zgbbrd (l)  Linux Man Pages
zgbbrd: reduces a complex general mbyn band matrix A to real upper bidiagonal form B by a unitary transformation
Command to display zgbbrd
manual in Linux: $ man l zgbbrd
NAME
ZGBBRD  reduces a complex general mbyn 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 mbyn band matrix A to real upper
bidiagonal form B by a unitary transformation: Qaq * A * P = B.
The routine computes B, and optionally forms Q or Paq, or computes
Qaq*C for a given matrix C.
ARGUMENTS
 VECT (input) CHARACTER*1

Specifies whether or not the matrices Q and Paq are to be
formed.
= aqNaq: do not form Q or Paq;
= aqQaq: form Q only;
= aqPaq: form Paq only;
= aqBaq: 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 mbyn band matrix A, stored in rows 1 to
KL+KU+1. The jth column of A is stored in the jth column of
the array AB as follows:
AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=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 = aqQaq or aqBaq, the mbym unitary matrix Q.
If VECT = aqNaq or aqPaq, the array Q is not referenced.
 LDQ (input) INTEGER

The leading dimension of the array Q.
LDQ >= max(1,M) if VECT = aqQaq or aqBaq; LDQ >= 1 otherwise.
 PT (output) COMPLEX*16 array, dimension (LDPT,N)

If VECT = aqPaq or aqBaq, the nbyn unitary matrix Paq.
If VECT = aqNaq or aqQaq, the array PT is not referenced.
 LDPT (input) INTEGER

The leading dimension of the array PT.
LDPT >= max(1,N) if VECT = aqPaq or aqBaq; LDPT >= 1 otherwise.
 C (input/output) COMPLEX*16 array, dimension (LDC,NCC)

On entry, an mbyncc matrix C.
On exit, C is overwritten by Qaq*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 ith argument had an illegal value.
Pages related to zgbbrd
 zgbbrd (3)
 zgbcon (l)  estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1norm or the infinitynorm,
 zgbequ (l)  computes row and column scalings intended to equilibrate an MbyN band matrix A and reduce its condition number
 zgbequb (l)  computes row and column scalings intended to equilibrate an MbyN matrix A and reduce its condition number
 zgbmv (l)  performs one of the matrixvector operations y := alpha*A*x + beta*y, or y := alpha*Aaq*x + beta*y, or y := alpha*conjg( Aaq )*x + beta*y,
 zgbrfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
 zgbrfsx (l)  ZGBRFSX improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
 zgbsv (l)  computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are NbyNRHS matrices