class 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)
To access elements:
To enumerate the elements:
Vector arithmetic:
-
#*(x) “is matrix or number”
-
#+(v)
-
#-(v)
Vector functions:
Conversion to other data types:
String representations:
Attributes
INSTANCE CREATION
Public Class Methods
Creates a Vector from a list of elements.
Vector[7, 4, ...]
# File lib/matrix.rb, line 1555 def Vector.[](*array) new convert_to_array(array, false) end
Creates a vector from an Array. The optional second argument specifies whether the array itself or a copy is used internally.
# File lib/matrix.rb, line 1563 def Vector.elements(array, copy = true) new convert_to_array(array, copy) end
::new is private; use Vector[] or ::elements to create.
# File lib/matrix.rb, line 1570 def initialize(array) # No checking is done at this point. @elements = array end
Public Instance Methods
Multiplies the vector by x
, where x
is a number
or another vector.
# File lib/matrix.rb, line 1677 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
Vector addition.
# File lib/matrix.rb, line 1694 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
Vector subtraction.
# File lib/matrix.rb, line 1712 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
Vector division.
# File lib/matrix.rb, line 1730 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
Returns true
iff the two vectors have the same elements in the
same order.
# File lib/matrix.rb, line 1646 def ==(other) return false unless Vector === other @elements == other.elements end
Returns element number i
(starting at zero) of the vector.
# File lib/matrix.rb, line 1580 def [](i) @elements[i] end
Return a copy of the vector.
# File lib/matrix.rb, line 1659 def clone self.class.elements(@elements) end
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 lib/matrix.rb, line 1854 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
Like Array#collect.
# File lib/matrix.rb, line 1774 def collect(&block) # :yield: e return to_enum(:collect) unless block_given? els = @elements.collect(&block) self.class.elements(els, false) end
Collects (as in Enumerable#collect) over the
elements of this vector and v
in conjunction.
# File lib/matrix.rb, line 1630 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
Creates a single-row matrix from this vector.
# File lib/matrix.rb, line 1821 def covector Matrix.row_vector(self) end
Returns the cross product of this vector with the other.
Vector[1, 0, 0].cross_product Vector[0, 1, 0] => Vector[0, 0, 1]
# File lib/matrix.rb, line 1764 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
Iterate over the elements of this vector
# File lib/matrix.rb, line 1607 def each(&block) return to_enum(:each) unless block_given? @elements.each(&block) self end
Iterate over the elements of this vector and v
in conjunction.
# File lib/matrix.rb, line 1616 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
# File lib/matrix.rb, line 1832 def elements_to_f warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated" map(&:to_f) end
# File lib/matrix.rb, line 1837 def elements_to_i warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated" map(&:to_i) end
# File lib/matrix.rb, line 1842 def elements_to_r warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated" map(&:to_r) end
# File lib/matrix.rb, line 1651 def eql?(other) return false unless Vector === other @elements.eql? other.elements end
Return a hash-code for the vector.
# File lib/matrix.rb, line 1666 def hash @elements.hash end
Returns the inner product of this vector with the other.
Vector[4,7].inner_product Vector[10,1] => 47
# File lib/matrix.rb, line 1750 def inner_product(v) Vector.Raise ErrDimensionMismatch if size != v.size p = 0 each2(v) {|v1, v2| p += v1 * v2.conj } p end
Overrides Object#inspect
# File lib/matrix.rb, line 1877 def inspect "Vector" + @elements.inspect end
Returns the modulus (Pythagorean distance) of the vector.
Vector[5,8,2].r => 9.643650761
# File lib/matrix.rb, line 1785 def magnitude Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2}) end
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 lib/matrix.rb, line 1808 def normalize n = magnitude raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0 self / n end
Returns the number of elements in the vector.
# File lib/matrix.rb, line 1596 def size @elements.size end
Returns the elements of the vector in an array.
# File lib/matrix.rb, line 1828 def to_a @elements.dup end
Overrides Object#to_s
# File lib/matrix.rb, line 1870 def to_s "Vector[" + @elements.join(", ") + "]" end
Private Instance Methods
# File lib/matrix.rb, line 1586 def []=(i, v) @elements[i]= v end