Class: Vector (Ruby 2.2.4)
Description: Class : Vector - Ruby 2.2.4

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Support for the Ruby 2.2 series has ended. See here for reference.

### Home Classes Methods

### In Files

- matrix.rb

### Parent

Object

### Namespace

- CLASS Vector::ZeroVectorError

### Methods

- ::[]
- ::basis
- ::elements
- ::independent?
- ::new
- #*
- #+
- #+@
- #-
- #-@
- #/
- #==
- #[]
- #angle_with
- #clone
- #coerce
- #collect
- #collect2
- #component
- #covector
- #cross
- #cross_product
- #dot
- #each
- #each2
- #element
- #elements_to_f
- #elements_to_i
- #elements_to_r
- #eql?
- #hash
- #independent?
- #inner_product
- #inspect
- #magnitude
- #map
- #map2
- #norm
- #normalize
- #r
- #size
- #to_a
- #to_s

### Included Modules

- Enumerable

### Class/Module Index

Quicksearch

- Matrix
- Matrix::EigenvalueDecomposition
- Matrix::LUPDecomposition
- Vector
- Vector::ZeroVectorError

No matching classes.

# 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:

- ::[]

- ::elements(array, copy = true)

- ::basis(size: n, index: k)

To access elements:

- [](i)

To enumerate the elements:

- each2(v)

- collect2(v)

Properties of vectors:

- angle_with(v)

- ::independent?

- independent?(*vs)

Vector arithmetic:

- #*(x) “is matrix or number”

- #+(v)

- #-(v)

- #+@

- #-@

Vector functions:

- inner_product(v), dot(v)

- cross_product(v), cross(v)

- collect

- magnitude

- map

- map2(v)

- norm

- normalize

- r

- size

Conversion to other data types:

- covector

- to_a

- coerce(other)

String representations:

- to_s

- inspect

### Attributes

elements[R]

INSTANCE CREATION

### Public Class Methods

[](*array) click to toggle source

Creates a Vector from a list of elements.

    Vector[7, 4, ...]

                   # File matrix.rb, line 1741
    def Vector.[](*array)
      new convert_to_array(array, false)
    end

basis(size:, index:) click to toggle source

Returns a standard basis `n`-vector, where k is the index.

    Vector.basis(size:, index:) # => Vector[0, 1, 0]

                   # File matrix.rb, line 1758
    def Vector.basis(size:, index:)
      raise ArgumentError, "invalid size (#{size} for 1..)" if size < 1
      raise ArgumentError, "invalid index (#{index} for 0...#{size})" unless 0 <= index && index < size
      array = Array.new(size, 0)
      array[index] = 1
      new convert_to_array(array, 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 1749
    def Vector.elements(array, copy = true)
      new convert_to_array(array, copy)
    end

independent?(*vs) click to toggle source

Returns `true` iff all of vectors are linearly independent.

    Vector.independent?(Vector[1,0], Vector[0,1])
      => true

    Vector.independent?(Vector[1,2], Vector[2,4])
      => false

                   # File matrix.rb, line 1851
    def Vector.independent?(*vs)
      vs.each do |v|
        raise TypeError, "expected Vector, got #{v.class}" unless v.is_a?(Vector)
        Vector.Raise ErrDimensionMismatch unless v.size == vs.first.size
      end
      return false if vs.count > vs.first.size
      Matrix[*vs].rank.eql?(vs.count)
    end

new(array) click to toggle source

::new is private; use Vector[] or ::elements to create.

                   # File matrix.rb, line 1769
    def initialize(array)
      # No checking is done at this point.
      @elements = array
    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 1911
    def *(x)
      case x
      when Numeric
        els = @elements.collect{|e| e * x}
        self.class.elements(els, false)
      when Matrix
        Matrix.column_vector(self) * x
      when Vector
        Vector.Raise ErrOperationNotDefined, "*", self.class, x.class
      else
        apply_through_coercion(x, __method__)
      end
    end

+(v) click to toggle source

Vector addition.

