Kronecker product: Difference between revisions
(→{{header|Fortran}}: Or, don't produce array AB as such.) |
(Add SuperCollider example) |
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[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0] |
[0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0] |
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[0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0] |
[0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0] |
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</pre> |
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=={{header|SuperCollider}}== |
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<lang SuperCollider>// the iterative version is derived from the javascript one here: |
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( |
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f = { |a, b| |
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var m = a.size; |
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var n = a[0].size; |
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var p = b.size; |
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var q = b[0].size; |
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var rtn = m * p; |
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var ctn = n * q; |
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var res = { 0.dup(ctn) }.dup(rtn); |
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m.do { |i| |
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n.do { |j| |
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p.do { |k| |
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q.do { |l| |
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res[p*i+k][q*j+l] = a[i][j] * b[k][l]; |
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} |
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} |
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} |
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}; |
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res |
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}; |
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) |
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// Like APL/J, SuperCollider has applicative operators, so here is a shorter version. |
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// the idea is to first replace every element of b with its product with all of a |
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// and then reshape the matrix appropriately |
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// note that +++ is lamination: [[1, 2, 3], [4, 5, 6]] +++ [100, 200] returns [ [ 1, 2, 3, 100 ], [ 4, 5, 6, 200 ] ]. |
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( |
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f = { |a, b| |
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a.collect { |x| |
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x.collect { |y| b * y }.reduce('+++') |
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}.reduce('++') |
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} |
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) |
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// to apply either of the two functions: |
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( |
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x = f.( |
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[ |
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[0, 1, 0], |
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[1, 1, 1], |
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[0, 1, 0] |
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], |
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[ |
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[1, 1, 1, 1], |
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[1, 0, 0, 1], |
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[1, 1, 1, 1] |
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] |
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) |
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) |
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</lang> |
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Results in: |
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<pre> |
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[ |
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[ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 ], |
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[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ], |
