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

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

10       SUBROUTINE DSBEV( 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           DOUBLE        PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, *
17                         )
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PURPOSE

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

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