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

6       DSTEQR  -  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 DSTEQR( 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( * ), Z( LDZ, * )
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PURPOSE

19       DSTEQR computes all eigenvalues and, optionally, eigenvectors of a sym‐
20       metric  tridiagonal  matrix  using  the  implicit QL or QR method.  The
21       eigenvectors of a full or band symmetric matrix can also  be  found  if
22       DSYTRD  or  DSPTRD  or  DSBTRD  has  been used to reduce this matrix to
23       tridiagonal form.
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ARGUMENTS

27       COMPZ   (input) CHARACTER*1
28               = 'N':  Compute eigenvalues only.
29               = 'V':  Compute eigenvalues and eigenvectors  of  the  original
30               symmetric  matrix.   On  entry,  Z  must contain the orthogonal
31               matrix used to reduce the original matrix to tridiagonal  form.
32               = 'I':  Compute eigenvalues and eigenvectors of the tridiagonal
33               matrix.  Z is initialized to the identity matrix.
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35       N       (input) INTEGER
36               The order of the matrix.  N >= 0.
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38       D       (input/output) DOUBLE PRECISION array, dimension (N)
39               On entry, the diagonal elements of the tridiagonal matrix.   On
40               exit, if INFO = 0, the eigenvalues in ascending order.
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42       E       (input/output) DOUBLE PRECISION array, dimension (N-1)
43               On  entry,  the  (n-1)  subdiagonal elements of the tridiagonal
44               matrix.  On exit, E has been destroyed.
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46       Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
47               On entry, if  COMPZ =  'V',  then  Z  contains  the  orthogonal
48               matrix  used in the reduction to tridiagonal form.  On exit, if
49               INFO = 0, then if  COMPZ =  'V',  Z  contains  the  orthonormal
50               eigenvectors  of  the original symmetric matrix, and if COMPZ =
51               'I', Z contains the orthonormal eigenvectors of  the  symmetric
52               tridiagonal matrix.  If COMPZ = 'N', then Z is not referenced.
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54       LDZ     (input) INTEGER
55               The  leading dimension of the array Z.  LDZ >= 1, and if eigen‐
56               vectors are desired, then  LDZ >= max(1,N).
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58       WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
59               If COMPZ = 'N', then WORK is not referenced.
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61       INFO    (output) INTEGER
62               = 0:  successful exit
63               < 0:  if INFO = -i, the i-th argument had an illegal value
64               > 0:  the algorithm has failed to find all the eigenvalues in a
65               total  of  30*N  iterations;  if INFO = i, then i elements of E
66               have not converged to zero; on exit, D and E contain  the  ele‐
67               ments  of  a symmetric tridiagonal matrix which is orthogonally
68               similar to the original matrix.
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72 LAPACK routine (version 3.1)    November 2006                       DSTEQR(1)