1SSBEV(1)              LAPACK driver routine (version 3.1)             SSBEV(1)
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NAME

6       SSBEV  -  all  the  eigenvalues and, optionally, eigenvectors of a real
7       symmetric band matrix A
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SYNOPSIS

10       SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO )
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12           CHARACTER     JOBZ, UPLO
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14           INTEGER       INFO, KD, LDAB, LDZ, N
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16           REAL          AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
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PURPOSE

19       SSBEV computes all the eigenvalues and, optionally, eigenvectors  of  a
20       real symmetric band matrix A.
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ARGUMENTS

24       JOBZ    (input) CHARACTER*1
25               = 'N':  Compute eigenvalues only;
26               = 'V':  Compute eigenvalues and eigenvectors.
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28       UPLO    (input) CHARACTER*1
29               = 'U':  Upper triangle of A is stored;
30               = 'L':  Lower triangle of A is stored.
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32       N       (input) INTEGER
33               The order of the matrix A.  N >= 0.
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35       KD      (input) INTEGER
36               The  number of superdiagonals of the matrix A if UPLO = 'U', or
37               the number of subdiagonals if UPLO = 'L'.  KD >= 0.
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39       AB      (input/output) REAL array, dimension (LDAB, N)
40               On entry, the upper or lower triangle  of  the  symmetric  band
41               matrix A, stored in the first KD+1 rows of the array.  The j-th
42               column of A is stored in the j-th column of  the  array  AB  as
43               follows:  if  UPLO  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
44               kd)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
45               j<=i<=min(n,j+kd).
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47               On  exit,  AB  is  overwritten  by  values generated during the
48               reduction to tridiagonal form.  If UPLO = 'U', the first super‐
49               diagonal  and  the  diagonal  of  the  tridiagonal matrix T are
50               returned in rows KD and KD+1 of AB, and  if  UPLO  =  'L',  the
51               diagonal  and  first subdiagonal of T are returned in the first
52               two rows of AB.
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54       LDAB    (input) INTEGER
55               The leading dimension of the array AB.  LDAB >= KD + 1.
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57       W       (output) REAL array, dimension (N)
58               If INFO = 0, the eigenvalues in ascending order.
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60       Z       (output) REAL array, dimension (LDZ, N)
61               If JOBZ = 'V', then if INFO = 0,  Z  contains  the  orthonormal
62               eigenvectors of the matrix A, with the i-th column of Z holding
63               the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
64               not referenced.
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66       LDZ     (input) INTEGER
67               The  leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
68               'V', LDZ >= max(1,N).
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70       WORK    (workspace) REAL array, dimension (max(1,3*N-2))
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72       INFO    (output) INTEGER
73               = 0:  successful exit
74               < 0:  if INFO = -i, the i-th argument had an illegal value
75               > 0:  if INFO = i, the algorithm failed  to  converge;  i  off-
76               diagonal  elements  of an intermediate tridiagonal form did not
77               converge to zero.
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81 LAPACK driver routine (version 3.N1o)vember 2006                        SSBEV(1)