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684 lines
23 KiB
684 lines
23 KiB
*> \brief \b CUNBDB
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download CUNBDB + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
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* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
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* TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER SIGNS, TRANS
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* INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
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* $ Q
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* ..
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* .. Array Arguments ..
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* REAL PHI( * ), THETA( * )
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* COMPLEX TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
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* $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
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* $ X21( LDX21, * ), X22( LDX22, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
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*> partitioned unitary matrix X:
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*>
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*> [ B11 | B12 0 0 ]
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*> [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
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*> X = [-----------] = [---------] [----------------] [---------] .
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*> [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
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*> [ 0 | 0 0 I ]
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*>
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*> X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
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*> not the case, then X must be transposed and/or permuted. This can be
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*> done in constant time using the TRANS and SIGNS options. See CUNCSD
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*> for details.)
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*>
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*> The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
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*> (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
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*> represented implicitly by Householder vectors.
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*>
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*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
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*> implicitly by angles THETA, PHI.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER
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*> = 'T': X, U1, U2, V1T, and V2T are stored in row-major
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*> order;
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*> otherwise: X, U1, U2, V1T, and V2T are stored in column-
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*> major order.
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*> \endverbatim
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*>
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*> \param[in] SIGNS
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*> \verbatim
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*> SIGNS is CHARACTER
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*> = 'O': The lower-left block is made nonpositive (the
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*> "other" convention);
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*> otherwise: The upper-right block is made nonpositive (the
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*> "default" convention).
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows and columns in X.
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*> \endverbatim
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*>
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*> \param[in] P
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*> \verbatim
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*> P is INTEGER
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*> The number of rows in X11 and X12. 0 <= P <= M.
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*> \endverbatim
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*>
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*> \param[in] Q
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*> \verbatim
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*> Q is INTEGER
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*> The number of columns in X11 and X21. 0 <= Q <=
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*> MIN(P,M-P,M-Q).
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*> \endverbatim
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*>
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*> \param[in,out] X11
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*> \verbatim
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*> X11 is COMPLEX array, dimension (LDX11,Q)
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*> On entry, the top-left block of the unitary matrix to be
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*> reduced. On exit, the form depends on TRANS:
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*> If TRANS = 'N', then
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*> the columns of tril(X11) specify reflectors for P1,
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*> the rows of triu(X11,1) specify reflectors for Q1;
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*> else TRANS = 'T', and
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*> the rows of triu(X11) specify reflectors for P1,
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*> the columns of tril(X11,-1) specify reflectors for Q1.
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*> \endverbatim
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*>
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*> \param[in] LDX11
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*> \verbatim
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*> LDX11 is INTEGER
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*> The leading dimension of X11. If TRANS = 'N', then LDX11 >=
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*> P; else LDX11 >= Q.
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*> \endverbatim
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*>
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*> \param[in,out] X12
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*> \verbatim
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*> X12 is COMPLEX array, dimension (LDX12,M-Q)
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*> On entry, the top-right block of the unitary matrix to
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*> be reduced. On exit, the form depends on TRANS:
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*> If TRANS = 'N', then
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*> the rows of triu(X12) specify the first P reflectors for
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*> Q2;
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*> else TRANS = 'T', and
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*> the columns of tril(X12) specify the first P reflectors
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*> for Q2.
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*> \endverbatim
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*>
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*> \param[in] LDX12
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*> \verbatim
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*> LDX12 is INTEGER
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*> The leading dimension of X12. If TRANS = 'N', then LDX12 >=
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*> P; else LDX11 >= M-Q.
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*> \endverbatim
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*>
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*> \param[in,out] X21
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*> \verbatim
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*> X21 is COMPLEX array, dimension (LDX21,Q)
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*> On entry, the bottom-left block of the unitary matrix to
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*> be reduced. On exit, the form depends on TRANS:
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*> If TRANS = 'N', then
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*> the columns of tril(X21) specify reflectors for P2;
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*> else TRANS = 'T', and
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*> the rows of triu(X21) specify reflectors for P2.
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*> \endverbatim
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*>
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*> \param[in] LDX21
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*> \verbatim
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*> LDX21 is INTEGER
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*> The leading dimension of X21. If TRANS = 'N', then LDX21 >=
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*> M-P; else LDX21 >= Q.
