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

6       SSBGST  - 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 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.
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24       B  must  have  been  previously factorized as S**T*S by SPBSTF, using a
25       split Cholesky factorization. A is overwritten by C = X**T*A*X, where X
26       =  S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the band‐
27       width of A.
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ARGUMENTS

31       VECT    (input) CHARACTER*1
32               = 'N':  do not form the transformation matrix X;
33               = 'V':  form X.
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35       UPLO    (input) CHARACTER*1
36               = 'U':  Upper triangle of A is stored;
37               = 'L':  Lower triangle of A is stored.
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39       N       (input) INTEGER
40               The order of the matrices A and B.  N >= 0.
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42       KA      (input) INTEGER
43               The number of superdiagonals of the matrix A if UPLO = 'U',  or
44               the number of subdiagonals if UPLO = 'L'.  KA >= 0.
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46       KB      (input) INTEGER
47               The  number of superdiagonals of the matrix B if UPLO = 'U', or
48               the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
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50       AB      (input/output) REAL array, dimension (LDAB,N)
51               On entry, the upper or lower triangle  of  the  symmetric  band
52               matrix A, stored in the first ka+1 rows of the array.  The j-th
53               column of A is stored in the j-th column of  the  array  AB  as
54               follows:  if  UPLO  = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
55               ka)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
56               j<=i<=min(n,j+ka).
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58               On  exit,  the  transformed matrix X**T*A*X, stored in the same
59               format as A.
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61       LDAB    (input) INTEGER
62               The leading dimension of the array AB.  LDAB >= KA+1.
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64       BB      (input) REAL array, dimension (LDBB,N)
65               The banded factor S from the split Cholesky factorization of B,
66               as  returned  by  SPBSTF,  stored in the first KB+1 rows of the
67               array.
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69       LDBB    (input) INTEGER
70               The leading dimension of the array BB.  LDBB >= KB+1.
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72       X       (output) REAL array, dimension (LDX,N)
73               If VECT = 'V', the n-by-n matrix X.  If VECT = 'N', the array X
74               is not referenced.
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76       LDX     (input) INTEGER
77               The  leading dimension of the array X.  LDX >= max(1,N) if VECT
78               = 'V'; LDX >= 1 otherwise.
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80       WORK    (workspace) REAL array, dimension (2*N)
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82       INFO    (output) INTEGER
83               = 0:  successful exit
84               < 0:  if INFO = -i, the i-th argument had an illegal value.
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88 LAPACK routine (version 3.1)    November 2006                       SSBGST(1)
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