                   # File matrix.rb, line 1928
    def +(v)
      case v
      when Vector
        Vector.Raise ErrDimensionMismatch if size != v.size
        els = collect2(v) {|v1, v2|
          v1 + v2
        }
        self.class.elements(els, false)
      when Matrix
        Matrix.column_vector(self) + v
      else
        apply_through_coercion(v, __method__)
      end
    end

+@() click to toggle source

                   # File matrix.rb, line 1976
    def +@
      self
    end

-(v) click to toggle source

Vector subtraction.

                   # File matrix.rb, line 1946
    def -(v)
      case v
      when Vector
        Vector.Raise ErrDimensionMismatch if size != v.size
        els = collect2(v) {|v1, v2|
          v1 - v2
        }
        self.class.elements(els, false)
      when Matrix
        Matrix.column_vector(self) - v
      else
        apply_through_coercion(v, __method__)
      end
    end

-@() click to toggle source

                   # File matrix.rb, line 1980
    def -@
      collect {|e| -e }
    end

/(x) click to toggle source

Vector division.

                   # File matrix.rb, line 1964
    def /(x)
      case x
      when Numeric
        els = @elements.collect{|e| e / x}
        self.class.elements(els, false)
      when Matrix, Vector
        Vector.Raise ErrOperationNotDefined, "/", self.class, x.class
      else
        apply_through_coercion(x, __method__)
      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 1880
    def ==(other)
      return false unless Vector === other
      @elements == other.elements
    end

[](i) click to toggle source

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

                   # File matrix.rb, line 1779
    def [](i)
      @elements[i]
    end

Also aliased as: element, component
angle_with(v) click to toggle source

Returns an angle with another vector. Result is within the [0…Math::PI].

    Vector[1,0].angle_with(Vector[0,1])
    # => Math::PI / 2

                   # File matrix.rb, line 2085
    def angle_with(v)
      raise TypeError, "Expected a Vector, got a #{v.class}" unless v.is_a?(Vector)
      Vector.Raise ErrDimensionMismatch if size != v.size
      prod = magnitude * v.magnitude
      raise ZeroVectorError, "Can't get angle of zero vector" if prod == 0

      Math.acos( inner_product(v) / prod )
    end

clone() click to toggle source

Returns a copy of the vector.

                   # File matrix.rb, line 1893
    def clone
      self.class.elements(@elements)
    end

coerce(other) click to toggle source

The coerce method provides support for Ruby type coercion. This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator. See also Numeric#coerce.

                   # File matrix.rb, line 2134
    def coerce(other)
      case other
      when Numeric
        return Matrix::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 2040
    def collect(&block) # :yield: e
      return to_enum(:collect) unless block_given?
      els = @elements.collect(&block)
      self.class.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 1829
    def collect2(v) # :yield: e1, e2
      raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
      Vector.Raise ErrDimensionMismatch if size != v.size
      return to_enum(:collect2, v) unless block_given?
      Array.new(size) do |i|
        yield @elements[i], v[i]
      end
    end

component(i) click to toggle source
Alias for: []
covector() click to toggle source

Creates a single-row matrix from this vector.

                   # File matrix.rb, line 2101
    def covector
      Matrix.row_vector(self)
    end

cross(*vs) click to toggle source
Alias for: cross_product
cross_product(*vs) click to toggle source

Returns the cross product of this vector with the others.

    Vector[1, 0, 0].cross_product Vector[0, 1, 0]   => Vector[0, 0, 1]

It is generalized to other dimensions to return a vector perpendicular to the arguments.

    Vector[1, 2].cross_product # => Vector[-2, 1]
    Vector[1, 0, 0, 0].cross_product(
       Vector[0, 1, 0, 0],
       Vector[0, 0, 1, 0]
    )  #=> Vector[0, 0, 0, 1]

