LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
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 
recursive subroutine dorcsd  (  character  JOBU1, 
character  JOBU2,  
character  JOBV1T,  
character  JOBV2T,  
character  TRANS,  
character  SIGNS,  
integer  M,  
integer  P,  
integer  Q,  
double precision, dimension( ldx11, * )  X11,  
integer  LDX11,  
double precision, dimension( ldx12, * )  X12,  
integer  LDX12,  
double precision, dimension( ldx21, * )  X21,  
integer  LDX21,  
double precision, dimension( ldx22, * )  X22,  
integer  LDX22,  
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( ldv2t, * )  V2T,  
integer  LDV2T,  
double precision, dimension( * )  WORK,  
integer  LWORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
DORCSD
Download DORCSD + dependencies [TGZ] [ZIP] [TXT]DORCSD 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).
[in]  JOBU1  JOBU1 is CHARACTER = 'Y': U1 is computed; otherwise: U1 is not computed. 
[in]  JOBU2  JOBU2 is CHARACTER = 'Y': U2 is computed; otherwise: U2 is not computed. 
[in]  JOBV1T  JOBV1T is CHARACTER = 'Y': V1T is computed; otherwise: V1T is not computed. 
[in]  JOBV2T  JOBV2T is CHARACTER = 'Y': V2T is computed; otherwise: V2T is not computed. 
[in]  TRANS  TRANS 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. 
[in]  SIGNS  SIGNS is CHARACTER = 'O': The lowerleft block is made nonpositive (the "other" convention); otherwise: The upperright block is made nonpositive (the "default" convention). 
[in]  M  M is INTEGER The number of rows and columns in X. 
[in]  P  P is INTEGER The number of rows in X11 and X12. 0 <= P <= M. 
[in]  Q  Q is INTEGER The number of columns in X11 and X21. 0 <= Q <= M. 
[in,out]  X11  X11 is DOUBLE PRECISION array, dimension (LDX11,Q) On entry, part of the orthogonal matrix whose CSD is desired. 
[in]  LDX11  LDX11 is INTEGER The leading dimension of X11. LDX11 >= MAX(1,P). 
[in,out]  X12  X12 is DOUBLE PRECISION array, dimension (LDX12,MQ) On entry, part of the orthogonal matrix whose CSD is desired. 
[in]  LDX12  LDX12 is INTEGER The leading dimension of X12. LDX12 >= MAX(1,P). 
[in,out]  X21  X21 is DOUBLE PRECISION array, dimension (LDX21,Q) On entry, part of the orthogonal matrix whose CSD is desired. 
[in]  LDX21  LDX21 is INTEGER The leading dimension of X11. LDX21 >= MAX(1,MP). 
[in,out]  X22  X22 is DOUBLE PRECISION array, dimension (LDX22,MQ) On entry, part of the orthogonal matrix whose CSD is desired. 
[in]  LDX22  LDX22 is INTEGER The leading dimension of X11. LDX22 >= MAX(1,MP). 
[out]  THETA  THETA is DOUBLE PRECISION 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)) ). 
[out]  U1  U1 is DOUBLE PRECISION array, dimension (P) If JOBU1 = 'Y', U1 contains the PbyP orthogonal matrix U1. 
[in]  LDU1  LDU1 is INTEGER The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= MAX(1,P). 
[out]  U2  U2 is DOUBLE PRECISION array, dimension (MP) If JOBU2 = 'Y', U2 contains the (MP)by(MP) orthogonal matrix U2. 
[in]  LDU2  LDU2 is INTEGER The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,MP). 
[out]  V1T  V1T is DOUBLE PRECISION array, dimension (Q) If JOBV1T = 'Y', V1T contains the QbyQ matrix orthogonal matrix V1**T. 
[in]  LDV1T  LDV1T is INTEGER The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q). 
[out]  V2T  V2T is DOUBLE PRECISION array, dimension (MQ) If JOBV2T = 'Y', V2T contains the (MQ)by(MQ) orthogonal matrix V2**T. 
[in]  LDV2T  LDV2T is INTEGER The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= MAX(1,MQ). 
[out]  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(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. 
[in]  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. 
[out]  IWORK  IWORK is INTEGER array, dimension (MMIN(P, MP, Q, MQ)) 
[out]  INFO  INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: DBBCSD did not converge. See the description of WORK above for details. 
Definition at line 297 of file dorcsd.f.