Arithmetic

basic operations¶

Shown previously arrays can do operations between eachother. allowing for basic operations like addition, subtraction, multiplication etc.

local a = numluau.array({1,2,3,4})
local b = numluau.array({2,4,6,8})

print(a + b) -- array([3 6 9 12])
print(a - b) -- array([-1 -2 -3 -4])
print(a * b) -- array([2 8 18 32])

math functions¶

numluau also provides access to math functions like square root or ceil.

local a = numluau.array({1,2.5,3.99})

print(numluau.sqrt(a)) -- array([1 1.5811388 1.9974984])
print(numluau.ceil(a)) -- array([1 3 4])
print(numluau.exp(a))  -- array([2.7182818 12.182494 54.054889])

scalar arithmetic¶

doing arithmetic between a scalar and a ndArray will apply that scalar to every item of that ndArray

local a = numluau.array({1,2,3,4})

print(a + 5) -- array([6 7 8 9])
print(a * 2) -- array([2 4 6 8])
print(a ^ 3) -- array([3 9 27 81])

heres an example of how you can use these

calculating the volumes of cylinders

local radii   = numluau.array({1,5,2.5,10})
local heights = numluau.array({2,10,22,100})

local volumes = (radii ^ 2) * math.pi * heights
volumes = numluau.round(volumes)

print(volumes) -- array([6 785 432 31416])

broadcasting¶

Numluau allows you to perform operations between arrays by virtually expanding dimensions, so that they match in shape. This process is called broadcasting.

Broadcasting can only be applied either if: 1. The dimensions are the same size. 2. Atleast one dimension is equal to one.

local a = numluau.array({
    {1,2,3},
})
local b = numluau.array({
    {0, 0, 0},
    {10,10,10},
    {20,20,20},
    {30,30,30},
})

print(a + b)

output

> array([
  [1 2 3]
  [11 12 13]
  [21 22 23]
  [31 32 33]
])

Danger

Doing a operation between arrays that dont follow these rules will produce a broadcasting error.

local a = numluau.array({
    {1,2,3},
    {4,5,6},
})
local b = numluau.array({
    {0, 0, 0},
    {10,10,10},
    {20,20,20},
    {30,30,30},
})

print(a + b)

output error

Error with broadcasting: Tried to broadcast incompatible arrays

If the two arrays have different dimensions, the missing dimensions are filled in with ones.

local a = numluau.array({2,5})
local b = numluau.array({
    {0,0},
    {1,1},
    {2,2},
    {3,3},
    {4,4},
})

-- a.Shape : [2]
-- b.Shape : [2, 5]

-- a.Shape has no 2nd dimension so it acts as if its 2nd dimension was 1
print(a * b)

output

> array([
  [0 0]
  [2 5]
  [4 10]
  [6 15]
  [8 20]
])

In some cases, both arrays will be expanded during broadcasting.

local a = numluau.array({1,2,3,4,5})
local b = numluau.array({
    {1},
    {2},
    {3},
    {4},
    {4},
})

print(a * b)

output

> array([
  [1 2 3 4 5]
  [2 4 6 8 10]
  [3 6 9 12 15]
  [4 8 12 16 20]
  [4 8 12 16 20]
])

aggregations¶

When working with data it is useful to reduce a collection of values into a single value. This is where aggregation functions come in.

local a = numluau.array({1,2,3,4,5})

print(numluau.sum(a)) -- array(15)

print(numluau.mean(a)) -- array(3)

With higher dimensional arrays, you can also specify a axis to aggregate across.

Info

Unlike indexing, Axes are 0 indexed. Meaning the 0^th axis is the first axis.

local a = numluau.array({
    {1,2,3,4,5},
    {10,9,8,7,6}
})

print(numluau.sum(a))  
print(numluau.sum(a,0))
print(numluau.sum(a,1))

output

> array(55)
> array([15 40])
> array([11 11 11 11 11])