Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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.

   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.

   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.

   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.

Author

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