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

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

10       SUBROUTINE CSTEQR( 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           REAL           D( * ), E( * ), WORK( * )
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18           COMPLEX        Z( LDZ, * )
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PURPOSE

21       CSTEQR 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 CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix
25       to tridiagonal form.
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ARGUMENTS

28       COMPZ   (input) CHARACTER*1
29               = 'N':  Compute eigenvalues only.
30               = 'V':  Compute eigenvalues and eigenvectors  of  the  original
31               Hermitian  matrix.  On entry, Z must contain the unitary matrix
32               used to reduce the original matrix to tridiagonal form.  = 'I':
33               Compute eigenvalues and eigenvectors of the tridiagonal matrix.
34               Z is initialized to the identity matrix.
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36       N       (input) INTEGER
37               The order of the matrix.  N >= 0.
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39       D       (input/output) REAL array, dimension (N)
40               On entry, the diagonal elements of the tridiagonal matrix.   On
41               exit, if INFO = 0, the eigenvalues in ascending order.
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43       E       (input/output) REAL array, dimension (N-1)
44               On  entry,  the  (n-1)  subdiagonal elements of the tridiagonal
45               matrix.  On exit, E has been destroyed.
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47       Z       (input/output) COMPLEX array, dimension (LDZ, N)
48               On entry, if  COMPZ = 'V', then Z contains the  unitary  matrix
49               used  in the reduction to tridiagonal form.  On exit, if INFO =
50               0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
51               of  the  original  Hermitian matrix, and if COMPZ = 'I', Z con‐
52               tains the orthonormal eigenvectors of the symmetric tridiagonal
53               matrix.  If COMPZ = 'N', then Z is not referenced.
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55       LDZ     (input) INTEGER
56               The  leading dimension of the array Z.  LDZ >= 1, and if eigen‐
57               vectors are desired, then  LDZ >= max(1,N).
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59       WORK    (workspace) REAL array, dimension (max(1,2*N-2))
60               If COMPZ = 'N', then WORK is not referenced.
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62       INFO    (output) INTEGER
63               = 0:  successful exit
64               < 0:  if INFO = -i, the i-th argument had an illegal value
65               > 0:  the algorithm has failed to find all the eigenvalues in a
66               total  of  30*N  iterations;  if INFO = i, then i elements of E
67               have not converged to zero; on exit, D and E contain  the  ele‐
68               ments of a symmetric tridiagonal matrix which is unitarily sim‐
69               ilar to the original matrix.
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73 LAPACK routine (version 3.2)    November 2008                       CSTEQR(1)