zbdsqr.f man page

zbdsqr.f —

Synopsis

Functions/Subroutines

subroutine zbdsqr (UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
ZBDSQR

Function/Subroutine Documentation

subroutine zbdsqr (characterUPLO, integerN, integerNCVT, integerNRU, integerNCC, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldvt, * )VT, integerLDVT, complex*16, dimension( ldu, * )U, integerLDU, complex*16, dimension( ldc, * )C, integerLDC, double precision, dimension( * )RWORK, integerINFO)

ZBDSQR

Purpose:

ZBDSQR computes the singular values and, optionally, the right and/or
left singular vectors from the singular value decomposition (SVD) of
a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
zero-shift QR algorithm.  The SVD of B has the form

   B = Q * S * P**H

where S is the diagonal matrix of singular values, Q is an orthogonal
matrix of left singular vectors, and P is an orthogonal matrix of
right singular vectors.  If left singular vectors are requested, this
subroutine actually returns U*Q instead of Q, and, if right singular
vectors are requested, this subroutine returns P**H*VT instead of
P**H, for given complex input matrices U and VT.  When U and VT are
the unitary matrices that reduce a general matrix A to bidiagonal
form: A = U*B*VT, as computed by ZGEBRD, then

   A = (U*Q) * S * (P**H*VT)

is the SVD of A.  Optionally, the subroutine may also compute Q**H*C
for a given complex input matrix C.

See "Computing  Small Singular Values of Bidiagonal Matrices With
Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11,
no. 5, pp. 873-912, Sept 1990) and
"Accurate singular values and differential qd algorithms," by
B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
Department, University of California at Berkeley, July 1992
for a detailed description of the algorithm.

Parameters:

UPLO

UPLO is CHARACTER*1
= 'U':  B is upper bidiagonal;
= 'L':  B is lower bidiagonal.

N

N is INTEGER
The order of the matrix B.  N >= 0.

NCVT

NCVT is INTEGER
The number of columns of the matrix VT. NCVT >= 0.

NRU

NRU is INTEGER
The number of rows of the matrix U. NRU >= 0.

NCC

NCC is INTEGER
The number of columns of the matrix C. NCC >= 0.

D

D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the bidiagonal matrix B.
On exit, if INFO=0, the singular values of B in decreasing
order.

E

E is DOUBLE PRECISION array, dimension (N-1)
On entry, the N-1 offdiagonal elements of the bidiagonal
matrix B.
On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
will contain the diagonal and superdiagonal elements of a
bidiagonal matrix orthogonally equivalent to the one given
as input.

VT

VT is COMPLEX*16 array, dimension (LDVT, NCVT)
On entry, an N-by-NCVT matrix VT.
On exit, VT is overwritten by P**H * VT.
Not referenced if NCVT = 0.

LDVT

LDVT is INTEGER
The leading dimension of the array VT.
LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0.

U

U is COMPLEX*16 array, dimension (LDU, N)
On entry, an NRU-by-N matrix U.
On exit, U is overwritten by U * Q.
Not referenced if NRU = 0.

LDU

LDU is INTEGER
The leading dimension of the array U.  LDU >= max(1,NRU).

C

C is COMPLEX*16 array, dimension (LDC, NCC)
On entry, an N-by-NCC matrix C.
On exit, C is overwritten by Q**H * C.
Not referenced if NCC = 0.

LDC

LDC is INTEGER
The leading dimension of the array C.
LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.

RWORK

RWORK is DOUBLE PRECISION array, dimension (2*N)
if NCVT = NRU = NCC = 0, (max(1, 4*N-4)) otherwise

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  If INFO = -i, the i-th argument had an illegal value
> 0:  the algorithm did not converge; D and E contain the
      elements of a bidiagonal matrix which is orthogonally
      similar to the input matrix B;  if INFO = i, i
      elements of E have not converged to zero.

Internal Parameters:

TOLMUL  DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8)))
        TOLMUL controls the convergence criterion of the QR loop.
        If it is positive, TOLMUL*EPS is the desired relative
           precision in the computed singular values.
        If it is negative, abs(TOLMUL*EPS*sigma_max) is the
           desired absolute accuracy in the computed singular
           values (corresponds to relative accuracy
           abs(TOLMUL*EPS) in the largest singular value.
        abs(TOLMUL) should be between 1 and 1/EPS, and preferably
           between 10 (for fast convergence) and .1/EPS
           (for there to be some accuracy in the results).
        Default is to lose at either one eighth or 2 of the
           available decimal digits in each computed singular value
           (whichever is smaller).

MAXITR  INTEGER, default = 6
        MAXITR controls the maximum number of passes of the
        algorithm through its inner loop. The algorithms stops
        (and so fails to converge) if the number of passes
        through the inner loop exceeds MAXITR*N**2.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 223 of file zbdsqr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zbdsqr(3) is an alias of zbdsqr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK