.TH "uncsd2by1" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
uncsd2by1 \- {un,or}csd2by1: ??
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcuncsd2by1\fP (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, rwork, lrwork, iwork, info)"
.br
.RI "\fBCUNCSD2BY1\fP "
.ti -1c
.RI "subroutine \fBdorcsd2by1\fP (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork, info)"
.br
.RI "\fBDORCSD2BY1\fP "
.ti -1c
.RI "subroutine \fBsorcsd2by1\fP (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork, info)"
.br
.RI "\fBSORCSD2BY1\fP "
.ti -1c
.RI "subroutine \fBzuncsd2by1\fP (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, rwork, lrwork, iwork, info)"
.br
.RI "\fBZUNCSD2BY1\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBCUNCSD2BY1\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBU1\fP 
.PP
.nf
!>          JOBU1 is CHARACTER
!>          = 'Y':      U1 is computed;
!>          otherwise:  U1 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBU2\fP 
.PP
.nf
!>          JOBU2 is CHARACTER
!>          = 'Y':      U2 is computed;
!>          otherwise:  U2 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBV1T\fP 
.PP
.nf
!>          JOBV1T is CHARACTER
!>          = 'Y':      V1T is computed;
!>          otherwise:  V1T is not computed\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows in X\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows in X11\&. 0 <= P <= M\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>          The number of columns in X11 and X21\&. 0 <= Q <= M\&.
!> 
.fi
.PP
.br
\fIX11\fP 
.PP
.nf
!>          X11 is COMPLEX array, dimension (LDX11,Q)
!>          On entry, part of the unitary matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX11\fP 
.PP
.nf
!>          LDX11 is INTEGER
!>          The leading dimension of X11\&. LDX11 >= MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIX21\fP 
.PP
.nf
!>          X21 is COMPLEX array, dimension (LDX21,Q)
!>          On entry, part of the unitary matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX21\fP 
.PP
.nf
!>          LDX21 is INTEGER
!>          The leading dimension of X21\&. LDX21 >= MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          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)) )\&.
!> 
.fi
.PP
.br
\fIU1\fP 
.PP
.nf
!>          U1 is COMPLEX array, dimension (P)
!>          If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1\&.
!> 
.fi
.PP
.br
\fILDU1\fP 
.PP
.nf
!>          LDU1 is INTEGER
!>          The leading dimension of U1\&. If JOBU1 = 'Y', LDU1 >=
!>          MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIU2\fP 
.PP
.nf
!>          U2 is COMPLEX array, dimension (M-P)
!>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
!>          matrix U2\&.
!> 
.fi
.PP
.br
\fILDU2\fP 
.PP
.nf
!>          LDU2 is INTEGER
!>          The leading dimension of U2\&. If JOBU2 = 'Y', LDU2 >=
!>          MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fIV1T\fP 
.PP
.nf
!>          V1T is COMPLEX array, dimension (Q)
!>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
!>          matrix V1**T\&.
!> 
.fi
.PP
.br
\fILDV1T\fP 
.PP
.nf
!>          LDV1T is INTEGER
!>          The leading dimension of V1T\&. If JOBV1T = 'Y', LDV1T >=
!>          MAX(1,Q)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBReferences:\fP
.RS 4
[1] Brian D\&. Sutton\&. Computing the complete CS decomposition\&. Numer\&. Algorithms, 50(1):33-65, 2009\&. 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB253\fP of file \fBcuncsd2by1\&.f\fP\&.
.SS "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)"

.PP
\fBDORCSD2BY1\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBU1\fP 
.PP
.nf
!>          JOBU1 is CHARACTER
!>          = 'Y':      U1 is computed;
!>          otherwise:  U1 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBU2\fP 
.PP
.nf
!>          JOBU2 is CHARACTER
!>          = 'Y':      U2 is computed;
!>          otherwise:  U2 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBV1T\fP 
.PP
.nf
!>          JOBV1T is CHARACTER
!>          = 'Y':      V1T is computed;
!>          otherwise:  V1T is not computed\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows in X\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows in X11\&. 0 <= P <= M\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>          The number of columns in X11 and X21\&. 0 <= Q <= M\&.
