MatLab Basics: Data type, Matrices, Graphics

Transcription

1 MatLa Basis: Data type, Matries, Graphis 1 Plotting Data os(t/10) X: 78 Y: t Figure y MIT OCW.

2 MatLa logial har NUMERIC ell struture funtion handle user lasses Java lasses int8, uint8, int16, uint16, int32, uint32, int64, uint64 single doule dapted from MTLB Help Setions. Figure y MIT OCW.

3 Numeri Types Numer representation Binary: 0, Deimal: Hexadeimal 0-9,,B,C,D,E,F 5D Bit: a single inary digit Byte: 8 inary digits Word: 16 inary digits Doule Word: 32 inary digits

4 Numeri Types In MatLa Integers: Floating points: 1.234e-72 Complex numer: i Infinity and NN: Inf (1/0), NN (not a numer)

5 MatLa Integer Type Data Type Range of Values Conversion Funtion Data Type Signed 8-it integer Signed 8-it integer Signed 16-it integer Signed 16-it integer Signed 32-it integer Signed 32-it integer Signed 64-it integer Signed 64-it integer Unsigned 8-it integer Unsigned 3-it integer Unsigned 16-it integer Unsigned 16-it integer Unsigned 32-it integer Unsigned 32-it integer Unsigned 64-it integer Unsigned 64-it integer Range of Values I Conversion Fundion I -2 7 to int to int to int to int64 0 to 2 O to uint8 uint~ 0 to 2 0 to I uint16 uint 16 0 to uint32 0 to O to IE4-1 uint64 uint 64 dapted from MTLB Help Setions. Figure y MIT OCW. I

6 MatLa Floating Point Type Uses IEEE Standard 754: Doule type, Single type e-34 Doule Single Bits Usage 63 I Sign 10 positive, 1 negative) 63 Sign (0 positive, 1 negative) 62 to 62 to 52 52I Exponent, iased y y I to 51 to U 0 Fration i f of the numer 1.f1. f I51 Bits Bits Usage Usage I 31 Sign Sign (U(0 positive, 11 negative) negative) 30 to 23 Exponent, iased y y to 0 Fration f of nf the numer 1.f1. f dapted from MTLB Help Setions. Figures y MIT OCW.

7 MatLa Complex Numer Type i or j are speially reserved symols in MatLa Complex numers are represented as: +Bi Complex(1,2) C1+2i Dreal(C) D1 Eimag(C) E2

8 Logial (oolean) Types In MatLa Logial state (e.g. 5>2) is represented y: 1 or 0 True or False Logial types are important in programming when deision must e made depending on the validity (true or false) of some onditions

9 Charater Types In MatLa -- a, z, 8 '&' are haraters De Hex Binary De Hex Binary SCII SCII X MatLa treat any symol 10 X 16 X 2 X 10 X 16 X E N F O P plaed inside SINGLE Q R quotes as an array S : T 059 3B : U of haraters! Internally, eah harater is represented y an 8-it numer using Uniode (SCII) deoding system C 3D 3E 3F B 4C 4D < B C D E F G H I J K L M B 5C 5D 5E 5F V W X Y Z [ \ ] ^ - ` a d e f g Figure y MIT OCW.

10 Logial (oolean) Types In MatLa Logial state (e.g. 5>2) is represented y: 1 or 0 True or False Logial types are important in programming when deision must e made depending on the validity (true or false) of some onditions

11 Construting Matrix in MatLa ones: matrix of all ones zeros: matrix of all zero eyes: Identity matrix randn: Random matrix ones(4, 6, uint32 ) reates a 4x6 matrix ontaining ones represented as unsigned 32 it integer randn(2) reates a 2x2 matrix ontaining random numers of standard normal distriution rand(2) reates a 2x2 matrix ontaining random numers uniformly distriuted etween 0 and 1

12 Basi Linear lgera ± ± ± ± ± a a a d ad I d a dh g df e h ag f ae h f g e d a h d f g a h f g e d a md m m ma d a m ]' [ Inverse Salar multi dd/su Matrix multi Transpose

13 MatLa Operators numeri Operator Desription + -.*./.\ + - :.^.' ' * / \ ^ ddition Sutration Multipliation Right division Left division Unary plus Unary minus Colon operator Power Transpose Complex onjugate transpose Matrix multipliation Matrix right division Matrix left division Matrix power dapted from MTLB Help Setions. Figure y MIT OCW. + C * C * B.* C./ C.\ C [ 1 2 ], B, C [ 5 6] 11 [ 6 8] ad! 3 4 [ 5 12] [ ] [ 5 3]

14 MatLa Operators - Relational, Logial Operator < C I < Desription I Less than Less than Less than or equal to > Greater than -- > Equal Greater to than or equal to - Not equal to Equal to ~ Not equal to dapted from MTLB Help Setions. Figure y MIT OCW. - Operator Desril ptio n Example Operator Desription Example & Returns 1 for every element loat~on that is true (nonzero) ~n oth arrays, n & E 0100i and 0 for all other elements & Returns 1 for every element loation that is true (nonzero) in oth arrays, and 0 for all other elements. & B I Returns 1 for every element loat~on that 1s true (nonzero) ~n e~ther one or I B Returns 1 for every element loation that is true (nonzero) in either one or the the other, other, or or oth arrays, and and 0 for 0 all for other all other elements. elements B ~ Complements eah eah element ofthe input aray, array,. n ~ xor xor Returns 1 for every element loation that is true (nonzero) in only one array, Returns and 10 for for every all other elements. loat~on that 1s true (nonzero) ~n only one xor (, B) xor [, E) array, and 0 for all other elements dapted from MTLB Help Setions. Figure y MIT OCW.

15 One more MatLa Operator Sequene : is the sequene operator that denote a range [ ] [ ] [ ] [] (:,2) (2 : 3,:) (:,2) (2,:) : 3: : 5 D D C C B B It is very useful to reate, deimate, and generate sumatrix

16 Basi Graphi Output in MatLa X [ ] Y [ ] plot(x,y)

17 More Graphi Output Plotting Data t1:1:100; plot(t,os(t/10)); os(t/10) X: 78 Y: t Figure y MIT OCW.

18 Graphi output an also e modified via sript t1:1:100; plot(t, os(t/10), o- ); title( Plotting Data2 ); xlael( t ); ylael( os(t/10) ); legend( sim data ); os(t/10) Plotting Data t sim data Figure y MIT OCW.

19 ouple more very useful graphi ommands (1) hold on/hold off determines whether the next plot ommand overwrites or not (2) figure Creates new figure window (3) From the figure window, under edit menu, the opy figure option allows you to opy the figure to the lipoard and then you an ut and paste it into other programs suh as MSWord.