MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Other Kinds of Arrays Chapter 11

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Objectives After studying this chapter, you should be able to: Understand the different kinds of data used in MATLAB Create and use both numeric and character arrays Create multidimensional arrays, and access data in those arrays Create and use cell and structure arrays

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Section 11.1 Data Types The primary data type (also called a class) in MATLAB is the array or matrix Within the array, MATLAB supports a number of different secondary data types (classes) The default is a double precision floating point number

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ MATLAB’s arrays can store different types of data Kinds of Data Stored in MATLAB Matrices NumericCharacterLogical Symbolic Objects - Symbolic Toolbox IntegerFloating Point multiple signed integer types multiple unsigned integer types single precision double precision complexreal

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ There are a variety of array types to store the data MATLAB Array Types Character Arrays Floating Point single precision double precision Logical Arrays Numeric Arrays Symbolic Arrays Cell Arrays Structure Arrays Other types, including user defined and JAVA types Cell and Structure arrays can store different types of data in the same array Integer multiple signed integer types multiple unsigned integer types Most of these arrays can only hold information of one data type

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ The difference between array types and data types may be confusing Consider the following analogy

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ There are lots of different places you could store your wealth They correspond to the array types

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ There are lots of different kinds of wealth you might store in a bank They correspond to the data types

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Numeric Data Types Numeric data is stored in numeric arrays The default data type is double precision floating point Every time you enter a number into MATLAB, the program assumes you’ve entered a double MATLAB conforms to the IEEE standards that specify the meaning of the double data type

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ When you define numeric values they default to doubles Each value in a double array needs 8 bytes of memory to store

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ There are 6 values in the C array – therefore it requires 6 x 8 = 48 bytes of memory

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Value limitations The biggest number you can store in a double can be found using the realmax function The smallest number you can store in a double can be found using the realmin function

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Single Precision floating point numbers Uses half the storage space of a double Each value requires 4 bytes = 32 bits

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ It’s necessary to use the single function to change the value of 5 (which is a double by default) into a single The grid symbol indicates a numeric array – double, single or integer

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Value limitations Since single precision numbers are allocated only half as much storage space, they can not cover as large a range of values as double numbers The biggest number you can store in a single can be found using the realmax(‘single’) function The smallest number you can store in a double can be found using the realmin(‘single’) function

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Engineers will rarely need to convert to single precision numbers, because today’s computers have plenty of storage space for most applications, and will execute most of the problems we pose in extremely short amounts of time

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ When would you use the short data type instead of double values? In some numerical analysis applications you may be able to improve the run time of a long problem by changing from double to single precision However, round off error becomes more of a problem.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Consider the harmonic series Shorthand for the harmonic series This series diverges -it just keeps getting bigger the more terms you add

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ For large numbers of steps the results are different using double and single data types double single

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Why? When the series gets big enough the value of 1/n is so small that the computer can’t distinguish it from 0 This occurs at the value of realmin Since doubles can differentiate between smaller numbers than singles the summation is valid for more steps

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Integers Integer arrays are new to MATLAB 7 Integers are stored in integer arrays MATLAB Integer Types 8-bit signed integer int88-bit unsigned integeruint8 16-bit signed integer int1616-bit unsigned integer uint16 32-bit signed integer int3232-bit unsigned integer uint32 64-bit signed integer int6464-bit unsigned integer uint64 Remember that 8 bits = 1 byte Each of these types require a different amount of storage

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You can determine the number of possible values allowed in the integer data type Each of the integer types uses a different amount of storage, and can thus save different ranges of values Determine the size range using intmax and intmin

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ When do we use integers Integer arrays can be used to store image information These arrays are often very large, but there are a limited number of colors used in many of these images to create the picture. Storing them as unsigned integer arrays reduces the storage requirement dramatically.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Complex numbers Default is double Twice as much storage is needed because the real and imaginary components must be stored Could also be stored as a single or integer

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Character and String Data Character arrays store character information A character array is produced from a string

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Each character is a separate element in the array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ The fifth element of the H array is the letter y

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Any string represents a character array in MATLAB Each character requires 2 bytes of storage

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Spaces are characters too The ‘ab’ symbol indicates a character array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ How are characters stored in MATLAB? All information in computers is stored using a series of zeros and ones ASCII – Used in small computers EBCDIC – Used in mainframes and super computers You can think of this list of 0’s and 1’s as a base two number

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Comparison between base 2 and base 10 Base 2 ”binary”Base 10 ”decimal”

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Every character stored using ASCII or EBCDIC code has both a binary representation and a decimal equivalent When we ask MATLAB to change a character to a double, the number we get is the decimal equivalent in the ASCII coding system

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Use the double function to convert to a double precision floating point number Use char to convert a number to a character MATLAB includes functions to change data types

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You shouldn’t mix data types in calculations or in arrays If you attempt to create an array with both character and numeric data, the array defaults to all characters There is no character equivalent to 3, so MATLAB adds a space to the array Notice that the ans array has two characters

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ If you try to perform arithmetic with a combination of character and numeric data, MATLAB converts the character to its decimal equivalent Remember that a has a decimal equivalent of 97

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Symbolic Data Covered in more detail in a separate chapter The symbolic toolbox uses symbolic data to perform symbolic algebraic calculations Create a symbolic variable using the sym function