!> 
.fi
.PP
.br
\fIX11\fP 
.PP
.nf
!>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
!>          On entry, part of the orthogonal matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX11\fP 
.PP
.nf
!>          LDX11 is INTEGER
!>          The leading dimension of X11\&. LDX11 >= MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIX21\fP 
.PP
.nf
!>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
!>          On entry, part of the orthogonal matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX21\fP 
.PP
.nf
!>          LDX21 is INTEGER
!>          The leading dimension of X21\&. LDX21 >= MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          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)) )\&.
!> 
.fi
.PP
.br
\fIU1\fP 
.PP
.nf
!>          U1 is DOUBLE PRECISION array, dimension (P)
!>          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1\&.
!> 
.fi
.PP
.br
\fILDU1\fP 
.PP
.nf
!>          LDU1 is INTEGER
!>          The leading dimension of U1\&. If JOBU1 = 'Y', LDU1 >=
!>          MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIU2\fP 
.PP
.nf
!>          U2 is DOUBLE PRECISION array, dimension (M-P)
!>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
!>          matrix U2\&.
!> 
.fi
.PP
.br
\fILDU2\fP 
.PP
.nf
!>          LDU2 is INTEGER
!>          The leading dimension of U2\&. If JOBU2 = 'Y', LDU2 >=
!>          MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fIV1T\fP 
.PP
.nf
!>          V1T is DOUBLE PRECISION array, dimension (Q)
!>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
!>          matrix V1**T\&.
!> 
.fi
.PP
.br
\fILDV1T\fP 
.PP
.nf
!>          LDV1T is INTEGER
!>          The leading dimension of V1T\&. If JOBV1T = 'Y', LDV1T >=
!>          MAX(1,Q)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBReferences:\fP
.RS 4
[1] Brian D\&. Sutton\&. Computing the complete CS decomposition\&. Numer\&. Algorithms, 50(1):33-65, 2009\&. 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB230\fP of file \fBdorcsd2by1\&.f\fP\&.
.SS "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)"

.PP
\fBSORCSD2BY1\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBU1\fP 
.PP
.nf
!>          JOBU1 is CHARACTER
!>          = 'Y':      U1 is computed;
!>          otherwise:  U1 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBU2\fP 
.PP
.nf
!>          JOBU2 is CHARACTER
!>          = 'Y':      U2 is computed;
!>          otherwise:  U2 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBV1T\fP 
.PP
.nf
!>          JOBV1T is CHARACTER
!>          = 'Y':      V1T is computed;
!>          otherwise:  V1T is not computed\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows in X\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows in X11\&. 0 <= P <= M\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>          The number of columns in X11 and X21\&. 0 <= Q <= M\&.
!> 
.fi
.PP
.br
\fIX11\fP 
.PP
.nf
!>          X11 is REAL array, dimension (LDX11,Q)
!>          On entry, part of the orthogonal matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX11\fP 
.PP
.nf
!>          LDX11 is INTEGER
!>          The leading dimension of X11\&. LDX11 >= MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIX21\fP 
.PP
.nf
!>          X21 is REAL array, dimension (LDX21,Q)
!>          On entry, part of the orthogonal matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX21\fP 
.PP
.nf
!>          LDX21 is INTEGER
!>           The leading dimension of X21\&. LDX21 >= MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          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)) )\&.
!> 
.fi
.PP
.br
\fIU1\fP 
.PP
.nf
!>          U1 is REAL array, dimension (P)
!>          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1\&.
!> 
.fi
.PP
.br
\fILDU1\fP 
.PP
.nf
!>          LDU1 is INTEGER
!>          The leading dimension of U1\&. If JOBU1 = 'Y', LDU1 >=
!>          MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIU2\fP 
.PP
.nf
!>          U2 is REAL array, dimension (M-P)
!>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
!>          matrix U2\&.
