1CGBBRD(1)                LAPACK routine (version 3.1)                CGBBRD(1)
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NAME

6       CGBBRD  - a complex general m-by-n band matrix A to real upper bidiago‐
7       nal form B by a unitary transformation
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SYNOPSIS

10       SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
11                          LDPT, C, LDC, WORK, RWORK, INFO )
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13           CHARACTER      VECT
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15           INTEGER        INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
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17           REAL           D( * ), E( * ), RWORK( * )
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19           COMPLEX        AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, *
20                          ), WORK( * )
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PURPOSE

23       CGBBRD reduces a complex general m-by-n band matrix  A  to  real  upper
24       bidiagonal form B by a unitary transformation: Q' * A * P = B.
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26       The  routine computes B, and optionally forms Q or P', or computes Q'*C
27       for a given matrix C.
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ARGUMENTS

31       VECT    (input) CHARACTER*1
32               Specifies whether or not the  matrices  Q  and  P'  are  to  be
33               formed.  = 'N': do not form Q or P';
34               = 'Q': form Q only;
35               = 'P': form P' only;
36               = 'B': form both.
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38       M       (input) INTEGER
39               The number of rows of the matrix A.  M >= 0.
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41       N       (input) INTEGER
42               The number of columns of the matrix A.  N >= 0.
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44       NCC     (input) INTEGER
45               The number of columns of the matrix C.  NCC >= 0.
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47       KL      (input) INTEGER
48               The number of subdiagonals of the matrix A. KL >= 0.
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50       KU      (input) INTEGER
51               The number of superdiagonals of the matrix A. KU >= 0.
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53       AB      (input/output) COMPLEX array, dimension (LDAB,N)
54               On  entry,  the  m-by-n  band  matrix  A,  stored  in rows 1 to
55               KL+KU+1. The j-th column of A is stored in the j-th  column  of
56               the  array  AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
57               ku)<=i<=min(m,j+kl).  On exit, A is overwritten by values  gen‐
58               erated during the reduction.
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60       LDAB    (input) INTEGER
61               The leading dimension of the array A. LDAB >= KL+KU+1.
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63       D       (output) REAL array, dimension (min(M,N))
64               The diagonal elements of the bidiagonal matrix B.
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66       E       (output) REAL array, dimension (min(M,N)-1)
67               The superdiagonal elements of the bidiagonal matrix B.
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69       Q       (output) COMPLEX array, dimension (LDQ,M)
70               If  VECT  = 'Q' or 'B', the m-by-m unitary matrix Q.  If VECT =
71               'N' or 'P', the array Q is not referenced.
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73       LDQ     (input) INTEGER
74               The leading dimension of the array Q.  LDQ >= max(1,M) if  VECT
75               = 'Q' or 'B'; LDQ >= 1 otherwise.
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77       PT      (output) COMPLEX array, dimension (LDPT,N)
78               If  VECT = 'P' or 'B', the n-by-n unitary matrix P'.  If VECT =
79               'N' or 'Q', the array PT is not referenced.
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81       LDPT    (input) INTEGER
82               The leading dimension of the array PT.   LDPT  >=  max(1,N)  if
83               VECT = 'P' or 'B'; LDPT >= 1 otherwise.
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85       C       (input/output) COMPLEX array, dimension (LDC,NCC)
86               On  entry,  an m-by-ncc matrix C.  On exit, C is overwritten by
87               Q'*C.  C is not referenced if NCC = 0.
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89       LDC     (input) INTEGER
90               The leading dimension of the array C.  LDC >= max(1,M) if NCC >
91               0; LDC >= 1 if NCC = 0.
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93       WORK    (workspace) COMPLEX array, dimension (max(M,N))
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95       RWORK   (workspace) REAL array, dimension (max(M,N))
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97       INFO    (output) INTEGER
98               = 0:  successful exit.
99               < 0:  if INFO = -i, the i-th argument had an illegal value.
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103 LAPACK routine (version 3.1)    November 2006                       CGBBRD(1)
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