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*> \endverbatim
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*>
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*> \param[in,out] X22
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*> \verbatim
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*> X22 is COMPLEX array, dimension (LDX22,M-Q)
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*> On entry, the bottom-right block of the unitary matrix to
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*> be reduced. On exit, the form depends on TRANS:
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*> If TRANS = 'N', then
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*> the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
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*> M-P-Q reflectors for Q2,
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*> else TRANS = 'T', and
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*> the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
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*> M-P-Q reflectors for P2.
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*> \endverbatim
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*>
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*> \param[in] LDX22
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*> \verbatim
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*> LDX22 is INTEGER
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*> The leading dimension of X22. If TRANS = 'N', then LDX22 >=
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*> M-P; else LDX22 >= M-Q.
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*> \endverbatim
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*>
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*> \param[out] THETA
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*> \verbatim
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*> THETA is REAL array, dimension (Q)
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*> The entries of the bidiagonal blocks B11, B12, B21, B22 can
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*> be computed from the angles THETA and PHI. See Further
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*> Details.
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*> \endverbatim
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*>
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*> \param[out] PHI
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*> \verbatim
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*> PHI is REAL array, dimension (Q-1)
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*> The entries of the bidiagonal blocks B11, B12, B21, B22 can
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*> be computed from the angles THETA and PHI. See Further
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*> Details.
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*> \endverbatim
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*>
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*> \param[out] TAUP1
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*> \verbatim
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*> TAUP1 is COMPLEX array, dimension (P)
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*> The scalar factors of the elementary reflectors that define
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*> P1.
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*> \endverbatim
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*>
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*> \param[out] TAUP2
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*> \verbatim
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*> TAUP2 is COMPLEX array, dimension (M-P)
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*> The scalar factors of the elementary reflectors that define
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*> P2.
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*> \endverbatim
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*>
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*> \param[out] TAUQ1
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*> \verbatim
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*> TAUQ1 is COMPLEX array, dimension (Q)
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*> The scalar factors of the elementary reflectors that define
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*> Q1.
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*> \endverbatim
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*>
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*> \param[out] TAUQ2
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*> \verbatim
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*> TAUQ2 is COMPLEX array, dimension (M-Q)
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*> The scalar factors of the elementary reflectors that define
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*> Q2.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= M-Q.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit.
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complexOTHERcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The bidiagonal blocks B11, B12, B21, and B22 are represented
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*> implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
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*> PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
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*> lower bidiagonal. Every entry in each bidiagonal band is a product
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*> of a sine or cosine of a THETA with a sine or cosine of a PHI. See
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*> [1] or CUNCSD for details.
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*>
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*> P1, P2, Q1, and Q2 are represented as products of elementary
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*> reflectors. See CUNCSD for details on generating P1, P2, Q1, and Q2
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*> using CUNGQR and CUNGLQ.
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*> \endverbatim
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*
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*> \par References:
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* ================
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*>
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*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
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*> Algorithms, 50(1):33-65, 2009.
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*>
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* =====================================================================
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SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
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$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
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$ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER SIGNS, TRANS
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INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
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$ Q
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* ..
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* .. Array Arguments ..
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REAL PHI( * ), THETA( * )
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COMPLEX TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
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$ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
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$ X21( LDX21, * ), X22( LDX22, * )
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* ..
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*
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* ====================================================================
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*
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* .. Parameters ..
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REAL REALONE
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PARAMETER ( REALONE = 1.0E0 )
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COMPLEX ONE
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PARAMETER ( ONE = (1.0E0,0.0E0) )
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* ..
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* .. Local Scalars ..
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LOGICAL COLMAJOR, LQUERY
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INTEGER I, LWORKMIN, LWORKOPT
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REAL Z1, Z2, Z3, Z4
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* ..
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* .. External Subroutines ..
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EXTERNAL CAXPY, CLARF, CLARFGP, CSCAL, XERBLA
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EXTERNAL CLACGV
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*
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* ..
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* .. External Functions ..
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REAL SCNRM2
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LOGICAL LSAME
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EXTERNAL SCNRM2, LSAME
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* ..
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* .. Intrinsic Functions
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INTRINSIC ATAN2, COS, MAX, MIN, SIN
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INTRINSIC CMPLX, CONJG
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* ..
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* .. Executable Statements ..
