1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
.TH CHBTRD l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
CHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
.SH SYNOPSIS
.TP 19
SUBROUTINE CHBTRD(
VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
WORK, INFO )
.TP 19
.ti +4
CHARACTER
UPLO, VECT
.TP 19
.ti +4
INTEGER
INFO, KD, LDAB, LDQ, N
.TP 19
.ti +4
REAL
D( * ), E( * )
.TP 19
.ti +4
COMPLEX
AB( LDAB, * ), Q( LDQ, * ), WORK( * )
.SH 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.
.br
.SH ARGUMENTS
.TP 8
VECT (input) CHARACTER*1
= 'N': do not form Q;
.br
= 'V': form Q;
.br
= 'U': update a matrix X, by forming X*Q.
.TP 8
UPLO (input) CHARACTER*1
.br
= 'U': Upper triangle of A is stored;
.br
= 'L': Lower triangle of A is stored.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
.TP 8
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.
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
.TP 8
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
.TP 8
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'.
.TP 8
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.
.TP 8
LDQ (input) INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
.TP 8
WORK (workspace) COMPLEX array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH FURTHER DETAILS
Modified by Linda Kaufman, Bell Labs.
.br
|
