LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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ssbgst.f File Reference

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Functions/Subroutines

subroutine ssbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO)
 SSBGST

Function/Subroutine Documentation

subroutine ssbgst ( character  VECT,
character  UPLO,
integer  N,
integer  KA,
integer  KB,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( ldbb, * )  BB,
integer  LDBB,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( * )  WORK,
integer  INFO 
)

SSBGST

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Purpose: 
 SSBGST reduces a real symmetric-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**T*S by SPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**T*A*X, where
 X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
 bandwidth of A.
Parameters:
[in]VECT
          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
[in]N
          N is INTEGER
          The order of the matrices A and B.  N >= 0.
[in]KA
          KA is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.
[in]KB
          KB is INTEGER
          The number of superdiagonals of the matrix B if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
[in,out]AB
          AB is REAL array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the symmetric band
          matrix A, stored in the first ka+1 rows of the array.  The
          j-th column of A is stored in the j-th column of the array AB
          as follows:
          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

          On exit, the transformed matrix X**T*A*X, stored in the same
          format as A.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KA+1.
[in]BB
          BB is REAL array, dimension (LDBB,N)
          The banded factor S from the split Cholesky factorization of
          B, as returned by SPBSTF, stored in the first KB+1 rows of
          the array.
[in]LDBB
          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.
[out]X
          X is REAL array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 159 of file ssbgst.f.

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