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dorcsd.f(3) LAPACK dorcsd.f(3)NAMEdorcsd.f-SYNOPSISFunctions/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) DORCSDFunction/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 | 00 ] [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0-S] [ V1 | ]**T X = [-I] = [-----------] [---------] [---------------------] . [ 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 =---------, 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 =-1, 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.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dorcsd.f(3)

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