LASQ1 - 5.2 English - 68552

LASQ1 computes the singular values of a real square bidiagonal matrix.

Used by sbdsqr.

Purpose:

 LASQ1 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.

Parameters:

• N – [in]

  N is INTEGER

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

• D – [inout]

  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 – [inout]

  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 – [out] WORK is REAL array, dimension (4*N)

• INFO – [out]

  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)