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[ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 ], |
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[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], |
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[ 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1 ], |
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[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], |
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[ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 ], |
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[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ], |
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[ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 ] |
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] |
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</pre> |
</pre> |
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Revision as of 19:09, 1 May 2017
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 two 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.
- Related task
360 Assembly
<lang 360asm>* Kronecker product 06/04/2017 KRONECK CSECT
USING KRONECK,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R1,1 first example
BAL R14,PRODUCT call product(a1,b1)
BAL R14,PRINT call print(r)
XPRNT =C'---',3 separator
LA R1,2 second example
BAL R14,PRODUCT call product(a2,b2)
BAL R14,PRINT call print(r)
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
- ------- ---- ----------------------------------------
PRODUCT EQU * product(o)
STC R1,OO store o
IF CLI,OO,EQ,X'01' THEN if o=1 then
MVC MM(8),DIM1 (m,n)=hbound(a1) (p,q)=hbound(b1)
LA R1,A1 @a1
LA R2,B1 @b1
ELSE , else
MVC MM(8),DIM2 (m,n)=hbound(a2) (p,q)=hbound(b2)
LA R1,A2 @a2
LA R2,B2 @b2
ENDIF , endif
ST R1,ADDRA addra=@a1
ST R2,ADDRB addrb=@b1
LH R1,MM m
MH R1,PP p
STH R1,RI ri=m*p
LH R2,NN n
MH R2,QQ *q
STH R2,RJ rj=n*q
LA R6,1 i=1
DO WHILE=(CH,R6,LE,MM) do i=1 to m
LA R7,1 j=1
DO WHILE=(CH,R7,LE,NN) do j=1 to n
LA R8,1 k=1
DO WHILE=(CH,R8,LE,PP) do k=1 to p
LA R9,1 l=1
DO WHILE=(CH,R9,LE,QQ) do l=1 to q
LR R1,R6 i
BCTR R1,0
MH R1,NN *hbound(a,2)
AR R1,R7 j
BCTR R1,0
SLA R1,2
L R4,ADDRA @a
L R2,0(R4,R1) r2=a(i,j)
LR R1,R8 k
BCTR R1,0
MH R1,QQ *hbound(b1,2)
AR R1,R9 l
BCTR R1,0
SLA R1,2
L R4,ADDRB @b
L R3,0(R4,R1) r3=b(k,l)
LR R5,R2 r2
MR R4,R3 *r3
LR R0,R5 r0=a(i,j)*b(k,l)
LR R1,R6 i
BCTR R1,0 i-1
MH R1,PP *p
AR R1,R8 r1=p*(i-1)+k
LR R2,R7 j
BCTR R2,0 j-1
MH R2,QQ *q
AR R2,R9 r2=q*(j-1)+l
BCTR R1,0
MH R1,=AL2(NR) *nr
AR R1,R2 r1=r1+r2
SLA R1,2
ST R0,R-4(R1) r(p*(i-1)+k,q*(j-1)+l)=r0
LA R9,1(R9) l++
ENDDO , enddo l
LA R8,1(R8) k++
ENDDO , enddo k
LA R7,1(R7) j++
ENDDO , enddo j
LA R6,1(R6) i++
ENDDO , enddo i
BR R14 return
- ------- ---- ----------------------------------------
PRINT EQU * print
LA R6,1 i
DO WHILE=(CH,R6,LE,RI) do i=1 to ri
MVC PG,=CL80' ' init buffer
LA R10,PG pgi=0
LA R7,1 j
DO WHILE=(CH,R7,LE,RJ) do j=1 to rj
LR R1,R6 i
BCTR R1,0
MH R1,=AL2(NR) *nr
AR R1,R7 +j
SLA R1,2
L R2,R-4(R1) r(i,j)
XDECO R2,XDEC edit
MVC 0(ND,R10),XDEC+12-ND output
LA R10,ND(R10) pgi=pgi+nd
LA R7,1(R7) j++
ENDDO , enddo j
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo j
BR R14 return
- ---- ----------------------------------------
NR EQU 32 dim result max ND EQU 3 digits to print A1 DC F'1',F'2' a1(2,2)
DC F'3',F'4'
B1 DC F'0',F'5' b1(2,2)
DC F'6',F'7'
DIM1 DC H'2',H'2',H'2',H'2' dim a1 , dim b1 A2 DC F'0',F'1',F'0' a2(3,3)
DC F'1',F'1',F'1'
DC F'0',F'1',F'0'
B2 DC F'1',F'1',F'1',F'1' b2(3,4)
DC F'1',F'0',F'0',F'1'
DC F'1',F'1',F'1',F'1'
DIM2 DC H'3',H'3',H'3',H'4' dim a2 , dim b2 ADDRA DS A @a ADDRB DS A @b RI DS H ri RJ DS H rj MM DS H m NN DS H n PP DS H p QQ DS H q OO DS X o PG DS CL80 buffer XDEC DS CL12
LTORG
R DS (NR*NR)F r(nr,nr)
YREGS
END KRONECK</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
ALGOL 68
<lang algol68>BEGIN
# multiplies in-place the elements of the matrix a by the scaler b #
OP *:= = ( REF[,]INT a, INT b )REF[,]INT:
BEGIN
FOR i FROM 1 LWB a TO 1 UPB a DO
FOR j FROM 2 LWB a TO 2 UPB a DO
a[ i, j ] *:= b
OD
OD;
a
END # *:= # ;
# returns the Kronecker Product of the two matrices a and b #
# the result will have lower bounds of 1 #
PRIO X = 6;
OP X = ( [,]INT a, b )[,]INT:
BEGIN
# normalise the matrices to have lower bounds of 1 #
[,]INT l = a[ AT 1, AT 1 ];
[,]INT r = b[ AT 1, AT 1 ];
# construct the result #
INT r 1 size = 1 UPB r;
INT r 2 size = 2 UPB r;
[ 1 : 1 UPB l * 1 UPB r, 1 : 2 UPB l * 2 UPB r ]INT k;
FOR i FROM 1 LWB l TO 1 UPB l DO
FOR j FROM 2 LWB l TO 2 UPB l DO
( k[ 1 + ( ( i - 1 ) * r 1 size ) : i * r 1 size
