Concatenation

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Concatenation

• MATLAB lets you construct a new vector by
  concatenating other vectors
• A B C D ... X Y Z
• where the individual items in the brackets may be
  any vector defined as a constant or variable, and
  the length of A will be the sum of the lengths of
  the individual vectors.
• A 1 2 3 42
• is a special case where all the component
  elements are scalar quantities.

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Slicing (generalized indexing)

• A(4) actually creates an anonymous 1 1 index
  vector, 4, and then using it to extract the
  specified element from the array A.
• In general,
• B(ltrangeBgt) A(ltrangeAgt)
• where ltrangeAgt and ltrangeBgt are both index
  vectors, A is an existing array, and B can be an
  existing array, a new array, or absent altogether
  (giving B the name ans). The values in B at the
  indices in ltrangeBgt are assigned the values of A
  from ltrangeAgt .

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Example
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Exercise Write Matlab code to create an array
oddv of odd indices from a vector v. For
example gtgt v 1 4 9 16 25 gtgt oddv lt your
code heregt gtgt oddv ans 1 9 25 etc.
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4.2. Matrices Example The following 2 x 3
matrix (matA) can be created in Matlab as
follows
Dimension of a matrix can be accessed by function
called size.
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Accessing and modifying array elements
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Accessing and modifying array elements
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Accessing and modifying array elements
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Matrix operations Matrix addition,
multiplication, inverse, determinant etc.
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Matrix operations Matrix addition,
multiplication, inverse, determinant, transpose
etc.
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Logical indexing in 2-dim matrices
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Exercise Solve a linear system of equations
3x 5y 6z 11 4x 6y z
9 -2x 3y 5z 13
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Sum, max, min, size etc.
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4.3. Mixed Data Types
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Discussions and exercises, Chapter 4
Exercise 4.1
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• Exercise 4.2
• Write statements to do the following operations
  on a vector x
• Return the odd indexed elements.

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Exercise 4.2 Write statements to do the
following operations on a vector x 2) Return
the first half of x.
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Exercise 4.2 Write statements to do the
following operations on a vector x 3) Return
the vector in the reverse order.
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Exercise 4.3 Given a vector v, and a vector k of
indices, write a one or two statement code in
Matlab that removes the elements of v in
positions specified by k. Example gtgt v 1, 3,
5, 7, 11, 9, 19 gtgt k 2, 4, 5 gtgt lt your code
heregt gtgt v ans 1, 5, 9, 19
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Exercise 4.3 Given a vector v, and a vector k of
indices, write a one or two statement code in
Matlab that removes the elements of v in
positions specified by k.
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Exercise 4.4 what does Matlab output for the
following commands? 1) 6 1 10 2) (6
1) 10
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Exercise 4.4 what does Matlab output for the
following commands? 1) 6 1 10 2) (6
1) 10
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Exercise 4.5. (This is quite tricky, especially
without using a loop construct like while or
for.) Write a statement to return the elements
of a vector randomly shuffled. Hint provided is
a useful one. First understand how sort function
works.
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Array Manipulation

• We consider the following basic operations on
  vectors
• Creating an array
• Extracting data from an array by indexing
• Shortening an array
• Mathematical and logical operations on arrays

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Creating an Array Constant Values

• Entering the values directly, e.g.
• A 2, 5, 7 1, 3, 42 the semicolon
  identifies the next row, as would a new line in
  the command
• Using the functions zeros( rows, cols),
  ones(rows, cols), rand(rows, cols) and
  randn(rows, cols) to create vectors filled with
  0, 1, or random values between 0 and 1

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Indexing an Array

• The process of extracting values from an array,
  or inserting values into an array
• Syntax
• A(row, col) returns the element(s) at the
  location(s) specified by the array row and column
  indices.
• A(row, col) value replaces the elements at the
  location(s) specified by the array row and column
  indices.
• The indexing row and column vectors may contain
  either numerical or logical values

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Operating on Arrays

• Four techniques extend directly from operations
  on vectors
• Arithmetic operations
• Logical operations
• Applying library functions
• Slicing (generalized indexing)
• The following deserves an additional word because
  of the nature of arrays
• Concatenation

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Array Concatenation

• Array concatenation can be accomplished
  horizontally or vertically
• R A B C succeeds as long as A, B and C have
  the same number of rows the columns in R will be
  the sum of the columns in A, B and C.
• R A B C succeeds as long as A, B and C have
  the same number of columns the rows in R will be
  the sum of the rows in A, B and C.

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Reshaping Arrays

• Arrays are actually stored in column order in
  Matlab. So internally, a 2 3 array is stored
  as a column vector A(1,1)
• A(2,1)
• A(1,2)
• A(2,2)
• A(1,3)
• A(2,3)
• Any n m array can be reshaped into any p q
  array as long as nm pq using the reshape
  function.

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Engineering ExampleComputing Soil Volume

• Consider the example where you are given the
  depth of soil from a survey in the form of a
  rectangular array of soil depth.
• You are also given the footprint of the
  foundations of a building to be built on that
  site and the depth of the foundation.
• Compute the volume of soil to be removed.

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Survey Data
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Building Footprint
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Solution

• clear
• clc
• soil depth data for each square produced
• by the survey
• dpth 8 8 9 8 8 8 8 8 7 8 7 7 7 7 8 8 8 7
• 8 8 8 8 8 8 8 7 7 7 7 7 8 7 8 8 8 7
• . . .
• 9 8 8 7 7 8 7 7 7 7 8 8 9 9 9 8 7 8
• estimated proportion of each square that should
  
• be excavated
• area 1 1 1 1 1 1 1 1 1 1 .3 0 0 0 0 0 0 0
• . . .
• 0 0 0 0 0 0 .4 .8 .9 1 1 1 1 1 1 1 1 .6
• square_volume dpth . area
• total_soil sum(sum(square_volume))

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Summary

• This chapter introduced you to vectors and
  arrays. For each collection, you saw how to
• Create them by concatenation and a variety of
  special-purpose functions
• Access and remove elements, rows, or columns
• Perform mathematical and logical operations on
  them
• Apply library functions, including those that
  summarize whole columns or rows
• Move arbitrary selected rows and columns from
  one array to another
• Reshape and linearize arrays