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Tutorial: Matrix and Vector operations

The following linear algebra operations are supported for tensors of rank 1 (vectors) and 2 (matrices):

  • dot product (Vector to Vector) using vtl.la.dot
  • addition and subtraction (any rank) using vtl.add and vtl.subtract
  • multiplication or division by a scalar using vtl.multiply and vtl.divide
  • matrix-matrix multiplication using vtl.la.matmul
  • . . .

Note: Matrix operations for floats are accelerated using vsl.blas. Unfortunately there is no acceleration routine for integers. Integer matrix-matrix and matrix-vector multiplications are implemented via semi-optimized routines.

Creating vectors and matrices

import vtl

// 1-D vector
v := vtl.from_1d([1.0, 2.0, 3.0])!

// 2-D matrix (3 rows × 3 columns)
a := vtl.from_2d([
	[1.0, 2.0, 3.0],
	[4.0, 5.0, 6.0],
	[7.0, 8.0, 9.0],
])!

Element-wise arithmetic

import vtl

a := vtl.from_2d([[1.0, 2.0], [3.0, 4.0]])!
b := vtl.from_2d([[5.0, 6.0], [7.0, 8.0]])!

sum := a.add(b)! // [[6, 8], [10, 12]]
diff := a.subtract(b)! // [[-4, -4], [-4, -4]]
prod := a.multiply(b)! // element-wise: [[5, 12], [21, 32]]
quot := a.divide(b)! // element-wise: [[0.2, 0.333], [0.428, 0.5]]

Scalar operations

import vtl

t := vtl.from_1d([2.0, 4.0, 6.0])!
s := vtl.tensor(2.0, [1])

scaled := t.multiply(s)! // [4.0, 8.0, 12.0]

Dot product (vectors)

import vtl
import vtl.la

u := vtl.from_1d([1.0, 2.0, 3.0])!
v := vtl.from_1d([4.0, 5.0, 6.0])!

d := la.dot(u, v)! // 1*4 + 2*5 + 3*6 = 32.0
println(d)

Matrix multiplication

import vtl
import vtl.la

a := vtl.from_2d([[1.0, 2.0], [3.0, 4.0]])! // 2×2
b := vtl.from_2d([[5.0, 6.0], [7.0, 8.0]])! // 2×2

c := la.matmul(a, b)! // 2×2
println(c)
// [[19, 22],
//  [43, 50]]

Transpose

Pass the desired axis order to transpose. For a 2-D matrix, swap axes [1, 0]:

import vtl

a := vtl.from_2d([[1, 2, 3], [4, 5, 6]])! // shape [2, 3]
t := a.transpose([1, 0])! // shape [3, 2]
println(t)
// [[1, 4],
//  [2, 5],
//  [3, 6]]

See also