12 Intro to Linear Algebra - DRAFT 🛠

In this tutorial, we introduce basic linear algebra concepts and the way they can be computed using Fastmath.

For additional backgrounds, see Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Stephen Boyd & Lieven Vandenberghe, Cambridge University Press, UK, 2018.

(ns noj-book.linear-algebra-intro
  (:require [fastmath.vector :as vec]))

util vars

(def java-double-array (double-array 5))

12.1 Addition

(vec/add [1 9]
         [0 -3])

[1.0 6.0]

(vec/mult [1 9]
          1000)

[1000.0 9000.0]

When we pass single vector to fastmath/sub function it will be multiplied by -1.0.

(vec/sub [10 5])

[-10.0 -5.0]

When we pass two vectors to fastmath/sub function it will perform basic vector subtraction.

(vec/sub [10 5]
         [8 4])

[2.0 1.0]

When we pass two vectors to fastmath/dot function it will perform dot product operation on them. a · b = a₁b₁ + a₂b₂ + … + anbn

(vec/dot [10 5]
         [8 4])

100.0

(vec/vec->array [10 5])

[10.0, 5.0]

(type (vec/vec->array [10 5]))

double/1

(identity java-double-array)

[0.0, 0.0, 0.0, 0.0, 0.0]

(type (vec/vec->seq java-double-array))

clojure.lang.ArraySeq$ArraySeq_double

(type (vec/vec->RealVector [10 5]))

org.apache.commons.math3.linear.ArrayRealVector

(identity java-double-array)

[0.0, 0.0, 0.0, 0.0, 0.0]

(type (vec/vec->RealVector java-double-array))

org.apache.commons.math3.linear.ArrayRealVector

(vec/vec->Vec [10 5])

[10.0 5.0]

(type (vec/vec->Vec [10 5]))

clojure.core.Vec

(identity java-double-array)

[0.0, 0.0, 0.0, 0.0, 0.0]

(type (vec/vec->Vec java-double-array))

clojure.core.Vec

(vec/as-vec [10 2] [5 10 15])

[5 10]

(vec/as-vec [5 10 15])

[0.0 0.0 0.0]

source: notebooks/noj_book/linear_algebra_intro.clj