cuncsd2by1.f3

!>
!> CUNCSD2BY1 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:
!>
!>                                [  I1 0  0 ]
!>                                [  0  C  0 ]
!>          [ X11 ]   [ U1 |    ] [  0  0  0 ]
!>      X = [-----] = [---------] [----------] V1**T .
!>          [ X21 ]   [    | U2 ] [  0  0  0 ]
!>                                [  0  S  0 ]
!>                                [  0  0  I2]
!>
!> X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P,
!> (M-P)-by-(M-P), and Q-by-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). I1 is a K1-by-K1 identity matrix and I2 is a
!> K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).
!>
!> 

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 in X.
!> 

P

!>          P is INTEGER
!>          The number of rows in X11. 0 <= P <= M.
!> 

Q

!>          Q is INTEGER
!>          The number of columns in X11 and X21. 0 <= Q <= M.
!> 

X11

!>          X11 is COMPLEX 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 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 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)) ).
!> 

U1

!>          U1 is COMPLEX 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 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 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 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 and RWORK
!>          arrays, returns this value as the first entry of the WORK
!>          and RWORK array, respectively, and no error message related
!>          to LWORK or LRWORK is issued by XERBLA.
!> 

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.
!> 

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 WORK and RWORK
!>          arrays, returns this value as the first entry of the WORK
!>          and RWORK array, respectively, and no error message related
!>          to LWORK or LRWORK 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 = -i, the i-th argument had an illegal value.
!>          > 0:  CBBCSD did not converge. See the description of WORK
!>                above for details.
!> 

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

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