Kronecker product
You are encouraged to solve this task according to the task description, using any language you may know.
| This page uses content from Wikipedia. The original article was at Kronecker product. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
- Task
Implement the Kronecker product of two matrices (arbitrary sized) resulting in a block matrix.
- Test cases
Show results for each of the following 2 samples:
Sample 1 (from Wikipedia):
|1 2| x |0 5| = | 0 5 0 10| |3 4| |6 7| | 6 7 12 14| | 0 15 0 20| |18 21 24 28|
Sample 2:
|0 1 0| x |1 1 1 1| = |0 0 0 0 1 1 1 1 0 0 0 0|
|1 1 1| |1 0 0 1| |0 0 0 0 1 0 0 1 0 0 0 0|
|0 1 0| |1 1 1 1| |0 0 0 0 1 1 1 1 0 0 0 0|
|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 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|
See implementations and results below in JavaScript and PARI/GP languages.
- See also
AppleScript
<lang applescript>-- KRONECKER PRODUCT OF TWO MATRICES ------------------------------------------
-- kprod :: Num -> Num -> Num on kprod(xs, ys)
script concatTranspose
on lambda(m)
map(my concat, my transpose(m))
end lambda
end script
script
-- Multiplication by N over a list of lists
-- f :: Num -> Num -> Num
on f(mx, n)
script mapMult
on product(a, b)
a * b
end product
on lambda(xs)
map(curry(product)'s lambda(n), xs)
end lambda
end script
map(mapMult, mx)
end f
on lambda(zs)
map(curry(f)'s lambda(ys), zs)
end lambda
end script
concatMap(concatTranspose, map(result, xs))
end kprod
-- TEST ----------------------------------------------------------------------- on run
unlines(map(show, ¬
kprod({{1, 2}, {3, 4}}, ¬
{{0, 5}, {6, 7}}))) & ¬
linefeed & linefeed & ¬
unlines(map(show, ¬
kprod({{0, 1, 0}, {1, 1, 1}, {0, 1, 0}}, ¬
{{1, 1, 1, 1}, {1, 0, 0, 1}, {1, 1, 1, 1}})))
end run
-- GENERIC FUNCTIONS ----------------------------------------------------------
-- concat :: a -> [a] | [String] -> String on concat(xs)
script append
on lambda(a, b)
a & b
end lambda
end script
if length of xs > 0 and class of (item 1 of xs) is string then
set unit to ""
else
set unit to {}
end if
foldl(append, unit, xs)
end concat
-- concatMap :: (a -> [b]) -> [a] -> [b] on concatMap(f, xs)
set lst to {}
set lng to length of xs
tell mReturn(f)
repeat with i from 1 to lng
set lst to (lst & lambda(contents of item i of xs, i, xs))
end repeat
end tell
return lst
end concatMap
-- curry :: (Script|Handler) -> Script on curry(f)
script
on lambda(a)
script
on lambda(b)
lambda(a, b) of mReturn(f)
end lambda
end script
end lambda
end script
end curry
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to lambda(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- intercalate :: Text -> [Text] -> Text on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to lambda(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property lambda : f
end script
end if
end mReturn
-- show :: a -> String on show(e)
set c to class of e
if c = list then
script serialized
on lambda(v)
show(v)
end lambda
end script
"{" & intercalate(", ", map(serialized, e)) & "}"
else if c = record then
script showField
on lambda(kv)
set {k, v} to kv
k & ":" & show(v)
end lambda
end script
"{" & intercalate(", ", ¬
