zunbdb3.f man page

zunbdb3.f —

Synopsis

Functions/Subroutines

subroutine zunbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
ZUNBDB3

Function/Subroutine Documentation

subroutine zunbdb3 (integerM, integerP, integerQ, complex*16, dimension(ldx11,*)X11, integerLDX11, complex*16, dimension(ldx21,*)X21, integerLDX21, double precision, dimension(*)THETA, double precision, dimension(*)PHI, complex*16, dimension(*)TAUP1, complex*16, dimension(*)TAUP2, complex*16, dimension(*)TAUQ1, complex*16, dimension(*)WORK, integerLWORK, integerINFO)

ZUNBDB3 .SH "Purpose:"

 ZUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
 matrix X with orthonomal columns:

                            [ B11 ]
      [ X11 ]   [ P1 |    ] [  0  ]
      [-----] = [---------] [-----] Q1**T .
      [ X21 ]   [    | P2 ] [ B21 ]
                            [  0  ]

 X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P,
 Q, or M-Q. Routines ZUNBDB1, ZUNBDB2, and ZUNBDB4 handle cases in
 which M-P is not the minimum dimension.

 The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
 and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
 Householder vectors.

 B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented
 implicitly by angles THETA, PHI..fi

 

Parameters:
M 

          M is INTEGER
           The number of rows X11 plus the number of rows in X21.

P

P is INTEGER
 The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q).

Q

Q is INTEGER
 The number of columns in X11 and X21. 0 <= Q <= M.

X11

X11 is COMPLEX*16 array, dimension (LDX11,Q)
 On entry, the top block of the matrix X to be reduced. On
 exit, the columns of tril(X11) specify reflectors for P1 and
 the rows of triu(X11,1) specify reflectors for Q1.

LDX11

LDX11 is INTEGER
 The leading dimension of X11. LDX11 >= P.

X21

X21 is COMPLEX*16 array, dimension (LDX21,Q)
 On entry, the bottom block of the matrix X to be reduced. On
 exit, the columns of tril(X21) specify reflectors for P2.

LDX21

LDX21 is INTEGER
 The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is DOUBLE PRECISION array, dimension (Q)
 The entries of the bidiagonal blocks B11, B21 are defined by
 THETA and PHI. See Further Details.

PHI

PHI is DOUBLE PRECISION array, dimension (Q-1)
 The entries of the bidiagonal blocks B11, B21 are defined by
 THETA and PHI. See Further Details.

TAUP1

TAUP1 is COMPLEX*16 array, dimension (P)
 The scalar factors of the elementary reflectors that define
 P1.

TAUP2

TAUP2 is COMPLEX*16 array, dimension (M-P)
 The scalar factors of the elementary reflectors that define
 P2.

TAUQ1

TAUQ1 is COMPLEX*16 array, dimension (Q)
 The scalar factors of the elementary reflectors that define
 Q1.

WORK

WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

         LWORK is INTEGER
          The dimension of the array WORK. LWORK >= M-Q.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

July 2012

Further Details:

The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or ZUNCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors.
See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
and ZUNGLQ.

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Definition at line 201 of file zunbdb3.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zunbdb3(3) is an alias of zunbdb3.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK