Class: Vector
- Inherits:
-
Object
- Object
- Vector
- 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)
-
Vector.basis(size: n, index: k)
To access elements:
-
#[](i)
To enumerate the elements:
-
#each2(v)
-
#collect2(v)
Properties of vectors:
-
#angle_with(v)
-
Vector.independent?(*vs)
-
#independent?(*vs)
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
Class Method Summary collapse
-
.[](*array) ⇒ Object
Creates a Vector from a list of elements.
-
.basis(size:, index:) ⇒ Object
Returns a standard basis
n
-vector, where k is the index. -
.elements(array, copy = true) ⇒ Object
Creates a vector from an Array.
-
.independent?(*vs) ⇒ Boolean
Returns
true
iff all of vectors are linearly independent.
Instance Method Summary collapse
-
#*(x) ⇒ Object
Multiplies the vector by
x
, wherex
is a number or a matrix. -
#+(v) ⇒ Object
Vector addition.
- #+@ ⇒ Object
-
#-(v) ⇒ Object
Vector subtraction.
- #-@ ⇒ Object
-
#/(x) ⇒ Object
Vector division.
-
#==(other) ⇒ Object
Returns
true
iff the two vectors have the same elements in the same order. -
#[](i) ⇒ Object
(also: #element, #component)
Returns element number
i
(starting at zero) of the vector. - #[]=(i, v) ⇒ Object (also: #set_element, #set_component)
-
#angle_with(v) ⇒ Object
Returns an angle with another vector.
-
#clone ⇒ Object
Returns a copy of the vector.
-
#coerce(other) ⇒ Object
The coerce method provides support for Ruby type coercion.
-
#collect(&block) ⇒ Object
(also: #map)
Like Array#collect.
-
#collect2(v) ⇒ Object
Collects (as in Enumerable#collect) over the elements of this vector and
v
in conjunction. -
#covector ⇒ Object
Creates a single-row matrix from this vector.
-
#cross_product(*vs) ⇒ Object
(also: #cross)
Returns the cross product of this vector with the others.
-
#each(&block) ⇒ Object
Iterate over the elements of this vector.
-
#each2(v) ⇒ Object
Iterate over the elements of this vector and
v
in conjunction. - #elements_to_f ⇒ Object
- #elements_to_i ⇒ Object
- #elements_to_r ⇒ Object
- #eql?(other) ⇒ Boolean
-
#hash ⇒ Object
Returns a hash-code for the vector.
-
#independent?(*vs) ⇒ Boolean
Returns
true
iff all of vectors are linearly independent. -
#initialize(array) ⇒ Vector
constructor
Vector.new is private; use Vector[] or Vector.elements to create.
-
#inner_product(v) ⇒ Object
(also: #dot)
Returns the inner product of this vector with the other.
-
#inspect ⇒ Object
Overrides Object#inspect.
-
#magnitude ⇒ Object
(also: #r, #norm)
Returns the modulus (Pythagorean distance) of the vector.
-
#map2(v, &block) ⇒ Object
Like Vector#collect2, but returns a Vector instead of an Array.
-
#normalize ⇒ Object
Returns a new vector with the same direction but with norm 1.
-
#round(ndigits = 0) ⇒ Object
Returns a vector with entries rounded to the given precision (see Float#round).
-
#size ⇒ Object
Returns the number of elements in the vector.
-
#to_a ⇒ Object
Returns the elements of the vector in an array.
-
#to_s ⇒ Object
Overrides Object#to_s.
Methods included from Matrix::CoercionHelper
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 1774 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 1746 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]
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# File 'lib/matrix.rb', line 1763 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 'lib/matrix.rb', line 1754 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
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# File 'lib/matrix.rb', line 1863 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 |
Instance Method Details
#*(x) ⇒ Object
Multiplies the vector by x
, where x
is a number or a matrix.
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# File 'lib/matrix.rb', line 1923 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 1940 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 'lib/matrix.rb', line 1988 def +@ self end |
#-(v) ⇒ Object
Vector subtraction.
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# File 'lib/matrix.rb', line 1958 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 'lib/matrix.rb', line 1992 def -@ collect {|e| -e } end |
#/(x) ⇒ Object
Vector division.
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# File 'lib/matrix.rb', line 1976 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 1892 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 1784 def [](i) @elements[i] end |
#[]=(i, v) ⇒ Object Also known as: set_element, set_component
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# File 'lib/matrix.rb', line 1790 def []=(i, v) @elements[i]= v end |
#angle_with(v) ⇒ Object
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# File 'lib/matrix.rb', line 2097 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 'lib/matrix.rb', line 1905 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 2146 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 2052 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.
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# File 'lib/matrix.rb', line 1841 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 'lib/matrix.rb', line 2113 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]
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# File 'lib/matrix.rb', line 2027 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 'lib/matrix.rb', line 1818 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.
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# File 'lib/matrix.rb', line 1827 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 'lib/matrix.rb', line 2124 def elements_to_f warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated" map(&:to_f) end |
#elements_to_i ⇒ Object
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# File 'lib/matrix.rb', line 2129 def elements_to_i warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated" map(&:to_i) end |
#elements_to_r ⇒ Object
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# File 'lib/matrix.rb', line 2134 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 1897 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 'lib/matrix.rb', line 1912 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
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# File 'lib/matrix.rb', line 1881 def independent?(*vs) self.class.independent?(self, *vs) end |
#inner_product(v) ⇒ Object Also known as: dot
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# File 'lib/matrix.rb', line 2004 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 'lib/matrix.rb', line 2169 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 'lib/matrix.rb', line 2063 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 2072 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
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# File 'lib/matrix.rb', line 2086 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 'lib/matrix.rb', line 1800 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 'lib/matrix.rb', line 1807 def size @elements.size end |
#to_a ⇒ Object
Returns the elements of the vector in an array.
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# File 'lib/matrix.rb', line 2120 def to_a @elements.dup end |
#to_s ⇒ Object
Overrides Object#to_s
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# File 'lib/matrix.rb', line 2162 def to_s "Vector[" + @elements.join(", ") + "]" end |