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

6       ZSTEQR  -  all eigenvalues and, optionally, eigenvectors of a symmetric
7       tridiagonal matrix using the implicit QL or QR method
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SYNOPSIS

10       SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
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12           CHARACTER      COMPZ
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14           INTEGER        INFO, LDZ, N
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16           DOUBLE         PRECISION D( * ), E( * ), WORK( * )
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18           COMPLEX*16     Z( LDZ, * )
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PURPOSE

21       ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a sym‐
22       metric  tridiagonal  matrix  using  the  implicit QL or QR method.  The
23       eigenvectors of a full or band complex Hermitian  matrix  can  also  be
24       found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix
25       to tridiagonal form.
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ARGUMENTS

29       COMPZ   (input) CHARACTER*1
30               = 'N':  Compute eigenvalues only.
31               = 'V':  Compute eigenvalues and eigenvectors  of  the  original
32               Hermitian  matrix.  On entry, Z must contain the unitary matrix
33               used to reduce the original matrix to tridiagonal form.  = 'I':
34               Compute eigenvalues and eigenvectors of the tridiagonal matrix.
35               Z is initialized to the identity matrix.
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37       N       (input) INTEGER
38               The order of the matrix.  N >= 0.
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40       D       (input/output) DOUBLE PRECISION array, dimension (N)
41               On entry, the diagonal elements of the tridiagonal matrix.   On
42               exit, if INFO = 0, the eigenvalues in ascending order.
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44       E       (input/output) DOUBLE PRECISION array, dimension (N-1)
45               On  entry,  the  (n-1)  subdiagonal elements of the tridiagonal
46               matrix.  On exit, E has been destroyed.
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48       Z       (input/output) COMPLEX*16 array, dimension (LDZ, N)
49               On entry, if  COMPZ = 'V', then Z contains the  unitary  matrix
50               used  in the reduction to tridiagonal form.  On exit, if INFO =
51               0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
52               of  the  original  Hermitian matrix, and if COMPZ = 'I', Z con‐
53               tains the orthonormal eigenvectors of the symmetric tridiagonal
54               matrix.  If COMPZ = 'N', then Z is not referenced.
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56       LDZ     (input) INTEGER
57               The  leading dimension of the array Z.  LDZ >= 1, and if eigen‐
58               vectors are desired, then  LDZ >= max(1,N).
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60       WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
61               If COMPZ = 'N', then WORK is not referenced.
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63       INFO    (output) INTEGER
64               = 0:  successful exit
65               < 0:  if INFO = -i, the i-th argument had an illegal value
66               > 0:  the algorithm has failed to find all the eigenvalues in a
67               total  of  30*N  iterations;  if INFO = i, then i elements of E
68               have not converged to zero; on exit, D and E contain  the  ele‐
69               ments of a symmetric tridiagonal matrix which is unitarily sim‐
70               ilar to the original matrix.
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74 LAPACK routine (version 3.1)    November 2006                       ZSTEQR(1)