!> 
.fi
.PP
.br
\fILDU2\fP 
.PP
.nf
!>          LDU2 is INTEGER
!>          The leading dimension of U2\&. If JOBU2 = 'Y', LDU2 >=
!>          MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fIV1T\fP 
.PP
.nf
!>          V1T is REAL array, dimension (Q)
!>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
!>          matrix V1**T\&.
!> 
.fi
.PP
.br
\fILDV1T\fP 
.PP
.nf
!>          LDV1T is INTEGER
!>          The leading dimension of V1T\&. If JOBV1T = 'Y', LDV1T >=
!>          MAX(1,Q)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBReferences:\fP
.RS 4
[1] Brian D\&. Sutton\&. Computing the complete CS decomposition\&. Numer\&. Algorithms, 50(1):33-65, 2009\&. 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB230\fP of file \fBsorcsd2by1\&.f\fP\&.
.SS "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)"

.PP
\fBZUNCSD2BY1\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBU1\fP 
.PP
.nf
!>          JOBU1 is CHARACTER
!>          = 'Y':      U1 is computed;
!>          otherwise:  U1 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBU2\fP 
.PP
.nf
!>          JOBU2 is CHARACTER
!>          = 'Y':      U2 is computed;
!>          otherwise:  U2 is not computed\&.
!> 
.fi
.PP
.br
\fIJOBV1T\fP 
.PP
.nf
!>          JOBV1T is CHARACTER
!>          = 'Y':      V1T is computed;
!>          otherwise:  V1T is not computed\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows in X\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows in X11\&. 0 <= P <= M\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>          The number of columns in X11 and X21\&. 0 <= Q <= M\&.
!> 
.fi
.PP
.br
\fIX11\fP 
.PP
.nf
!>          X11 is COMPLEX*16 array, dimension (LDX11,Q)
!>          On entry, part of the unitary matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX11\fP 
.PP
.nf
!>          LDX11 is INTEGER
!>          The leading dimension of X11\&. LDX11 >= MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIX21\fP 
.PP
.nf
!>          X21 is COMPLEX*16 array, dimension (LDX21,Q)
!>          On entry, part of the unitary matrix whose CSD is desired\&.
!> 
.fi
.PP
.br
\fILDX21\fP 
.PP
.nf
!>          LDX21 is INTEGER
!>          The leading dimension of X21\&. LDX21 >= MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          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)) )\&.
!> 
.fi
.PP
.br
\fIU1\fP 
.PP
.nf
!>          U1 is COMPLEX*16 array, dimension (P)
!>          If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1\&.
!> 
.fi
.PP
.br
\fILDU1\fP 
.PP
.nf
!>          LDU1 is INTEGER
!>          The leading dimension of U1\&. If JOBU1 = 'Y', LDU1 >=
!>          MAX(1,P)\&.
!> 
.fi
.PP
.br
\fIU2\fP 
.PP
.nf
!>          U2 is COMPLEX*16 array, dimension (M-P)
!>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
!>          matrix U2\&.
!> 
.fi
.PP
.br
\fILDU2\fP 
.PP
.nf
!>          LDU2 is INTEGER
!>          The leading dimension of U2\&. If JOBU2 = 'Y', LDU2 >=
!>          MAX(1,M-P)\&.
!> 
.fi
.PP
.br
\fIV1T\fP 
.PP
.nf
!>          V1T is COMPLEX*16 array, dimension (Q)
!>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
!>          matrix V1**T\&.
!> 
.fi
.PP
.br
\fILDV1T\fP 
.PP
.nf
!>          LDV1T is INTEGER
!>          The leading dimension of V1T\&. If JOBV1T = 'Y', LDV1T >=
!>          MAX(1,Q)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBReferences:\fP
.RS 4
[1] Brian D\&. Sutton\&. Computing the complete CS decomposition\&. Numer\&. Algorithms, 50(1):33-65, 2009\&. 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB252\fP of file \fBzuncsd2by1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.