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zhbgst (3)
  • >> zhbgst (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zhbgst - reduce a complex Hermitian-definite banded general-
         ized  eigenproblem  A*x  = lambda*B*x to standard form C*y =
         lambda*y,
    
    SYNOPSIS
         SUBROUTINE ZHBGST( VECT, UPLO, N,  KA,  KB,  AB,  LDAB,  BB,
                   LDBB, X, LDX, WORK, RWORK, INFO )
    
         CHARACTER UPLO, VECT
    
         INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N
    
         DOUBLE PRECISION RWORK( * )
    
         COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X(  LDX,
                   * )
    
    
    
         #include <sunperf.h>
    
         void zhbgst(char vect, char uplo, int n,  int  ka,  int  kb,
                   doublecomplex  *zab,  int ldab, doublecomplex *bb,
                   int ldbb, doublecomplex *zx, int ldx, int *info) ;
    
    PURPOSE
         ZHBGST reduces a complex Hermitian-definite banded  general-
         ized 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**H*S by  ZPBSTF,
         using  a split Cholesky factorization. A is overwritten by C
         = X**H*A*X, where X = S**(-1)*Q and Q is  a  unitary  matrix
         chosen to preserve the bandwidth of A.
    
    
    ARGUMENTS
         VECT      (input) CHARACTER*1
                   = 'N':  do not form the transformation matrix X;
                   = 'V':  form X.
    
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrices A and B.  N >= 0.
    
         KA        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KA >= 0.
    
         KB        (input) INTEGER
                   The number of superdiagonals of the  matrix  B  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KA >= KB >= 0.
    
         AB        (input/output)   COMPLEX*16    array,    dimension
                   (LDAB,N)
                   On entry, the upper or lower triangle of the  Her-
                   mitian  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**H*A*X,  stored
                   in the same format as A.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KA+1.
    
         BB        (input) COMPLEX*16 array, dimension (LDBB,N)
                   The banded factor S from the split  Cholesky  fac-
                   torization  of B, as returned by ZPBSTF, stored in
                   the first kb+1 rows of the array.
    
         LDBB      (input) INTEGER
                   The leading dimension of the array  BB.   LDBB  >=
                   KB+1.
    
         X         (output) COMPLEX*16 array, dimension (LDX,N)
                   If VECT = 'V', the n-by-n matrix  X.   If  VECT  =
                   'N', the array X is not referenced.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
    
         WORK      (workspace) COMPLEX*16 array, dimension (N)
    
         RWORK     (workspace) DOUBLE PRECISION array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    
    
    


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