NAME

SYNOPSIS

  SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, 
 *      INFO)
  CHARACTER * 1 VECT, UPLO
  DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*)
  INTEGER N, KD, LDAB, LDQ, INFO
  DOUBLE PRECISION D(*), E(*)
 
  SUBROUTINE ZHBTRD_64( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, 
 *      WORK, INFO)
  CHARACTER * 1 VECT, UPLO
  DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*)
  INTEGER*8 N, KD, LDAB, LDQ, INFO
  DOUBLE PRECISION D(*), E(*)
 

F95 INTERFACE

  SUBROUTINE HBTRD( VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, Q
  INTEGER :: N, KD, LDAB, LDQ, INFO
  REAL(8), DIMENSION(:) :: D, E
 
  SUBROUTINE HBTRD_64( VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, Q
  INTEGER(8) :: N, KD, LDAB, LDQ, INFO
  REAL(8), DIMENSION(:) :: D, E
 

C INTERFACE

void zhbtrd(char vect, char uplo, int n, int kd, doublecomplex *ab, int ldab, double *d, double *e, doublecomplex *q, int ldq, int *info);

void zhbtrd_64(char vect, char uplo, long n, long kd, doublecomplex *ab, long ldab, double *d, double *e, doublecomplex *q, long ldq, long *info);

PURPOSE

ARGUMENTS

* VECT (input)

* UPLO (input)

* N (input)

The order of the matrix A. N >= 0.

* KD (input)

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

* AB (input/output)

On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction.

* LDAB (input)

The leading dimension of the array AB. LDAB >= KD+1.

* D (output)

The diagonal elements of the tridiagonal matrix T.

* E (output)

The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

* Q (input/output)

On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set.

On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced.

* LDQ (input)

The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

* WORK (workspace)

dimension(N)

* INFO (output)