Kronecker product: Difference between revisions

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=={{header|Frink}}==

The Frink library [https://frinklang.org/fsp/colorize.fsp?f=Matrix.frink Matrix.frink] contains an implementation of Kronecker product. ~~The~~ following example demonstrates calculating the Kronecker product and typesetting the equations using ~~Frink's~~ ~~layout~~ ~~routines~~.

The Frink library [https://frinklang.org/fsp/colorize.fsp?f=Matrix.frink Matrix.frink] contains an implementation of Kronecker product. However, the following example demonstrates calculating the Kronecker product and typesetting the equations using multidimensional arrays and no external libraries.

<lang frink>~~use~~ ~~Matrix.frink~~

<lang frink>a = [[1,2],[3,4]]

a = ~~new Matrix~~[ [[1,2],[3,4] ]]

b = [[0,5],[6,7]]

b = new Matrix[ [[0,5],[6,7] ]]

println[formatProd[a,b]]

c = ~~new Matrix[~~ [[0,1,0],[1,1,1],[0,1,0] ]]

c = [[0,1,0],[1,1,1],[0,1,0]]

d = ~~new Matrix[~~ [[1,1,1,1],[1,0,0,1],[1,1,1,1]] ]

d = [[1,1,1,1],[1,0,0,1],[1,1,1,1]]

println[formatProd[c,d]]

formatProd[a,b] := formatTable[[[a.formatMatrix[], "\u2297", b.formatMatrix[], "=", a.KroneckerProduct[b]~~.formatMatrix[~~]]]]~~</lang>~~

formatProd[a,b] := formatTable[[[formatMatrix[a], "\u2297", formatMatrix[b], "=", formatMatrix[KroneckerProduct[a,b]]]]]

KroneckerProduct[a, b] :=

{

[m,n] = a.dimensions[]

[p,q] = b.dimensions[]

rows = m p

cols = n q

n = new array[[rows, cols], 0]

for i=0 to rows-1

for j=0 to cols-1

n@i@j = a@(i div p)@(j div q) * b@(i mod p)@(j mod q)

return n

}</lang>

<pre>

┌ ┐

┌ ┐ ┌ ┐ │ 0 5 0 10│

│ 0 5 0 10│

│1 2│ │0 5│ │ 6 7 12 ~~14│~~

┌ ┐ ┌ ┐ │ │

│3 4│ ⊗ │6 7│ = │ 0 15 0 ~~20│~~

│1 2│ │0 5│ │ 6 7 12 14│

└ ┘ └ ┘ ~~│18~~ 21 24 ~~28│~~

│ │ ⊗ │ │ = │ │

└ ┘

│3 4│ │6 7│ │ 0 15 0 20│

┌ ┐

└ ┘ └ ┘ │ │

│0 0 ~~0 0 1 1 1 1 0 0 0 0│~~

│18 21 24 28│

│0 0 0 0 1 0 0 1 0 0 ~~0 0│~~

└ ┘

┌ ┐ ┌ ┐ │0 0 0 0 1 1 1 1 0 0 0 0│

┌ ┐

│0 1 0│ │1 1 1 1│ │1 1 1 1 1 1 1 1 1 1 1 1│

│0 0 0 0 1 1 1 1 0 0 0 0│

│ │

⚫

│1 1 1│ ⊗ │1 0 0 1│ = │1 0 0 1 1 0 0 1 1 0 0 1│

│0 1 0│ │1 1 1 1│ │1 1 1 1 1 1 1 1 1 1 1 1│

│0 0 0 0 1 0 0 1 0 0 0 0│

└ ┘ └ ┘ │0 0 0 0 1 1 1 1 0 0 0 0│

│ │

│0 0 0 0 1 0 0 1 0 0 0 0│

│0 0 0 0 1 1 1 1 0 0 0 0│

┌ ┐ ┌ ┐ │ │

└ ┘

│0 1 0│ │1 1 1 1│ │1 1 1 1 1 1 1 1 1 1 1 1│

│ │ │ │ │ │

⚫

│1 1 1│ ⊗ │1 0 0 1│ = │1 0 0 1 1 0 0 1 1 0 0 1│

│ │ │ │ │ │

│0 1 0│ │1 1 1 1│ │1 1 1 1 1 1 1 1 1 1 1 1│

└ ┘ └ ┘ │ │

│0 0 0 0 1 1 1 1 0 0 0 0│

│ │

│0 0 0 0 1 0 0 1 0 0 0 0│

│ │

│0 0 0 0 1 1 1 1 0 0 0 0│

└ ┘

</pre>