NAME
Sidef::Types::Array::Vector - Mathematical vector operations in Sidef
DESCRIPTION
This class implements mathematical vectors with support for common vector operations including arithmetic, comparison, and geometric calculations. Vectors are ordered collections of numeric elements that support element-wise operations and various distance metrics.
A Vector is similar to an Array but is optimized for mathematical operations and always contains numeric elements. Operations between vectors are performed element-wise.
SYNOPSIS
# Create vectors
var v1 = Vector(1, 2, 3)
var v2 = Vector(4, 5, 6)
# Basic arithmetic
var sum = v1 + v2 # Vector(5, 7, 9)
var diff = v1 - v2 # Vector(-3, -3, -3)
var prod = v1 * v2 # Element-wise: Vector(4, 10, 18)
var quot = v1 / v2 # Element-wise: Vector(0.25, 0.4, 0.5)
# Scalar operations
var scaled = v1 * 2 # Vector(2, 4, 6)
var powered = v1 ** 2 # Vector(1, 4, 9)
# Vector operations
say v1.norm # Euclidean norm (magnitude)
say v1.abs # Absolute value of each element
say v1.dist(v2) # Euclidean distance between vectors
# Create special vectors
var zeros = Vector.zero(5) # Vector of 5 zerosINHERITS
Inherits methods from:
* Sidef::Types::Array::ArrayMETHODS
&
v1 & v2Returns a new vector with element-wise bitwise AND operation between two vectors. Each element of the result is the bitwise AND of the corresponding elements.
Vector(5, 7, 3) & Vector(3, 5, 1) #=> Vector(1, 5, 1)Aliases: and
*
v1 * v2
v * scalarReturns a new vector with element-wise multiplication. When multiplying with a scalar, each element is multiplied by that scalar. When multiplying two vectors, corresponding elements are multiplied together (Hadamard product).
Vector(1, 2, 3) * 2 #=> Vector(2, 4, 6)
Vector(1, 2, 3) * Vector(2, 3, 4) #=> Vector(2, 6, 12)Aliases: mul
**
v ** nReturns a new vector where each element is raised to the power n. The exponent can be a scalar or another vector for element-wise exponentiation.
Vector(2, 3, 4) ** 2 #=> Vector(4, 9, 16)
Vector(2, 3, 4) ** Vector(1, 2, 3) #=> Vector(2, 9, 64)Aliases: pow
+
v1 + v2
v + scalarReturns a new vector with element-wise addition. When adding a scalar, it is added to each element. When adding two vectors, corresponding elements are added together.
Vector(1, 2, 3) + 5 #=> Vector(6, 7, 8)
Vector(1, 2, 3) + Vector(4, 5, 6) #=> Vector(5, 7, 9)Aliases: add
-
v1 - v2
v - scalarReturns a new vector with element-wise subtraction. When subtracting a scalar, it is subtracted from each element. When subtracting two vectors, corresponding elements are subtracted.
Vector(5, 7, 9) - 2 #=> Vector(3, 5, 7)
Vector(5, 7, 9) - Vector(1, 2, 3) #=> Vector(4, 5, 6)Aliases: sub
/
v1 / v2
v / scalarReturns a new vector with element-wise division. When dividing by a scalar, each element is divided by that scalar. When dividing two vectors, corresponding elements are divided.
Vector(10, 20, 30) / 2 #=> Vector(5, 10, 15)
Vector(10, 20, 30) / Vector(2, 4, 5) #=> Vector(5, 5, 6)Aliases: ÷, div
^
v1 ^ v2Returns a new vector with element-wise bitwise XOR operation between two vectors. Each element of the result is the bitwise XOR of the corresponding elements.
Vector(5, 7, 3) ^ Vector(3, 5, 1) #=> Vector(6, 2, 2)Aliases: xor
|
v1 | v2Returns a new vector with element-wise bitwise OR operation between two vectors. Each element of the result is the bitwise OR of the corresponding elements.
Vector(5, 7, 3) | Vector(3, 5, 1) #=> Vector(7, 7, 3)Aliases: or
abs
v.absReturns a new vector where each element is the absolute value of the corresponding element in the original vector.
Vector(-1, 2, -3).abs #=> Vector(1, 2, 3)atan2
v1.atan2(v2)Returns a new vector containing the element-wise arctangent of the quotient of corresponding elements from v1 and v2. This is useful for computing angles in two-dimensional space.
Vector(1, 0).atan2(Vector(0, 1)) #=> Vector(atan(∞), 0)ceil
v.ceilReturns a new vector where each element is rounded up to the nearest integer (ceiling function).
