---
name: "zgbbrd"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zgbbrd/3lapack"
---

# zgbbrd(3lapack)

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

## NAME

ZGBBRD - reduces 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 generated 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.