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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:

  • #*(x) "is matrix or number"
  • #+(v)
  • #-(v)
  • #/(v)
  • #+@
  • #-@

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

#+@ ⇒ Object 

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

#-@ ⇒ Object 

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

#clone ⇒ Object

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

#covector ⇒ Object

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_f ⇒ Object 

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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_i ⇒ Object 

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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_r ⇒ Object 

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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

#hash ⇒ Object

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

#inspect ⇒ Object

Overrides Object#inspect

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# File 'opal/stdlib/matrix.rb', line 2166
def inspect
 "Vector" + @elements.inspect
end

#magnitude ⇒ Object 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

#normalize ⇒ Object

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

#size ⇒ Object

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_a ⇒ Object

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_matrix ⇒ Object

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_s ⇒ Object

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

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