, 1 + ( ( j - 1 ) * r 2 size ) : j * r 2 size
] := r
) *:= l[ i, j ]
OD
OD;
k
END # X # ;
# prints matrix a with the specified field width #
PROC print matrix = ( [,]INT a, INT field width )VOID:
FOR i FROM 1 LWB a TO 1 UPB a DO
FOR j FROM 2 LWB a TO 2 UPB a DO
print( ( " ", whole( a[ i, j ], field width ) ) )
OD;
print( ( newline ) )
OD # print matrix # ;
# task test cases #
print matrix( [,]INT( ( 1, 2 )
, ( 3, 4 )
)
X [,]INT( ( 0, 5 )
, ( 6, 7 )
)
, -2
);
print( ( newline ) );
print matrix( [,]INT( ( 0, 1, 0 )
, ( 1, 1, 1 )
, ( 0, 1, 0 )
)
X [,]INT( ( 1, 1, 1, 1 )
, ( 1, 0, 0, 1 )
, ( 1, 1, 1, 1 )
)
, -1
)
END </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
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
on product(a, b)
a * b
end product
on lambda(xs)
map(curry(product)'s lambda(n), xs)
end lambda
end script
map(result, 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}
AWK
<lang AWK>
- syntax: GAWK -f KRONECKER_PRODUCT.AWK
BEGIN {
A[++a] = "1 2" ; B[++b] = "0 5"
A[++a] = "3 4" ; B[++b] = "6 7"
main("sample 1",1234)
A[++a] = "0 1 0" ; B[++b] = "1 1 1 1"
A[++a] = "1 1 1" ; B[++b] = "1 0 0 1"
A[++a] = "0 1 0" ; B[++b] = "1 1 1 1"
main("sample 2",3)
exit(0)
} function main(desc,option) {
- option: allows complete flexibility of output; they may be combined
- 1 show A and B matrix
- 2 show A x B
- 3 show product
- 4 show Arow,Acol x Brow,Bcol
printf("%s\n\n",desc)
if (option ~ /[1234]/) {
a_rows = show_array(A,"A",option)
b_rows = show_array(B,"B",option)
if (option ~ /2/) { prn("A x B",2) }
if (option ~ /3/) { prn("Product",3) }
if (option ~ /4/) { prn("Arow,Acol x Brow,Bcol",4) }
}
else {
print("nothing to print")
}
print("")
a = b = 0 # reset
delete A
delete B
} function prn(desc,option, a_cols,b_cols,w,x,y,z,AA,BB) {
printf("%s:\n",desc)
for (w=1; w<=a_rows; w++) {
a_cols = split(A[w],AA," ")
for (x=1; x<=b_rows; x++) {
b_cols = split(B[x],BB," ")
printf("[ ")
for (y=1; y<=a_cols; y++) {
for (z=1; z<=b_cols; z++) {
if (option ~ /2/) { printf("%sx%s ",AA[y],BB[z]) }
if (option ~ /3/) { printf("%2s ",AA[y] * BB[z]) }
if (option ~ /4/) { printf("%s,%sx%s,%s ",w,y,x,z) }
}
}
printf("]\n")
}
}
} function show_array(arr,desc,option, i,n) {
for (i in arr) {
n++
}
if (option ~ /1/) {
printf("Matrix %s:\n",desc)
for (i=1; i<=n; i++) {
printf("[ %s ]\n",arr[i])
}
}
return(n)
} </lang>
- Output:
sample 1 Matrix A: [ 1 2 ] [ 3 4 ] Matrix B: [ 0 5 ] [ 6 7 ] A x B: [ 1x0 1x5 2x0 2x5 ] [ 1x6 1x7 2x6 2x7 ] [ 3x0 3x5 4x0 4x5 ] [ 3x6 3x7 4x6 4x7 ] Product: [ 0 5 0 10 ] [ 6 7 12 14 ] [ 0 15 0 20 ] [ 18 21 24 28 ] Arow,Acol x Brow,Bcol: [ 1,1x1,1 1,1x1,2 1,2x1,1 1,2x1,2 ] [ 1,1x2,1 1,1x2,2 1,2x2,1 1,2x2,2 ] [ 2,1x1,1 2,1x1,2 2,2x1,1 2,2x1,2 ] [ 2,1x2,1 2,1x2,2 2,2x2,1 2,2x2,2 ] sample 2 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 ]
Fortran
The plan is to pass the two arrays to a subroutine, which will return their Kronecker product as a third parameter. This relies on the expanded array-handling facilities introduced with F90, especially the ability of a subroutine to allocate an array of a size of its choosing, this array being a parameter to the subroutine. Some compilers offering the "allocate" statement do not handle this! Further features of the MODULE protocol of F90 allow arrays passed to a subroutine to have their sizes ascertained in the subroutine (via function UBOUND, etc.) rather than this information being supplied via the programmer coding additional parameters. This is not all to the good: multi-dimensional arrays must therefore be the actual size of their usage rather than say A(100,100) but only using the first fifty elements (in one place) and the first thirty in another. Thus, for such usage the array must be re-allocated the correct size each time, and, the speed of access to such arrays is reduced - see Sequence_of_primorial_primes#Fixed-size_data_aggregates for an example. Similarly, suppose a portion of a large array is to be passed as a parameter, as is enabled by F90 syntax such as A(3:7,9:12) to select a 5x4 block: those elements will not be in contiguous memory locations, as is expected by the subroutine, so they will be copied into a temporary storage area that will become the parameter and their values will be copied back on return. Copy-in copy-out, instead of by reference. With large arrays, this imposes a large overhead. A further detail of the MODULE protocol when passing arrays is that if the parameter's declaration does not specify the lower bound, it will be treated as if it were one even if the actual array is declared otherwise - see Array_length#Fortran for example.
