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## cuncsd()

recursive subroutine cuncsd | ( | character | jobu1,
|  | character | jobu2,
|  | character | jobv1t,
|  | character | jobv2t,
|  | character | trans,
|  | character | signs,
|  | integer | m,
|  | integer | p,
|  | integer | q,
|  | complex, dimension( ldx11, * ) | x11,
|  | integer | ldx11,
|  | complex, dimension( ldx12, * ) | x12,
|  | integer | ldx12,
|  | complex, dimension( ldx21, * ) | x21,
|  | integer | ldx21,
|  | complex, dimension( ldx22, * ) | x22,
|  | integer | ldx22,
|  | real, dimension( * ) | theta,
|  | complex, dimension( ldu1, * ) | u1,
|  | integer | ldu1,
|  | complex, dimension( ldu2, * ) | u2,
|  | integer | ldu2,
|  | complex, dimension( ldv1t, * ) | v1t,
|  | integer | ldv1t,
|  | complex, dimension( ldv2t, * ) | v2t,
|  | integer | ldv2t,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | real, dimension( * ) | rwork,
|  | integer | lrwork,
|  | integer, dimension( * ) | iwork,
|  | integer | info )

CUNCSD

Download CUNCSD + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CUNCSD computes the CS decomposition of an M-by-M 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 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).
      !>

Parameters

  [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 row-major
      !>                      order;
      !>          otherwise:  X, U1, U2, V1T, and V2T are stored in column-
      !>                      major order.
      !>

  [in]

  SIGNS

      !>          SIGNS is CHARACTER
      !>          = 'O':      The lower-left block is made nonpositive (the
      !>                       convention);
      !>          otherwise:  The upper-right block is made nonpositive (the
      !>                       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 COMPLEX array, dimension (LDX11,Q)
      !>          On entry, part of the unitary matrix whose CSD is desired.
      !>

  [in]

  LDX11

      !>          LDX11 is INTEGER
      !>          The leading dimension of X11. LDX11 >= MAX(1,P).
      !>

  [in,out]

  X12

      !>          X12 is COMPLEX array, dimension (LDX12,M-Q)
      !>          On entry, part of the unitary matrix whose CSD is desired.
      !>

  [in]

  LDX12

      !>          LDX12 is INTEGER
      !>          The leading dimension of X12. LDX12 >= MAX(1,P).
      !>

  [in,out]

  X21

      !>          X21 is COMPLEX array, dimension (LDX21,Q)
      !>          On entry, part of the unitary matrix whose CSD is desired.
      !>

  [in]

  LDX21

      !>          LDX21 is INTEGER
      !>          The leading dimension of X11. LDX21 >= MAX(1,M-P).
      !>

  [in,out]

  X22

      !>          X22 is COMPLEX array, dimension (LDX22,M-Q)
      !>          On entry, part of the unitary matrix whose CSD is desired.
      !>

  [in]

  LDX22

      !>          LDX22 is INTEGER
      !>          The leading dimension of X11. LDX22 >= MAX(1,M-P).
      !>

  [out]

  THETA

      !>          THETA is REAL 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)) ).
      !>

  [out]

  U1

      !>          U1 is COMPLEX array, dimension (LDU1,P)
      !>          If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
      !>

  [in]

  LDU1

      !>          LDU1 is INTEGER
      !>          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
      !>          MAX(1,P).
      !>

  [out]

  U2

      !>          U2 is COMPLEX array, dimension (LDU2,M-P)
      !>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
      !>          matrix U2.
      !>

  [in]

  LDU2

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

  [out]

  V1T

      !>          V1T is COMPLEX array, dimension (LDV1T,Q)
      !>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
      !>          matrix V1**H.
      !>

  [in]

  LDV1T

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

  [out]

  V2T

      !>          V2T is COMPLEX array, dimension (LDV2T,M-Q)
      !>          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
      !>          matrix V2**H.
      !>

  [in]

  LDV2T

      !>          LDV2T is INTEGER
      !>          The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
      !>          MAX(1,M-Q).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
      !>

  [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]

  RWORK

      !>          RWORK is REAL 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.
      !>

  [in]

  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.
      !>

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit.
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
      !>          > 0:  CBBCSD did not converge. See the description of RWORK
      !>                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.