# Ubuntu Feisty 7.04 manual page repository

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Provided by: lapack3-doc_3.0.20000531a-6ubuntu3_all

### NAME

ZGBBRD - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation

### SYNOPSIS

SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO ) CHARACTER VECT INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC DOUBLE PRECISION D( * ), E( * ), RWORK( * ) COMPLEX*16 AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, * ), WORK( * )

### PURPOSE

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

### ARGUMENTS

VECT (input) CHARACTER*1 Specifies whether or not the matrices Q and P’ are to be formed. = ’N’: do not form Q or P’; = ’Q’: form Q only; = ’P’: form P’ only; = ’B’: form both. M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. NCC (input) INTEGER The number of columns of the matrix C. NCC >= 0. KL (input) INTEGER The number of subdiagonals of the matrix A. KL >= 0. KU (input) INTEGER The number of superdiagonals of the matrix A. KU >= 0. AB (input/output) COMPLEX*16 array, dimension (LDAB,N) On entry, the m-by-n band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j- ku)<=i<=min(m,j+kl). On exit, A is overwritten by values gen‐ erated during the reduction. LDAB (input) INTEGER The leading dimension of the array A. LDAB >= KL+KU+1. D (output) DOUBLE PRECISION array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B. E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) The superdiagonal elements of the bidiagonal matrix B. Q (output) COMPLEX*16 array, dimension (LDQ,M) If VECT = ’Q’ or ’B’, the m-by-m unitary matrix Q. If VECT = ’N’ or ’P’, the array Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if VECT = ’Q’ or ’B’; LDQ >= 1 otherwise. PT (output) COMPLEX*16 array, dimension (LDPT,N) If VECT = ’P’ or ’B’, the n-by-n unitary matrix P’. If VECT = ’N’ or ’Q’, the array PT is not referenced. LDPT (input) INTEGER The leading dimension of the array PT. LDPT >= max(1,N) if VECT = ’P’ or ’B’; LDPT >= 1 otherwise. C (input/output) COMPLEX*16 array, dimension (LDC,NCC) On entry, an m-by-ncc matrix C. On exit, C is overwritten by Q’*C. C is not referenced if NCC = 0. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. WORK (workspace) COMPLEX*16 array, dimension (max(M,N)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.