1SSBGST(1)                LAPACK routine (version 3.2)                SSBGST(1)
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NAME

6       SSBGST  -  reduces  a real symmetric-definite banded generalized eigen‐
7       problem A*x = lambda*B*x to standard form C*y = lambda*y,
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SYNOPSIS

10       SUBROUTINE SSBGST( 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           REAL           AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )
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PURPOSE

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

29       VECT    (input) CHARACTER*1
30               = 'N':  do not form the transformation matrix X;
31               = 'V':  form X.
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33       UPLO    (input) CHARACTER*1
34               = 'U':  Upper triangle of A is stored;
35               = 'L':  Lower triangle of A is stored.
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37       N       (input) INTEGER
38               The order of the matrices A and B.  N >= 0.
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40       KA      (input) INTEGER
41               The number of superdiagonals of the matrix A if UPLO = 'U',  or
42               the number of subdiagonals if UPLO = 'L'.  KA >= 0.
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44       KB      (input) INTEGER
45               The  number of superdiagonals of the matrix B if UPLO = 'U', or
46               the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
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48       AB      (input/output) REAL array, dimension (LDAB,N)
49               On entry, the upper or lower triangle  of  the  symmetric  band
50               matrix A, stored in the first ka+1 rows of the array.  The j-th
51               column of A is stored in the j-th column of  the  array  AB  as
52               follows:  if  UPLO  = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
53               ka)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
54               j<=i<=min(n,j+ka).   On  exit, the transformed matrix X**T*A*X,
55               stored in the same format as A.
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57       LDAB    (input) INTEGER
58               The leading dimension of the array AB.  LDAB >= KA+1.
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60       BB      (input) REAL array, dimension (LDBB,N)
61               The banded factor S from the split Cholesky factorization of B,
62               as  returned  by  SPBSTF,  stored in the first KB+1 rows of the
63               array.
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65       LDBB    (input) INTEGER
66               The leading dimension of the array BB.  LDBB >= KB+1.
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68       X       (output) REAL array, dimension (LDX,N)
69               If VECT = 'V', the n-by-n matrix X.  If VECT = 'N', the array X
70               is not referenced.
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72       LDX     (input) INTEGER
73               The  leading dimension of the array X.  LDX >= max(1,N) if VECT
74               = 'V'; LDX >= 1 otherwise.
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76       WORK    (workspace) REAL array, dimension (2*N)
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78       INFO    (output) INTEGER
79               = 0:  successful exit
80               < 0:  if INFO = -i, the i-th argument had an illegal value.
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84 LAPACK routine (version 3.2)    November 2008                       SSBGST(1)