1SGBBRD(1)                LAPACK routine (version 3.2)                SGBBRD(1)
2
3
4

NAME

6       SGBBRD  - reduces a real general m-by-n band matrix A to upper bidiago‐
7       nal form B by an orthogonal transformation
8

SYNOPSIS

10       SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
11                          LDPT, C, LDC, WORK, INFO )
12
13           CHARACTER      VECT
14
15           INTEGER        INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
16
17           REAL           AB(  LDAB,  *  ),  C(  LDC, * ), D( * ), E( * ), PT(
18                          LDPT, * ), Q( LDQ, * ), WORK( * )
19

PURPOSE

21       SGBBRD reduces a real general m-by-n band matrix A to upper  bidiagonal
22       form  B  by  an orthogonal transformation: Q' * A * P = B.  The routine
23       computes B, and optionally forms Q or P', or computes Q'*C for a  given
24       matrix C.
25

ARGUMENTS

27       VECT    (input) CHARACTER*1
28               Specifies  whether  or  not  the  matrices  Q  and P' are to be
29               formed.  = 'N': do not form Q or P';
30               = 'Q': form Q only;
31               = 'P': form P' only;
32               = 'B': form both.
33
34       M       (input) INTEGER
35               The number of rows of the matrix A.  M >= 0.
36
37       N       (input) INTEGER
38               The number of columns of the matrix A.  N >= 0.
39
40       NCC     (input) INTEGER
41               The number of columns of the matrix C.  NCC >= 0.
42
43       KL      (input) INTEGER
44               The number of subdiagonals of the matrix A. KL >= 0.
45
46       KU      (input) INTEGER
47               The number of superdiagonals of the matrix A. KU >= 0.
48
49       AB      (input/output) REAL array, dimension (LDAB,N)
50               On entry, the m-by-n  band  matrix  A,  stored  in  rows  1  to
51               KL+KU+1.  The  j-th column of A is stored in the j-th column of
52               the array AB as follows: AB(ku+1+i-j,j) = A(i,j)  for  max(1,j-
53               ku)<=i<=min(m,j+kl).   On exit, A is overwritten by values gen‐
54               erated during the reduction.
55
56       LDAB    (input) INTEGER
57               The leading dimension of the array A. LDAB >= KL+KU+1.
58
59       D       (output) REAL array, dimension (min(M,N))
60               The diagonal elements of the bidiagonal matrix B.
61
62       E       (output) REAL array, dimension (min(M,N)-1)
63               The superdiagonal elements of the bidiagonal matrix B.
64
65       Q       (output) REAL array, dimension (LDQ,M)
66               If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.  If  VECT
67               = 'N' or 'P', the array Q is not referenced.
68
69       LDQ     (input) INTEGER
70               The  leading dimension of the array Q.  LDQ >= max(1,M) if VECT
71               = 'Q' or 'B'; LDQ >= 1 otherwise.
72
73       PT      (output) REAL array, dimension (LDPT,N)
74               If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.  If VECT
75               = 'N' or 'Q', the array PT is not referenced.
76
77       LDPT    (input) INTEGER
78               The  leading  dimension  of  the array PT.  LDPT >= max(1,N) if
79               VECT = 'P' or 'B'; LDPT >= 1 otherwise.
80
81       C       (input/output) REAL array, dimension (LDC,NCC)
82               On entry, an m-by-ncc matrix C.  On exit, C is  overwritten  by
83               Q'*C.  C is not referenced if NCC = 0.
84
85       LDC     (input) INTEGER
86               The leading dimension of the array C.  LDC >= max(1,M) if NCC >
87               0; LDC >= 1 if NCC = 0.
88
89       WORK    (workspace) REAL array, dimension (2*max(M,N))
90
91       INFO    (output) INTEGER
92               = 0:  successful exit.
93               < 0:  if INFO = -i, the i-th argument had an illegal value.
94
95
96
97 LAPACK routine (version 3.2)    November 2008                       SGBBRD(1)
Impressum