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

6       DSBTRD - a real symmetric band matrix A to symmetric tridiagonal form T
7       by an orthogonal similarity transformation
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SYNOPSIS

10       SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D,  E,  Q,  LDQ,  WORK,
11                          INFO )
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13           CHARACTER      UPLO, VECT
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15           INTEGER        INFO, KD, LDAB, LDQ, N
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17           DOUBLE         PRECISION  AB(  LDAB, * ), D( * ), E( * ), Q( LDQ, *
18                          ), WORK( * )
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PURPOSE

21       DSBTRD reduces a real symmetric band matrix A to symmetric  tridiagonal
22       form T by an orthogonal similarity transformation: Q**T * A * Q = T.
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ARGUMENTS

26       VECT    (input) CHARACTER*1
27               = 'N':  do not form Q;
28               = 'V':  form Q;
29               = 'U':  update a matrix X, by forming X*Q.
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31       UPLO    (input) CHARACTER*1
32               = 'U':  Upper triangle of A is stored;
33               = 'L':  Lower triangle of A is stored.
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35       N       (input) INTEGER
36               The order of the matrix A.  N >= 0.
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38       KD      (input) INTEGER
39               The  number of superdiagonals of the matrix A if UPLO = 'U', or
40               the number of subdiagonals if UPLO = 'L'.  KD >= 0.
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42       AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
43               On entry, the upper or lower triangle  of  the  symmetric  band
44               matrix A, stored in the first KD+1 rows of the array.  The j-th
45               column of A is stored in the j-th column of  the  array  AB  as
46               follows:  if  UPLO  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
47               kd)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
48               j<=i<=min(n,j+kd).   On  exit,  the diagonal elements of AB are
49               overwritten by the diagonal elements of the tridiagonal  matrix
50               T;  if KD > 0, the elements on the first superdiagonal (if UPLO
51               = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten
52               by  the off-diagonal elements of T; the rest of AB is overwrit‐
53               ten by values generated during the reduction.
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55       LDAB    (input) INTEGER
56               The leading dimension of the array AB.  LDAB >= KD+1.
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58       D       (output) DOUBLE PRECISION array, dimension (N)
59               The diagonal elements of the tridiagonal matrix T.
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61       E       (output) DOUBLE PRECISION array, dimension (N-1)
62               The off-diagonal elements of the tridiagonal matrix T:  E(i)  =
63               T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
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65       Q       (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
66               On  entry,  if VECT = 'U', then Q must contain an N-by-N matrix
67               X; if VECT = 'N' or 'V', then Q need not be set.
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69               On exit: if VECT = 'V', Q contains the N-by-N orthogonal matrix
70               Q;  if  VECT  = 'U', Q contains the product X*Q; if VECT = 'N',
71               the array Q is not referenced.
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73       LDQ     (input) INTEGER
74               The leading dimension of the array Q.  LDQ >= 1, and LDQ  >=  N
75               if VECT = 'V' or 'U'.
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77       WORK    (workspace) DOUBLE PRECISION array, dimension (N)
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79       INFO    (output) INTEGER
80               = 0:  successful exit
81               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

84       Modified by Linda Kaufman, Bell Labs.
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89 LAPACK routine (version 3.1)    November 2006                       DSBTRD(1)