In older-style Fortran, the arrays would be of some "surely-big-enough" size, fixed at compile time, and there would be additional parameters describing the bounds in use for each invocation. Since no array-assignment statements were available, there would be additional DO-loops to copy each block of values. In all versions of Fortran, the ordering of array elements in storage is "column-major" so that the DATA statement appears to initialise the arrays with their transpose - see Matrix_transposition#Fortran for example. As a result, the default output order for an array, if written as just WRITE (6,*) A will be that of the transposed order, just as with the default order of the DATA statement's data. To show the desired order of A(row,column), the array must be written with explicit specification of the order of elements, as is done by subroutine SHOW: columns across the page, rows running down the page. <lang Fortran> MODULE ARRAYMUSH !A rather small collection.
CONTAINS !For the specific problem only.
SUBROUTINE KPRODUCT(A,B,AB) !AB = Kronecker product of A and B, both two-dimensional arrays.
Considers the arrays to be addressed as A(row,column), despite any storage order arrangements. . Creating array AB to fit here, adjusting the caller's array AB, may not work on some compilers.
INTEGER A(:,:),B(:,:) !Two-dimensional arrays, lower bound one.
INTEGER, ALLOCATABLE:: AB(:,:) !To be created to fit.
INTEGER R,RA,RB,C,CA,CB,I !Assistants.
RA = UBOUND(A,DIM = 1) !Ascertain the upper bounds of the incoming arrays.
CA = UBOUND(A,DIM = 2) !Their lower bounds will be deemed one,
RB = UBOUND(B,DIM = 1) !And the upper bound as reported will correspond.
CB = UBOUND(B,DIM = 2) !UBOUND(A) would give an array of two values, RA and CA, more for higher dimensionality.
WRITE (6,1) "A",RA,CA,"B",RB,CB,"A.k.B",RA*RB,CA*CB !Announce.
1 FORMAT (3(A," is ",I0,"x",I0,1X)) !Three sets of sizes.
IF (ALLOCATED(AB)) DEALLOCATE(AB) !Discard any lingering storage.
ALLOCATE (AB(RA*RB,CA*CB)) !Obtain the exact desired size.
R = 0 !Syncopation: start the row offset.
DO I = 1,RA !Step down the rows of A.
C = 0 !For each row, start the column offset.
DO J = 1,CA !Step along the columns of A.
AB(R + 1:R + RB,C + 1:C + CB) = A(I,J)*B !Place a block of B values.
C = C + CB !Advance a block of columns.
END DO !On to the next column of A.
R = R + RB !Advance a block of rows.
END DO !On to the next row of A.
END SUBROUTINE KPRODUCT !No tests for bad parameters, or lack of storage...
SUBROUTINE SHOW(F,A) !Write array A in row,column order.
INTEGER F !Output file unit number.
INTEGER A(:,:) !The 2-D array, lower bound one.
INTEGER R !The row stepper.
DO R = 1,UBOUND(A,DIM = 1) !Each row gets its own line.
WRITE (F,1) A(R,:) !Write all the columns of that row.
1 FORMAT (666I3) !This suffices for the example.
END DO !On to the next row.
END SUBROUTINE SHOW !WRITE (F,*) A or similar would show A as if transposed.
END MODULE ARRAYMUSH !That was simple enough.
PROGRAM POKE
USE ARRAYMUSH
INTEGER A(2,2),B(2,2) !First test: square arrays.
INTEGER, ALLOCATABLE:: AB(:,:) !To be created for each result.