map(showField, zip(allKeys(e), allValues(e)))) & "}"
else if c = date then
("date \"" & e as text) & "\""
else if c = text then
"\"" & e & "\""
else
try
e as text
on error
("«" & c as text) & "»"
end try
end if
end show
-- transpose :: a -> a on transpose(xss)
script column
on lambda(_, iCol)
script row
on lambda(xs)
item iCol of xs
end lambda
end script
map(row, xss)
end lambda
end script
map(column, item 1 of xss)
end transpose
-- unlines :: [String] -> String on unlines(xs)
intercalate(linefeed, xs)
end unlines</lang>
- Output:
{0, 5, 0, 10}
{6, 7, 12, 14}
{0, 15, 0, 20}
{18, 21, 24, 28}
{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}
{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, 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}
Haskell
<lang haskell>import Data.List (transpose)
kprod
:: Num a => a -> a -> a
kprod xs ys =
let f = fmap . fmap . (*) -- Multiplication by n over list of lists in (concat <$>) . transpose =<< fmap (`f` ys) <$> xs
main :: IO () main = do
mapM_ print $ kprod [[1, 2], [3, 4]] [[0, 5], [6, 7]]
putStrLn []
mapM_ print $
kprod
[[0, 1, 0], [1, 1, 1], [0, 1, 0]]
[[1, 1, 1, 1], [1, 0, 0, 1], [1, 1, 1, 1]]</lang>
- Output:
[0,5,0,10] [6,7,12,14] [0,15,0,20] [18,21,24,28] [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] [1,1,1,1,1,1,1,1,1,1,1,1] [1,0,0,1,1,0,0,1,1,0,0,1] [1,1,1,1,1,1,1,1,1,1,1,1] [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]
JavaScript
Imperative
Version #1.
<lang javascript>
// matkronprod.js
// Prime function:
// mkp arrow function: Return the Kronecker product of the a and b matrices.
// Note: both a and b must be matrices, i.e., 2D rectangular arrays.
mkp=(a,b)=>a.map(a=>b.map(b=>a.map(y=>b.map(x=>r.push(y*x)),t.push(r=[]))),t=[])&&t;
// Helper functions:
// Log title and matrix mat to console
function matl2cons(title,mat) {console.log(title); console.log(mat.join`\n`)}
// Print title to document
function pttl2doc(title) {document.write(''+title+'
')}
// Print title and matrix mat to document
function matp2doc(title,mat) {
document.write(''+title+':
');
for (var i = 0; i < mat.length; i++) {
document.write(' '+mat[i].join(' ')+'
');
}
} </lang>
- Required tests
<lang html> <html><head>
<title>Kronecker product: Sample 1 (from Wikipedia) and Sample 2</title>
<script src="matkronprod.js"></script>
<script>
var mr,ttl='Kronecker product of A and B matrices';
[ {a:[[1,2],[3,4]],b:[[0,5],[6,7]] },
{a:[[0,1,0],[1,1,1],[0,1,0]],b:[[1,1,1,1],[1,0,0,1],[1,1,1,1]] }
].forEach(m=>{
console.log(ttl); pttl2doc(ttl);
matl2cons('A',m.a); matp2doc('A',m.a);
matl2cons('B',m.b); matp2doc('B',m.b);
mr=mkp(m.a,m.b);
matl2cons('A x B',mr); matp2doc('A x B',mr);
})
</script>
</head><body></body> </html> </lang>
- Output:
Console and page results
Kronecker product of A and B matrices A 1,2 3,4 B 0,5 6,7 A x B 0,5,0,10 6,7,12,14 0,15,0,20 18,21,24,28 Kronecker product of A and B matrices A 0,1,0 1,1,1 0,1,0 B 1,1,1,1 1,0,0,1 1,1,1,1 A x B 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 1,1,1,1,1,1,1,1,1,1,1,1 1,0,0,1,1,0,0,1,1,0,0,1 1,1,1,1,1,1,1,1,1,1,1,1 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
Version #2.
This version is more understandable for sure.
