1DLASD0(1)           LAPACK auxiliary routine (version 3.1)           DLASD0(1)
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NAME

6       DLASD0  -  divide  and  conquer  approach, DLASD0 computes the singular
7       value decomposition (SVD) of a real upper bidiagonal  N-by-M  matrix  B
8       with diagonal D and offdiagonal E, where M = N + SQRE
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SYNOPSIS

11       SUBROUTINE DLASD0( N,  SQRE,  D,  E,  U,  LDU, VT, LDVT, SMLSIZ, IWORK,
12                          WORK, INFO )
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14           INTEGER        INFO, LDU, LDVT, N, SMLSIZ, SQRE
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16           INTEGER        IWORK( * )
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18           DOUBLE         PRECISION D( * ), E( * ), U( LDU, * ), VT(  LDVT,  *
19                          ), WORK( * )
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PURPOSE

22       Using a divide and conquer approach, DLASD0 computes the singular value
23       decomposition (SVD) of a real upper bidiagonal  N-by-M  matrix  B  with
24       diagonal  D  and offdiagonal E, where M = N + SQRE.  The algorithm com‐
25       putes orthogonal matrices U and VT such that B = U * S * VT. The singu‐
26       lar values S are overwritten on D.
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28       A  related  subroutine,  DLASDA, computes only the singular values, and
29       optionally, the singular vectors in compact form.
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ARGUMENTS

33       N      (input) INTEGER
34              On entry, the row dimension  of  the  upper  bidiagonal  matrix.
35              This is also the dimension of the main diagonal array D.
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37       SQRE   (input) INTEGER
38              Specifies  the  column dimension of the bidiagonal matrix.  = 0:
39              The bidiagonal matrix has column dimension M = N;
40              = 1: The bidiagonal matrix has column dimension M = N+1;
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42       D      (input/output) DOUBLE PRECISION array, dimension (N)
43              On entry D contains the main diagonal of the bidiagonal  matrix.
44              On exit D, if INFO = 0, contains its singular values.
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46       E      (input) DOUBLE PRECISION array, dimension (M-1)
47              Contains  the  subdiagonal entries of the bidiagonal matrix.  On
48              exit, E has been destroyed.
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50       U      (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
51              On exit, U contains the left singular vectors.
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53       LDU    (input) INTEGER
54              On entry, leading dimension of U.
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56       VT     (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
57              On exit, VT' contains the right singular vectors.
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59       LDVT   (input) INTEGER
60              On entry, leading dimension of VT.
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62              SMLSIZ (input) INTEGER On entry, maximum size of the subproblems
63              at the bottom of the computation tree.
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65       IWORK  (workspace) INTEGER work array.
66              Dimension must be at least (8 * N)
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68       WORK   (workspace) DOUBLE PRECISION work array.
69              Dimension must be at least (3 * M**2 + 2 * M)
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71       INFO   (output) INTEGER
72              = 0:  successful exit.
73              < 0:  if INFO = -i, the i-th argument had an illegal value.
74              > 0:  if INFO = 1, an singular value did not converge
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FURTHER DETAILS

77       Based on contributions by
78          Ming Gu and Huan Ren, Computer Science Division, University of
79          California at Berkeley, USA
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84 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLASD0(1)