Kronecker product: Difference between revisions

</pre>

=={{header|Simula}}==

<lang simula>BEGIN

PROCEDURE OUTMATRIX(A, W); INTEGER ARRAY A; INTEGER W;

BEGIN

INTEGER I, J;

INTEGER LA1, UA1;

INTEGER LA2, UA2;

LA1 := LOWERBOUND(A, 1); UA1 := UPPERBOUND(A, 1);

LA2 := LOWERBOUND(A, 2); UA2 := UPPERBOUND(A, 2);

FOR I := LA1 STEP 1 UNTIL UA1 DO

BEGIN

OUTTEXT("[");

FOR J := LA2 STEP 1 UNTIL UA2 DO

BEGIN

IF NOT (J = LA2) THEN OUTCHAR(' ');

OUTINT(A(I, J), W)

END;

OUTTEXT("]");

OUTIMAGE

END

END OUTMATRIX;

PROCEDURE KRONECKERPRODUCT(A, B, C); INTEGER ARRAY A, B, C;

BEGIN

INTEGER I, J, K, L, CI, CJ;

INTEGER LA1, UA1;

INTEGER LA2, UA2;

INTEGER LB1, UB1;

INTEGER LB2, UB2;

LA1 := LOWERBOUND(A, 1); UA1 := UPPERBOUND(A, 1);

LA2 := LOWERBOUND(A, 2); UA2 := UPPERBOUND(A, 2);

LB1 := LOWERBOUND(B, 1); UB1 := UPPERBOUND(B, 1);

LB2 := LOWERBOUND(B, 2); UB2 := UPPERBOUND(B, 2);

CI := 1;

FOR I := LA1 STEP 1 UNTIL UA1 DO

FOR K := LB1 STEP 1 UNTIL UB1 DO

BEGIN

CJ := 1;

FOR J := LA2 STEP 1 UNTIL UA2 DO

FOR L := LB2 STEP 1 UNTIL UB2 DO

BEGIN

C(CI, CJ) := A(I, J) * B(K, L);

CJ := CJ + 1

END;

CI := CI + 1

END

END KRONECKERPRODUCT;

! --- EXAMPLE 1 --- ;

BEGIN

INTEGER ARRAY A(1:2, 1:2);

INTEGER ARRAY B(1:2, 1:2);

INTEGER ARRAY C(1:4, 1:4);

! {{1, 2}, {3, 4}} ;

A(1, 1) := 1;

A(1, 2) := 2;

A(2, 1) := 3;

A(2, 2) := 4;

! {{0, 5}, {6, 7}} ;

B(1, 1) := 0;

B(1, 2) := 5;

B(2, 1) := 6;

B(2, 2) := 7;

OUTMATRIX(A, 2); OUTTEXT(" *"); OUTIMAGE;

OUTMATRIX(B, 2); OUTTEXT(" ="); OUTIMAGE;

KRONECKERPRODUCT(A, B, C);

OUTMATRIX(C, 2); OUTIMAGE

! OUTPUT:

! [ 0 5 0 10]

! [ 6 7 12 14]

! [ 0 15 0 20]

! [18 21 24 28] ;

END EXAMPLE 1;

! --- EXAMPLE 2 --- ;

BEGIN

INTEGER ARRAY X(1:3, 1:3);

INTEGER ARRAY Y(1:3, 1:4);

INTEGER ARRAY C(1:9, 1:12);

! {{0, 1, 0}, {1, 1, 1}, {0, 1, 0}} ;

X(1,1) := 0;

X(1,2) := 1;

X(1,3) := 0;

X(2,1) := 1;

X(2,2) := 1;

X(2,3) := 1;

X(3,1) := 0;

X(3,2) := 1;

X(3,3) := 0;

! {{1, 1, 1, 1}, {1, 0, 0, 1}, {1, 1, 1, 1}} ;

Y(1,1) := 1;

Y(1,2) := 1;

Y(1,3) := 1;

Y(1,4) := 1;

Y(2,1) := 1;

Y(2,2) := 0;

Y(2,3) := 0;

Y(2,4) := 1;

Y(3,1) := 1;

Y(3,2) := 1;

Y(3,3) := 1;

Y(3,4) := 1;

OUTIMAGE;

OUTMATRIX(X, 1); OUTTEXT(" *"); OUTIMAGE;

OUTMATRIX(Y, 1); OUTTEXT(" ="); OUTIMAGE;

KRONECKERPRODUCT(X, Y, C);

OUTMATRIX(C, 1); OUTIMAGE;

! OUTPUT:

! [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] ;

END EXAMPLE 2;

END</lang>

{{out}}

<pre>

[ 1 2]

[ 3 4]

*

[ 0 5]

[ 6 7]

=

[ 0 5 0 10]

[ 6 7 12 14]

[ 0 15 0 20]

[18 21 24 28]

[0 1 0]

[1 1 1]

[0 1 0]

*

[1 1 1 1]

[1 0 0 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]

[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]