Class: Vector

Relationships & Source Files
Namespace Children
Exceptions: `ZeroVectorError`
Super Chains via Extension / Inclusion / Inheritance
Class Chain: self, `::Matrix::ConversionHelper`
Instance Chain: self, `::Matrix::CoercionHelper`, Enumerable, `::ExceptionForMatrix`
Inherits:	Object
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)
.elements(array, copy = true)
.basis(size: n, index: k)
.zero(n)

To access elements:

#[](i)

To set elements:

#[]=(i, v)

To enumerate the elements:

#each2(v)
#collect2(v)

Properties of vectors:

#angle_with(v)
.independent?(*vs)
#independent?(*vs)
#zero?

Vector arithmetic:

#*(x) “is matrix or number”
#+(v)
#-(v)
#/(v)
#+@
#-@

Vector functions:

#inner_product(v), #dot(v)
#cross_product(v), #cross(v)
#collect
#collect!
#magnitude
#map
#map!
#map2(v)
#norm
#normalize
#r
#round
#size

Conversion to other data types:

#covector
#to_a
#coerce(other)

String representations:

#to_s
#inspect

Class Method Summary

.[](*array)

Creates a Vector from a list of elements.
.basis(size:, index:)

Returns a standard basis n-vector, where k is the index.
.elements(array, copy = true)

Creates a vector from an Array.
.independent?(*vs) ⇒ Boolean

Returns true iff all of vectors are linearly independent.
.new(array) ⇒ Vector constructor

new is private; use Vector[] or .elements to create.
.zero(size)

Return a zero vector.

`::Matrix::ConversionHelper` - Extended

convert_to_array

Converts the obj to an Array.

Instance Attribute Summary

#zero? ⇒ Boolean readonly

Returns true iff all elements are zero.
#elements readonly protected

Instance Method Summary

#*(x)

Multiplies the vector by x, where x is a number or a matrix.
#+(v)

Vector addition.
#+@
#-(v)

Vector subtraction.
#-@
#/(x)

Vector division.
#==(other)

Returns true iff the two vectors have the same elements in the same order.
#[](range) (also: #element, #component)

Returns element or elements of the vector.
#[]=(range, new_vector) (also: #set_element, #set_component)

Set element or elements of vector.
#angle_with(v)

Returns an angle with another vector.
#coerce(other)

The coerce method provides support for Ruby type coercion.
#collect(&block) (also: #map)

Like Array#collect.
#collect!(&block) (also: #map!)

Like Array#collect!
#collect2(v)

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

Alias for #[].
#covector

Creates a single-row matrix from this vector.
#cross(*vs)

Alias for #cross_product.
#cross_product(*vs) (also: #cross)

Returns the cross product of this vector with the others.
#dot(v)

Alias for #inner_product.
#each(&block)

Iterate over the elements of this vector.
#each2(v)

Iterate over the elements of this vector and v in conjunction.
#element(i)

Alias for #[].
#elements_to_f
#elements_to_i
#elements_to_r
#eql?(other) ⇒ Boolean
#freeze

Makes the matrix frozen and Ractor-shareable.
#hash

Returns a hash-code for the vector.
#independent?(*vs) ⇒ Boolean

Returns true iff all of vectors are linearly independent.
#inner_product(v) (also: #dot)

Returns the inner product of this vector with the other.
#inspect

Overrides Object#inspect
#magnitude (also: #r, #norm)

Returns the modulus (Pythagorean distance) of the vector.
#map(&block)

Alias for #collect.
#map!(&block)

Alias for #collect!.
#map2(v, &block)

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

Alias for #magnitude.
#normalize

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

Alias for #magnitude.
#round(ndigits = 0)

Returns a vector with entries rounded to the given precision (see Float#round).
#size

Returns the number of elements in the vector.
#to_a

Returns the elements of the vector in an array.
#to_matrix

Return a single-column matrix from this vector.
#to_s

Overrides Object#to_s
#initialize_copy(v) private

Called for dup & clone.
#set_component(i, v) private

Alias for #[]=.
#set_element(i, v) private

Alias for #[]=.
#set_range(range, value) private
#set_value(index, value) private

`::Matrix::CoercionHelper` - Included

#apply_through_coercion

Applies the operator oper with argument obj through coercion of obj

Constructor Details

.new(array) ⇒ `Vector`

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

[ GitHub ]

# File 'lib/matrix.rb', line 1991


def initialize(array)
  # No checking is done at this point.
  @elements = array
end

Class Method Details

.[](*array)

Creates a Vector from a list of elements.

