Class: Vector

Inherits:
Object show all
Extended by:
Matrix::ConversionHelper
Includes:
Enumerable, ExceptionForMatrix, Matrix::CoercionHelper
Defined in:
opal/stdlib/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.
  • Vector.elements(array, copy = true)
  • Vector.basis(size: n, index: k)
  • Vector.zero(n)

To access elements:

  • #

To enumerate the elements:

  • #each2(v)
  • #collect2(v)

Properties of vectors:

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

Vector arithmetic:

Vector functions:

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

Conversion to other data types:

  • #covector
  • #to_a
  • #coerce(other)

String representations:

  • #to_s
  • #inspect

Defined Under Namespace

Classes: ZeroVectorError

Constant Summary

Constants included from Exception2MessageMapper

Exception2MessageMapper::E2MM

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Matrix::CoercionHelper

coerce_to, coerce_to_int, coerce_to_matrix

Methods included from Enumerable

#to_json, #to_set

Methods included from Exception2MessageMapper

#Fail, Raise, #Raise, #bind, def_e2message, #def_e2message, #def_exception, def_exception, e2mm_message, extend_object, #fail

Constructor Details

#initialize(array) ⇒ Vector

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


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# File 'opal/stdlib/matrix.rb', line 1757

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

Class Method Details

.[](*array) ⇒ Object

Creates a Vector from a list of elements. Vector[7, 4, ...]


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# File 'opal/stdlib/matrix.rb', line 1718

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

.basis(size:, index:) ⇒ Object

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

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

Raises:

  • (ArgumentError)

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# File 'opal/stdlib/matrix.rb', line 1735

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) ⇒ 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 'opal/stdlib/matrix.rb', line 1726

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

Returns:


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# File 'opal/stdlib/matrix.rb', line 1846

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

.zero(size) ⇒ Object

Return a zero vector.

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

Raises:

  • (ArgumentError)

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# File 'opal/stdlib/matrix.rb', line 1748

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 Method Details

#*(x) ⇒ Object

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


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# File 'opal/stdlib/matrix.rb', line 1913

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) ⇒ Object

Vector addition.


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# File 'opal/stdlib/matrix.rb', line 1930

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

#[email protected]Object


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# File 'opal/stdlib/matrix.rb', line 1978

def [email protected]
  self
end

#-(v) ⇒ Object

Vector subtraction.


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# File 'opal/stdlib/matrix.rb', line 1948

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

#[email protected]Object


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# File 'opal/stdlib/matrix.rb', line 1982

def [email protected]
  collect {|e| -e }
end

#/(x) ⇒ Object

Vector division.


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# File 'opal/stdlib/matrix.rb', line 1966

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) ⇒ Object

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


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# File 'opal/stdlib/matrix.rb', line 1882

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

#[](i) ⇒ Object Also known as: element, component

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


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# File 'opal/stdlib/matrix.rb', line 1767

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

#[]=(i, v) ⇒ Object Also known as: set_element, set_component


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# File 'opal/stdlib/matrix.rb', line 1773

def []=(i, v)
  @elements[i]= v
end

#angle_with(v) ⇒ Object

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)

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# File 'opal/stdlib/matrix.rb', line 2087

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

#cloneObject

Returns a copy of the vector.


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# File 'opal/stdlib/matrix.rb', line 1895

def clone
  self.class.elements(@elements)
end

#coerce(other) ⇒ Object

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.


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# File 'opal/stdlib/matrix.rb', line 2143

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) ⇒ Object Also known as: map

Like Array#collect.


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# File 'opal/stdlib/matrix.rb', line 2042

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

#collect2(v) ⇒ Object

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

Raises:

  • (TypeError)

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# File 'opal/stdlib/matrix.rb', line 1824

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

#covectorObject

Creates a single-row matrix from this vector.


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# File 'opal/stdlib/matrix.rb', line 2103

def covector
  Matrix.row_vector(self)
end

#cross_product(*vs) ⇒ Object 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)

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# File 'opal/stdlib/matrix.rb', line 2017

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

#each(&block) ⇒ Object

Iterate over the elements of this vector


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# File 'opal/stdlib/matrix.rb', line 1801

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

#each2(v) ⇒ Object

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

Raises:

  • (TypeError)

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# File 'opal/stdlib/matrix.rb', line 1810

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

#elements_to_fObject


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# File 'opal/stdlib/matrix.rb', line 2121

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

#elements_to_iObject


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# File 'opal/stdlib/matrix.rb', line 2126

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

#elements_to_rObject


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# File 'opal/stdlib/matrix.rb', line 2131

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

#eql?(other) ⇒ Boolean

Returns:


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# File 'opal/stdlib/matrix.rb', line 1887

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

#hashObject

Returns a hash-code for the vector.


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# File 'opal/stdlib/matrix.rb', line 1902

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

Returns:


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# File 'opal/stdlib/matrix.rb', line 1864

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

#inner_product(v) ⇒ Object Also known as: dot

Returns the inner product of this vector with the other. Vector[4,7].inner_product Vector[10,1] => 47


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# File 'opal/stdlib/matrix.rb', line 1994

def inner_product(v)
  Vector.Raise ErrDimensionMismatch if size != v.size

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

#inspectObject

Overrides Object#inspect


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# File 'opal/stdlib/matrix.rb', line 2166

def inspect
  "Vector" + @elements.inspect
end

#magnitudeObject Also known as: r, norm

Returns the modulus (Pythagorean distance) of the vector. Vector[5,8,2].r => 9.643650761


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# File 'opal/stdlib/matrix.rb', line 2053

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

#map2(v, &block) ⇒ Object

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


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# File 'opal/stdlib/matrix.rb', line 2062

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

#normalizeObject

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:


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# File 'opal/stdlib/matrix.rb', line 2076

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

#round(ndigits = 0) ⇒ Object

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


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# File 'opal/stdlib/matrix.rb', line 1783

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

#sizeObject

Returns the number of elements in the vector.


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# File 'opal/stdlib/matrix.rb', line 1790

def size
  @elements.size
end

#to_aObject

Returns the elements of the vector in an array.


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# File 'opal/stdlib/matrix.rb', line 2110

def to_a
  @elements.dup
end

#to_matrixObject

Return a single-column matrix from this vector


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# File 'opal/stdlib/matrix.rb', line 2117

def to_matrix
  Matrix.column_vector(self)
end

#to_sObject

Overrides Object#to_s


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# File 'opal/stdlib/matrix.rb', line 2159

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

#zero?Boolean

Returns +true+ iff all elements are zero.

Returns:


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# File 'opal/stdlib/matrix.rb', line 1871

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