 DGBBRD(3) reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

## SYNOPSIS

SUBROUTINE DGBBRD(
VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, INFO )

CHARACTER VECT

INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

DOUBLE PRECISION AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), PT( LDPT, * ), Q( LDQ, * ), WORK( * )

## PURPOSE

DGBBRD reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDQ,M)
If VECT = 'Q' or 'B', the m-by-m orthogonal 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) DOUBLE PRECISION array, dimension (LDPT,N)
If VECT = 'P' or 'B', the n-by-n orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*max(M,N))
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.