Vector[7, 4, ...]

[ GitHub ]

# File 'lib/matrix.rb', line 1952


def Vector.[](*array)
  new convert_to_array(array, false)
end

.basis(size:, index:)

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

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

Raises:

(ArgumentError)

[ GitHub ]

# File 'lib/matrix.rb', line 1969


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)

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

[ GitHub ]

# File 'lib/matrix.rb', line 1960


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

.independent?(*vs) ⇒ `Boolean`

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

[ GitHub ]

# File 'lib/matrix.rb', line 2116


def Vector.independent?(*vs)
  vs.each do |v|
    raise TypeError, "expected Vector, got #{v.class}" unless v.is_a?(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

.zero(size)

Return a zero vector.

Vector.zero(3) # => Vector[0, 0, 0]

Raises:

(ArgumentError)

[ GitHub ]

# File 'lib/matrix.rb', line 1982


def Vector.zero(size)
  raise ArgumentError, "invalid size (#{size} for 0..)" if size < 0
  array = Array.new(size, 0)
  new convert_to_array(array, false)
end

Instance Attribute Details

#elements (readonly, protected)

[ GitHub ]

# File 'lib/matrix.rb', line 1945


attr_reader :elements

#zero? ⇒ `Boolean` (readonly)

Returns true iff all elements are zero.

[ GitHub ]

# File 'lib/matrix.rb', line 2141


def zero?
  all?(&:zero?)
end

Instance Method Details

#*(x)

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

[ GitHub ]

# File 'lib/matrix.rb', line 2193


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
    raise ErrOperationNotDefined, ["*", self.class, x.class]
  else
    apply_through_coercion(x, __method__)
  end
end

#+(v)

Vector addition.

[ GitHub ]

# File 'lib/matrix.rb', line 2210


def +(v)
  case v
  when 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

#+@

[ GitHub ]

# File 'lib/matrix.rb', line 2258


def +@
  self
end

#-(v)

Vector subtraction.

[ GitHub ]

# File 'lib/matrix.rb', line 2228


def -(v)
  case v
  when 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

#-@

[ GitHub ]

# File 'lib/matrix.rb', line 2262


def -@
  collect {|e| -e }
end

#/(x)

Vector division.

[ GitHub ]

# File 'lib/matrix.rb', line 2246


def /(x)
  case x
  when Numeric
    els = @elements.collect{|e| e / x}
    self.class.elements(els, false)
  when Matrix, Vector
    raise ErrOperationNotDefined, ["/", self.class, x.class]
  else
    apply_through_coercion(x, __method__)
  end
end

#==(other)

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

[ GitHub ]

# File 'lib/matrix.rb', line 2169


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

#[](range) #[](integer)
Also known as: #element, #component

Returns element or elements of the vector.

[ GitHub ]

# File 'lib/matrix.rb', line 2005


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

#[]=(range, new_vector) #[]=(range, row_matrix) #[]=(range, new_element) #[]=(integer, new_element)
Also known as: #set_element, #set_component

Set element or elements of vector.

Raises:

(FrozenError)

[ GitHub ]

# File 'lib/matrix.rb', line 2020


def []=(i, v)
  raise FrozenError, "can't modify frozen Vector" if frozen?
  if i.is_a?(Range)
    range = Matrix::CoercionHelper.check_range(i, size, :vector)
    set_range(range, v)
  else
    index = Matrix::CoercionHelper.check_int(i, size, :index)
    set_value(index, v)
  end
end

#angle_with(v)

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

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

Raises:

(TypeError)

[ GitHub ]

# File 'lib/matrix.rb', line 2378


def angle_with(v)
  raise TypeError, "Expected a Vector, got a #{v.class}" unless v.is_a?(Vector)
  raise ErrDimensionMismatch if size != v.size
  prod = magnitude * v.magnitude
  raise ZeroVectorError, "Can't get angle of zero vector" if prod == 0
  dot = inner_product(v)
  if dot.abs >= prod
    dot.positive? ? 0 : Math::PI
  else
    Math.acos(dot / prod)
  end
end

#coerce(other)

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.

[ GitHub ]

# File 'lib/matrix.rb', line 2438


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(&block) Also known as: #map

Like Array#collect.

[ GitHub ]

# File 'lib/matrix.rb', line 2322


def collect(&block) # :yield: e
  return to_enum(:collect) unless block_given?
  els = @elements.collect(&block)
  self.class.elements(els, false)
end

#collect!(&block) Also known as: #map!

