sorcsd (3)  Linux Manuals
NAME
sorcsd.f 
SYNOPSIS
Functions/Subroutines
recursive subroutine sorcsd (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)
SORCSD
Function/Subroutine Documentation
recursive subroutine sorcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM, integerP, integerQ, real, dimension( ldx11, * )X11, integerLDX11, real, dimension( ldx12, * )X12, integerLDX12, real, dimension( ldx21, * )X21, integerLDX21, real, dimension( ldx22, * )X22, integerLDX22, real, dimension( * )THETA, real, dimension( ldu1, * )U1, integerLDU1, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldv1t, * )V1T, integerLDV1T, real, dimension( ldv2t, * )V2T, integerLDV2T, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
SORCSD
Purpose:

SORCSD computes the CS decomposition of an MbyM 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 PbyQ. The orthogonal matrices U1, U2, V1, and V2 are PbyP, (MP)by(MP), QbyQ, and (MQ)by(MQ), respectively. C and S are RbyR nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which R = MIN(P,MP,Q,MQ).
Parameters:

JOBU1
JOBU1 is CHARACTER = 'Y': U1 is computed; otherwise: U1 is not computed.
JOBU2JOBU2 is CHARACTER = 'Y': U2 is computed; otherwise: U2 is not computed.
JOBV1TJOBV1T is CHARACTER = 'Y': V1T is computed; otherwise: V1T is not computed.
JOBV2TJOBV2T is CHARACTER = 'Y': V2T is computed; otherwise: V2T is not computed.
TRANSTRANS is CHARACTER = 'T': X, U1, U2, V1T, and V2T are stored in rowmajor order; otherwise: X, U1, U2, V1T, and V2T are stored in column major order.
SIGNSSIGNS is CHARACTER = 'O': The lowerleft block is made nonpositive (the "other" convention); otherwise: The upperright block is made nonpositive (the "default" convention).
MM is INTEGER The number of rows and columns in X.
PP is INTEGER The number of rows in X11 and X12. 0 <= P <= M.
QQ is INTEGER The number of columns in X11 and X21. 0 <= Q <= M.
X11X11 is REAL array, dimension (LDX11,Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX11LDX11 is INTEGER The leading dimension of X11. LDX11 >= MAX(1,P).
X12X12 is REAL array, dimension (LDX12,MQ) On entry, part of the orthogonal matrix whose CSD is desired.
LDX12LDX12 is INTEGER The leading dimension of X12. LDX12 >= MAX(1,P).
X21X21 is REAL array, dimension (LDX21,Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX21LDX21 is INTEGER The leading dimension of X11. LDX21 >= MAX(1,MP).
X22X22 is REAL array, dimension (LDX22,MQ) On entry, part of the orthogonal matrix whose CSD is desired.
LDX22LDX22 is INTEGER The leading dimension of X11. LDX22 >= MAX(1,MP).
THETATHETA is REAL array, dimension (R), in which R = MIN(P,MP,Q,MQ). C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
U1U1 is REAL array, dimension (P) If JOBU1 = 'Y', U1 contains the PbyP orthogonal matrix U1.
LDU1LDU1 is INTEGER The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= MAX(1,P).
U2U2 is REAL array, dimension (MP) If JOBU2 = 'Y', U2 contains the (MP)by(MP) orthogonal matrix U2.
LDU2LDU2 is INTEGER The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,MP).
V1TV1T is REAL array, dimension (Q) If JOBV1T = 'Y', V1T contains the QbyQ matrix orthogonal matrix V1**T.
LDV1TLDV1T is INTEGER The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q).
V2TV2T is REAL array, dimension (MQ) If JOBV2T = 'Y', V2T contains the (MQ)by(MQ) orthogonal matrix V2**T.
LDV2TLDV2T is INTEGER The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= MAX(1,MQ).
WORKWORK 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(R1) that, together with THETA(1), ..., THETA(R), define the matrix in intermediate bidiagonalblock form remaining after nonconvergence. INFO specifies the number of nonzero PHI's.
LWORKLWORK 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.
IWORKIWORK is INTEGER array, dimension (MMIN(P, MP, Q, MQ))
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith 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):3365, 2009.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2013
Definition at line 297 of file sorcsd.f.
Author
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