NAME

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

SYNOPSIS

SUBROUTINE CGBBRD(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

REAL D( ∗ ), E( ∗ ), RWORK( ∗ )

COMPLEX AB( LDAB, ∗ ), C( LDC, ∗ ), PT( LDPT, ∗ ), Q( LDQ, ∗ ), WORK( ∗ )

#include <sunperf.h>

void cgbbrd(char vect, int m, int n, int ncc, int kl, int ku, complex ∗cab, int ldab, float ∗d, float ∗e, complex ∗q, int ldq, complex ∗pt, int ldpt, complex ∗cc, int ldc, int ∗info);

PURPOSE

CGBBRD 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 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) REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.

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

Q (output) COMPLEX 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 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 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 array, dimension (max(M,N))

RWORK (workspace) REAL array, dimension (max(M,N))

INFO (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.

SunOS 5.0  —  Last change: 10 Dec 1998