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¶

Often you will have a 1D array thats a measurement and another 2D array that represent multiple measurements. Instead of manually copying the 1D array, numluau will expand that array's dimensions to be compatible with the 2D array.

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])