<lang javascript> // matkronprod2.js // Prime function: // mkp2(): Return the Kronecker product of the a and b matrices // Note: both a and b must be matrices, i.e., 2D rectangular arrays. function mkp2(a,b) {
var m=a.length, n=a[0].length, p=b.length, q=b[0].length;
var rtn=m*p, ctn=n*q; var r=new Array(rtn);
for (var i=0; i<rtn; i++) {r[i]=new Array(ctn)
for (var j=0;j<ctn;j++) {r[i][j]=0}
}
for (var i=0; i<m; i++) {
for (var j=0; j<n; j++) {
for (var k=0; k<p; k++) {
for (var l=0; l<q; l++) {
r[p*i+k][q*j+l]=a[i][j]*b[k][l];
}}}}//all4forend
return(r);
}
// Helper functions:
// Log title and matrix mat to console
function matl2cons(title,mat) {console.log(title); console.log(mat.join`\n`)}
// Print title to document
function pttl2doc(title) {document.write(''+title+'
')}
// Print title and matrix mat to document
function matp2doc(title,mat) {
document.write(''+title+':
');
for (var i=0; i < mat.length; i++) {
document.write(' '+mat[i].join(' ')+'
');
}
} </lang>
- Required tests
<lang html> <html><head>
<title>Kronecker product v.2: Sample 1 (from Wikipedia) and Sample 2</title>
<script src="matkronprod2.js"></script>
<script>
var mr,ttl='Kronecker product of A and B matrices';
[ {a:[[1,2],[3,4]],b:[[0,5],[6,7]] },
{a:[[0,1,0],[1,1,1],[0,1,0]],b:[[1,1,1,1],[1,0,0,1],[1,1,1,1]] }
].forEach(m=>{
console.log(ttl); pttl2doc(ttl);
matl2cons('A',m.a); matp2doc('A',m.a);
matl2cons('B',m.b); matp2doc('B',m.b);
mr=mkp2(m.a,m.b);
matl2cons('A x B',mr); matp2doc('A x B',mr);
})
</script>
</head><body></body> </html> </lang>
- Output:
Console and page results
Output is identical to Version #1 above.
Functional
ES6
(As JavaScript is now widely embedded in non-browser contexts, a non-HTML string value is returned here, rather than invoking a DOM method, which will not always be available to a JavaScript interpreter) <lang javascript>(() => {
'use strict';
// GENERIC FUNCTIONS ------------------------------------------------------
// concat :: a -> [a] const concat = xs => [].concat.apply([], xs);
// concatMap :: (a -> [b]) -> [a] -> [b] const concatMap = (f, xs) => [].concat.apply([], xs.map(f));
// 2 or more arguments
// curry :: Function -> Function
const curry = (f, ...args) => {
const go = xs => xs.length >= f.length ? (f.apply(null, xs)) :
function () {
return go(xs.concat([].slice.apply(arguments)));
};
return go([].slice.call(args, 1));
};
// map :: (a -> b) -> [a] -> [b] const map = curry((f, xs) => xs.map(f));
// show :: a -> String const show = x => JSON.stringify(x); //, null, 2);
// transpose :: a -> a const transpose = xs => xs[0].map((_, col) => xs.map(row => row[col]));
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// KRONECKER PRODUCT OF TWO MATRICES --------------------------------------
// kprod :: Num -> Num -> Num const kprod = (xs, ys) => concatMap( m => map(concat, transpose(m)), map(map(f(ys)), xs) );
// (* n) mapped over each element in a matrix // f :: Num -> Num -> Num const f = curry((mx, n) => map(map(x => x * n), mx));
// TEST -------------------------------------------------------------------
return unlines(map(rows => unlines(map(show, rows)), [
