Chapter 3 Review: Built In MATLAB Functions

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Chapter 3 Review Built In MATLAB Functions

• Introduction to MATLAB 7
• Engineering 161

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Predefined MATLAB functions

• MATLAB is rich in predefined or built in
  functions that you can use in your expressions
  and calculations
• x 16, 25, 9, 4
• y sqrt ( x )
• yields the vector y with values 4, 5, 3, 2
• sqrt is a built in MATLAB function that operates
  on scalars and vectors and matrices.

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Predefined MATLAB functions II

• Use the help command to learn how to use a
  particular function gtgt help sqrt
• Use MATLAB Help feature to see a list of all
  MATLAB functions that are available and read the
  documentation about each of them.
• MATLAB functions are varied and powerful and can
  be nested, sqrt(sin(abs(x)))
• where x can be a matrix, vector or scalar.

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Using MATLAB functions

• MATLAB functions come built in to MATLAB, sqrt,
  sin, abs, max, exp, etc.
• MATLAB functions come in specialized toolboxes
  for special fields of work the financial
  toolbox, statistical toolbox, symbolic math
  toolbox are examples.
• And, you will be able to write your own functions
  and use them just like built in ones.

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Some Elementary Math and Rounding Functions

• abs(x) absolute value
• sqrt(x) square root
• round(x) rounds to nearest
• fix(x) truncates toward 0
• floor(x) rounds down
• ceil(x) rounds up

• sign(x) sign of x
• rem(x,y) remainder of x/y
• exp(x) e raised to x power
• log(x) natural log of x
• log10(x) log to the base 10
• log2(x) log to the base 2

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Some Trigonometric Functions

• sin(x) computes the sine of x, x in
  radians,
• cos(x) computes the cosine of x, x in
  radians
• tan(x) computes the tangent of x, x in
  radians
• asin(y) computes the inverse sine, -1 lt x lt
  1
• atan(y) computes the inverse tangent, i.e.,
• computes the angle whose tangent is y
• Notice that MATLAB wants angles to be expressed
  in radians, not degrees. To convert use the
  relationship
• 1 degree pi/180 radians
• angle_radians angle_degrees(pi/180)
• angle_degrees angle_radians(180/pi)
• (sind(x) permits x to be in degrees)

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Other Useful Elementary Analysis Functions

• See our text for more detailed explanations see
  Appendix A for a list of some of the MATLAB
  functions.
• max(x), min(x), mean(x), median(x), std(x),
  sum(x), prod(x), cumsum(x), cumprod(x), sort(x),
  size(x), length(x) are just a few.
• Note that x may be a vector (row or column) or a
  matrix. For matrices, functions typically work
  on the columns of the matrix to yield their
  results. (Always best to use help feature to
  check and make sure.)

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Functions with Multiple Outputs

• Some functions return multiple results, for
  example, consider the max function
• a,b max(x) where x is a row vector of
  arbitrary length, returns two values, a will be
  the maximum value while b will be the index in
  the row vector of the maximum value

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Functions with Multiple Outputs

• x 2,4,6.5,-3, 7.9, 4.1
• a,b max(x)
• a
• 7.9
• b
• 5

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Functions used in Discrete Mathematics

• factor(x)- finds the factors of x
• gcd(x,y)- finds the greatest common denominator
  of x and y
• lcm(x,y)- finds the least common multiple of x
  and y
• rats(x)- represents x as a fraction
• factorial(x)- for x4 implies factorial(x) 24
• primes(x)- finds all the prime numbers lt x
• isprime(x)- checks to see if x is a prime number,
  function returns 1 if yes 0 if no.

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Random Number Generators I

• MATLAB contains two random number generators,
  rand(n,m) for uniformly distributed random
  numbers and randn(n,m) for normal or Gaussian
  distributed random numbers.
• Random number sequences can be scaled for
  different mean and standard deviation
  requirements.
• Sequences of random numbers are often used in
  engineering problem solving.
• x 10rand(1,100) 5 creates a row vector x
  with 100 random numbers uniformly distributed
  between -5 and 5.
• Enter the above command followed by the command
  plot (x) to see what happens.

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Random Number Generators II

• rand(n)- nxn matrix uniformly distributed (0 to
  1)
• rand(m,n)- mxn matrix uniformly distributed (0 to
  1)
• randn(n)- nxn matrix Gaussian distributed
• randn(mxn)- mxn matrix Gaussian distributed
• mean (x)- computes mean value of a vector x
• median(x)- finds the median of the elements of x
• std(x)- computes the standard deviation of the
  elements of x
• var(x)- computes the variance of the elements of x

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More on Matrices

• Weve seen ways to define matrices
• A 1,3,5 A 1 3 5 are equivalent
• t -10.52 yields t -1, -0.5, 0, .5, 1, 1.5,
  2
• B 1,2,53,4,6 yields the 2X3 matrix of two
  rows and three columns
• x linspace(-5,5,10) creates the vector x of
• 10 values equally spaced between -5 and 5

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More on Matrices II

• Also consider
• gtgt a 3,5
• gtgt b 1,a creates the row vector
• where b 1,3,5
• gtgt b(2) is the scalar with value 3
• gtgt a' is the column vector, 2 rows and
• one column (we say a transpose)

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More on the colon operator

• For M1,2,3,4,52,3,4,5,63,4,5,6,7
• x M(,1) is the column vector, the 1st column
  of M
• x M(,3) is a column vector, the 3rd column of
  M
• y M(2,) is a row vector, the second row of M
• w M(23,) is a 2 rows and 5 columns matrix
  made up of the last two rows of M
• w M(23,45) is a 2 rows and 2 columns matrix
  made up the elements, 5,66,7
• And dont forget, z M(2,4), then z 5

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Special Values

• MATLAB includes a number of predefined constants,
  special values and special matrices.
• Some examples include, pi, i and j sqrt (-1),
  Inf, NaN, clock, date, eps, and ans.
• MATLAB allows the following statement, pi 3,
  but be careful, pi will take in the value of 3
  not 3.14159.. until it is reset to the value of
  pi. Clearing the Workspace reestablishes the
  value of pi.
• Same is true for built in function names, avoid
  it.

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Other Useful Functions

• abs(z)- computes the absolute value of a complex
  number
• angle(z)- computes the angle in radians of a
  complex number used in its polar representation
• complex(x,y)- generates a complex number, you can
  also write z 5 i7
• real(z)- extracts the real part of a complex
  number
• imag(z)- extracts the imaginary component of a
  complex number
• isreal(z)- determines if z is real or not
• conj(z)- generates the complex conjugate of z

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Other Functions

• See the Table on pages 112 - 113 for a list of
  basic functions described in Chp. 3. This is a
  very small subset of MATLAB built in functions.
  Dont forget to use the Help feature to learn
  more about these functions and to find functions
  that will help you solve problems.
• Also see Table 3.16 on page 110 for special
  MATLAB functions and symbols.

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Example Problem 3.3

• Joe Mixsell
• Problem 3.3
• Calculate the number of rabbits after 10 years
  with a
• starting number of 100 and breeding at a rate
  of 90 percent/yr
• R 0.9 Breeding rate
• P0 100 Initial population
• t 0110 10 years in increments of 1 year
• P P0exp(Rt) Calculate population for
  years 0 to 10
• disp ( Years Population) Display column
  labels
• t,P Output table of values
• plot ( t, P)
• xlabel (Years), ylabel ( Annual Population)
• title ( Rabbit Population Calculation)

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Chapter 3 Assignments

• Assignments in Chapter 3 include problems 3.5,
  3.10, 3.22, 3.23.