dorcsd2by1.f man page

dorcsd2by1.f

Synopsis

Functions/Subroutines

subroutine dorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO)
DORCSD2BY1

Function/Subroutine Documentation

subroutine dorcsd2by1 (character JOBU1, character JOBU2, character JOBV1T, 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(ldu1,*) U1, integer LDU1, double precision, dimension(ldu2,*) U2, integer LDU2, double precision, dimension(ldv1t,*) V1T, integer LDV1T, double precision, dimension(*) WORK, integer LWORK, integer, dimension(*) IWORK, integer INFO)

DORCSD2BY1

Purpose:

DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
orthonormal columns that has been partitioned into a 2-by-1 block
structure:

[  I1 0  0 ]
[  0  C  0 ]
[ X11 ]   [ U1 |    ] [  0  0  0 ]
X = [-----] = [---------] [----------] V1**T .
[ X21 ]   [    | U2 ] [  0  0  0 ]
[  0  S  0 ]
[  0  0  I2]

X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
(M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a
K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).
Parameters:

JOBU1

JOBU1 is CHARACTER
= 'Y':      U1 is computed;
otherwise:  U1 is not computed.

JOBU2

JOBU2 is CHARACTER
= 'Y':      U2 is computed;
otherwise:  U2 is not computed.

JOBV1T

JOBV1T is CHARACTER
= 'Y':      V1T is computed;
otherwise:  V1T is not computed.

M

M is INTEGER
The number of rows in X.

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.

X11

X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
On entry, part of the orthogonal matrix whose CSD is desired.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= MAX(1,P).

X21

X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
On entry, part of the orthogonal matrix whose CSD is desired.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= MAX(1,M-P).

THETA

THETA is DOUBLE PRECISION array, dimension (R), in which R =
MIN(P,M-P,Q,M-Q).
C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).

U1

U1 is DOUBLE PRECISION array, dimension (P)
If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

LDU1

LDU1 is INTEGER
The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
MAX(1,P).

U2

U2 is DOUBLE PRECISION array, dimension (M-P)
If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
matrix U2.

LDU2

LDU2 is INTEGER
The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
MAX(1,M-P).

V1T

V1T is DOUBLE PRECISION array, dimension (Q)
If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
matrix V1**T.

LDV1T

LDV1T is INTEGER
The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
MAX(1,Q).

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
define the matrix in intermediate bidiagonal-block form
remaining after nonconvergence. INFO specifies the number
of nonzero PHI's.

LWORK

LWORK is INTEGER
The dimension of the array WORK.

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.

IWORK

IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

INFO

INFO is INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  DBBCSD did not converge. See the description of WORK
above for details.

References:

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

July 2012

Definition at line 235 of file dorcsd2by1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page dorcsd2by1(3) is an alias of dorcsd2by1.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK