2 COMMENT THIRD EXAMPLE PROGRAM FROM BALGOL MANUAL, MARCH 1963.
2
2 THE SHORT PROGRAM WHICH FOLLOWS IS FOR A REDUCTION OF A SQUARE MATRIX
2 TO TRIDIAGONAL FORM, USING THE METHOD OF HOUSEHOLDER;
2
2 COMMENT HOUSEHOLDER REDUCTION TO TRIDIAGONAL FORM;
2 INTEGER I, J, K, L, R, N;
2 ARRAY A(50,50), X(50), P(50);
2 INPUT
2   ELEMENT (I, J, Q);
2 OUTPUT
2   AOUT (A(R,R)),
2   BOUT (-0.5/S);
2 FORMAT
2   AF (B10, X10.5, W),
2   BF (B40, X10.5, W);
2
2   N = 5;
2 IN..
2   READ (;; ELEMENT);
2   IF I NEQ 0;
2     BEGIN
2     A(I,J) = Q;
2     GO TO IN
2     END;
2
2   FOR R = (1,1,N-1);
2     BEGIN
2     WRITE (;; AOUT, AF);
2     L = R+1;
2     S = 0;
2     FOR J = (L,1,N);
2       S = S + A(R,J)*2;
2
2     S = SIGN(A(R,L))/2SQRT(S);
2     WRITE (;; BOUT, BF);
2     X(L) = SQRT(0.5 + A(R,L).S);
2     S = S/X(L);
2     FOR J = (R+2,1,N);
2       X(J) = S.A(R,J);
2     FOR J = (R,1,N);
2       BEGIN
2       S = 0;
2       FOR K = (L,1,N);
2         S = S + A(MIN(J,K), MAX(J,K)).X(K);
2       P(J) = S
2       END;
2
2     S = 0;
2     FOR J = (L,1,N);
2       S = S + X(J).P(J);                                                      * X(J) WAS K(J)
2     FOR J = (L,1,N);
2       P(J) = P(J) - S.X(J);
2     FOR J = (L,1,N);
2       FOR K = (J,1,N);
2         A(J,K) = A(J,K) - 2(X(J).P(K) + X(K).P(J))
2     END;
2
2   WRITE (;; AOUT, AF);
2   STOP;
2   GO TO IN;
2 FINISH;
5 1 1   4.0
5 1 2   1.0
5 1 3  -2.0
5 1 4   2.0
5 1 5   1.0
5 2 1   1.0
5 2 2   2.0
5 2 3   0.0
5 2 4   1.0
5 2 5   1.0
5 3 1  -2.0
5 3 2   0.0
5 3 3   3.0
5 3 4  -2.0
5 3 5   1.0
5 4 1   2.0
5 4 2   1.0
5 4 3  -2.0
5 4 4  -1.0
5 4 5   1.0
5 5 1   1.0
5 5 2   1.0
5 5 3   1.0
5 5 4   1.0
5 5 5   1.0
5 0 0   0.0