DGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

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( * )

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.

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.