Like Array#collect!

Raises:

(FrozenError)

[ GitHub ]

# File 'lib/matrix.rb', line 2332


def collect!(&block)
  return to_enum(:collect!) unless block_given?
  raise FrozenError, "can't modify frozen Vector" if frozen?
  @elements.collect!(&block)
  self
end

#collect2(v)

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

Raises:

(TypeError)

[ GitHub ]

# File 'lib/matrix.rb', line 2094


def collect2(v) # :yield: e1, e2
  raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
  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)

Alias for #[].

[ GitHub ]

# File 'lib/matrix.rb', line 2009


alias component []

#covector

Creates a single-row matrix from this vector.

[ GitHub ]

# File 'lib/matrix.rb', line 2398


def covector
  Matrix.row_vector(self)
end

#cross(*vs)

Alias for #cross_product.

[ GitHub ]

# File 'lib/matrix.rb', line 2317


alias_method :cross, :cross_product

#cross_product(*vs) Also known as: #cross

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]

Raises:

(ErrOperationNotDefined)

[ GitHub ]

# File 'lib/matrix.rb', line 2297


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
    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

#dot(v)

Alias for #inner_product.

[ GitHub ]

# File 'lib/matrix.rb', line 2283


alias_method :dot, :inner_product

#each(&block)

Iterate over the elements of this vector

[ GitHub ]

# File 'lib/matrix.rb', line 2071


def each(&block)
  return to_enum(:each) unless block_given?
  @elements.each(&block)
  self
end

#each2(v)

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

Raises:

(TypeError)

[ GitHub ]

# File 'lib/matrix.rb', line 2080


def each2(v) # :yield: e1, e2
  raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
  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)

Alias for #[].

[ GitHub ]

# File 'lib/matrix.rb', line 2008


alias element []

#elements_to_f

[ GitHub ]

# File 'lib/matrix.rb', line 2416


def elements_to_f
  warn "Vector#elements_to_f is deprecated", uplevel: 1
  map(&:to_f)
end

#elements_to_i

[ GitHub ]

# File 'lib/matrix.rb', line 2421


def elements_to_i
  warn "Vector#elements_to_i is deprecated", uplevel: 1
  map(&:to_i)
end

#elements_to_r

[ GitHub ]

# File 'lib/matrix.rb', line 2426


def elements_to_r
  warn "Vector#elements_to_r is deprecated", uplevel: 1
  map(&:to_r)
end

#eql?(other) ⇒ `Boolean`

[ GitHub ]

# File 'lib/matrix.rb', line 2174


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

#freeze

Makes the matrix frozen and Ractor-shareable

[ GitHub ]

# File 'lib/matrix.rb', line 2148


def freeze
  @elements.freeze
  super
end

#hash

Returns a hash-code for the vector.

[ GitHub ]

# File 'lib/matrix.rb', line 2182


def hash
  @elements.hash
end

#independent?(*vs) ⇒ `Boolean`

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

[ GitHub ]

# File 'lib/matrix.rb', line 2134


def independent?(*vs)
  self.class.independent?(self, *vs)
end

#initialize_copy(v) (private)

Called for dup & clone.

[ GitHub ]

# File 'lib/matrix.rb', line 2156


private def initialize_copy(v)
  super
  @elements = @elements.dup unless frozen?
end

#inner_product(v) Also known as: #dot

Returns the inner product of this vector with the other.

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

Raises:

(ErrDimensionMismatch)

[ GitHub ]

# File 'lib/matrix.rb', line 2274


def inner_product(v)
  raise ErrDimensionMismatch if size != v.size

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

#inspect

Overrides Object#inspect

[ GitHub ]

# File 'lib/matrix.rb', line 2461


def inspect
  "Vector" + @elements.inspect
end

#magnitude Also known as: #r, #norm

Returns the modulus (Pythagorean distance) of the vector.

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

[ GitHub ]

# File 'lib/matrix.rb', line 2344


def magnitude
  Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2})
end

#map(&block)

Alias for #collect.

[ GitHub ]

# File 'lib/matrix.rb', line 2327


alias_method :map, :collect

#map!(&block)

Alias for #collect!.

[ GitHub ]

# File 'lib/matrix.rb', line 2338


alias map! collect!

#map2(v, &block)

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

[ GitHub ]

# File 'lib/matrix.rb', line 2353


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

Alias for #magnitude.

