Matlab Training Session 14: Improving Program Efficiency

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Matlab Training Session 14Improving Program
Efficiency
Course Website http//www.queensu.ca/neurosci/Mat
lab Training Sessions.htm
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• Course Outline
• Term 1
• Introduction to Matlab and its Interface
• Fundamentals (Operators)
• Fundamentals (Flow)
• Importing Data
• Functions and M-Files
• Plotting (2D and 3D)
• Term 2
• Term 1 review
• Plotting (2D and 3D)
• Statistical Tools in Matlab
• Nonlinear Curve Fitting
• Statistical Tools in Matlab II
• GUIs
• Improving Code Efficiency

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• Week 14 Lecture Outline
• Programming Efficiency
• Data types in Matlab
• B. Assigning Appropriate Data Resolution
• Downsampling from 64 bit data structures
• B. Assessing Execution Time
• tic, toc functions
• Eliminating/Minimizing Loops
• Compiling Code

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Part A Data types in Matlab
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Part A Data types in Matlab
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Part A Data types in Matlab
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Part A Assigning Appropriate Data Resolution

• By default, numeric values are saved in matlab as
  64 bit floating point values
• Large data sets recorded experimentally generally
  utilizes smaller or more specific data resolution
• Down-sampling large datasets can significantly
  save on memory and dramatically improve execution
  time

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Binary Precision

• The number of bits used to represent a value
  determines how large or small that value can be
• 8 bits 0 to 256
• 16 bits 0 to 65536
• 32 bits 0 to 4.2950e009
• 64 bits 1.8447e019!
• Precision also determines how many decimal places
  can be represented

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Numeric Formats Integers and Characters
'schar' Signed character 8 bits 'uchar'
Unsigned character 8 bits 'int8' Integer 8
bits 'int16' Integer 16 bits 'int32'
Integer 32 bits 'int64' Integer 64
bits 'uint8' Unsigned integer 8 bits 'uint16'
Unsigned integer 16 bits 'uint32' Unsigned
integer 32 bits 'uint64' Unsigned integer 64
bits
The first bit denotes the sign if the integer
or character is signed.
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Readable Binary Data Formats Floating Point
Representation

• By default matlab stores all values with double
  precision
• The functions realmax and realmin return max and
  min value representations
• 'float32, single Floating-point 32 bits
• 'float64', 'double' Floating-point 64 bits

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Part B Assigning Appropriate Data Resolution

• The following functions can be used to convert
  between numeric formats in matlab
• single, double, uint8, uint16, int8, int16,
  int32
• eg. single(x) will convert matrix x to 32 bit
  IEEE floating point representation
• Operations on numeric formats are defined for
  matlab version 7 and later
• BE CARFUL, EXCESSIVE DOWNSAMPLING CAN LEAD TO
  ROUNDING ERRORS

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Part B Assigning Appropriate Data Resolution

• Lets look at an example
• testmatrix magic(1000)
• testmatrix single(testmatrix)
• rowdim, coldim size(testmatrix)
• tic
• for rowloop 1rowdim
• for colloop 1coldim
• testmatrix(rowloop,colloop)
  testmatrix(rowloop,colloop) 50
• end
• end
• toc

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Part B Assessing Execution Time

• The tic and toc functions quantitatively assess
  how long it takes to run any series of commands
  in Matlab
• tic starts a stopwatch timer.
• toc prints the elapsed time since tic was used.

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Part C Assessing Execution Time

• The tic and toc functions work together to
  measure elapsed time. tic saves the current time
  that toc uses later to measure the elapsed time.
• The sequence of commands
• tic
• operations
• toc
• measures the amount of time MATLAB takes to
  complete one or more operations, and displays the
  time in seconds.

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Part C Assessing Execution Time

• For example, add 50 to every element of some 2D
  matrix
• testmatrix magic(1000)
• rowdim, coldim size(testmatrix)
• tic
• for rowloop 1rowdim
• for colloop 1coldim
• testmatrix(rowloop,colloop)
  testmatrix(rowloop,colloop) 50
• end
• end
• toc

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Part C Assessing Execution Time

• The tic, toc functions allow for the direct
  comparison of execution time when assessing the
  efficiency of different programming algorithms

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Part C Eliminating/Simplifying Loops

• Since Matlab is an interpreted language, certain
  common programming techniques (especially for
  loops) are intrinsically inefficient.
• Whenever possible, you should try to find a
  vector function (or the composition of a few
  vector functions) that will accomplish the same
  result as a for loop.
• The process of converting a for loop to vector
  function is referred to as vectorization
• The difference in processing time between
  vectorization and a for loop can be astounding!

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Part C Eliminating/Simplifying Loops

• For example, eliminate the for loop in the
  earlier example
• testmatrix magic(1000)
• rowdim, coldim size(testmatrix)
• tic
• for rowloop 1rowdim
• for colloop 1coldim
• testmatrix(rowloop,colloop)
  testmatrix(rowloop,colloop) 50
• end
• end
• toc

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Part C Eliminating/Simplifying Loops

• For example, eliminate the for loop in the
  earlier example
• testmatrix magic(1000)
• tic
• testmatrix(,) testmatrix(,) 50
• toc

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Part C Eliminating/Simplifying Loops

• Lets look at some other common examples and then
  list some common functions that aid in
  eliminating for loops through vectorization
• Two generic algorithms in matlab are
• 1. Find a subset of a matrix that satisfies a
  condition, and do something to it.
• 2. Do something different to each column of a
  matrix without a loop.

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Part C Eliminating/Simplifying Loops

• Find a subset of a matrix that satisfies a
  condition, and do something to it.
• Say you have a matrix
• M magic(3)
• and you want to negate every element greater than
  4.

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Part C Eliminating/Simplifying Loops

• Slow looping method
• rowdim, coldim size(M)
• for i1rowdim,
• for j1coldim,
• if (M(i,j) gt 4),
• M(i,j) -M(i,j)
• end
• end
• end

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Part C Eliminating/Simplifying Loops

• Fast Vectorized Matlab Method
• ind find(M gt 4)
• M(ind)-M(ind)

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Part C Eliminating/Simplifying Loops

• 2. Do something different to each column of a
  matrix without a loop.
• In this case, let's subtract the mean from each
  column of the matrix M
• M rand(10,5)
• V mean(M)
• Slow looping method
• for i15,
• M(i,)M(i,)-V(i)
• end

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Part C Eliminating/Simplifying Loops

• M rand(10,5)
• V mean(M)
• Fast Vectorized Matlab Method
• MM-V(ones(10,1),)
• That is, V is turned into a matrix the size of M
  and the matrices are subtracted in one operation.

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Part C Eliminating/Simplifying Loops

• Handy functions that aid in avoiding for loops
  through vectorization are
• find (find values that meet some criteria)
• sum, prod, diff (sum, product, difference)
• . ./ (element by element matrix
  operations)
• min, max (find min or max values)
• zeros, ones (for initializing arrays)

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Part C Eliminating/Simplifying Loops

• One other little tidbit Avoid using 's when
  they aren't necessary.
• MATLAB has to create temporary storage for the
  results of what it believes to be concatenation.
• Eg
• tic tic
• for i11000 for i11000
• a17 a17
• end end
• toc toc
• elapsed_time 0.1987 elapsed_time 0.0435

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Part D Compiling Code

• MATLAB programs can be compiled has to create
  temporary storage for the results of what it
  believes to be concatenation.
• Eg
• tic tic
• for i11000 for i11000
• a17 a17
• end end
• toc toc
• elapsed_time 0.1987 elapsed_time 0.0435