INTEGER C(3,3),D(3,4) !Second test: some rectilinearity.
DATA A/1,3, 2,4/,B/0,6, 5,7/ !Furrytran uses "column-major" order for successive storage elements.
DATA C/0,1,0, 1,1,1, 0,1,0/ !So, the first three values go down the rows of the first column.
DATA D/1,1,1, 1,0,1, 1,0,1, 1,1,1/!And then follow the values for the next column, etc.
WRITE (6,*) "First test..."
CALL KPRODUCT(A,B,AB)
CALL SHOW (6,AB)
WRITE (6,*)
WRITE (6,*) "Second test..."
CALL KPRODUCT(C,D,AB)
CALL SHOW (6,AB)
END</lang>
Output:
First test... A is 2x2 B is 2x2 A.k.B is 4x4 0 5 0 10 6 7 12 14 0 15 0 20 18 21 24 28 Second test... A is 3x3 B is 3x4 A.k.B is 9x12 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
An alternative approach is not to produce the array AB at all, just calculate its elements as needed. Using the array dimension variables as defined above, <lang Fortran>AB(i,j) = A((i - 1)/RB + 1,(j - 1)/CB + 1)*B(MOD(i - 1,RB) + 1,MOD(j - 1,CB) + 1))</lang> with the subtracting and adding of one necessary because array indexing starts with row one and column one. With F90, they could start at zero (or any desired value) but if so, you will have to be very careful with counting. For instance, DO I = 1,RA must become DO I = 0,RA - 1 and so forth.
FreeBASIC
<lang freebasic>' version 06-04-2017 ' compile with: fbc -s console
Sub kronecker_product(a() As Long, b() As Long, frmt As String = "#")
Dim As Long i, j, k, l Dim As Long la1 = LBound(a, 1) : Dim As Long ua1 = UBound(a, 1) Dim As Long la2 = LBound(a, 2) : Dim As Long ua2 = UBound(a, 2) Dim As Long lb1 = LBound(b, 1) : Dim As Long ub1 = UBound(b, 1) Dim As Long lb2 = LBound(b, 2) : Dim As Long ub2 = UBound(b, 2)
For i = la1 To ua1
For k = lb1 To ub1
Print "[";
For j = la2 To ua2
For l = lb2 To ub2
Print Using frmt; a(i, j) * b(k, l);
If j = ua1 And l = ub2 Then
Print "]"
Else
Print " ";
End If
Next
Next
Next
Next
End Sub
' ------=< MAIN >=-----
Dim As Long a(1 To 2, 1 To 2) = {{1, 2}, _
{3, 4}}
Dim As Long b(1 To 2, 1 To 2) = {{0, 5}, _
{6, 7}}
kronecker_product(a(), b(), "##")
Print Dim As Long x(1 To 3, 1 To 3) = {{0, 1, 0}, _
{1, 1, 1}, _
{0, 1, 0}}
Dim As Long y(1 To 3, 1 To 4) = {{1, 1, 1, 1}, _
{1, 0, 0, 1}, _
{1, 1, 1, 1}}
kronecker_product(x(), y())
' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</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]
Perl 6
<lang perl6>sub kronecker_product ( @a, @b ) {
return (@a X @b).map: { .[0].list X* .[1].list };
}
.say for kronecker_product([ <1 2>, <3 4> ],
[ <0 5>, <6 7> ]);
say ; .say for kronecker_product([ <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)
PureBasic
<lang PureBasic>EnableExplicit DataSection
Matrix_A_B_Dimension_Bsp1: Data.i 2,2,?MatrixA_Werte_Bsp1,2,2,?MatrixB_Werte_Bsp1 Matrix_A_B_Dimension_Bsp2: Data.i 3,3,?MatrixA_Werte_Bsp2,3,4,?MatrixB_Werte_Bsp2 MatrixA_Werte_Bsp1: Data.i 1,2,3,4 MatrixA_Werte_Bsp2: Data.i 0,1,0,1,1,1,0,1,0 MatrixB_Werte_Bsp1: Data.i 0,5,6,7 MatrixB_Werte_Bsp2: Data.i 1,1,1,1,1,0,0,1,1,1,1,1
