dorbdb4 (3) Linux Manual Page

dorbdb4.f –

Synopsis

Functions/Subroutines

subroutine dorbdb4 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
DORBDB4

Function/Subroutine Documentation

subroutine dorbdb4 (integerM, integerP, integerQ, double precision, dimension(ldx11,*)X11, integerLDX11, double precision, dimension(ldx21,*)X21, integerLDX21, double precision, dimension(*)THETA, double precision, dimension(*)PHI, double precision, dimension(*)TAUP1, double precision, dimension(*)TAUP2, double precision, dimension(*)TAUQ1, double precision, dimension(*)PHANTOM, double precision, dimension(*)WORK, integerLWORK, integerINFO)

DORBDB4 .SH "Purpose:"

 DORBDB4 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-Q must be no larger than P,

 M-P, or Q. Routines DORBDB1, DORBDB2, and DORBDB3 handle cases in

 which M-Q 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-Q)-by-(M-Q) 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.

Q

 Q is INTEGER

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

 M-Q <= min(P,M-P,Q).

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.

PHANTOM

 PHANTOM is DOUBLE PRECISION array, dimension (M)

 The routine computes an M-by-1 column vector Y that is

 orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and

 PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and

 Y(P+1:M), respectively.

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 212 of file dorbdb4.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.