.TH "SRC/dorbdb3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dorbdb3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdorbdb3\fP (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)"
.br
.RI "\fBDORBDB3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBDORBDB3\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
!> matrix X with orthonormal 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\&.
!>
!>
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>           The number of rows X11 plus the number of rows in X21\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>           The number of rows in X11\&. 0 <= P <= M\&. M-P <= min(P,Q,M-Q)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>           The number of columns in X11 and X21\&. 0 <= Q <= M\&.
!> 
.fi
.PP
.br
\fIX11\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDX11\fP 
.PP
.nf
!>          LDX11 is INTEGER
!>           The leading dimension of X11\&. LDX11 >= P\&.
!> 
.fi
.PP
.br
\fIX21\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDX21\fP 
.PP
.nf
!>          LDX21 is INTEGER
!>           The leading dimension of X21\&. LDX21 >= M-P\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          THETA is DOUBLE PRECISION array, dimension (Q)
!>           The entries of the bidiagonal blocks B11, B21 are defined by
!>           THETA and PHI\&. See Further Details\&.
!> 
.fi
.PP
.br
\fIPHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fITAUP1\fP 
.PP
.nf
!>          TAUP1 is DOUBLE PRECISION array, dimension (P)
!>           The scalar factors of the elementary reflectors that define
!>           P1\&.
!> 
.fi
.PP
.br
\fITAUP2\fP 
.PP
.nf
!>          TAUP2 is DOUBLE PRECISION array, dimension (M-P)
!>           The scalar factors of the elementary reflectors that define
!>           P2\&.
!> 
.fi
.PP
.br
\fITAUQ1\fP 
.PP
.nf
!>          TAUQ1 is DOUBLE PRECISION array, dimension (Q)
!>           The scalar factors of the elementary reflectors that define
!>           Q1\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>           = 0:  successful exit\&.
!>           < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBReferences:\fP
.RS 4
[1] Brian D\&. Sutton\&. Computing the complete CS decomposition\&. Numer\&. Algorithms, 50(1):33-65, 2009\&. 
.RE
.PP

.PP
Definition at line \fB199\fP of file \fBdorbdb3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.