DLASQ1 computes the singular values of a real N-by-N bidiagonal


 matrix with diagonal D and off-diagonal E. The singular values


 are computed to high relative accuracy, in the absence of


 denormalization, underflow and overflow. The algorithm was first


 presented in


 'Accurate singular values and differential qd algorithms' by K. V.


 Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,


 1994,


 and the present implementation is described in 'An implementation of


 the dqds Algorithm (Positive Case)', LAPACK Working Note.

N

          N is INTEGER


        The number of rows and columns in the matrix. N >= 0.

D

          D is DOUBLE PRECISION array, dimension (N)


        On entry, D contains the diagonal elements of the


        bidiagonal matrix whose SVD is desired. On normal exit,


        D contains the singular values in decreasing order.

E

          E is DOUBLE PRECISION array, dimension (N)


        On entry, elements E(1:N-1) contain the off-diagonal elements


        of the bidiagonal matrix whose SVD is desired.


        On exit, E is overwritten.

WORK

          WORK is DOUBLE PRECISION array, dimension (4*N)

INFO

          INFO is INTEGER


        = 0: successful exit


        < 0: if INFO = -i, the i-th argument had an illegal value


        > 0: the algorithm failed


             = 1, a split was marked by a positive value in E


             = 2, current block of Z not diagonalized after 100*N


                  iterations (in inner while loop)  On exit D and E


                  represent a matrix with the same singular values


                  which the calling subroutine could use to finish the


                  computation, or even feed back into DLASQ1


             = 3, termination criterion of outer while loop not met


                  (program created more than N unreduced blocks)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 SLASQ1 computes the singular values of a real N-by-N bidiagonal


 matrix with diagonal D and off-diagonal E. The singular values


 are computed to high relative accuracy, in the absence of


 denormalization, underflow and overflow. The algorithm was first


 presented in


 'Accurate singular values and differential qd algorithms' by K. V.


 Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,


 1994,


 and the present implementation is described in 'An implementation of


 the dqds Algorithm (Positive Case)', LAPACK Working Note.

N

          N is INTEGER


        The number of rows and columns in the matrix. N >= 0.

D

          D is REAL array, dimension (N)


        On entry, D contains the diagonal elements of the


        bidiagonal matrix whose SVD is desired. On normal exit,


        D contains the singular values in decreasing order.

E

          E is REAL array, dimension (N)


        On entry, elements E(1:N-1) contain the off-diagonal elements


        of the bidiagonal matrix whose SVD is desired.


        On exit, E is overwritten.

WORK

          WORK is REAL array, dimension (4*N)

INFO

          INFO is INTEGER


        = 0: successful exit


        < 0: if INFO = -i, the i-th argument had an illegal value


        > 0: the algorithm failed


             = 1, a split was marked by a positive value in E


             = 2, current block of Z not diagonalized after 100*N


                  iterations (in inner while loop)  On exit D and E


                  represent a matrix with the same singular values


                  which the calling subroutine could use to finish the


                  computation, or even feed back into SLASQ1


             = 3, termination criterion of outer while loop not met


                  (program created more than N unreduced blocks)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.