dorbdb3.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEdorbdb3.f
SYNOPSIS
Functions/Subroutinessubroutine dorbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
DORBDB3
Function/Subroutine Documentation
subroutine dorbdb3 (integer M, integer P, integer Q, double precision, dimension(ldx11,*) X11, integer LDX11, double precision, dimension(ldx21,*) X21, integer LDX21, double precision, dimension(*) THETA, double precision, dimension(*) PHI, double precision, dimension(*) TAUP1, double precision, dimension(*) TAUP2, double precision, dimension(*) TAUQ1, double precision, dimension(*) WORK, integer LWORK, integer INFO)DORBDB3 Purpose: DORBDB3 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 DORBDB1, DORBDB2, and DORBDB4 handle cases in
which M-P is not the minimum dimension.
The orthogonal 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.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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (P)
The scalar factors of the elementary reflectors that define
P1.
TAUP2 TAUP2 is DOUBLE PRECISION array, dimension (M-P)
The scalar factors of the elementary reflectors that define
P2.
TAUQ1 TAUQ1 is DOUBLE PRECISION array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.
WORK WORK is DOUBLE PRECISION 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 DORCSD for details.
P1, P2, and Q1 are represented as products of elementary reflectors.
See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
and DORGLQ.References: [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009. Definition at line 203 of file dorbdb3.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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