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*
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* Test input arguments
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*
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INFO = 0
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COLMAJOR = .NOT. LSAME( TRANS, 'T' )
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IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
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Z1 = REALONE
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Z2 = REALONE
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Z3 = REALONE
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Z4 = REALONE
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ELSE
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Z1 = REALONE
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Z2 = -REALONE
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Z3 = REALONE
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Z4 = -REALONE
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END IF
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LQUERY = LWORK .EQ. -1
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*
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IF( M .LT. 0 ) THEN
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INFO = -3
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ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
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INFO = -4
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ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
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$ Q .GT. M-Q ) THEN
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INFO = -5
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ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
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INFO = -7
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ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
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INFO = -7
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ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
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INFO = -9
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ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
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INFO = -9
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ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
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INFO = -11
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ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
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INFO = -11
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ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
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INFO = -13
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ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
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INFO = -13
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END IF
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*
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* Compute workspace
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*
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IF( INFO .EQ. 0 ) THEN
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LWORKOPT = M - Q
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LWORKMIN = M - Q
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WORK(1) = LWORKOPT
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IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
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INFO = -21
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END IF
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END IF
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IF( INFO .NE. 0 ) THEN
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CALL XERBLA( 'xORBDB', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Handle column-major and row-major separately
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*
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IF( COLMAJOR ) THEN
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*
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* Reduce columns 1, ..., Q of X11, X12, X21, and X22
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*
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DO I = 1, Q
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*
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IF( I .EQ. 1 ) THEN
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CALL CSCAL( P-I+1, CMPLX( Z1, 0.0E0 ), X11(I,I), 1 )
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ELSE
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CALL CSCAL( P-I+1, CMPLX( Z1*COS(PHI(I-1)), 0.0E0 ),
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$ X11(I,I), 1 )
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CALL CAXPY( P-I+1, CMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
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$ 0.0E0 ), X12(I,I-1), 1, X11(I,I), 1 )
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END IF
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IF( I .EQ. 1 ) THEN