EndDataSection
Define.i ma, na, mb, nb, adr1, adr2, i, j, k, l Define mk$
Gosub Bsp1_Matrix_A_B : Gosub LoadMatrix : Gosub Bsp2_Matrix_A_B : Gosub LoadMatrix : End
LoadMatrix: Read.i ma Read.i na Read.i adr1 Read.i mb Read.i nb Read.i adr2
Dim mxa.i(ma,na) Dim mxb.i(mb,nb) NewMap mxc.i()
For i=1 To ma
For j=1 To na mxa(i,j)=PeekI(adr1) adr1+SizeOf(Integer) Next
Next
For i=1 To mb
For j=1 To nb mxb(i,j)=PeekI(adr2) adr2+SizeOf(Integer) Next
Next
OpenConsole("Kronecker product") PrintN("Matrix A:") For i=1 To ma ; Zeile
Print("|")
For j=1 To na ; Spalte
Print(RSet(Str(mxa(i,j)),2," ")+" ")
Next
PrintN("|")
Next PrintN("")
PrintN("Matrix B:") For i=1 To mb ; Zeile
Print("|")
For j=1 To nb ; Spalte
Print(RSet(Str(mxb(i,j)),2," ")+" ")
Next
PrintN("|")
Next PrintN("")
PrintN("Matrix C=AxB") For i=1 To ma ; Zeile MA
For j=1 To na ; Spalte MA
For k=1 To mb ; Zeile MB
For l=1 To nb ; Spalte MB
mxc(Str(i)+","+Str(j)+","+Str(k)+","+Str(l))=mxa(i,j)*mxb(k,l)
Next
Next
Next
Next
For i=1 To ma ; Zeile MA
For k=1 To mb; Zeile MB
Print("|")
For j=1 To na ; Spalte MA
For l=1 To nb ; Spalte MB
mk$=Str(i)+","+Str(j)+","+Str(k)+","+Str(l)
If FindMapElement(mxc(),mk$)
Print(RSet(Str(mxc()),2," ")+" ")
EndIf
Next
Next
PrintN("|")
Next
Next PrintN("Press return") : Input() Return
Bsp1_Matrix_A_B:
Restore Matrix_A_B_Dimension_Bsp1
Return
Bsp2_Matrix_A_B:
Restore Matrix_A_B_Dimension_Bsp2
Return</lang>
- Output:
Matrix A: | 1 2 | | 3 4 | Matrix B: | 0 5 | | 6 7 | Matrix C=AxB | 0 5 0 10 | | 6 7 12 14 | | 0 15 0 20 | |18 21 24 28 | Press return 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 | Matrix C=AxB | 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 | Press return
Python
<lang Python>
- !/usr/bin/env python3
- Sample 1
a1 = [[1, 2], [3, 4]] b1 = [[0, 5], [6, 7]]
- Sample 2
a2 = [[0, 1, 0], [1, 1, 1], [0, 1, 0]] b2 = [[1, 1, 1, 1], [1, 0, 0, 1], [1, 1, 1, 1]]
def kronecker(matrix1, matrix2):
final_list = [] sub_list = []
count = len(matrix2)
for elem1 in matrix1:
counter = 0
check = 0
while check < count:
for num1 in elem1:
for num2 in matrix2[counter]:
sub_list.append(num1 * num2)
counter += 1
final_list.append(sub_list)
sub_list = []
check +=1
return final_list
- Result 1
result1 = kronecker(a1, b1) for elem in result1:
print(elem)
print("")
- Result 2
result2 = kronecker(a2, b2) for elem in result2:
print(elem)
</lang>
Result:
[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]
R
R has built-in Kronecker product operator for a and b matrices: a %x% b. <lang r>
- Sample using:
a <- matrix(c(1,1,1,1), ncol=2, nrow=2, byrow=TRUE); b <- matrix(c(0,1,1,0), ncol=2, nrow=2, byrow=TRUE); a %x% b </lang>
- Output:
[,1] [,2] [,3] [,4] [1,] 0 1 0 1 [2,] 1 0 1 0 [3,] 0 1 0 1 [4,] 1 0 1 0 Note: This resultant matrix could be used as initial for Checkerboard fractal.
