1CHBTRD(1) LAPACK routine (version 3.1) CHBTRD(1)
2
6 CHBTRD - a complex Hermitian band matrix A to real symmetric tridiago‐
7 nal form T by a unitary similarity transformation
8
10 SUBROUTINE CHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK,
11 INFO )
12 CHARACTER UPLO, VECT
14 INTEGER INFO, KD, LDAB, LDQ, N
16 REAL D( * ), E( * )
18 COMPLEX AB( LDAB, * ), Q( LDQ, * ), WORK( * )
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22 CHBTRD reduces a complex Hermitian band matrix A to real symmetric
23 tridiagonal form T by a unitary similarity transformation: Q**H * A * Q
24 = T.
25
28 VECT (input) CHARACTER*1
29 = 'N': do not form Q;
30 = 'V': form Q;
31 = 'U': update a matrix X, by forming X*Q.
32 UPLO (input) CHARACTER*1
34 = 'U': Upper triangle of A is stored;
35 = 'L': Lower triangle of A is stored.
36 N (input) INTEGER
38 The order of the matrix A. N >= 0.
39 KD (input) INTEGER
41 The number of superdiagonals of the matrix A if UPLO = 'U', or
42 the number of subdiagonals if UPLO = 'L'. KD >= 0.
43 AB (input/output) COMPLEX array, dimension (LDAB,N)
45 On entry, the upper or lower triangle of the Hermitian band
46 matrix A, stored in the first KD+1 rows of the array. The j-th
47 column of A is stored in the j-th column of the array AB as
48 follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
49 kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
50 j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are
51 overwritten by the diagonal elements of the tridiagonal matrix
52 T; if KD > 0, the elements on the first superdiagonal (if UPLO
53 = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten
54 by the off-diagonal elements of T; the rest of AB is overwrit‐
55 ten by values generated during the reduction.
56 LDAB (input) INTEGER
58 The leading dimension of the array AB. LDAB >= KD+1.
59 D (output) REAL array, dimension (N)
61 The diagonal elements of the tridiagonal matrix T.
62 E (output) REAL array, dimension (N-1)
64 The off-diagonal elements of the tridiagonal matrix T: E(i) =
65 T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
66 Q (input/output) COMPLEX array, dimension (LDQ,N)
68 On entry, if VECT = 'U', then Q must contain an N-by-N matrix
69 X; if VECT = 'N' or 'V', then Q need not be set.
70 On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q;
72 if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the
73 array Q is not referenced.
74 LDQ (input) INTEGER
76 The leading dimension of the array Q. LDQ >= 1, and LDQ >= N
77 if VECT = 'V' or 'U'.
78 WORK (workspace) COMPLEX array, dimension (N)
80 INFO (output) INTEGER
82 = 0: successful exit
83 < 0: if INFO = -i, the i-th argument had an illegal value
84
86 Modified by Linda Kaufman, Bell Labs.
87 LAPACK routine (version 3.1) November 2006 CHBTRD(1)