1ZGBBRD(1) LAPACK routine (version 3.2) ZGBBRD(1)
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6 ZGBBRD - reduces a complex general m-by-n band matrix A to real upper
7 bidiagonal form B by a unitary transformation
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10 SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
11 LDPT, C, LDC, WORK, RWORK, INFO )
12 CHARACTER VECT
14 INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
16 DOUBLE PRECISION D( * ), E( * ), RWORK( * )
18 COMPLEX*16 AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, *
20 ), WORK( * )
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23 ZGBBRD 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. The
25 routine computes B, and optionally forms Q or P', or computes Q'*C for
26 a given matrix C.
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29 VECT (input) CHARACTER*1
30 Specifies whether or not the matrices Q and P' are to be
31 formed. = 'N': do not form Q or P';
32 = 'Q': form Q only;
33 = 'P': form P' only;
34 = 'B': form both.
35 M (input) INTEGER
37 The number of rows of the matrix A. M >= 0.
38 N (input) INTEGER
40 The number of columns of the matrix A. N >= 0.
41 NCC (input) INTEGER
43 The number of columns of the matrix C. NCC >= 0.
44 KL (input) INTEGER
46 The number of subdiagonals of the matrix A. KL >= 0.
47 KU (input) INTEGER
49 The number of superdiagonals of the matrix A. KU >= 0.
50 AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
52 On entry, the m-by-n band matrix A, stored in rows 1 to
53 KL+KU+1. The j-th column of A is stored in the j-th column of
54 the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
55 ku)<=i<=min(m,j+kl). On exit, A is overwritten by values gen‐
56 erated during the reduction.
57 LDAB (input) INTEGER
59 The leading dimension of the array A. LDAB >= KL+KU+1.
60 D (output) DOUBLE PRECISION array, dimension (min(M,N))
62 The diagonal elements of the bidiagonal matrix B.
63 E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
65 The superdiagonal elements of the bidiagonal matrix B.
66 Q (output) COMPLEX*16 array, dimension (LDQ,M)
68 If VECT = 'Q' or 'B', the m-by-m unitary matrix Q. If VECT =
69 'N' or 'P', the array Q is not referenced.
70 LDQ (input) INTEGER
72 The leading dimension of the array Q. LDQ >= max(1,M) if VECT
73 = 'Q' or 'B'; LDQ >= 1 otherwise.
74 PT (output) COMPLEX*16 array, dimension (LDPT,N)
76 If VECT = 'P' or 'B', the n-by-n unitary matrix P'. If VECT =
77 'N' or 'Q', the array PT is not referenced.
78 LDPT (input) INTEGER
80 The leading dimension of the array PT. LDPT >= max(1,N) if
81 VECT = 'P' or 'B'; LDPT >= 1 otherwise.
82 C (input/output) COMPLEX*16 array, dimension (LDC,NCC)
84 On entry, an m-by-ncc matrix C. On exit, C is overwritten by
85 Q'*C. C is not referenced if NCC = 0.
86 LDC (input) INTEGER
88 The leading dimension of the array C. LDC >= max(1,M) if NCC >
89 0; LDC >= 1 if NCC = 0.
90 WORK (workspace) COMPLEX*16 array, dimension (max(M,N))
92 RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))
94 INFO (output) INTEGER
96 = 0: successful exit.
97 < 0: if INFO = -i, the i-th argument had an illegal value.
98 LAPACK routine (version 3.2) November 2008 ZGBBRD(1)