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Engineering
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ENG 6
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Lecture 5

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Engineering

ENG 6

Professor Rajeevan Amirtharajah

Spring

Description

ENG 06 – Lecture #5; 1/22/2013
Plotting
• ginput
o displays coordinates where a user clicked on a graph
• Saving plots
o File -> save as
Change file to format like jpg
• Histogram
o hist function
o two arguments: data set, followed by number of bins (default is 10)
o also functions for pie charts, box and whisker plots
o search “specialized plotting”
• 3-D Plotting
o plot3() command
o 3 vectors, x, y, and z
o You can also plot surfaces
o Use meshgrid to generate matrices of points for z
o Use mesh or surf functions to plot surface
o Create top-down view of surface’s elevations using pcolour or contour
• 3-D Line Plot
• 3_D surfaces: meshgrid
o 1 variable as a function of x and y
o for every possible combo of x and y, you need a z value
o plot a surface for x and y from 0 10 10, create meshgrid
o [x y] = meshgrid(-10:10, -10:10);
o z = x.^2-y.^2;
o mesh(x,y,z);
• 3_D surfaces: surf
o fills in surface
• 3-D surfaces: Pseudo color plot
o 2 d value represented by color
o use pcolour
• 3-D surfaces: contour plot
o if you want to just display lines that connect points of the same z elevation
o additional examples: type demo in command window, scroll down to graphics
Review/Advanced/Details: Vectors
• Vectors: Indexing
o Process of extracting or inserting values in a vector
o Syntax:
V(index) returns element(s) at location specified by index
V(index) = value replaces elements at specified locations • Numerical Indexing
o Indexing vector can be any length of integers
• Replacement Rules:
o Either
All dimensions on either side of replacement instruction must be equal, or
There must be a single element on right side of replacement
o If you replace beyond end of existing vector, vector length is increased
Other elements become 0
• Caution: shortening a vector
o Better to extract what you want by indexing than removing what you don’t want
o Assign empty vector [] to elements of a vector
• Operating on vectors
o Arithmetic operations, logical operations, and applying library functions
• Library Functions:
o Sum(v) and mean(v) consume a vector and return a number
o Min(v) and max(v) return two quantities: minimum or maximum value and the
position in the vector
o Round, ceil,floor, fix remove fractional part of numbers
• Concatenation
o You can construct a new vector by concatenating (combining) other vectors
o A= [B C D…X Y Z]
o Individual items in brackets may be any vector defined as a constant or variable
o Length of Awill be sum of lengths of individual vectors
• Slicing (generalized indexing)
o B()=A()
Ais an existing array, B can be an existing array or a new array
Values in B at indices in are assigned values ofAfrom
Review/Advanced/Details:Arrays
• Resources: create elementary matrices:
o Zeros
o Ones
o Eye: identity matrix
o Linspace: linearly spaced vector
o Logspace: logarithmically spaced vector
o Meshgrid: x and y arrays for 3-D plots
• Arrays: Indexing
o A(row, col) returns elements at location specified
o A(row, col) = value replaces elements at specified location
o Indexing row and column vectors may contain either numerical or logical values
• Arrays: Numerical Indexing
o Indexing vectors can be of any length, include integers
o For reading elements: 1<=element<=length(array dimension) o For replacing elements: 1<=element
• Arrays: Replacement Rules
o Same as vectors
• Operating on Arrays
o Same techniques as vectors with:
Arithmetic operations, logical operations, library functions, slicing
o Concatenation is treated slightly differently
R = [AB C] is fine as long asA,B, and C have the same number of rows
R = [A;B;C] is fine as long asA, B, and C have the same number of
columns
• Matrix Multiplication’
o Using * by itself on matrices performs matrix multiplication
o A*b element in first row, second column of result is sum of each

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