1DLASQ1(1)                LAPACK routine (version 3.1)                DLASQ1(1)
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NAME

6       DLASQ1  -  the  singular values of a real N-by-N bidiagonal matrix with
7       diagonal D and off-diagonal E
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SYNOPSIS

10       SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
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12           INTEGER        INFO, N
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14           DOUBLE         PRECISION D( * ), E( * ), WORK( * )
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PURPOSE

17       DLASQ1 computes the singular values of a real N-by-N bidiagonal  matrix
18       with diagonal D and off-diagonal E. The singular values are computed to
19       high relative accuracy, in the absence  of  denormalization,  underflow
20       and overflow. The algorithm was first presented in
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22       "Accurate  singular  values  and  differential  qd algorithms" by K. V.
23       Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2,  pp.  191-230,
24       1994,
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26       and  the  present  implementation is described in "An implementation of
27       the dqds Algorithm (Positive Case)", LAPACK Working Note.
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ARGUMENTS

31       N     (input) INTEGER
32             The number of rows and columns in the matrix. N >= 0.
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34       D     (input/output) DOUBLE PRECISION array, dimension (N)
35             On entry, D contains the  diagonal  elements  of  the  bidiagonal
36             matrix  whose SVD is desired. On normal exit, D contains the sin‐
37             gular values in decreasing order.
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39       E     (input/output) DOUBLE PRECISION array, dimension (N)
40             On entry, elements E(1:N-1) contain the off-diagonal elements  of
41             the  bidiagonal matrix whose SVD is desired.  On exit, E is over‐
42             written.
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44       WORK  (workspace) DOUBLE PRECISION array, dimension (4*N)
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46       INFO  (output) INTEGER
47             = 0: successful exit
48             < 0: if INFO = -i, the i-th argument had an illegal value
49             > 0: the algorithm failed = 1, a split was marked by  a  positive
50             value  in  E  = 2, current block of Z not diagonalized after 30*N
51             iterations (in inner while loop) = 3,  termination  criterion  of
52             outer  while  loop not met (program created more than N unreduced
53             blocks)
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57 LAPACK routine (version 3.1)    November 2006                       DLASQ1(1)