cuncsd2by1.f man page

cuncsd2by1.f —

Synopsis

Functions/Subroutines

subroutine cuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD2BY1

Function/Subroutine Documentation

subroutine cuncsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, complex, dimension(ldx11,*)X11, integerLDX11, complex, dimension(ldx21,*)X21, integerLDX21, real, dimension(*)THETA, complex, dimension(ldu1,*)U1, integerLDU1, complex, dimension(ldu2,*)U2, integerLDU2, complex, dimension(ldv1t,*)V1T, integerLDV1T, complex, dimension(*)WORK, integerLWORK, real, dimension(*)RWORK, integerLRWORK, integer, dimension(*)IWORK, integerINFO)

CUNCSD2BY1 .SH "Purpose:"

 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:

                                [  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 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 COMPLEX 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.
 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 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 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:  CBBCSD 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 260 of file cuncsd2by1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

cuncsd2by1(3) is an alias of cuncsd2by1.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK