1ZLAED0(1)                LAPACK routine (version 3.2)                ZLAED0(1)
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NAME

6       ZLAED0 - the divide and conquer method, ZLAED0 computes all eigenvalues
7       of a symmetric tridiagonal matrix which is one diagonal block of  those
8       from reducing a dense or band Hermitian matrix and corresponding eigen‐
9       vectors of the dense or band matrix
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SYNOPSIS

12       SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,  RWORK,  IWORK,
13                          INFO )
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15           INTEGER        INFO, LDQ, LDQS, N, QSIZ
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17           INTEGER        IWORK( * )
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19           DOUBLE         PRECISION D( * ), E( * ), RWORK( * )
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21           COMPLEX*16     Q( LDQ, * ), QSTORE( LDQS, * )
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PURPOSE

24       Using the divide and conquer method, ZLAED0 computes all eigenvalues of
25       a symmetric tridiagonal matrix which is one  diagonal  block  of  those
26       from reducing a dense or band Hermitian matrix and corresponding eigen‐
27       vectors of the dense or band matrix.
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ARGUMENTS

30       QSIZ   (input) INTEGER
31              The dimension of the unitary matrix  used  to  reduce  the  full
32              matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
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34       N      (input) INTEGER
35              The dimension of the symmetric tridiagonal matrix.  N >= 0.
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37       D      (input/output) DOUBLE PRECISION array, dimension (N)
38              On  entry,  the diagonal elements of the tridiagonal matrix.  On
39              exit, the eigenvalues in ascending order.
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41       E      (input/output) DOUBLE PRECISION array, dimension (N-1)
42              On entry, the off-diagonal elements of the  tridiagonal  matrix.
43              On exit, E has been destroyed.
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45       Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
46              On  entry,  Q must contain an QSIZ x N matrix whose columns uni‐
47              tarily orthonormal. It is a part  of  the  unitary  matrix  that
48              reduces the full dense Hermitian matrix to a (reducible) symmet‐
49              ric tridiagonal matrix.
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51       LDQ    (input) INTEGER
52              The leading dimension of the array Q.  LDQ >= max(1,N).
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54       IWORK  (workspace) INTEGER array,
55              the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N ( lg(
56              N ) = smallest integer k such that 2^k >= N )
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58       RWORK  (workspace) DOUBLE PRECISION array,
59              dimension  (1  +  3*N  + 2*N*lg N + 3*N**2) ( lg( N ) = smallest
60              integer k such that 2^k >= N  )  QSTORE  (workspace)  COMPLEX*16
61              array,  dimension (LDQS, N) Used to store parts of the eigenvec‐
62              tor matrix when the updating matrix multiplies take place.
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64       LDQS   (input) INTEGER
65              The leading dimension of the array QSTORE.  LDQS >= max(1,N).
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67       INFO   (output) INTEGER
68              = 0:  successful exit.
69              < 0:  if INFO = -i, the i-th argument had an illegal value.
70              > 0:  The algorithm failed to compute an eigenvalue while  work‐
71              ing  on  the  submatrix  lying  in  rows  and columns INFO/(N+1)
72              through mod(INFO,N+1).
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76 LAPACK routine (version 3.2)    November 2008                       ZLAED0(1)
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