CHBTRD
November 2006
Purpose
CHBTRD reduces a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.
Arguments
| VECT |
(input) CHARACTER*1
= 'N': do not form Q;
= 'V': form Q; = 'U': update a matrix X, by forming X*Q. |
| 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 matrix A. N >= 0.
|
| KD |
(input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
| AB |
(input/output) COMPLEX 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. |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
|
| D |
(output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
|
| E |
(output) REAL 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'. |
| Q |
(input/output) COMPLEX 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. |
| LDQ |
(input) INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. |
| WORK |
(workspace) COMPLEX array, dimension (N)
|
| INFO |
(output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
Further Details
Modified by Linda Kaufman, Bell Labs.