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dorcsd.f(3) LAPACK dorcsd.f(3)

NAME

dorcsd.f -

SYNOPSIS

Functions/Subroutines


recursive subroutine dorcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO)
DORCSD

Function/Subroutine Documentation

recursive subroutine dorcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM, integerP, integerQ, double precision, dimension( ldx11, * )X11, integerLDX11, double precision, dimension( ldx12, * )X12, integerLDX12, double precision, dimension( ldx21, * )X21, integerLDX21, double precision, dimension( ldx22, * )X22, integerLDX22, double precision, dimension( * )THETA, double precision, dimension( ldu1, * )U1, integerLDU1, double precision, dimension( ldu2, * )U2, integerLDU2, double precision, dimension( ldv1t, * )V1T, integerLDV1T, double precision, dimension( ldv2t, * )V2T, integerLDV2T, double precision, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)

DORCSD

Purpose:


DORCSD computes the CS decomposition of an M-by-M partitioned
orthogonal matrix X:
[ I 0 0 | 0 0 0 ]
[ 0 C 0 | 0 -S 0 ]
[ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T
X = [-----------] = [---------] [---------------------] [---------] .
[ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
[ 0 S 0 | 0 C 0 ]
[ 0 0 I | 0 0 0 ]
X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
(M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-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).

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.

JOBV2T


JOBV2T is CHARACTER
= 'Y': V2T is computed;
otherwise: V2T is not computed.

TRANS


TRANS is CHARACTER
= 'T': X, U1, U2, V1T, and V2T are stored in row-major
order;
otherwise: X, U1, U2, V1T, and V2T are stored in column-
major order.

SIGNS


SIGNS is CHARACTER
= 'O': The lower-left block is made nonpositive (the
"other" convention);
otherwise: The upper-right block is made nonpositive (the
"default" convention).

M


M is INTEGER
The number of rows and columns in X.

P


P is INTEGER
The number of rows in X11 and X12. 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).

X12


X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q)
On entry, part of the orthogonal matrix whose CSD is desired.

LDX12


LDX12 is INTEGER
The leading dimension of X12. LDX12 >= 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 X11. LDX21 >= MAX(1,M-P).

X22


X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q)
On entry, part of the orthogonal matrix whose CSD is desired.

LDX22


LDX22 is INTEGER
The leading dimension of X11. LDX22 >= 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).

V2T


V2T is DOUBLE PRECISION array, dimension (M-Q)
If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
matrix V2**T.

LDV2T


LDV2T is INTEGER
The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
MAX(1,M-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:

[1] 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:

November 2011

Definition at line 297 of file dorcsd.f.

Author

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Tue Sep 25 2012 Version 3.4.2