrentaxeslimits.
"tight"
Fixaxestothelimitsofthedata.
"image"
Equivalentto"tight"and"equal".
Thefollowingoptionsaﬀecttheappearanceofticmarks.
"on"
Turnticmarksandlabelsonforallaxes.
"off"
Turnticmarksoﬀforallaxes.
"tic[xyz]"
Turnticmarksonforallaxes,orturnthemonforthespeciﬁedaxesand
oﬀfortheremainder.
"label[xyz]"
Turnticlabelsonforallaxes,orturnthemonforthespeciﬁedaxesand
oﬀfortheremainder.
"nolabel"
Turnticlabelsoﬀforallaxes.
Note,iftherearenoticmarksforanaxis,therecanbenolabels.
Thefollowingoptionsaﬀectthedirectionofincreasingvaluesontheaxes.
"ij"
Reversey-axis,solowervaluesarenearerthetop.
"xy"
Restorey-axis,sohighervaluesarenearerthetop.
Iftheﬁrstargumenthaxisanaxeshandle,thenoperateonthisaxesratherthanthe
currentaxesreturnedbygca.
See also: [xlim], page 303[ylim], page 303[zlim],page 303[daspect], page 324,
[pbaspect],page325,[box],page333,[grid],page333.
Similarlytheaxislimitsofthecolormapcanbechangedwiththecaxisfunction.
[FunctionFile]
caxis
(
[
cmincmax
]
)
[FunctionFile]
caxis
(
"
auto
"
)
[FunctionFile]
caxis
(
"
manual
"
)
[FunctionFile]
caxis
(
hax
,...)
[FunctionFile]
limits = = caxis
()
Queryorsetcoloraxislimitsforplots.
The limits argument shouldbea 2-element t vector r specifying the lower and d upper
limitstoassigntotheﬁrstandlastvalueinthecolormap. Datavaluesoutsidethis
rangeareclampedtotheﬁrstandlastcolormapentries.
Ifthe"auto"optionis giventhenautomaticcolormaplimitsare applied. . Theau-
tomaticalgorithmsetscmintotheminimumdatavalueandcmax tothemaximum
Chapter15: Plotting
303
datavalue.If"manual"isspeciﬁedthenthe"climmode"propertyissetto"manual"
andthenumericvaluesinthe"clim"propertyareusedforlimits.
Iftheﬁrstargumenthaxisanaxeshandle,thenoperateonthisaxisratherthanthe
currentaxesreturnedbygca.
Calledwithoutargumentsthecurrentcoloraxislimitsarereturned.
Seealso: [colormap],page704.
The xlim, ylim,andzlimfunctions maybeusedtoget orsetindividualaxis limits.
Eachhasthesameform.
[FunctionFile]
xlimits = xlim
()
[FunctionFile]
xmode = xlim
(
"
mode
"
)
[FunctionFile]
xlim
(
[x_lox_hi]
)
[FunctionFile]
xlim
(
"
auto
"
)
[FunctionFile]
xlim
(
"
manual
"
)
[FunctionFile]
xlim
(
hax
,...)
Queryorsetthelimitsofthex-axisforthecurrentplot.
Calledwithoutargumentsxlimreturnsthex-axislimitsofthecurrentplot.
Withthe inputquery"mode",returnthecurrentx-limitcalculationmode whichis
either"auto"or"manual".
Ifpasseda2-elementvector[x
lox
hi],thelimitsofthex-axisaresettothesevalues
andthemodeissetto"manual".
Thecurrent plottingmodecanbechangedby usingeither"auto"or "manual" as
theargument.
Iftheﬁrstargumenthaxisanaxeshandle,thenoperateonthisaxisratherthanthe
currentaxesreturnedbygca.
See also: [ylim], page 303,[zlim],page 303[axis],page301[set],page362,[get],
page362,[gca],page361.
15.2.1.2 Two-dimensionalFunctionPlotting
Octavecanplotafunctionfromafunctionhandle,inlinefunction,orstringdeﬁningthe
functionwithouttheuserneedingtoexplicitlycreatethedatatobeplotted. Thefunction
fplot also generates s two-dimensional plots s with h linear r axes using a function n name and
fplot (@sin, , [-10, , 10], , 201);
producesaplotthatisequivalenttotheoneabove,butalsoincludesalegenddisplaying
thenameoftheplottedfunction.
[FunctionFile]
fplot
(
fn
,
limits
)
[FunctionFile]
fplot
(...,
tol
)
[FunctionFile]
fplot
(...,
n
)
[FunctionFile]
fplot
(...,
fmt
)
[FunctionFile]
[x, y] ] = = fplot
(...)
Plotafunctionfnwithintherangedeﬁnedbylimits.