zhbgst

NAME

zhbgst - reduce a complex Hermitian-definite banded generalized 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 * 1 VECT, UPLO
  DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
  INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO
  DOUBLE PRECISION RWORK(*)
 
  SUBROUTINE ZHBGST_64( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, 
 *      LDX, WORK, RWORK, INFO)
  CHARACTER * 1 VECT, UPLO
  DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO
  DOUBLE PRECISION RWORK(*)

F95 INTERFACE 

  SUBROUTINE HBGST( VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], 
 *       X, [LDX], [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, BB, X
  INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO
  REAL(8), DIMENSION(:) :: RWORK
 
  SUBROUTINE HBGST_64( VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], 
 *       X, [LDX], [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, BB, X
  INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO
  REAL(8), DIMENSION(:) :: RWORK

C INTERFACE

#include <sunperf.h>

void zhbgst(char vect, char uplo, int n, int ka, int kb, doublecomplex *ab, int ldab, doublecomplex *bb, int ldbb, doublecomplex *x, int ldx, int *info);

void zhbgst_64(char vect, char uplo, long n, long ka, long kb, doublecomplex *ab, long ldab, doublecomplex *bb, long ldbb, doublecomplex *x, long ldx, long *info);

PURPOSE

zhbgst reduces a complex Hermitian-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**H*S by CPBSTF, 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)
* UPLO (input)

* N (input)
The order of the matrices A and B. N >= 0.

* KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.

* KB (input)
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)
On entry, the upper or lower triangle of the Hermitian 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)
The leading dimension of the array AB. LDAB >= KA+1.

* BB (input)
The banded factor S from the split Cholesky factorization of B, as returned by CPBSTF, stored in the first kb+1 rows of the array.

* LDBB (input)
The leading dimension of the array BB. LDBB >= KB+1.

* X (output)
If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.

* LDX (input)
The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

* WORK (workspace)
dimension(N)

* RWORK (workspace)
dimension(N)

* INFO (output)