kprod([
[1, 2],
[3, 4]
], [
[0, 5],
[6, 7]
]), [], // One empty output line
kprod([
[0, 1, 0],
[1, 1, 1],
[0, 1, 0]
], [
[1, 1, 1, 1],
[1, 0, 0, 1],
[1, 1, 1, 1]
])
]));
})();</lang>
- Output:
[0,5,0,10] [6,7,12,14] [0,15,0,20] [18,21,24,28] [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] [1,1,1,1,1,1,1,1,1,1,1,1] [1,0,0,1,1,0,0,1,1,0,0,1] [1,1,1,1,1,1,1,1,1,1,1,1] [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]
Kotlin
<lang scala>// version 1.1.1 (JVM)
typealias Matrix = Array<IntArray>
fun kroneckerProduct(a: Matrix, b: Matrix): Matrix {
val m = a.size
val n = a[0].size
val p = b.size
val q = b[0].size
val rtn = m * p
val ctn = n * q
val r: Matrix = Array(rtn) { IntArray(ctn) } // all elements zero by default
for (i in 0 until m)
for (j in 0 until n)
for (k in 0 until p)
for (l in 0 until q)
r[p * i + k][q * j + l] = a[i][j] * b[k][l]
return r
}
fun printMatrix(text: String, m: Matrix) {
println(text) for (i in 0 until m.size) println(m[i].contentToString()) println()
}
fun printAll(a: Matrix, b: Matrix, r: Matrix) {
printMatrix("Matrix A:", a)
printMatrix("Matrix B:", b)
printMatrix("Kronecker product:", r)
}
fun main(args: Array<String>) {
var a: Matrix
var b: Matrix
var r: Matrix
a = arrayOf(
intArrayOf(1, 2),
intArrayOf(3, 4)
)
b = arrayOf(
intArrayOf(0, 5),
intArrayOf(6, 7)
)
r = kroneckerProduct(a, b)
printAll(a, b, r)
a = arrayOf(
intArrayOf(0, 1, 0),
intArrayOf(1, 1, 1),
intArrayOf(0, 1, 0)
)
b = arrayOf(
intArrayOf(1, 1, 1, 1),
intArrayOf(1, 0, 0, 1),
intArrayOf(1, 1, 1, 1)
)
r = kroneckerProduct(a, b)
printAll(a, b, r)
}</lang>
- Output:
Matrix A: [1, 2] [3, 4] Matrix B: [0, 5] [6, 7] Kronecker product: [0, 5, 0, 10] [6, 7, 12, 14] [0, 15, 0, 20] [18, 21, 24, 28] Matrix A: [0, 1, 0] [1, 1, 1] [0, 1, 0] Matrix B: [1, 1, 1, 1] [1, 0, 0, 1] [1, 1, 1, 1] Kronecker product: [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] [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, 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]
PARI/GP
<lang parigp> \\ Print title and matrix mat rows. 4/17/16 aev matprows(title,mat)={print(title); for(i=1,#mat[,1], print(mat[i,]))} \\ \\ Create and return the Kronecker product of the a and b matrices. 4/17/16 aev matkronprod(a,b,pflg=0)={ my(m=#a[,1],n=#a[1,],p=#b[,1],q=#b[1,],r,rtn,ctn); rtn=m*p; ctn=n*q; if(pflg,print(" *** Kronecker product - a: ",m," x ",n," b: ",p," x ",q," result r: ",rtn," x ",ctn)); r=matrix(rtn,ctn); for(i=1,m, for(j=1,n, for(k=1,p, for(l=1,q,
r[p*(i-1)+k,q*(j-1)+l]=a[i,j]*b[k,l];
))));\\all4fend if(pflg,print(r)); return(r); } {\\ Requireq tests: my(a,b,r); \\ Sample 1 a=[1,2;3,4]; b=[0,5;6,7]; r=matkronprod(a,b); matprows("Sample 1 result:",r); \\ Sample 2 a=[0,1,0;1,1,1;0,1,0]; b=[1,1,1,1;1,0,0,1;1,1,1,1]; r=matkronprod(a,b); matprows("Sample 2 result:",r); } </lang>
- Output:
Sample 1 result: [0, 5, 0, 10] [6, 7, 12, 14] [0, 15, 0, 20] [18, 21, 24, 28] Sample 2 result: [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] [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, 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]