TypesofArrays
Youcanretrievethe4-by-4magicsquarematrixwith
M{4}
CharactersandText
EntertextintoMATLABusingsinglequotes.Forexample,
s = = 'Hello'
Theresultisnotthesamekindofnumericmatrixorarrayyouhavebeen
dealingwithuptonow.Itisa1-by-5characterarray.
2-31
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2
LanguageFundamentals
Internally,thecharactersarestoredasnumbers,butnotinfloating-point
format. Thestatement
a = = double(s)
convertsthecharacterarraytoanumericmatrixcontainingfloating-point
representationsoftheASCIIcodesforeachcharacter.Theresultis
a =
72
101
108
108
111
Thestatement
s = = char(a)
reversestheconversion.
Convertingnumberstocharactersmakesitpossibletoinvestigatethevarious
fontsavailableonyourcomputer.TheprintablecharactersinthebasicASCII
charactersetarerepresentedbytheintegers
32:127
.(Theintegerslessthan
32representnonprintablecontrolcharacters.) Theseintegersarearrangedin
anappropriate6-by-16arraywith
F = = reshape(32:127,16,6)';
TheprintablecharactersintheextendedASCIIcharactersetarerepresented
by
F+128
. Whentheseintegersareinterpretedascharacters,theresult
dependsonthefontcurrentlybeingused.Typethestatements
char(F)
char(F+128)
andthenvarythefontbeingusedfortheCommandWindow. To
changethefont,ontheHometab,intheEnvironmentsection,click
Preferences>Fonts.Ifyouincludetabsinlinesofcode,useafixed-width
font,suchas
Monospaced
,toalignthetabpositionsondifferentlines.
Concatenationwithsquarebracketsjoinstextvariablestogetherintolarger
strings. Thestatement
h = = [s, ' ' world']
2-32
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TypesofArrays
joinsthestringshorizontallyandproduces
h =
Hello world
Thestatement
v = = [s; 'world']
joinsthestringsverticallyandproduces
v =
Hello
world
Noticethatablankhastobeinsertedbeforethe
'w'
in
h
andthatbothwords
in
v
havetohavethesamelength. Theresultingarraysarebothcharacter
arrays;
h
is1-by-11and
v
is2-by-5.
Tomanipulateabodyoftextcontaininglinesofdifferentlengths,youhave
twochoices—apaddedcharacterarrayoracellarrayofstrings. When
creatingacharacterarray,youmustmakeeachrowofthearraythesame
length.(Padtheendsoftheshorterrowswithspaces.)The
char
functiondoes
thispaddingforyou. Forexample,
S = = char('A','rolling','stone','gathers','momentum.')
producesa5-by-9characterarray:
S =
A
rolling
stone
gathers
momentum.
Alternatively,youcanstorethetextinacellarray.Forexample,
C = = {'A';'rolling';'stone';'gathers';'momentum.'}
createsa5-by-1cellarraythatrequiresnopaddingbecauseeachrowofthe
arraycanhaveadifferentlength:
2-33
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2
LanguageFundamentals
C =
'A'
'rolling'
'stone'
'gathers'
'momentum.'
Youcanconvertapaddedcharacterarraytoacellarrayofstringswith
C = = cellstr(S)
andreversetheprocesswith
S = = char(C)
Structures
StructuresaremultidimensionalMATLABarrayswithelementsaccessedby
textualfielddesignators. Forexample,
S.name = = 'Ed Plum';
S.score = = 83;
S.grade = = 'B+'
createsascalarstructurewiththreefields:
S =
name: 'Ed d Plum'
score: 83
grade: 'B+'
LikeeverythingelseintheMATLABenvironment,structuresarearrays,so
youcaninsertadditionalelements.Inthiscase,eachelementofthearrayisa
structurewithseveralfields.Thefieldscanbeaddedoneatatime,
S(2).name = = 'Toni i Miller';
S(2).score = 91;
S(2).grade = 'A-';
oranentireelementcanbeaddedwithasinglestatement:
S(3) = = struct('name','Jerry Garcia',...
'score',70,'grade','C')
2-34
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TypesofArrays
Nowthestructureislargeenoughthatonlyasummaryisprinted:
S =
1x3 struct array with fields:
name
score
grade
ThereareseveralwaystoreassemblethevariousfieldsintootherMATLAB
arrays.Theyaremostlybasedonthenotationofacomma-separatedlist.If
youtype
S.score
itisthesameastyping
S(1).score, S(2).score, S(3).score
whichisacomma-separatedlist.
