
NAMEzuncsd.f SYNOPSISFunctions/Subroutinesrecursive subroutine zuncsd (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, RWORK, LRWORK, IWORK, INFO) Function/Subroutine Documentationrecursive subroutine zuncsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM, integerP, integerQ, complex*16, dimension( ldx11, * )X11, integerLDX11, complex*16, dimension( ldx12, * )X12, integerLDX12, complex*16, dimension( ldx21, * )X21, integerLDX21, complex*16, dimension( ldx22, * )X22, integerLDX22, double precision, dimension( * )THETA, complex*16, dimension( ldu1, * )U1, integerLDU1, complex*16, dimension( ldu2, * )U2, integerLDU2, complex*16, dimension( ldv1t, * )V1T, integerLDV1T, complex*16, dimension( ldv2t, * )V2T, integerLDV2T, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerINFO)ZUNCSD Purpose:ZUNCSD computes the CS decomposition of an MbyM partitioned unitary matrix X: [ I 0 0  0 0 0 ] [ 0 C 0  0 S 0 ] [ X11  X12 ] [ U1  ] [ 0 0 0  0 0 I ] [ V1  ]**H 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 unitary 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). JOBU1
References:
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 rowmajor order; otherwise: X, U1, U2, V1T, and V2T are stored in column major order.SIGNS SIGNS is CHARACTER = 'O': The lowerleft block is made nonpositive (the "other" convention); otherwise: The upperright 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 COMPLEX*16 array, dimension (LDX11,Q) On entry, part of the unitary matrix whose CSD is desired.LDX11 LDX11 is INTEGER The leading dimension of X11. LDX11 >= MAX(1,P).X12 X12 is COMPLEX*16 array, dimension (LDX12,MQ) On entry, part of the unitary matrix whose CSD is desired.LDX12 LDX12 is INTEGER The leading dimension of X12. LDX12 >= MAX(1,P).X21 X21 is COMPLEX*16 array, dimension (LDX21,Q) On entry, part of the unitary matrix whose CSD is desired.LDX21 LDX21 is INTEGER The leading dimension of X11. LDX21 >= MAX(1,MP).X22 X22 is COMPLEX*16 array, dimension (LDX22,MQ) On entry, part of the unitary matrix whose CSD is desired.LDX22 LDX22 is INTEGER The leading dimension of X11. LDX22 >= MAX(1,MP).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)) ).U1 U1 is COMPLEX*16 array, dimension (P) If JOBU1 = 'Y', U1 contains the PbyP unitary matrix U1.LDU1 LDU1 is INTEGER The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= MAX(1,P).U2 U2 is COMPLEX*16 array, dimension (MP) If JOBU2 = 'Y', U2 contains the (MP)by(MP) unitary matrix U2.LDU2 LDU2 is INTEGER The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,MP).V1T V1T is COMPLEX*16 array, dimension (Q) If JOBV1T = 'Y', V1T contains the QbyQ matrix unitary matrix V1**H.LDV1T LDV1T is INTEGER The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q).V2T V2T is COMPLEX*16 array, dimension (MQ) If JOBV2T = 'Y', V2T contains the (MQ)by(MQ) unitary matrix V2**H.LDV2T LDV2T is INTEGER The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= MAX(1,MQ).WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.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.RWORK RWORK is DOUBLE PRECISION array, dimension MAX(1,LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. If INFO > 0 on exit, RWORK(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.LRWORK LRWORK is INTEGER The dimension of the array RWORK. If LRWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the work array, and no error message related to LRWORK is issued by XERBLA.IWORK IWORK is INTEGER array, dimension (MMIN(P,MP,Q,MQ))INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: ZBBCSD did not converge. See the description of RWORK above for details. [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 316 of file zuncsd.f.
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