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CALL CSCAL( M-P-I+1, CMPLX( Z2, 0.0E0 ), X21(I,I), 1 )
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ELSE
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CALL CSCAL( M-P-I+1, CMPLX( Z2*COS(PHI(I-1)), 0.0E0 ),
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$ X21(I,I), 1 )
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CALL CAXPY( M-P-I+1, CMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
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$ 0.0E0 ), X22(I,I-1), 1, X21(I,I), 1 )
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END IF
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*
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THETA(I) = ATAN2( SCNRM2( M-P-I+1, X21(I,I), 1 ),
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$ SCNRM2( P-I+1, X11(I,I), 1 ) )
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*
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IF( P .GT. I ) THEN
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CALL CLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
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ELSE IF ( P .EQ. I ) THEN
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CALL CLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
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END IF
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X11(I,I) = ONE
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IF ( M-P .GT. I ) THEN
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CALL CLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1,
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$ TAUP2(I) )
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ELSE IF ( M-P .EQ. I ) THEN
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CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1,
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$ TAUP2(I) )
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END IF
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X21(I,I) = ONE
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*
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IF ( Q .GT. I ) THEN
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CALL CLARF( 'L', P-I+1, Q-I, X11(I,I), 1,
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$ CONJG(TAUP1(I)), X11(I,I+1), LDX11, WORK )
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CALL CLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
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$ CONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
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END IF
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IF ( M-Q+1 .GT. I ) THEN
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CALL CLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
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$ CONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
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CALL CLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
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$ CONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
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END IF
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*
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IF( I .LT. Q ) THEN
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CALL CSCAL( Q-I, CMPLX( -Z1*Z3*SIN(THETA(I)), 0.0E0 ),
|
|
$ X11(I,I+1), LDX11 )
|
|
CALL CAXPY( Q-I, CMPLX( Z2*Z3*COS(THETA(I)), 0.0E0 ),
|
|
$ X21(I,I+1), LDX21, X11(I,I+1), LDX11 )
|
|
END IF
|
|
CALL CSCAL( M-Q-I+1, CMPLX( -Z1*Z4*SIN(THETA(I)), 0.0E0 ),
|
|
$ X12(I,I), LDX12 )
|
|
CALL CAXPY( M-Q-I+1, CMPLX( Z2*Z4*COS(THETA(I)), 0.0E0 ),
|
|
$ X22(I,I), LDX22, X12(I,I), LDX12 )
|
|
*
|
|
IF( I .LT. Q )
|
|
$ PHI(I) = ATAN2( SCNRM2( Q-I, X11(I,I+1), LDX11 ),
|
|
$ SCNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
|
|
*
|
|
IF( I .LT. Q ) THEN
|
|
CALL CLACGV( Q-I, X11(I,I+1), LDX11 )
|
|
IF ( I .EQ. Q-1 ) THEN
|
|
CALL CLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
|
|
$ TAUQ1(I) )
|
|
ELSE
|
|
CALL CLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
|
|
$ TAUQ1(I) )
|
|
END IF
|
|
X11(I,I+1) = ONE
|
|
END IF
|
|
IF ( M-Q+1 .GT. I ) THEN
|
|
CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
|
|
IF ( M-Q .EQ. I ) THEN
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
|
|
$ TAUQ2(I) )
|
|
ELSE
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
|
|
$ TAUQ2(I) )
|
|
END IF
|
|
END IF
|
|
X12(I,I) = ONE
|
|
*
|
|
IF( I .LT. Q ) THEN
|
|
CALL CLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
|
|
$ X11(I+1,I+1), LDX11, WORK )
|
|
CALL CLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
|
|
$ X21(I+1,I+1), LDX21, WORK )
|
|
END IF
|
|
IF ( P .GT. I ) THEN
|
|
CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
|
|
$ X12(I+1,I), LDX12, WORK )
|
|
END IF
|
|
IF ( M-P .GT. I ) THEN
|
|
CALL CLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
|
|
$ TAUQ2(I), X22(I+1,I), LDX22, WORK )
|
|
END IF
|
|
*
|
|
IF( I .LT. Q )
|
|
$ CALL CLACGV( Q-I, X11(I,I+1), LDX11 )
|
|
CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
|
|
*
|
|
END DO
|
|
*
|
|
* Reduce columns Q + 1, ..., P of X12, X22
|
|
*
|
|
DO I = Q + 1, P
|
|
*
|
|
CALL CSCAL( M-Q-I+1, CMPLX( -Z1*Z4, 0.0E0 ), X12(I,I),
