Vector

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

Public Class Methods

[](*array) click to toggle source

Creates a Vector from a list of elements.

Vector[7, 4, ...]

 
               # File matrix.rb, line 999
def Vector.[](*array)
  new(:init_elements, array, copy = false)
end

elements(array, copy = true) click to toggle source

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

 
               # File matrix.rb, line 1007
def Vector.elements(array, copy = true)
  new(:init_elements, array, copy)
end

new(method, array, copy) click to toggle source

For internal use.

 
               # File matrix.rb, line 1014
def initialize(method, array, copy)
  self.send(method, array, copy)
end

Public Instance Methods

*(x) click to toggle source

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

 
               # File 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) click to toggle source

Vector addition.

 
               # File 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) click to toggle source

Vector subtraction.

 
               # File 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) click to toggle source

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

 
               # File matrix.rb, line 1079
def ==(other)
  return false unless Vector === other
  
  other.compare_by(@elements)
end

Also aliased as: eql?

[](i) click to toggle source

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

 
               # File matrix.rb, line 1034
def [](i)
  @elements[i]
end

clone() click to toggle source

Return a copy of the vector.

 
               # File matrix.rb, line 1096
def clone
  Vector.elements(@elements)
end

coerce(other) click to toggle source

FIXME: describe #coerce.

 
               # File 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() click to toggle source

Like Array#collect.

 
               # File matrix.rb, line 1189
def collect # :yield: e
  els = @elements.collect {
    |v|
    yield v
  }
  Vector.elements(els, false)
end

Also aliased as: map

collect2(v) click to toggle source

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

 
               # File 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) click to toggle source

For internal use.

 
               # File matrix.rb, line 1089
def compare_by(elements)
  @elements == elements
end

covector() click to toggle source

Creates a single-row matrix from this vector.

 
               # File matrix.rb, line 1228
def covector
  Matrix.row_vector(self)
end

each2(v) click to toggle source

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

 
               # File 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

eql?(other) click to toggle source

Alias for: ==

hash() click to toggle source

Return a hash-code for the vector.

 
               # File matrix.rb, line 1103
def hash
  @elements.hash
end

init_elements(array, copy) click to toggle source

For internal use.

 
               # File matrix.rb, line 1021
def init_elements(array, copy)
  if copy
    @elements = array.dup
  else
    @elements = array
  end
end

inner_product(v) click to toggle source

Returns the inner product of this vector with the other.

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

 
               # File 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() click to toggle source

Overrides Object#inspect

 
               # File matrix.rb, line 1265
def inspect
  str = "Vector"+@elements.inspect
end

map() click to toggle source

Alias for: collect

map2(v) click to toggle source

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

 
               # File matrix.rb, line 1201
def map2(v) # :yield: e1, e2
  els = collect2(v) {
    |v1, v2|
    yield v1, v2
  }
  Vector.elements(els, false)
end

r() click to toggle source

Returns the modulus (Pythagorean distance) of the vector.

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

 
               # File matrix.rb, line 1213
def r
  v = 0
  for e in @elements
    v += e*e
  end
  return Math.sqrt(v)
end

size() click to toggle source

Returns the number of elements in the vector.

 
               # File matrix.rb, line 1041
def size
  @elements.size
end

to_a() click to toggle source

Returns the elements of the vector in an array.

 
               # File matrix.rb, line 1235
def to_a
  @elements.dup
end

to_s() click to toggle source

Overrides Object#to_s

 
               # File matrix.rb, line 1258
def to_s
  "Vector[" + @elements.join(", ") + "]"
end

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