dgbbrd (l)  Linux Man Pages
dgbbrd: reduces a real general mbyn band matrix A to upper bidiagonal form B by an orthogonal transformation
Command to display dgbbrd
manual in Linux: $ man l dgbbrd
NAME
DGBBRD  reduces a real general mbyn 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 mbyn band matrix A to upper
bidiagonal form B by an orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDQ,M)

If VECT = aqQaq or aqBaq, the mbym orthogonal 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) DOUBLE PRECISION array, dimension (LDPT,N)

If VECT = aqPaq or aqBaq, the nbyn orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*max(M,N))

 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
Pages related to dgbbrd
 dgbbrd (3)
 dgbcon (l)  estimates the reciprocal of the condition number of a real general band matrix A, in either the 1norm or the infinitynorm,
 dgbequ (l)  computes row and column scalings intended to equilibrate an MbyN band matrix A and reduce its condition number
 dgbequb (l)  computes row and column scalings intended to equilibrate an MbyN matrix A and reduce its condition number
 dgbmv (l)  performs one of the matrixvector operations y := alpha*A*x + beta*y, or y := alpha*Aaq*x + beta*y,
 dgbrfs (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
 dgbrfsx (l)  DGBRFSX improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
 dgbsv (l)  computes the solution to a real 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