LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ sorcsd2by1()

subroutine sorcsd2by1 ( character  JOBU1,
character  JOBU2,
character  JOBV1T,
integer  M,
integer  P,
integer  Q,
real, dimension(ldx11,*)  X11,
integer  LDX11,
real, dimension(ldx21,*)  X21,
integer  LDX21,
real, dimension(*)  THETA,
real, dimension(ldu1,*)  U1,
integer  LDU1,
real, dimension(ldu2,*)  U2,
integer  LDU2,
real, dimension(ldv1t,*)  V1T,
integer  LDV1T,
real, dimension(*)  WORK,
integer  LWORK,
integer, dimension(*)  IWORK,
integer  INFO 
)

SORCSD2BY1

Download SORCSD2BY1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SORCSD2BY1 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 orthogonal 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).
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]M
          M is INTEGER
          The number of rows in X.
[in]P
          P is INTEGER
          The number of rows in X11. 0 <= P <= M.
[in]Q
          Q is INTEGER
          The number of columns in X11 and X21. 0 <= Q <= M.
[in,out]X11
          X11 is REAL array, dimension (LDX11,Q)
          On entry, part of the orthogonal matrix whose CSD is desired.
[in]LDX11
          LDX11 is INTEGER
          The leading dimension of X11. LDX11 >= MAX(1,P).
[in,out]X21
          X21 is REAL array, dimension (LDX21,Q)
          On entry, part of the orthogonal matrix whose CSD is desired.
[in]LDX21
          LDX21 is INTEGER
           The leading dimension of X21. LDX21 >= 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 REAL array, dimension (P)
          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
[in]LDU1
          LDU1 is INTEGER
          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
          MAX(1,P).
[out]U2
          U2 is REAL array, dimension (M-P)
          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
          matrix U2.
[in]LDU2
          LDU2 is INTEGER
          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
          MAX(1,M-P).
[out]V1T
          V1T is REAL array, dimension (Q)
          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
          matrix V1**T.
[in]LDV1T
          LDV1T is INTEGER
          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
          MAX(1,Q).
[out]WORK
          WORK is REAL 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.
[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]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:  SBBCSD 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.