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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| subroutine zhbtrd | ( | character | VECT, |
| character | UPLO, | ||
| integer | N, | ||
| integer | KD, | ||
| complex*16, dimension( ldab, * ) | AB, | ||
| integer | LDAB, | ||
| double precision, dimension( * ) | D, | ||
| double precision, dimension( * ) | E, | ||
| complex*16, dimension( ldq, * ) | Q, | ||
| integer | LDQ, | ||
| complex*16, dimension( * ) | WORK, | ||
| integer | INFO | ||
| ) |
ZHBTRD
Download ZHBTRD + dependencies [TGZ] [ZIP] [TXT]
ZHBTRD reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.
| [in] | VECT | VECT is CHARACTER*1
= 'N': do not form Q;
= 'V': form Q;
= 'U': update a matrix X, by forming X*Q. |
| [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 matrix A. N >= 0. |
| [in] | KD | KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
| [in,out] | AB | AB is COMPLEX*16 array, dimension (LDAB,N)
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. |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1. |
| [out] | D | D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T. |
| [out] | E | E is DOUBLE PRECISION array, dimension (N-1)
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'. |
| [in,out] | Q | Q is COMPLEX*16 array, dimension (LDQ,N)
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. |
| [in] | LDQ | LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. |
| [out] | WORK | WORK is COMPLEX*16 array, dimension (N) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
Modified by Linda Kaufman, Bell Labs.
Definition at line 165 of file zhbtrd.f.
1.8.10 
