zuncsd2by1.f (3)

Functions/Subroutines

subroutine zuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)

ZUNCSD2BY1

subroutine zuncsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, complex*16, dimension(ldx11,*)X11, integerLDX11, complex*16, dimension(ldx21,*)X21, integerLDX21, 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(*)WORK, integerLWORK, double precision, dimension(*)RWORK, integerLRWORK, integer, dimension(*)IWORK, integerINFO)

ZUNCSD2BY1

 ZUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
 orthonormal columns that has been partitioned into a 2-by-1 block
 structure:

                                [  I  0  0 ]
                                [  0  C  0 ]
          [ X11 ]   [ U1 |    ] [  0  0  0 ]
      X = [-----] = [---------] [----------] V1**T .
          [ X21 ]   [    | U2 ] [  0  0  0 ]
                                [  0  S  0 ]
                                [  0  0  I ]

 X11 is P-by-Q. The unitary 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)..fi



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.

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).

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 X21. LDX21 >= MAX(1,M-P).

THETA

          THETA is COMPLEX*16 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 COMPLEX*16 array, dimension (P)
           If JOBU1 = 'Y', U1 contains the P-by-P 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 (M-P)
           If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
           matrix U2.

LDU2

          LDU2 is INTEGER
           The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
           MAX(1,M-P).

V1T

          V1T is COMPLEX*16 array, dimension (Q)
           If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
           matrix V1**T.

LDV1T

          LDV1T is INTEGER
           The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
           MAX(1,Q).

WORK

          WORK is COMPLEX*16 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 = -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(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.

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.
 \param[out] IWORK
 \verbatim
          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

INFO

          INFO is INTEGER
           = 0:  successful exit.
           < 0:  if INFO = -i, the i-th argument had an illegal value.
           > 0:  ZBBCSD 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:

July 2012

Definition at line 259 of file zuncsd2by1.f.

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