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Symbolic variables can be grouped into arrays, just like other data types The cube symbol indicates a symbolic array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Logical Data Types Logical data can have only one of two values True False MATLAB uses 0 to represent false and 1 to represent true

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Although a logical array contains the information true and false, MATLAB represents it as 0 and 1 The check mark indicates a logical array We don’t usually create logical arrays by entering true and false values. Usually they are the result of logical operations

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Notice that x and y are numeric arrays and z is a logical array We can interpret this result to mean that x>y is false for elements 1 and 3, and true for elements 2,3 and 5 These arrays are used in logical functions, and are not usually even seen by the user.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ In this example the find command used the result of the comparison x>y to determine that elements 2, 3, and 4 met the criteria

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Sparse Arrays Both double precision arrays and logical arrays can be stored in either full matrices, or as sparse matrices. Sparse matrices are “sparsely populated”, meaning many or most of the values in the array are zero Identity matrices are examples of sparse matrices

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Sparse matrices require less space than the corresponding numeric or logical matrices If we store sparse arrays in the full matrix format, it takes 8 bytes of storage for every data value, whether they are zeros or not The sparse matrix format only stores the non-zero values, and remembers where they are this strategy saves a lot of space

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Compare the size of N and P N is a 1000x1000 identity matrix P is the same matrix, stored using the sparse strategy

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Section 11.2 Multidimensional Arrays Sometimes you may want to store data in multidimensional arrays Rows Columns Pages Additional dimensions are possible

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Multidimensional arrays are grouped into pages rows columns pages

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Imagine that you would like to store each of these 4 two- dimensional arrays into 1 three- dimensional array with four pages. Page 1 Page 2 Page 3 Page 4

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You must define each page separately. Read the first definition statement as “all the rows, all the columns, in page 1”

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Section 11.3 Creating Character Arrays We can create two dimensional character arrays only if the number of elements in each row is the same

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ This statement doesn’t work, because the number of characters in each line is different

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ The char functions “pads” the array with blanks. Notice that the array size is 6 rows by 7 columns Character arrays can store any of the characters defined in the ASCII coding scheme – including the symbols for numbers

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Character arrays can only hold character data We can take advantage of this to create tables that look like they include both character and numeric information, but really are composed of just characters The number 1 is different from the character 1

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Let’s combine an array of test scores and names Test scores Names Holly Steven Meagan David Michael Heidi Numeric information Character information

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ When we tried to store the two different data types into the same array, MATLAB interpreted the numbers as the ASCII equivalent of characters Notice that table is a character array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ num2str In order to store the two different data types in the same array, we’ll need to convert the numbers into the corresponding characters num2str

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ The num2str function converted the array of scores into the corresponding characters

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Creation of file names A useful application of character arrays and the num2str function is the creation of file names There are occasions when you may want to save data into.dat or.mat files, but you don’t know ahead of time how many files will be required my_data1.dat my_data2.dat my_data3.dat Etc.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ For example…. Load a file of unknown size called some_data Create a number of new files, one for each column from the input file

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Input and Output Data from input file Data in File Data in File Data in File3 Output files

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Load the input file Determine the number of rows and columns Create the file names Extract the data Save the data into the new files

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Section 11.4 Cell Arrays The cell array can store different types of data inside the same array Each element in the array is also an array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ These three arrays all store different data types

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Create a cell array using curly braces

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Indexing The indexing system used for cell arrays is the same as that used in other arrays. You may either use a single index, or a row and column indexing scheme. There are two approaches to retrieving information from cell arrays. Parentheses – results in a description Curly braces – results in the values

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ To access a particular element inside an array stored in a cell array, you must use a combination of curly braces and parentheses

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Section 11.5 Structure Arrays Similar to Cell Arrays Multiple arrays of differing data types can be stored in structure arrays Instead of using content indexing each of the matrices is given a location called a field

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ This structure array (struct) contains three fields This is still a 1x1 structure array – however it has three fields

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ We can add more content to the structure, and expand its size, by adding more matrices to the fields we’ve defined.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You can access the information using… Matrix name Field name Index numbers

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Just calling the matrix name returns a description of the array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You can access the actual arrays you’ve stored in the structure by using an index number to identify which set of data you’re interested in

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ You can use the field name to access just the data in certain fields. This example returns the arrays in the first field of each member of the structure

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Combining an index number and the field name allows you to access one particular array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Finally, if you want to know the content of one particular element in a field you must specify the element index number after the field name.

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Variable Editor You can use the variable editor to access the content of a structure array Double click the structure array name in the workspace window

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ If you double click on one of the elements of the structure in the variable editor, the editor expands to show you the contents of that element

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Summary MATLAB’s primary data structure is the array MATLAB supports a number of different array types, each of which can store a particular type of data Cell and structure arrays can store more than one data type in the same array

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Summary-Data Type MATLAB supports the following data types Numeric double single 8 different types of integers Character Symbolic Logical

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Summary - Array Types Numeric double single 8 different integer arrays Character Symbolic Logical Sparse Cell Structure

MATLAB for Engineers 4E, by Holly Moore. © 2014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ Summary – Multidimensional Arrays Additional dimensions can be stored in MATLAB arrays The third dimension is called a page Each page must be entered separately as a two-dimensional array