sorcsd2by1.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEsorcsd2by1.f
SYNOPSIS
Functions/Subroutinessubroutine sorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO)
SORCSD2BY1
Function/Subroutine Documentation
subroutine sorcsd2by1 (character JOBU1, character JOBU2, character JOBV1T, integer M, integer P, integer Q, real, dimension(ldx11,*) X11, integer LDX11, real, dimension(ldx21,*) X21, integer LDX21, real, dimension(*) THETA, real, dimension(ldu1,*) U1, integer LDU1, real, dimension(ldu2,*) U2, integer LDU2, real, dimension(ldv1t,*) V1T, integer LDV1T, real, dimension(*) WORK, integer LWORK, integer, dimension(*) IWORK, integer INFO)SORCSD2BY1 Purpose: SORCSD2BY1 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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: SBBCSD 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: July 2012 Definition at line 235 of file sorcsd2by1.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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