Object
The Vector
class represents a mathematical vector, which is
useful in its own right, and also constitutes a row or column of a Matrix.
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)
#collect
#map
#map2(v)
#r
#size
Conversion to other data types:
#covector
#to_a
#coerce(other)
String representations:
#to_s
#inspect
Creates a Vector from a list of elements.
Vector[7, 4, ...]
# File matrix.rb, line 999 def Vector.[](*array) new(:init_elements, array, copy = false) end
Multiplies the vector by x
, where x
is a number
or another vector.
# File matrix.rb, line 1114 def *(x) case x when Numeric els = @elements.collect{|e| e * x} Vector.elements(els, false) when Matrix Matrix.column_vector(self) * x else s, x = x.coerce(self) s * x end end
Vector addition.
# File matrix.rb, line 1130 def +(v) case v when Vector Vector.Raise ErrDimensionMismatch if size != v.size els = collect2(v) { |v1, v2| v1 + v2 } Vector.elements(els, false) when Matrix Matrix.column_vector(self) + v else s, x = v.coerce(self) s + x end end
Vector subtraction.
# File matrix.rb, line 1150 def -(v) case v when Vector Vector.Raise ErrDimensionMismatch if size != v.size els = collect2(v) { |v1, v2| v1 - v2 } Vector.elements(els, false) when Matrix Matrix.column_vector(self) - v else s, x = v.coerce(self) s - x end end
Returns true
iff the two vectors have the same elements in the
same order.
# File matrix.rb, line 1079 def ==(other) return false unless Vector === other other.compare_by(@elements) end
Returns element number i
(starting at zero) of the vector.
# File matrix.rb, line 1034 def [](i) @elements[i] end
Return a copy of the vector.
# File matrix.rb, line 1096 def clone Vector.elements(@elements) end
FIXME: describe #coerce.
# File matrix.rb, line 1242 def coerce(other) case other when Numeric return Scalar.new(other), self else raise TypeError, "#{self.class} can't be coerced into #{other.class}" end end
Like Array#collect.
# File matrix.rb, line 1189 def collect # :yield: e els = @elements.collect { |v| yield v } Vector.elements(els, false) end
Collects (as in Enumerable#collect) over the elements of this vector and
v
in conjunction.
# File matrix.rb, line 1064 def collect2(v) # :yield: e1, e2 Vector.Raise ErrDimensionMismatch if size != v.size (0 .. size - 1).collect do |i| yield @elements[i], v[i] end end
For internal use.
# File matrix.rb, line 1089 def compare_by(elements) @elements == elements end
Creates a single-row matrix from this vector.
# File matrix.rb, line 1228 def covector Matrix.row_vector(self) end
Iterate over the elements of this vector and v
in conjunction.
# File matrix.rb, line 1052 def each2(v) # :yield: e1, e2 Vector.Raise ErrDimensionMismatch if size != v.size 0.upto(size - 1) do |i| yield @elements[i], v[i] end end
Return a hash-code for the vector.
# File matrix.rb, line 1103 def hash @elements.hash end
For internal use.
# File matrix.rb, line 1021 def init_elements(array, copy) if copy @elements = array.dup else @elements = array end end
Returns the inner product of this vector with the other.
Vector[4,7].inner_product Vector[10,1] => 47
# File matrix.rb, line 1175 def inner_product(v) Vector.Raise ErrDimensionMismatch if size != v.size p = 0 each2(v) { |v1, v2| p += v1 * v2 } p end
Overrides Object#inspect
# File matrix.rb, line 1265 def inspect str = "Vector"+@elements.inspect end
Returns the modulus (Pythagorean distance) of the vector.
Vector[5,8,2].r => 9.643650761
# File matrix.rb, line 1213 def r v = 0 for e in @elements v += e*e end return Math.sqrt(v) end
Returns the number of elements in the vector.
# File matrix.rb, line 1041 def size @elements.size end