                   # File matrix.rb, line 2015
    def cross_product(*vs)
      raise ErrOperationNotDefined, "cross product is not defined on vectors of dimension #{size}" unless size >= 2
      raise ArgumentError, "wrong number of arguments (#{vs.size} for #{size - 2})" unless vs.size == size - 2
      vs.each do |v|
        raise TypeError, "expected Vector, got #{v.class}" unless v.is_a? Vector
        Vector.Raise ErrDimensionMismatch unless v.size == size
      end
      case size
      when 2
        Vector[-@elements[1], @elements[0]]
      when 3
        v = vs[0]
        Vector[ v[2]*@elements[1] - v[1]*@elements[2],
          v[0]*@elements[2] - v[2]*@elements[0],
          v[1]*@elements[0] - v[0]*@elements[1] ]
      else
        rows = self, *vs, Array.new(size) {|i| Vector.basis(size: size, index: i) }
        Matrix.rows(rows).laplace_expansion(row: size - 1)
      end
    end

Also aliased as: cross
dot(v) click to toggle source
Alias for: inner_product
each(&block) click to toggle source

Iterate over the elements of this vector

                   # File matrix.rb, line 1806
    def each(&block)
      return to_enum(:each) unless block_given?
      @elements.each(&block)
      self
    end

each2(v) click to toggle source

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

                   # File matrix.rb, line 1815
    def each2(v) # :yield: e1, e2
      raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
      Vector.Raise ErrDimensionMismatch if size != v.size
      return to_enum(:each2, v) unless block_given?
      size.times do |i|
        yield @elements[i], v[i]
      end
      self
    end

element(i) click to toggle source
Alias for: []
elements_to_f() click to toggle source

                   # File matrix.rb, line 2112
    def elements_to_f
      warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated"
      map(&:to_f)
    end

elements_to_i() click to toggle source

                   # File matrix.rb, line 2117
    def elements_to_i
      warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated"
      map(&:to_i)
    end

elements_to_r() click to toggle source

                   # File matrix.rb, line 2122
    def elements_to_r
      warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated"
      map(&:to_r)
    end

eql?(other) click to toggle source

                   # File matrix.rb, line 1885
    def eql?(other)
      return false unless Vector === other
      @elements.eql? other.elements
    end

hash() click to toggle source

Returns a hash-code for the vector.

                   # File matrix.rb, line 1900
    def hash
      @elements.hash
    end

independent?(*vs) click to toggle source

Returns `true` iff all of vectors are linearly independent.

    Vector[1,0].independent?(Vector[0,1])
      => true

    Vector[1,2].independent?(Vector[2,4])
      => false

                   # File matrix.rb, line 1869
    def independent?(*vs)
      self.class.independent?(self, *vs)
    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 1992
    def inner_product(v)
      Vector.Raise ErrDimensionMismatch if size != v.size

      p = 0
      each2(v) {|v1, v2|
        p += v1 * v2.conj
      }
      p
    end

Also aliased as: dot
inspect() click to toggle source

Overrides Object#inspect

                   # File matrix.rb, line 2157
    def inspect
      "Vector" + @elements.inspect
    end

magnitude() click to toggle source

Returns the modulus (Pythagorean distance) of the vector.

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

                   # File matrix.rb, line 2051
    def magnitude
      Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2})
    end

Also aliased as: r, norm
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 2060
    def map2(v, &block) # :yield: e1, e2
      return to_enum(:map2, v) unless block_given?
      els = collect2(v, &block)
      self.class.elements(els, false)
    end

norm() click to toggle source
Alias for: magnitude
normalize() click to toggle source

Returns a new vector with the same direction but with norm 1.

    v = Vector[5,8,2].normalize
    # => Vector[0.5184758473652127, 0.8295613557843402, 0.20739033894608505]
    v.norm => 1.0

                   # File matrix.rb, line 2074
    def normalize
      n = magnitude
      raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0
      self / n
    end

r() click to toggle source
Alias for: magnitude
size() click to toggle source

Returns the number of elements in the vector.

                   # File matrix.rb, line 1795
    def size
      @elements.size
    end

to_a() click to toggle source

Returns the elements of the vector in an array.

                   # File matrix.rb, line 2108
    def to_a
      @elements.dup
    end

to_s() click to toggle source

Overrides Object#to_s

                   # File matrix.rb, line 2150
    def to_s
      "Vector[" + @elements.join(", ") + "]"
    end