1ZGBBRD(1) LAPACK routine (version 3.1) ZGBBRD(1)
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6 ZGBBRD - 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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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.
25 The routine computes B, and optionally forms Q or P', or computes Q'*C
27 for a given matrix C.
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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.
37 M (input) INTEGER
39 The number of rows of the matrix A. M >= 0.
40 N (input) INTEGER
42 The number of columns of the matrix A. N >= 0.
43 NCC (input) INTEGER
45 The number of columns of the matrix C. NCC >= 0.
46 KL (input) INTEGER
48 The number of subdiagonals of the matrix A. KL >= 0.
49 KU (input) INTEGER
51 The number of superdiagonals of the matrix A. KU >= 0.
52 AB (input/output) COMPLEX*16 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.
59 LDAB (input) INTEGER
61 The leading dimension of the array A. LDAB >= KL+KU+1.
62 D (output) DOUBLE PRECISION array, dimension (min(M,N))
64 The diagonal elements of the bidiagonal matrix B.
65 E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
67 The superdiagonal elements of the bidiagonal matrix B.
68 Q (output) COMPLEX*16 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.
72 LDQ (input) INTEGER
74 The leading dimension of the array Q. LDQ >= max(1,M) if VECT
75 = 'Q' or 'B'; LDQ >= 1 otherwise.
76 PT (output) COMPLEX*16 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.
80 LDPT (input) INTEGER
82 The leading dimension of the array PT. LDPT >= max(1,N) if
83 VECT = 'P' or 'B'; LDPT >= 1 otherwise.
84 C (input/output) COMPLEX*16 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.
88 LDC (input) INTEGER
90 The leading dimension of the array C. LDC >= max(1,M) if NCC >
91 0; LDC >= 1 if NCC = 0.
92 WORK (workspace) COMPLEX*16 array, dimension (max(M,N))
94 RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))
96 INFO (output) INTEGER
98 = 0: successful exit.
99 < 0: if INFO = -i, the i-th argument had an illegal value.
100 LAPACK routine (version 3.1) November 2006 ZGBBRD(1)