LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zgbbrd()

subroutine zgbbrd ( character vect,
integer m,
integer n,
integer ncc,
integer kl,
integer ku,
complex*16, dimension( ldab, * ) ab,
integer ldab,
double precision, dimension( * ) d,
double precision, dimension( * ) e,
complex*16, dimension( ldq, * ) q,
integer ldq,
complex*16, dimension( ldpt, * ) pt,
integer ldpt,
complex*16, dimension( ldc, * ) c,
integer ldc,
complex*16, dimension( * ) work,
double precision, dimension( * ) rwork,
integer info )

ZGBBRD

Download ZGBBRD + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> ZGBBRD reduces a complex general m-by-n band matrix A to real upper
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
!>
!> The routine computes B, and optionally forms Q or P**H, or computes
!> Q**H*C for a given matrix C.
!>
Parameters
[in]VECT
!>          VECT is CHARACTER*1
!>          Specifies whether or not the matrices Q and P**H are to be
!>          formed.
!>          = 'N': do not form Q or P**H;
!>          = 'Q': form Q only;
!>          = 'P': form P**H only;
!>          = 'B': form both.
!>
[in]M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>
[in]N
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
[in]NCC
!>          NCC is INTEGER
!>          The number of columns of the matrix C.  NCC >= 0.
!>
[in]KL
!>          KL is INTEGER
!>          The number of subdiagonals of the matrix A. KL >= 0.
!>
[in]KU
!>          KU is INTEGER
!>          The number of superdiagonals of the matrix A. KU >= 0.
!>
[in,out]AB
!>          AB is 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 generated during the
!>          reduction.
!>
[in]LDAB
!>          LDAB is INTEGER
!>          The leading dimension of the array A. LDAB >= KL+KU+1.
!>
[out]D
!>          D is DOUBLE PRECISION array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B.
!>
[out]E
!>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
!>          The superdiagonal elements of the bidiagonal matrix B.
!>
[out]Q
!>          Q is 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.
!>
[in]LDQ
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.
!>          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
!>
[out]PT
!>          PT is 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.
!>
[in]LDPT
!>          LDPT is INTEGER
!>          The leading dimension of the array PT.
!>          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
!>
[in,out]C
!>          C is COMPLEX*16 array, dimension (LDC,NCC)
!>          On entry, an m-by-ncc matrix C.
!>          On exit, C is overwritten by Q**H*C.
!>          C is not referenced if NCC = 0.
!>
[in]LDC
!>          LDC is INTEGER
!>          The leading dimension of the array C.
!>          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
!>
[out]WORK
!>          WORK is COMPLEX*16 array, dimension (max(M,N))
!>
[out]RWORK
!>          RWORK is DOUBLE PRECISION array, dimension (max(M,N))
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.