• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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)
  

   = 'N':  do not form the transformation matrix X;

   = 'V':  form X.

• UPLO (input)
  

   = 'U':  Upper triangle of A is stored;

   = 'L':  Lower triangle of A is stored.

• 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)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value.