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sorbdb3.f(3) LAPACK sorbdb3.f(3)

NAME

sorbdb3.f -

SYNOPSIS

Functions/Subroutines


subroutine sorbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
 
SORBDB3

Function/Subroutine Documentation

subroutine sorbdb3 (integerM, integerP, integerQ, real, dimension(ldx11,*)X11, integerLDX11, real, dimension(ldx21,*)X21, integerLDX21, real, dimension(*)THETA, real, dimension(*)PHI, real, dimension(*)TAUP1, real, dimension(*)TAUP2, real, dimension(*)TAUQ1, real, dimension(*)WORK, integerLWORK, integerINFO)

SORBDB3

Purpose:

 SORBDB3 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 SORBDB1, SORBDB2, and SORBDB4 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
 
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 REAL 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 REAL 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 REAL array, dimension (Q)
           The entries of the bidiagonal blocks B11, B21 are defined by
           THETA and PHI. See Further Details.
PHI
          PHI is REAL array, dimension (Q-1)
           The entries of the bidiagonal blocks B11, B21 are defined by
           THETA and PHI. See Further Details.
TAUP1
          TAUP1 is REAL array, dimension (P)
           The scalar factors of the elementary reflectors that define
           P1.
TAUP2
          TAUP2 is REAL array, dimension (M-P)
           The scalar factors of the elementary reflectors that define
           P2.
TAUQ1
          TAUQ1 is REAL array, dimension (Q)
           The scalar factors of the elementary reflectors that define
           Q1.
WORK
          WORK is REAL 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 SORCSD for details.
P1, P2, and Q1 are represented as products of elementary reflectors. See SORCSD2BY1 for details on generating P1, P2, and Q1 using SORGQR and SORGLQ.
References:
[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.
Definition at line 202 of file sorbdb3.f.

Author

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