REXX
A little extra coding was added to make the matrix glyphs and element alignment look nicer. <lang rexx>/*REXX program calculates the Kronecker product of two arbitrary size matrices. */ w=0 /*W: max width of any matrix element. */
aMat= 2x2 1 2 3 4 /*define A matrix size and elements.*/
bMat= 2x2 0 5 6 7 /* " B " " " " */
call makeMat 'A', aMat /*construct A matrix from elements.*/ call makeMat 'B', bMat /* " B " " " */ call KronMat 'Kronecker product' /*calculate the Kronecker produect. */ w=0; say; say copies('░', 55); say /*display a fence between the 2 outputs*/
aMat= 3x3 0 1 0 1 1 1 0 1 0 /*define A matrix size and elements.*/
bMat= 3x4 1 1 1 1 1 0 0 1 1 1 1 1 /* " B " " " " */
call makeMat 'A', aMat /*construct A matrix from elements.*/ call makeMat 'B', bMat /* " B " " " */ call KronMat 'Kronecker product' /*calculate the Kronecker produect. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ KronMat: parse arg what; #=0; parse var @.a.shape aRows aCols
parse var @.b.shape bRows bCols
do rA=1 for aRows
do rB=1 for bRows; #=#+1; ##=0; _=
do cA=1 for aCols; x=@.a.rA.cA
do cB=1 for bCols; y=@.b.rB.cB; ##=##+1; xy=x*y; _=_ xy
@.what.#.##=xy; w=max(w, length(xy) )
end /*cB*/
end /*cA*/
end /*rB*/
end /*rA*/
call showMat what, aRows*bRows || 'X' || aRows*bCols; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ makeMat: parse arg what, size elements; arg , row 'X' col .; @.what.shape= row col
#=0; do r=1 for row /* [↓] bump item#; get item; max width*/
do c=1 for col; #=#+1; _=word(elements, #); w=max(w, length(_) )
@.what.r.c=_
end /*c*/ /* [↑] define an element of WHAT matrix*/
end /*r*/
call showMat what, size; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ showMat: parse arg what, size .; z='┌'; parse var size row 'X' col; $=left(, 6)
say; say $ copies('═',7) 'matrix' what copies('═',7)
do r=1 for row; _= '│'
do c=1 for col; _=_ right(@.what.r.c, w); if r==1 then z=z left(,w)
end /*c*/
if r==1 then do; z=z '┐'; say $ $ z; end /*show the top part of matrix.*/
say $ $ _ '│'
end /*r*/
say $ $ translate(z, '└┘', "┌┐"); return /*show the bot part of matrix.*/</lang>
- output when using the default inputs:
═══════ matrix A ═══════
┌ ┐
│ 1 2 │
│ 3 4 │
└ ┘
═══════ matrix B ═══════
┌ ┐
│ 0 5 │
│ 6 7 │
└ ┘
═══════ matrix 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 │
└ ┘
═══════ matrix 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 │
└ ┘
Sidef
<lang ruby>func kronecker_product(a, b) {
a ~X b -> map { _[0] ~X* _[1] }
}
kronecker_product([[1, 2], [3, 4]],
[[0, 5], [6, 7]]).each { .say }
say kronecker_product([[0,1,0], [1,1,1], [0,1,0]],
[[1,1,1,1],[1,0,0,1], [1,1,1,1]]).each { .say }</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]
SuperCollider
<lang SuperCollider>// the iterative version is derived from the javascript one here: ( f = { |a, b| var m = a.size; var n = a[0].size; var p = b.size; var q = b[0].size; var rtn = m * p; var ctn = n * q; var res = { 0.dup(ctn) }.dup(rtn); m.do { |i| n.do { |j| p.do { |k| q.do { |l| res[p*i+k][q*j+l] = a[i][j] * b[k][l]; } } } }; res }; )
// Like APL/J, SuperCollider has applicative operators, so here is a shorter version. // the idea is to first replace every element of b with its product with all of a // and then reshape the matrix appropriately // note that +++ is lamination: [[1, 2, 3], [4, 5, 6]] +++ [100, 200] returns [ [ 1, 2, 3, 100 ], [ 4, 5, 6, 200 ] ].