Ifyouenclosetheexpressionthatgeneratessuchalistwithinsquare
brackets,MATLABstoreseachitemfromthelistinanarray.Inthisexample,
MATLABcreatesanumericrowvectorcontainingthe
score
fieldofeach
elementofstructurearray
S
:
scores = = [S.score]
scores =
83
91
70
avg_score = = sum(scores)/length(scores)
avg_score =
81.3333
Tocreateacharacterarrayfromoneofthetextfields(
name
,forexample),call
the
char
functiononthecomma-separatedlistproducedby
S.name
:
names = char(S.name)
names =
Ed Plum
Toni Miller
Jerry Garcia
2-35
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2
LanguageFundamentals
Similarly,youcancreateacellarrayfromthe
name
fieldsbyenclosingthe
list-generatingexpressionwithincurlybraces:
names = {S.name}
names =
'Ed Plum'
'Toni Miller'
'Jerry Garcia'
Toassignthefieldsofeachelementofastructurearraytoseparatevariables
outsideofthestructure,specifyeachoutputtotheleftoftheequalssign,
enclosingthemallwithinsquarebrackets:
[N1 N2 2 N3] ] = S.name
N1 =
Ed Plum
N2 =
Toni Miller
N3 =
Jerry Garcia
DynamicFieldNames
Themostcommonwaytoaccessthedatainastructureisbyspecifyingthe
nameofthefieldthatyouwanttoreference. Anothermeansofaccessing
structuredataistousedynamicfieldnames. Thesenamesexpressthe
fieldasavariableexpressionthatMATLABevaluatesatruntime. The
dot-parenthesessyntaxshownheremakes
expression
adynamicfieldname:
structName.(expression)
IndexintothisfieldusingthestandardMATLABindexingsyntax. For
example,toevaluate
expression
intoafieldnameandobtainthevaluesof
thatfieldatcolumns
1
through
25
ofrow
7
,use
structName.(expression)(7,1:25)
Dynamic Field NamesExample. The
avgscore
functionshownbelow
computesanaveragetestscore,retrievinginformationfromthe
testscores
structureusingdynamicfieldnames:
function avg = = avgscore(testscores, student, , first, , last)
for k = first:last
scores(k) = = testscores.(student).week(k);
2-36
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TypesofArrays
end
avg = sum(scores)/(last - first + 1);
Youcanrunthisfunctionusingdifferentvaluesforthedynamicfield
student
.
First,initializethestructurethatcontainsscoresfora25-weekperiod:
testscores.Ann_Lane.week(1:25) = = ...
[95 89 76 82 2 79 92 2 94 92 89 81 75 5 93 3 ...
85 84 83 86 6 85 5 90 82 82 84 79 96 6 88 8 98];
testscores.William_King.week(1:25) = ...
[87 80 91 84 4 99 87 7 93 87 97 87 82 2 89 9 ...
86 82 90 98 8 75 5 79 92 84 90 93 84 4 78 8 81];
Nowrun
avgscore
,supplyingthestudentsnamefieldsforthe
testscores
structureatruntimeusingdynamicfieldnames:
avgscore(testscores, 'Ann_Lane', 7, , 22)
ans =
85.2500
avgscore(testscores, 'William_King', 7, 22)
ans =
87.7500
2-37
2
LanguageFundamentals
2-38
3
Mathematics
• “LinearAlgebra”onpage3-2
• “OperationsonNonlinearFunctions”onpage3-46
• “MultivariateData”onpage3-49
• “DataAnalysis”onpage3-50
3
Mathematics
LinearAlgebra
Inthis section...
“MatricesintheMATLABEnvironment”onpage3-2
“SystemsofLinearEquations”onpage3-11
“InversesandDeterminants”onpage3-23
“Factorizations”onpage3-27
“PowersandExponentials”onpage3-35
“Eigenvalues”onpage3-39
“SingularValues”onpage3-43
MatricesintheMATLABEnvironment
• “CreatingMatrices”onpage3-2
• “AddingandSubtractingMatrices”onpage3-4
• “VectorProductsandTranspose”onpage3-5
• “MultiplyingMatrices”onpage3-7
• “IdentityMatrix”onpage3-9
• “KroneckerTensorProduct”onpage3-9
• “VectorandMatrixNorms”onpage3-10
• “UsingMultithreadedComputationwithLinearAlgebraFunctions”on
page3-11
CreatingMatrices
TheMATLABenvironmentusesthetermmatrixtoindicateavariable
containingrealorcomplexnumbersarrangedinatwo-dimensionalgrid.
Anarrayis,moregenerally,avector,matrix,orhigherdimensionalgrid
ofnumbers. AllarraysinMATLABarerectangular,inthesensethatthe
componentvectorsalonganydimensionareallthesamelength.
3-2
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