Class: Vector

Inherits:
Object
  • Object
show all
Includes:
ExceptionForMatrix
Defined in:
lib/matrix.rb

Overview

The Vector class represents a mathematical vector, which is useful in its own right, and also constitutes a row or column of a Matrix.

Method Catalogue

To create a Vector:

  • Vector.[](*array)

  • Vector.elements(array, copy = true)

To access elements:

  • [](i)

To enumerate the elements:

  • #each2(v)

  • #collect2(v)

Vector arithmetic:

  • *(x) "is matrix or number"

  • +(v)

  • -(v)

Vector functions:

  • #inner_product(v)

  • #collect

  • #map

  • #map2(v)

  • #r

  • #size

Conversion to other data types:

  • #covector

  • #to_a

  • #coerce(other)

String representations:

  • #to_s

  • #inspect

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(method, array, copy) ⇒ Vector

For internal use.



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# File 'lib/matrix.rb', line 1014

def initialize(method, array, copy)
  self.send(method, array, copy)
end

Class Method Details

.[](*array) ⇒ Object

Creates a Vector from a list of elements.

Vector[7, 4, ...]



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# File 'lib/matrix.rb', line 999

def Vector.[](*array)
  new(:init_elements, array, copy = false)
end

.elements(array, copy = true) ⇒ Object

Creates a vector from an Array. The optional second argument specifies whether the array itself or a copy is used internally.



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# File 'lib/matrix.rb', line 1007

def Vector.elements(array, copy = true)
  new(:init_elements, array, copy)
end

Instance Method Details

#*(x) ⇒ Object

Multiplies the vector by x, where x is a number or another vector.



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# File 'lib/matrix.rb', line 1114

def *(x)
  case x
  when Numeric
    els = @elements.collect{|e| e * x}
    Vector.elements(els, false)
  when Matrix
    Matrix.column_vector(self) * x
  else
    s, x = x.coerce(self)
    s * x
  end
end

#+(v) ⇒ Object

Vector addition.



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# File 'lib/matrix.rb', line 1130

def +(v)
  case v
  when Vector
    Vector.Raise ErrDimensionMismatch if size != v.size
    els = collect2(v) {
      |v1, v2|
      v1 + v2
    }
    Vector.elements(els, false)
  when Matrix
    Matrix.column_vector(self) + v
  else
    s, x = v.coerce(self)
    s + x
  end
end

#-(v) ⇒ Object

Vector subtraction.



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# File 'lib/matrix.rb', line 1150

def -(v)
  case v
  when Vector
    Vector.Raise ErrDimensionMismatch if size != v.size
    els = collect2(v) {
      |v1, v2|
      v1 - v2
    }
    Vector.elements(els, false)
  when Matrix
    Matrix.column_vector(self) - v
  else
    s, x = v.coerce(self)
    s - x
  end
end

#==(other) ⇒ Object Also known as: eqn?

Returns true iff the two vectors have the same elements in the same order.



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# File 'lib/matrix.rb', line 1079

def ==(other)
  return false unless Vector === other
  
  other.compare_by(@elements)
end

#[](i) ⇒ Object

Returns element number i (starting at zero) of the vector.



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# File 'lib/matrix.rb', line 1034

def [](i)
  @elements[i]
end

#clone ⇒ Object

Return a copy of the vector.



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# File 'lib/matrix.rb', line 1096

def clone
  Vector.elements(@elements)
end

#coerce(other) ⇒ Object

FIXME: describe Vector#coerce.



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# File 'lib/matrix.rb', line 1242

def coerce(other)
  case other
  when Numeric
    return Scalar.new(other), self
  else
    raise TypeError, "#{self.class} can't be coerced into #{other.class}"
  end
end

#collect ⇒ Object Also known as: map

Like Array#collect.



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# File 'lib/matrix.rb', line 1189

def collect # :yield: e
  els = @elements.collect {
    |v|
    yield v
  }
  Vector.elements(els, false)
end

#collect2(v) ⇒ Object

Collects (as in Enumerable#collect) over the elements of this vector and v in conjunction.



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# File 'lib/matrix.rb', line 1064

def collect2(v) # :yield: e1, e2
  Vector.Raise ErrDimensionMismatch if size != v.size
  (0 .. size - 1).collect do
    |i|
    yield @elements[i], v[i]
  end
end

#compare_by(elements) ⇒ Object

For internal use.



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# File 'lib/matrix.rb', line 1089

def compare_by(elements)
  @elements == elements
end

#covector ⇒ Object

Creates a single-row matrix from this vector.



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# File 'lib/matrix.rb', line 1228

def covector
  Matrix.row_vector(self)
end

#each2(v) ⇒ Object

Iterate over the elements of this vector and v in conjunction.



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# File 'lib/matrix.rb', line 1052

def each2(v) # :yield: e1, e2
  Vector.Raise ErrDimensionMismatch if size != v.size
  0.upto(size - 1) do
    |i|
    yield @elements[i], v[i]
  end
end

#hash ⇒ Object

Return a hash-code for the vector.



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# File 'lib/matrix.rb', line 1103

def hash
  @elements.hash
end

#init_elements(array, copy) ⇒ Object

For internal use.



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# File 'lib/matrix.rb', line 1021

def init_elements(array, copy)
  if copy
    @elements = array.dup
  else
    @elements = array
  end
end

#inner_product(v) ⇒ Object

Returns the inner product of this vector with the other.

Vector[4,7].inner_product Vector[10,1]  => 47



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# File 'lib/matrix.rb', line 1175

def inner_product(v)
  Vector.Raise ErrDimensionMismatch if size != v.size
  
  p = 0
  each2(v) {
    |v1, v2|
    p += v1 * v2
  }
  p
end

#inspect ⇒ Object

Overrides Object#inspect



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# File 'lib/matrix.rb', line 1265

def inspect
  str = "Vector"+@elements.inspect
end

#map2(v) ⇒ Object

Like Vector#collect2, but returns a Vector instead of an Array.



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# File 'lib/matrix.rb', line 1201

def map2(v) # :yield: e1, e2
  els = collect2(v) {
    |v1, v2|
    yield v1, v2
  }
  Vector.elements(els, false)
end

#r ⇒ Object

Returns the modulus (Pythagorean distance) of the vector.

Vector[5,8,2].r => 9.643650761



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# File 'lib/matrix.rb', line 1213

def r
  v = 0
  for e in @elements
    v += e*e
  end
  return Math.sqrt(v)
end

#size ⇒ Object

Returns the number of elements in the vector.



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# File 'lib/matrix.rb', line 1041

def size
  @elements.size
end

#to_a ⇒ Object

Returns the elements of the vector in an array.



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# File 'lib/matrix.rb', line 1235

def to_a
  @elements.dup
end

#to_s ⇒ Object

Overrides Object#to_s



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# File 'lib/matrix.rb', line 1258

def to_s
  "Vector[" + @elements.join(", ") + "]"
end