CS100A Lecture 19

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CS100A Lecture 19

• Previous Lecture
• Representation Rules of Thumb.
• Transform problems to simpler equivalent problems
• Maintain duplicate representations if helpful
• Choose representations that limit search spaces
• Find representations that yield uniform
  algorithms.
• The Next Several Lectures
• MatLab
• Learn MatLab
• Implement (a piece of MatLab) in Java
• Get an appreciation for what MatLab does for you
• Learn to implement a class of some complexity
• Handout The CS100 MatLab Syllabus
• Java Concepts
• Overloading
• this as a constructor

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MatLab

• Each "primitive" arithmetic value is a complex
  number, i.e., a pair of real numbers, known
  respectively as the real part and the imaginary
  part.
• gtgt sqrt(-2)
• ans
• 0 1.4142i
• A complex number with a zero imaginary part is
  displayed as a real number.
• gtgt sqrt(2)
• ans
• 1.4142
• A complex number with a zero imaginary part and
  an integral real part is displayed as an integer.
• gtgt sqrt(4)
• ans
• 2
• Operators - . ./ . lt lt gt gt
• Example
• gtgt sqrt(-2) sqrt(2)

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Class ml Representation

• Development strategy Represent primitive MatLab
  arithmetic values as objects of class ml.
• Development strategy Dont get hung up doing all
  operations now. Just implement a few and trust
  that the rest will be similar.
• // Primitive MatLab arithmetic values.
• class ml
• double re // Real part
• double im // Imaginary part
• // Constructors
• . . .
• // Methods
• . . .

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Class ml Constructors

• ml(double re, double im)
• this.re re
• this.im im
• ml(double re)
• this( re, 0.0 )
• ml(int re)
• this( (double)re, 0.0 )
• ml(int re, double im)
• this( (double)re, im )

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Overloading in Java

• Signature . The name of a constructor or method
  and the types of its parameters is called its
  signature.
• Overloading. If two constructors or methods of a
  class have the same name, but different
  signatures, then the method name is said to be
  overloaded.
• Invocation. When a method is invoked, the number
  of arguments and their types are used to
  determine the signature of the method that will
  be invoked.
• Sample invocations
• // Each of the following constructs 1.0 0.0i
• ml( 1.0, 0.0 ) // Invokes first constructor.
• ml( 1.0 ) // Invokes second constructor.
• ml( 1 ) // Invokes third constructor.
• ml( 1, 0.0 ) // Invokes fourth constructor.
• ml( 1.0, 0 ) // Invokes fifth constructor.
• this() can be used in a constructor definition
  to invoke another constructor of the same class.

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Class ml Method toString

• // Convert MatLab real to String.
• private String toStringReal(double x)
• if ( (x - Math.floor(x)) 0 )
• return (int)x ""
• else
• return x ""
• // Convert MatLab complex value to String.
• public String toString()
• if ( im 0 )
• return toStringReal(re)
• else
• return toStringReal(re) " "
• toStringReal(im) "i"

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Class ml Arithmetic Methods

• public static ml add(ml x, ml y)
• return new ml(x.re y.re, x.im y.im)
• public static ml sub(ml x, ml y)
• return new ml(x.re - y.re, x.im - y.im)
• / other operators
• . ./ lt lt gt gt unary- etc.
• /

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Matrix

• A matrix is a rectangular table of values.
• gtgt ones(2,3)
• ans
• 1 1 1
• 1 1 1
• The elements of two matrices with the same
  dimensions can be added (), subtracted (-),
  multiplied (.), and divided(./).
• gtgt ones(2,3) ones(2,3)
• ans
• 2 2 2
• 2 2 2
• Other operators . lt lt gt gt
• The empty matrix, written , has height and
  width 0. The empty matrix results from requesting
  a non-positive height or width.
• gtgt ones(2,-1)

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Scalars

• A scalar is just a 1-by-1 matrix.
• gtgt ones(1,1)
• ans
• 1
• Scalar operations are just special cases of
  matrix operations, i.e., operations on 1-by-1
  matrices.
• gtgt 1 2
• ans
• 3
• A scalar operand s is treated as a matrix with
  the same dimensions as the other operand and the
  value s everywhere.
• gtgt 5 ones(2,3)
• ans
• 6 6 6
• 6 6 6

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class ML

• Class ML implements MatLab matrix values.
• Development strategy Dont get hung up doing all
  matrix operations now. Just implement a few, and
  trust that the rest will be similar.
• Development strategy Dont get hung up about
  efficiency now.

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class ML Representation

• // MatLab Matrix
• public class ML
• private int h // height of matrix
• private int w // width of matrix
• private ml values // elements of matrix
• // Constructors.
• . . .
• // Methods.
• . . .

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class ML Constructors

• // Construct h-by-w uninitialized matrix.
• private ML(int h, int w)
• this.h h
• this.w w
• values new ml hw
• // Construct h-by-w matrix initialized with v.
• public ML(int h, int w, ml v)
• this(h,w)
• for (int r0 rlth r)
• for (int c 0 c lt w c)
• valuesrc v
• // Construct scalar matrix v.
• public ML(ml v)
• this(1,1)

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class ML Methods ones, zeros, toString

• // Construct matrix of all ones.
• public static ML ones(int h, int w)
• return new ML( h, w, new ml(1.0))
• // Construct matrix of all zeros.
• public static ML zeros(int h, int w)
• return new ML( h, w, new ml(0.0))
• // Convert this matrix to String.
• public String toString()
• String result ""
• for (int r 0 r lt h r)
• for (int c 0 c lt w c)
• result result valuesrc " "

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class ML Utility methods

• // this is empty if either height or width is 0.
• private boolean isEmpty()
• return h0 w 0
• // this is scalar if both height and width are 1.
• private boolean isScalar()
• return h1 w 1

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class ML Method add

• // x y
• public static ML add(ML x, ML y)
• if ( x.isEmpty() y.isEmpty() )
• return new ML(0,0)
• else if ( x.isScalar() )
• ML result new ML(y.h, y.w)
• ml scalarValue x.values00
• for (int r 0 r lt y.h r)
• for (int c 0 c lt y.w c)
• result.valuesrc
• ml.add( scalarValue,
• y.valuesrc )
• return result
• else if ( y.isScalar() )
• ML result new ML(x.h, x.w)

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class ML Method add, continued

• else if (x.h ! y.h x.w ! y.w)
• throw new RuntimeException(
• matrix dimensions do not match")
• else
• ML result new ML(x.h, x.w)
• for (int r 0 r lt x.h r)
• for (int c 0 c lt x.w c)
• result.valuesrc
• ml.add( x.valuesrc,
• y.valuesrc)
• return result
• // end of method add