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- matrix.rb
Class/Module Index
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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:
Public Class Methods
Creates a Vector from a list of elements.
Vector[7, 4, ...]
# File matrix.rb, line 1554
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 matrix.rb, line 1562
def Vector.elements(array, copy = true)
new convert_to_array(array, copy)
end
::new is private; use Vector[] or ::elements to create.
# File matrix.rb, line 1569
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 matrix.rb, line 1676
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 matrix.rb, line 1693
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 matrix.rb, line 1711
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 matrix.rb, line 1729
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 matrix.rb, line 1645
def ==(other)
return false unless Vector === other
@elements == other.elements
end
Returns element number i (starting at zero) of the vector.
# File matrix.rb, line 1579
def [](i)
@elements[i]
end
Return a copy of the vector.
# File matrix.rb, line 1658
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 matrix.rb, line 1842
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 matrix.rb, line 1762
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 matrix.rb, line 1629
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 matrix.rb, line 1809
def covector
Matrix.row_vector(self)
end
Iterate over the elements of this vector
# File matrix.rb, line 1606
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 matrix.rb, line 1615
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 matrix.rb, line 1820
def elements_to_f
warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated"
map(&:to_f)
end
# File matrix.rb, line 1825
def elements_to_i
warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated"
map(&:to_i)
end
# File matrix.rb, line 1830
def elements_to_r
warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated"
map(&:to_r)
end
# File matrix.rb, line 1650
def eql?(other)
return false unless Vector === other
@elements.eql? other.elements
end
Return a hash-code for the vector.
# File matrix.rb, line 1665
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 matrix.rb, line 1749
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 matrix.rb, line 1865
def inspect
"Vector" + @elements.inspect
end
Returns the modulus (Pythagorean distance) of the vector.
Vector[5,8,2].r => 9.643650761
# File matrix.rb, line 1773
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 matrix.rb, line 1796
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 matrix.rb, line 1595
def size
@elements.size
end