|
|
$ LDX12 )
|
|
CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
|
|
IF ( I .GE. M-Q ) THEN
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
|
|
$ TAUQ2(I) )
|
|
ELSE
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
|
|
$ TAUQ2(I) )
|
|
END IF
|
|
X12(I,I) = ONE
|
|
*
|
|
IF ( P .GT. I ) THEN
|
|
CALL CLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
|
|
$ X12(I+1,I), LDX12, WORK )
|
|
END IF
|
|
IF( M-P-Q .GE. 1 )
|
|
$ CALL CLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
|
|
$ TAUQ2(I), X22(Q+1,I), LDX22, WORK )
|
|
*
|
|
CALL CLACGV( M-Q-I+1, X12(I,I), LDX12 )
|
|
*
|
|
END DO
|
|
*
|
|
* Reduce columns P + 1, ..., M - Q of X12, X22
|
|
*
|
|
DO I = 1, M - P - Q
|
|
*
|
|
CALL CSCAL( M-P-Q-I+1, CMPLX( Z2*Z4, 0.0E0 ),
|
|
$ X22(Q+I,P+I), LDX22 )
|
|
CALL CLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
|
|
CALL CLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
|
|
$ LDX22, TAUQ2(P+I) )
|
|
X22(Q+I,P+I) = ONE
|
|
CALL CLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
|
|
$ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
|
|
*
|
|
CALL CLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
|
|
*
|
|
END DO
|
|
*
|
|
ELSE
|
|
*
|
|
* Reduce columns 1, ..., Q of X11, X12, X21, X22
|
|
*
|
|
DO I = 1, Q
|
|
*
|
|
IF( I .EQ. 1 ) THEN
|
|
CALL CSCAL( P-I+1, CMPLX( Z1, 0.0E0 ), X11(I,I),
|
|
$ LDX11 )
|
|
ELSE
|
|
CALL CSCAL( P-I+1, CMPLX( Z1*COS(PHI(I-1)), 0.0E0 ),
|
|
$ X11(I,I), LDX11 )
|
|
CALL CAXPY( P-I+1, CMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
|
|
$ 0.0E0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 )
|
|
END IF
|
|
IF( I .EQ. 1 ) THEN
|
|
CALL CSCAL( M-P-I+1, CMPLX( Z2, 0.0E0 ), X21(I,I),
|
|
$ LDX21 )
|
|
ELSE
|
|
CALL CSCAL( M-P-I+1, CMPLX( Z2*COS(PHI(I-1)), 0.0E0 ),
|
|
$ X21(I,I), LDX21 )
|
|
CALL CAXPY( M-P-I+1, CMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
|
|
$ 0.0E0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 )
|
|
END IF
|
|
*
|
|
THETA(I) = ATAN2( SCNRM2( M-P-I+1, X21(I,I), LDX21 ),
|
|
$ SCNRM2( P-I+1, X11(I,I), LDX11 ) )
|
|
*
|
|
CALL CLACGV( P-I+1, X11(I,I), LDX11 )
|
|
CALL CLACGV( M-P-I+1, X21(I,I), LDX21 )
|
|
*
|
|
CALL CLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
|
|
X11(I,I) = ONE
|
|
IF ( I .EQ. M-P ) THEN
|
|
CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
|
|
$ TAUP2(I) )
|
|
ELSE
|
|
CALL CLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
|
|
$ TAUP2(I) )
|
|
END IF
|
|
X21(I,I) = ONE
|
|
*
|
|
CALL CLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
|
|
$ X11(I+1,I), LDX11, WORK )
|
|
CALL CLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
|
|
$ X12(I,I), LDX12, WORK )
|
|
CALL CLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
|
|
$ X21(I+1,I), LDX21, WORK )
|
|
CALL CLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
|
|
$ TAUP2(I), X22(I,I), LDX22, WORK )
|
|
*
|
|
CALL CLACGV( P-I+1, X11(I,I), LDX11 )
|
|
CALL CLACGV( M-P-I+1, X21(I,I), LDX21 )
|
|
*
|
|
IF( I .LT. Q ) THEN
|
|
CALL CSCAL( Q-I, CMPLX( -Z1*Z3*SIN(THETA(I)), 0.0E0 ),
|
|
$ X11(I+1,I), 1 )
|
|
CALL CAXPY( Q-I, CMPLX( Z2*Z3*COS(THETA(I)), 0.0E0 ),
|
|
$ X21(I+1,I), 1, X11(I+1,I), 1 )
|
|
END IF
|
|
CALL CSCAL( M-Q-I+1, CMPLX( -Z1*Z4*SIN(THETA(I)), 0.0E0 ),
|
|
$ X12(I,I), 1 )
|
|
CALL CAXPY( M-Q-I+1, CMPLX( Z2*Z4*COS(THETA(I)), 0.0E0 ),
|
|
$ X22(I,I), 1, X12(I,I), 1 )
|
|
*
|
|
IF( I .LT. Q )
|
|
$ PHI(I) = ATAN2( SCNRM2( Q-I, X11(I+1,I), 1 ),
|
|
$ SCNRM2( M-Q-I+1, X12(I,I), 1 ) )
|
|
*
|
|
IF( I .LT. Q ) THEN
|
|
CALL CLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
|
|
X11(I+1,I) = ONE
|
|
END IF
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
|
|
X12(I,I) = ONE
|
|
*
|
|
IF( I .LT. Q ) THEN
|
|
CALL CLARF( 'L', Q-I, P-I, X11(I+1,I), 1,
|
|
$ CONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK )
|
|
CALL CLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1,
|
|
$ CONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK )
|
|
END IF
|
|
CALL CLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, CONJG(TAUQ2(I)),
|
|
$ X12(I,I+1), LDX12, WORK )
|
|
|
|
IF ( M-P .GT. I ) THEN
|
|
CALL CLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
|
|
$ CONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
|
|
END IF
|
|
END DO
|
|
*
|
|
* Reduce columns Q + 1, ..., P of X12, X22
|
|
*
|
|
DO I = Q + 1, P
|
|
*
|
|
CALL CSCAL( M-Q-I+1, CMPLX( -Z1*Z4, 0.0E0 ), X12(I,I), 1 )
|
|
CALL CLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
|
|
X12(I,I) = ONE
|
|
*
|
|
IF ( P .GT. I ) THEN
|
|
CALL CLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
|
|
$ CONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
|
|
END IF
|
|
IF( M-P-Q .GE. 1 )
|
|
$ CALL CLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
|
|
$ CONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
|
|
*
|
|
END DO
|
|
*
|
|
* Reduce columns P + 1, ..., M - Q of X12, X22
|
|
*
|
|
DO I = 1, M - P - Q
|
|
*
|
|
CALL CSCAL( M-P-Q-I+1, CMPLX( Z2*Z4, 0.0E0 ),
|
|
$ X22(P+I,Q+I), 1 )
|
|
CALL CLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
|
|
$ TAUQ2(P+I) )
|
|
X22(P+I,Q+I) = ONE
|
|
IF ( M-P-Q .NE. I ) THEN
|
|
CALL CLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
|
|
$ CONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
|
|
$ WORK )
|
|
END IF
|
|
END DO
|
|
*
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CUNBDB
|
|
*
|
|
END
|
|
|
|
|