Class: Vector

Inherits:
Object
  • Object
show all
Extended by:
Matrix::ConversionHelper
Includes:
Enumerable, ExceptionForMatrix, Matrix::CoercionHelper
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)

  • 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)

  • #cross_product(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

Defined Under Namespace

Classes: ZeroVectorError

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Matrix::CoercionHelper

coerce_to, coerce_to_int

Constructor Details

#initialize(array) ⇒ Vector

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


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# File 'lib/matrix.rb', line 1571

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 'lib/matrix.rb', line 1556

def Vector.[](*array)
  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 'lib/matrix.rb', line 1564

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

Instance Method Details

#*(x) ⇒ Object

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


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# File 'lib/matrix.rb', line 1678

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 'lib/matrix.rb', line 1695

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

#-(v) ⇒ Object

Vector subtraction.


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# File 'lib/matrix.rb', line 1713

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

#/(x) ⇒ Object

Vector division.


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# File 'lib/matrix.rb', line 1731

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 'lib/matrix.rb', line 1647

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 'lib/matrix.rb', line 1581

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

#cloneObject

Return a copy of the vector.


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# File 'lib/matrix.rb', line 1660

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 'lib/matrix.rb', line 1855

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 'lib/matrix.rb', line 1775

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 'lib/matrix.rb', line 1631

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 'lib/matrix.rb', line 1822

def covector
  Matrix.row_vector(self)
end

#cross_product(v) ⇒ Object

Returns the cross product of this vector with the other.

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

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# File 'lib/matrix.rb', line 1765

def cross_product(v)
  Vector.Raise ErrDimensionMismatch unless size == v.size && v.size == 3
  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] ]
end

#each(&block) ⇒ Object

Iterate over the elements of this vector


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# File 'lib/matrix.rb', line 1608

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 'lib/matrix.rb', line 1617

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 'lib/matrix.rb', line 1833

def elements_to_f
  warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated"
  map(&:to_f)
end

#elements_to_iObject


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# File 'lib/matrix.rb', line 1838

def elements_to_i
  warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated"
  map(&:to_i)
end

#elements_to_rObject


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# File 'lib/matrix.rb', line 1843

def elements_to_r
  warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated"
  map(&:to_r)
end

#eql?(other) ⇒ Boolean


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# File 'lib/matrix.rb', line 1652

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

#hashObject

Return a hash-code for the vector.


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# File 'lib/matrix.rb', line 1667

def hash
  @elements.hash
end

#inner_product(v) ⇒ Object

Returns the inner product of this vector with the other.

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

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# File 'lib/matrix.rb', line 1751

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 'lib/matrix.rb', line 1878

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 'lib/matrix.rb', line 1786

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 'lib/matrix.rb', line 1795

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 'lib/matrix.rb', line 1809

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

#sizeObject

Returns the number of elements in the vector.


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# File 'lib/matrix.rb', line 1597

def size
  @elements.size
end

#to_aObject

Returns the elements of the vector in an array.


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# File 'lib/matrix.rb', line 1829

def to_a
  @elements.dup
end

#to_sObject

Overrides Object#to_s


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# File 'lib/matrix.rb', line 1871

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