zgbbrd.f - Man Page

subroutine zgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, rwork, info)
ZGBBRD

ZGBBRD  

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

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.

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

NCC

          NCC is INTEGER
          The number of columns of the matrix C.  NCC >= 0.

KL

          KL is INTEGER
          The number of subdiagonals of the matrix A. KL >= 0.

KU

          KU is INTEGER
          The number of superdiagonals of the matrix A. KU >= 0.

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.

LDAB

          LDAB is INTEGER
          The leading dimension of the array A. LDAB >= KL+KU+1.

D

          D is DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B.

E

          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B.

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.

LDQ

          LDQ is INTEGER
          The leading dimension of the array Q.
          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.

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.

LDPT

          LDPT is INTEGER
          The leading dimension of the array PT.
          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.

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.

LDC

          LDC is INTEGER
          The leading dimension of the array C.
          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.

WORK

          WORK is COMPLEX*16 array, dimension (max(M,N))

RWORK

          RWORK is DOUBLE PRECISION array, dimension (max(M,N))

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.

Definition at line 191 of file zgbbrd.f.