1CLAED0(1)                LAPACK routine (version 3.1)                CLAED0(1)
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NAME

6       CLAED0  - divide and conquer method, CLAED0 computes all eigenvalues of
7       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 CLAED0( 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           REAL           D( * ), E( * ), RWORK( * )
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21           COMPLEX        Q( LDQ, * ), QSTORE( LDQS, * )
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PURPOSE

24       Using the divide and conquer method, CLAED0 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

31       QSIZ   (input) INTEGER
32              The dimension of the unitary matrix  used  to  reduce  the  full
33              matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
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35       N      (input) INTEGER
36              The dimension of the symmetric tridiagonal matrix.  N >= 0.
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38       D      (input/output) REAL array, dimension (N)
39              On  entry,  the diagonal elements of the tridiagonal matrix.  On
40              exit, the eigenvalues in ascending order.
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42       E      (input/output) REAL array, dimension (N-1)
43              On entry, the off-diagonal elements of the  tridiagonal  matrix.
44              On exit, E has been destroyed.
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46       Q      (input/output) COMPLEX array, dimension (LDQ,N)
47              On  entry,  Q must contain an QSIZ x N matrix whose columns uni‐
48              tarily orthonormal. It is a part  of  the  unitary  matrix  that
49              reduces the full dense Hermitian matrix to a (reducible) symmet‐
50              ric tridiagonal matrix.
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52       LDQ    (input) INTEGER
53              The leading dimension of the array Q.  LDQ >= max(1,N).
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55       IWORK  (workspace) INTEGER array,
56              the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N ( lg(
57              N ) = smallest integer k such that 2^k >= N )
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59       RWORK  (workspace) REAL array,
60              dimension  (1  +  3*N  + 2*N*lg N + 3*N**2) ( lg( N ) = smallest
61              integer k such that 2^k >= N )
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63              QSTORE (workspace) COMPLEX array, dimension (LDQS,  N)  Used  to
64              store  parts  of the eigenvector matrix when the updating matrix
65              multiplies take place.
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67       LDQS   (input) INTEGER
68              The leading dimension of the array QSTORE.  LDQS >= max(1,N).
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70       INFO   (output) INTEGER
71              = 0:  successful exit.
72              < 0:  if INFO = -i, the i-th argument had an illegal value.
73              > 0:  The algorithm failed to compute an eigenvalue while  work‐
74              ing  on  the  submatrix  lying  in  rows  and columns INFO/(N+1)
75              through mod(INFO,N+1).
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79 LAPACK routine (version 3.1)    November 2006                       CLAED0(1)
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