# 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:

• ` 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 `

• ` #magnitude `

• ` #map `

• ` #map2(v) `

• ` #norm `

• ` #normalize `

• ` #r `

• ` #size `

Conversion to other data types:

• ` #covector `

• ` #to_a `

• ` #coerce(other) `

String representations:

• ` #to_s `

• ` #inspect `

### Attributes

elements[R]

INSTANCE CREATION

### Public Class Methods

[](*array) click to toggle source

Creates a Vector from a list of elements.

`Vector[7, 4, ...]`
```# File rake/lib/matrix.rb, line 1551
def Vector.[](*array)
new convert_to_array(array, false)
end```
elements(array, copy = true) click to toggle source

Creates a vector from an Array. The optional second argument specifies whether the array itself or a copy is used internally.

```# File rake/lib/matrix.rb, line 1559
def Vector.elements(array, copy = true)
new convert_to_array(array, copy)
end```
new(array) click to toggle source

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

```# File rake/lib/matrix.rb, line 1566
def initialize(array)
# No checking is done at this point.
@elements = array
end```

### Public Instance Methods

*(x) click to toggle source

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

```# File rake/lib/matrix.rb, line 1673
def *(x)
case x
when Numeric
els = @elements.collect{|e| e * x}
Vector.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) click to toggle source

```# File rake/lib/matrix.rb, line 1690
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
apply_through_coercion(v, __method__)
end
end```
-(v) click to toggle source

Vector subtraction.

```# File rake/lib/matrix.rb, line 1708
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
apply_through_coercion(v, __method__)
end
end```
/(x) click to toggle source

Vector division.

```# File rake/lib/matrix.rb, line 1726
def /(x)
case x
when Numeric
els = @elements.collect{|e| e / x}
Vector.elements(els, false)
when Matrix, Vector
Vector.Raise ErrOperationNotDefined, "/", self.class, x.class
else
apply_through_coercion(x, __method__)
end
end```
==(other) click to toggle source

Returns `true` iff the two vectors have the same elements in the same order.

```# File rake/lib/matrix.rb, line 1642
def ==(other)
return false unless Vector === other
@elements == other.elements
end```
[](i) click to toggle source

Returns element number `i` (starting at zero) of the vector.

```# File rake/lib/matrix.rb, line 1576
def [](i)
@elements[i]
end```
Also aliased as: element, component
clone() click to toggle source

Return a copy of the vector.

```# File rake/lib/matrix.rb, line 1655
def clone
Vector.elements(@elements)
end```
coerce(other) click to toggle source

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 rake/lib/matrix.rb, line 1839
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() { |e| ... } click to toggle source

Like Array#collect.

```# File rake/lib/matrix.rb, line 1759
def collect(&block) # :yield: e
els = @elements.collect(&block)
Vector.elements(els, false)
end```
Also aliased as: map
collect2(v) { |e1, e2| ... } click to toggle source

Collects (as in Enumerable#collect) over the elements of this vector and `v` in conjunction.

```# File rake/lib/matrix.rb, line 1626
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
Array.new(size) do |i|
yield @elements[i], v[i]
end
end```
component(i)
Alias for: []
covector() click to toggle source

Creates a single-row matrix from this vector.

```# File rake/lib/matrix.rb, line 1806
def covector
Matrix.row_vector(self)
end```
each(&block) click to toggle source

Iterate over the elements of this vector

```# File rake/lib/matrix.rb, line 1603
def each(&block)
@elements.each(&block)
self
end```
each2(v) { |e1, e2| ... } click to toggle source

Iterate over the elements of this vector and `v` in conjunction.

```# File rake/lib/matrix.rb, line 1612
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
size.times do |i|
yield @elements[i], v[i]
end
self
end```
element(i)
Alias for: []
elements_to_f() click to toggle source
```# File rake/lib/matrix.rb, line 1817
def elements_to_f
warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated"
map(&:to_f)
end```
elements_to_i() click to toggle source
```# File rake/lib/matrix.rb, line 1822
def elements_to_i
warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated"
map(&:to_i)
end```
elements_to_r() click to toggle source
```# File rake/lib/matrix.rb, line 1827
def elements_to_r
warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated"
map(&:to_r)
end```
eql?(other) click to toggle source
```# File rake/lib/matrix.rb, line 1647
def eql?(other)
return false unless Vector === other
@elements.eql? other.elements
end```
hash() click to toggle source

Return a hash-code for the vector.

```# File rake/lib/matrix.rb, line 1662
def hash
@elements.hash
end```
inner_product(v) click to toggle source

Returns the inner product of this vector with the other.

```Vector[4,7].inner_product Vector[10,1]  => 47
```
```# File rake/lib/matrix.rb, line 1746
def inner_product(v)
Vector.Raise ErrDimensionMismatch if size != v.size

p = 0
each2(v) {|v1, v2|
p += v1 * v2
}
p
end```
inspect() click to toggle source

Overrides Object#inspect

```# File rake/lib/matrix.rb, line 1862
def inspect
"Vector" + @elements.inspect
end```
magnitude() click to toggle source

Returns the modulus (Pythagorean distance) of the vector.

```Vector[5,8,2].r => 9.643650761
```
```# File rake/lib/matrix.rb, line 1770
def magnitude
Math.sqrt(@elements.inject(0) {|v, e| v + e*e})
end```
Also aliased as: r, norm
map()
Alias for: collect
map2(v) { |e1, e2| ... } click to toggle source

Like #collect2, but returns a Vector instead of an Array.

```# File rake/lib/matrix.rb, line 1779
def map2(v, &block) # :yield: e1, e2
els = collect2(v, &block)
Vector.elements(els, false)
end```
norm()
Alias for: magnitude
normalize() click to toggle source

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 rake/lib/matrix.rb, line 1793
def normalize
n = magnitude
raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0
self / n
end```
r()
Alias for: magnitude
size() click to toggle source

Returns the number of elements in the vector.

```# File rake/lib/matrix.rb, line 1592
def size
@elements.size
end```
to_a() click to toggle source

Returns the elements of the vector in an array.

```# File rake/lib/matrix.rb, line 1813
def to_a
@elements.dup
end```
to_s() click to toggle source

Overrides Object#to_s

```# File rake/lib/matrix.rb, line 1855
def to_s
"Vector[" + @elements.join(", ") + "]"
end```