Vector(1.2, 2.8, -0.5).ceil #=> Vector(2, 3, 0)chebyshev_dist
v1.chebyshev_dist(v2)Returns the Chebyshev distance (L∞ metric) between two vectors. This is the maximum absolute difference between corresponding elements. Also known as the chessboard distance or maximum metric.
Vector(1, 2, 3).chebyshev_dist(Vector(4, 5, 6)) #=> 3dist
v1.dist(v2)Returns the Euclidean distance (L2 metric) between two vectors. This is the straight-line distance in n-dimensional space, calculated as the square root of the sum of squared differences between corresponding elements.
Vector(1, 2, 3).dist(Vector(4, 5, 6)) #=> sqrt(27) ≈ 5.196dist_norm
v1.dist_norm(p, v2)Returns the Lp-norm distance between two vectors. The parameter p specifies the norm degree. Common values are p=1 (Manhattan), p=2 (Euclidean), and p=∞ (Chebyshev).
Vector(1, 2, 3).dist_norm(1, Vector(4, 5, 6)) #=> 9 (Manhattan)
Vector(1, 2, 3).dist_norm(2, Vector(4, 5, 6)) #=> 5.196... (Euclidean)floor
v.floorReturns a new vector where each element is rounded down to the nearest integer (floor function).
Vector(1.8, 2.3, -0.5).floor #=> Vector(1, 2, -1)manhattan_dist
v1.manhattan_dist(v2)Returns the Manhattan distance (L1 metric) between two vectors. This is the sum of absolute differences between corresponding elements. Also known as taxicab distance or city block distance.
Vector(1, 2, 3).manhattan_dist(Vector(4, 5, 6)) #=> 9manhattan_norm
v.manhattan_normReturns the Manhattan norm (L1 norm) of the vector. This is the sum of the absolute values of all elements.
Vector(1, -2, 3).manhattan_norm #=> 6neg
v.negReturns a new vector where each element is the negation of the corresponding element in the original vector. Equivalent to multiplying by -1.
Vector(1, -2, 3).neg #=> Vector(-1, 2, -3)new
Vector.new(elements...)
Vector(elements...)Creates a new Vector object from the given elements. Elements should be numeric values.
var v1 = Vector.new(1, 2, 3)
var v2 = Vector(1, 2, 3) # Same as aboveAliases: call
norm
v.normReturns the Euclidean norm (L2 norm, magnitude, or length) of the vector. This is the square root of the sum of squares of all elements.
Vector(3, 4).norm #=> 5
Vector(1, 2, 3).norm #=> sqrt(14) ≈ 3.742not
v.notReturns a new vector where each element is the bitwise NOT of the corresponding element in the original vector.
Vector(5, 7, 3).not #=> Vector with bitwise complement of each elementround
v.round(digits=-1)Returns a new vector where each element is rounded to the specified number of digits. If digits is negative (default), rounds to the nearest integer. If digits is positive, rounds to that many decimal places.
Vector(1.234, 2.567, 3.891).round #=> Vector(1, 3, 4)
Vector(1.234, 2.567, 3.891).round(2) #=> Vector(1.23, 2.57, 3.89)to_a
v.to_aConverts the vector to a regular Array object, preserving all elements in order.
Vector(1, 2, 3).to_a #=> [1, 2, 3]Aliases: to_array
to_s
v.to_sReturns a string representation of the vector, showing all elements.
Vector(1, 2, 3).to_s #=> "Vector(1, 2, 3)"Aliases: dump, to_str
zero
Vector.zero(n)Creates a new vector of length n with all elements initialized to zero. This is a class method used to create zero vectors of a specified dimension.
Vector.zero(3) #=> Vector(0, 0, 0)
Vector.zero(5) #=> Vector(0, 0, 0, 0, 0)EXAMPLES
# Vector arithmetic and operations
var v1 = Vector(1, 2, 3)
var v2 = Vector(4, 5, 6)
# Element-wise operations
say (v1 + v2) # Vector(5, 7, 9)
say (v1 * v2) # Vector(4, 10, 18)
# Scalar operations
say (v1 * 2) # Vector(2, 4, 6)
say (v1 + 10) # Vector(11, 12, 13)
# Norms and distances
say v1.norm # Magnitude of v1
say v1.manhattan_norm # L1 norm
say v1.dist(v2) # Euclidean distance
say v1.manhattan_dist(v2) # Manhattan distance
say v1.chebyshev_dist(v2) # Chebyshev distance
# Transformations
say v1.abs # Absolute values
say v1.neg # Negation
say v1.round(2) # Round to 2 decimals
say v1.ceil # Ceiling
say v1.floor # Floor
# Creating special vectors
var zeros = Vector.zero(5)
say zeros # Vector(0, 0, 0, 0, 0)