
NAMEzbbcsd.f SYNOPSISFunctions/Subroutinessubroutine zbbcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO) Function/Subroutine Documentationsubroutine zbbcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, integerM, integerP, integerQ, double precision, dimension( * )THETA, double precision, dimension( * )PHI, complex*16, dimension( ldu1, * )U1, integerLDU1, complex*16, dimension( ldu2, * )U2, integerLDU2, complex*16, dimension( ldv1t, * )V1T, integerLDV1T, complex*16, dimension( ldv2t, * )V2T, integerLDV2T, double precision, dimension( * )B11D, double precision, dimension( * )B11E, double precision, dimension( * )B12D, double precision, dimension( * )B12E, double precision, dimension( * )B21D, double precision, dimension( * )B21E, double precision, dimension( * )B22D, double precision, dimension( * )B22E, double precision, dimension( * )RWORK, integerLRWORK, integerINFO)ZBBCSD Purpose:ZBBCSD computes the CS decomposition of a unitary matrix in bidiagonalblock form, [ B11  B12 0 0 ] [ 0  0 I 0 ] X = [] [ B21  B22 0 0 ] [ 0  0 0 I ] [ C  S 0 0 ] [ U1  ] [ 0  0 I 0 ] [ V1  ]**H = [] [] [] . [  U2 ] [ S  C 0 0 ] [  V2 ] [ 0  0 0 I ] X is MbyM, its topleft block is PbyQ, and Q must be no larger than P, MP, or MQ. (If Q is not the smallest index, then X must be transposed and/or permuted. This can be done in constant time using the TRANS and SIGNS options. See ZUNCSD for details.) The bidiagonal matrices B11, B12, B21, and B22 are represented implicitly by angles THETA(1:Q) and PHI(1:Q1). The unitary matrices U1, U2, V1T, and V2T are input/output. The input matrices are pre or postmultiplied by the appropriate singular vector matrices. JOBU1
Internal Parameters:
JOBU1 is CHARACTER = 'Y': U1 is updated; otherwise: U1 is not updated.JOBU2 JOBU2 is CHARACTER = 'Y': U2 is updated; otherwise: U2 is not updated.JOBV1T JOBV1T is CHARACTER = 'Y': V1T is updated; otherwise: V1T is not updated.JOBV2T JOBV2T is CHARACTER = 'Y': V2T is updated; otherwise: V2T is not updated.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.M M is INTEGER The number of rows and columns in X, the unitary matrix in bidiagonalblock form.P P is INTEGER The number of rows in the topleft block of X. 0 <= P <= M.Q Q is INTEGER The number of columns in the topleft block of X. 0 <= Q <= MIN(P,MP,MQ).THETA THETA is DOUBLE PRECISION array, dimension (Q) On entry, the angles THETA(1),...,THETA(Q) that, along with PHI(1), ...,PHI(Q1), define the matrix in bidiagonalblock form. On exit, the angles whose cosines and sines define the diagonal blocks in the CS decomposition.PHI PHI is DOUBLE PRECISION array, dimension (Q1) The angles PHI(1),...,PHI(Q1) that, along with THETA(1),..., THETA(Q), define the matrix in bidiagonalblock form.U1 U1 is COMPLEX*16 array, dimension (LDU1,P) On entry, an LDU1byP matrix. On exit, U1 is postmultiplied by the left singular vector matrix common to [ B11 ; 0 ] and [ B12 0 0 ; 0 I 0 0 ].LDU1 LDU1 is INTEGER The leading dimension of the array U1.U2 U2 is COMPLEX*16 array, dimension (LDU2,MP) On entry, an LDU2by(MP) matrix. On exit, U2 is postmultiplied by the left singular vector matrix common to [ B21 ; 0 ] and [ B22 0 0 ; 0 0 I ].LDU2 LDU2 is INTEGER The leading dimension of the array U2.V1T V1T is COMPLEX*16 array, dimension (LDV1T,Q) On entry, a LDV1TbyQ matrix. On exit, V1T is premultiplied by the conjugate transpose of the right singular vector matrix common to [ B11 ; 0 ] and [ B21 ; 0 ].LDV1T LDV1T is INTEGER The leading dimension of the array V1T.V2T V2T is COMPLEX*16 array, dimenison (LDV2T,MQ) On entry, a LDV2Tby(MQ) matrix. On exit, V2T is premultiplied by the conjugate transpose of the right singular vector matrix common to [ B12 0 0 ; 0 I 0 ] and [ B22 0 0 ; 0 0 I ].LDV2T LDV2T is INTEGER The leading dimension of the array V2T.B11D B11D is DOUBLE PRECISION array, dimension (Q) When ZBBCSD converges, B11D contains the cosines of THETA(1), ..., THETA(Q). If ZBBCSD fails to converge, then B11D contains the diagonal of the partially reduced topleft block.B11E B11E is DOUBLE PRECISION array, dimension (Q1) When ZBBCSD converges, B11E contains zeros. If ZBBCSD fails to converge, then B11E contains the superdiagonal of the partially reduced topleft block.B12D B12D is DOUBLE PRECISION array, dimension (Q) When ZBBCSD converges, B12D contains the negative sines of THETA(1), ..., THETA(Q). If ZBBCSD fails to converge, then B12D contains the diagonal of the partially reduced topright block.B12E B12E is DOUBLE PRECISION array, dimension (Q1) When ZBBCSD converges, B12E contains zeros. If ZBBCSD fails to converge, then B12E contains the subdiagonal of the partially reduced topright block.B21D B21D is DOUBLE PRECISION array, dimension (Q) When CBBCSD converges, B21D contains the negative sines of THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then B21D contains the diagonal of the partially reduced bottomleft block.B21E B21E is DOUBLE PRECISION array, dimension (Q1) When CBBCSD converges, B21E contains zeros. If CBBCSD fails to converge, then B21E contains the subdiagonal of the partially reduced bottomleft block.B22D B22D is DOUBLE PRECISION array, dimension (Q) When CBBCSD converges, B22D contains the negative sines of THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then B22D contains the diagonal of the partially reduced bottomright block.B22E B22E is DOUBLE PRECISION array, dimension (Q1) When CBBCSD converges, B22E contains zeros. If CBBCSD fails to converge, then B22E contains the subdiagonal of the partially reduced bottomright block.RWORK RWORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LRWORK LRWORK is INTEGER The dimension of the array RWORK. LRWORK >= MAX(1,8*Q). 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.INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: if ZBBCSD did not converge, INFO specifies the number of nonzero entries in PHI, and B11D, B11E, etc., contain the partially reduced matrix. TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(1/8))) TOLMUL controls the convergence criterion of the QR loop. Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they are within TOLMUL*EPS of either bound. [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 330 of file zbbcsd.f.
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