( f = { |a, b| a.collect { |x| x.collect { |y| b * y }.reduce('+++') }.reduce('++') } )
// to apply either of the two functions: ( x = f.( [ [0, 1, 0], [1, 1, 1], [0, 1, 0] ], [ [1, 1, 1, 1], [1, 0, 0, 1], [1, 1, 1, 1] ] ) ) </lang>
Results in:
[ [ 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 ] ]
Tcl
<lang Tcl># some helpers for matrices in nice string form: proc parse_matrix {s} {
split [string trim $s] \n
}
proc print_matrix {m} {
foreach row $m {
puts [join [lmap x $row {format %3s $x}]]
}
}
- obvious imperative version using [foreach]
proc kroenecker {A B} {
foreach arow $A {
foreach brow $B {
set row {}
foreach a $arow {
foreach b $brow {
lappend row [expr {$a * $b}]
}
}
lappend result $row
}
}
return $result
}
proc lolcat {args} { ;# see https://wiki.tcl.tk/41507
concat {*}[uplevel 1 lmap $args]
}
- more compact but obtuse, using [lmap] and [lolcat]
proc kroenecker {A B} {
lolcat arow $A {
lmap brow $B {
lolcat a $arow {
lmap b $brow {
expr {$a * $b}
}
}
}
}
}
- demo:
set inputs {
{1 2
3 4}
{0 5
6 7}
{0 1 0
1 1 1
0 1 0}
{1 1 1 1
1 0 0 1
1 1 1 1}
}
foreach {a b} $inputs {
set a [parse_matrix $a] set b [parse_matrix $b] print_matrix [kroenecker $a $b] puts ""
}</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
VBScript
<lang vb>' Kronecker product - 05/04/2017 dim a(),b(),r()
sub kroneckerproduct '(a,b)
m=ubound(a,1): n=ubound(a,2)
p=ubound(b,1): q=ubound(b,2)
rtn=m*p
ctn=n*q
redim r(rtn,ctn)
for i=1 to m
for j=1 to n
for k=1 to p
for l=1 to q
r(p*(i-1)+k,q*(j-1)+l)=a(i,j)*b(k,l)
next: next: next: next
end sub 'kroneckerproduct
sub printmatrix(text,m,w)
wscript.stdout.writeline text
select case m
case "a": ni=ubound(a,1): nj=ubound(a,2)
case "b": ni=ubound(b,1): nj=ubound(b,2)
case "r": ni=ubound(r,1): nj=ubound(r,2)
end select
for i=1 to ni
for j=1 to nj
select case m
case "a": k=a(i,j)
case "b": k=b(i,j)
case "r": k=r(i,j)
end select
wscript.stdout.write right(space(w)&k,w)
next
wscript.stdout.writeline
next
end sub 'printmatrix
sub printall(w)
printmatrix "matrix a:", "a", w printmatrix "matrix b:", "b", w printmatrix "kronecker product:", "r", w
end sub 'printall
sub main()
xa=array( 1, 2, _
3, 4)
redim a(2,2)
k=0: for i=1 to ubound(a,1): for j=1 to ubound(a,1)
a(i,j)=xa(k): k=k+1
next:next
xb=array( 0, 5, _
6, 7)
redim b(2,2)
k=0: for i=1 to ubound(b,1): for j=1 to ubound(b,1)
b(i,j)=xb(k): k=k+1
next:next
kroneckerproduct
printall 3
xa=array( 0, 1, 0, _
1, 1, 1, _
0, 1, 0)
redim a(3,3)
k=0: for i=1 to ubound(a,1): for j=1 to ubound(a,1)
a(i,j)=xa(k): k=k+1
next:next
xb=array( 1, 1, 1, 1, _
1, 0, 0, 1, _
1, 1, 1, 1)
redim b(3,4)
k=0: for i=1 to ubound(b,1): for j=1 to ubound(b,1)
b(i,j)=xb(k): k=k+1
next:next
kroneckerproduct
printall 2
end sub 'main
main</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 kronecker product: 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
zkl
<lang zkl>var [const] GSL=Import.lib("zklGSL"); // libGSL (GNU Scientific Library) fcn kronecker(A,B){
m,n, p,q := A.rows,A.cols, B.rows,B.cols;
r:=GSL.Matrix(m*p, n*q);
foreach i,j,k,l in (m,n,p,q){ r[p*i + k, q*j + l]=A[i,j]*B[k,l] }
r
}</lang> <lang zkl>A:=GSL.Matrix(2,2).set(1,2, 3,4); B:=GSL.Matrix(2,2).set(0,5, 6,7); kronecker(A,B).format(3,0).println(); // format(width,precision)
A:=GSL.Matrix(3,3).set(0,1,0, 1,1,1, 0,1,0); B:=GSL.Matrix(3,4).set(1,1,1,1, 1,0,0,1, 1,1,1,1); kronecker(A,B).format(2,0).println();</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