uncsd2by1(3)

NAME
uncsd2by1 - {un,or}csd2by1: ??

SYNOPSIS

  Functions
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
subroutine dorcsd2by1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork, info)
DORCSD2BY1
subroutine sorcsd2by1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork, info)
SORCSD2BY1
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

Detailed Description

Function Documentation

  subroutine cuncsd2by1 (character jobu1, character jobu2, character jobv1t, integer m, integer p, integer q, complex, dimension(ldx11,*) x11, integer ldx11, complex, dimension(ldx21,*) x21, integer ldx21, real, dimension(*) theta, complex, dimension(ldu1,*) u1, integer ldu1, complex, dimension(ldu2,*) u2, integer ldu2, complex, dimension(ldv1t,*) v1t, integer ldv1t, complex, dimension(*) work, integer lwork, real, dimension(*) rwork, integer lrwork, integer, dimension(*) iwork, integer info)

CUNCSD2BY1

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:
                                    [  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).

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 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.

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.

Definition at line 253 of file cuncsd2by1.f.

  subroutine dorcsd2by1 (character jobu1, character jobu2, character jobv1t, integer m, integer p, integer q, double precision, dimension(ldx11,*) x11, integer ldx11, double precision, dimension(ldx21,*) x21, integer ldx21, double precision, dimension(*) theta, double precision, dimension(ldu1,*) u1, integer ldu1, double precision, dimension(ldu2,*) u2, integer ldu2, double precision, dimension(ldv1t,*) v1t, integer ldv1t, double precision, dimension(*) work, integer lwork, integer, dimension(*) iwork, integer info)

DORCSD2BY1

Purpose:

     DORCSD2BY1 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
    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 DOUBLE PRECISION array, dimension (LDX11,Q)
              On entry, part of the orthogonal matrix whose CSD is desired.

    LDX11

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

    X21

              X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
              On entry, part of the orthogonal matrix whose CSD is desired.

    LDX21

              LDX21 is INTEGER
              The leading dimension of X21. LDX21 >= MAX(1,M-P).

    THETA

              THETA is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (P)
              If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

    LDU1

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

    U2

              U2 is DOUBLE PRECISION array, dimension (M-P)
              If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
              matrix U2.

    LDU2

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

    V1T

              V1T is DOUBLE PRECISION array, dimension (Q)
              If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
              matrix V1**T.

    LDV1T

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

    WORK

              WORK is DOUBLE PRECISION 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.

    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:  DBBCSD 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.

Definition at line 230 of file dorcsd2by1.f.

  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

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
    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 REAL array, dimension (LDX11,Q)
              On entry, part of the orthogonal matrix whose CSD is desired.

    LDX11

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

    X21

              X21 is REAL array, dimension (LDX21,Q)
              On entry, part of the orthogonal 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 REAL array, dimension (P)
              If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

    LDU1

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

    U2

              U2 is REAL array, dimension (M-P)
              If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
              matrix U2.

    LDU2

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

    V1T

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

    LDV1T

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

    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.

    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.

    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:  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.

Definition at line 230 of file sorcsd2by1.f.

  subroutine zuncsd2by1 (character jobu1, character jobu2, character jobv1t, integer m, integer p, integer q, complex*16, dimension(ldx11,*) x11, integer ldx11, complex*16, dimension(ldx21,*) x21, integer ldx21, double precision, dimension(*) theta, complex*16, dimension(ldu1,*) u1, integer ldu1, complex*16, dimension(ldu2,*) u2, integer ldu2, complex*16, dimension(ldv1t,*) v1t, integer ldv1t, complex*16, dimension(*) work, integer lwork, double precision, dimension(*) rwork, integer lrwork, integer, dimension(*) iwork, integer info)

ZUNCSD2BY1

Purpose:

     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:
                                    [  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).

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 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*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 DOUBLE PRECISION 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.

    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 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 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:  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.

Definition at line 252 of file zuncsd2by1.f.

Author

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