[ GitHub ]

# File 'lib/matrix.rb', line 2348


alias_method :norm, :magnitude

#normalize

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

Raises:

(ZeroVectorError)

[ GitHub ]

# File 'lib/matrix.rb', line 2367


def normalize
  n = magnitude
  raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0
  self / n
end

#r

Alias for #magnitude.

[ GitHub ]

# File 'lib/matrix.rb', line 2347


alias_method :r, :magnitude

#round(ndigits = 0)

Returns a vector with entries rounded to the given precision (see Float#round)

[ GitHub ]

# File 'lib/matrix.rb', line 2053


def round(ndigits=0)
  map{|e| e.round(ndigits)}
end

#set_component(i, v) (private)

Alias for #[]=.

[ GitHub ]

# File 'lib/matrix.rb', line 2031


alias set_component []=

#set_element(i, v) (private)

Alias for #[]=.

[ GitHub ]

# File 'lib/matrix.rb', line 2030


alias set_element []=

#set_range(range, value) (private)

[ GitHub ]

# File 'lib/matrix.rb', line 2038


private def set_range(range, value)
  if value.is_a?(Vector)
    raise ArgumentError, "vector to be set has wrong size" unless range.size == value.size
    @elements[range] = value.elements
  elsif value.is_a?(Matrix)
    raise ErrDimensionMismatch unless value.row_count == 1
    @elements[range] = value.row(0).elements
  else
    @elements[range] = Array.new(range.size, value)
  end
end

#set_value(index, value) (private)

[ GitHub ]

# File 'lib/matrix.rb', line 2034


private def set_value(index, value)
  @elements[index] = value
end

#size

Returns the number of elements in the vector.

[ GitHub ]

# File 'lib/matrix.rb', line 2060


def size
  @elements.size
end

#to_a

Returns the elements of the vector in an array.

[ GitHub ]

# File 'lib/matrix.rb', line 2405


def to_a
  @elements.dup
end

#to_matrix

Return a single-column matrix from this vector

[ GitHub ]

# File 'lib/matrix.rb', line 2412


def to_matrix
  Matrix.column_vector(self)
end

#to_s

Overrides Object#to_s

[ GitHub ]

# File 'lib/matrix.rb', line 2454


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

Class: Vector

Overview

Method Catalogue

Class Method Summary

::Matrix::ConversionHelper - Extended

Instance Attribute Summary

Instance Method Summary

::Matrix::CoercionHelper - Included

Constructor Details

.new(array) ⇒ Vector

Class Method Details

.[](*array)

.basis(size:, index:)

.elements(array, copy = true)

.independent?(*vs) ⇒ Boolean

.zero(size)

Instance Attribute Details

#elements (readonly, protected)

#zero? ⇒ Boolean (readonly)

Instance Method Details

#*(x)

#+(v)

#+@

#-(v)

#-@

#/(x)

#==(other)

#[](range) #[](integer) Also known as: #element, #component

#[]=(range, new_vector) #[]=(range, row_matrix) #[]=(range, new_element) #[]=(integer, new_element) Also known as: #set_element, #set_component

#angle_with(v)

#coerce(other)

#collect(&block) Also known as: #map

#collect!(&block) Also known as: #map!

#collect2(v)

#component(i)

#covector

#cross(*vs)

#cross_product(*vs) Also known as: #cross

#dot(v)

#each(&block)

#each2(v)

#element(i)

#elements_to_f

#elements_to_i

#elements_to_r

#eql?(other) ⇒ Boolean

#freeze

#hash

#independent?(*vs) ⇒ Boolean

#initialize_copy(v) (private)

#inner_product(v) Also known as: #dot

#inspect

#magnitude Also known as: #r, #norm

#map(&block)

#map!(&block)

#map2(v, &block)

#norm

#normalize

#r

#round(ndigits = 0)

#set_component(i, v) (private)

#set_element(i, v) (private)

#set_range(range, value) (private)

#set_value(index, value) (private)

#size

#to_a

#to_matrix

#to_s

`::Matrix::ConversionHelper` - Extended

`::Matrix::CoercionHelper` - Included

.new(array) ⇒ `Vector`

.independent?(*vs) ⇒ `Boolean`

#zero? ⇒ `Boolean` (readonly)

#[](range) #[](integer)
Also known as: #element, #component

#[]=(range, new_vector) #[]=(range, row_matrix) #[]=(range, new_element) #[]=(integer, new_element)
Also known as: #set_element, #set_component

#eql?(other) ⇒ `Boolean`

#independent?(*vs) ⇒ `Boolean`