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

6       DSBGST  - a real symmetric-definite banded generalized eigenproblem A*x
7       = lambda*B*x to standard form C*y = lambda*y,
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SYNOPSIS

10       SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,  X,  LDX,
11                          WORK, INFO )
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13           CHARACTER      UPLO, VECT
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15           INTEGER        INFO, KA, KB, LDAB, LDBB, LDX, N
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17           DOUBLE         PRECISION  AB(  LDAB, * ), BB( LDBB, * ), WORK( * ),
18                          X( LDX, * )
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PURPOSE

21       DSBGST reduces a real symmetric-definite banded generalized  eigenprob‐
22       lem   A*x  =  lambda*B*x  to standard form  C*y = lambda*y, such that C
23       has the same bandwidth as A.
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25       B must have been previously factorized as S**T*S  by  DPBSTF,  using  a
26       split Cholesky factorization. A is overwritten by C = X**T*A*X, where X
27       = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the  band‐
28       width of A.
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ARGUMENTS

32       VECT    (input) CHARACTER*1
33               = 'N':  do not form the transformation matrix X;
34               = 'V':  form X.
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36       UPLO    (input) CHARACTER*1
37               = 'U':  Upper triangle of A is stored;
38               = 'L':  Lower triangle of A is stored.
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40       N       (input) INTEGER
41               The order of the matrices A and B.  N >= 0.
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43       KA      (input) INTEGER
44               The  number of superdiagonals of the matrix A if UPLO = 'U', or
45               the number of subdiagonals if UPLO = 'L'.  KA >= 0.
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47       KB      (input) INTEGER
48               The number of superdiagonals of the matrix B if UPLO = 'U',  or
49               the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
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51       AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
52               On  entry,  the  upper  or lower triangle of the symmetric band
53               matrix A, stored in the first ka+1 rows of the array.  The j-th
54               column  of  A  is  stored in the j-th column of the array AB as
55               follows: if UPLO = 'U', AB(ka+1+i-j,j) =  A(i,j)  for  max(1,j-
56               ka)<=i<=j;   if   UPLO  =  'L',  AB(1+i-j,j)     =  A(i,j)  for
57               j<=i<=min(n,j+ka).
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59               On exit, the transformed matrix X**T*A*X, stored  in  the  same
60               format as A.
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62       LDAB    (input) INTEGER
63               The leading dimension of the array AB.  LDAB >= KA+1.
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65       BB      (input) DOUBLE PRECISION array, dimension (LDBB,N)
66               The banded factor S from the split Cholesky factorization of B,
67               as returned by DPBSTF, stored in the first  KB+1  rows  of  the
68               array.
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70       LDBB    (input) INTEGER
71               The leading dimension of the array BB.  LDBB >= KB+1.
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73       X       (output) DOUBLE PRECISION array, dimension (LDX,N)
74               If VECT = 'V', the n-by-n matrix X.  If VECT = 'N', the array X
75               is not referenced.
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77       LDX     (input) INTEGER
78               The leading dimension of the array X.  LDX >= max(1,N) if  VECT
79               = 'V'; LDX >= 1 otherwise.
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81       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
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83       INFO    (output) INTEGER
84               = 0:  successful exit
85               < 0:  if INFO = -i, the i-th argument had an illegal value.
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89 LAPACK routine (version 3.1)    November 2006                       DSBGST(1)
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