--- rpl/lapack/lapack/zunbdb.f 2011/07/22 07:40:27 1.3
+++ rpl/lapack/lapack/zunbdb.f 2011/11/21 20:43:23 1.4
@@ -1,15 +1,296 @@
+*> \brief \b ZUNBDB
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZUNBDB + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
+* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
+* TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER SIGNS, TRANS
+* INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
+* $ Q
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION PHI( * ), THETA( * )
+* COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
+* $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
+* $ X21( LDX21, * ), X22( LDX22, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
+*> partitioned unitary matrix X:
+*>
+*> [ B11 | B12 0 0 ]
+*> [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
+*> X = [-----------] = [---------] [----------------] [---------] .
+*> [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
+*> [ 0 | 0 0 I ]
+*>
+*> X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
+*> not the case, then X must be transposed and/or permuted. This can be
+*> done in constant time using the TRANS and SIGNS options. See ZUNCSD
+*> for details.)
+*>
+*> The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
+*> (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
+*> represented implicitly by Householder vectors.
+*>
+*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
+*> implicitly by angles THETA, PHI.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER
+*> = 'T': X, U1, U2, V1T, and V2T are stored in row-major
+*> order;
+*> otherwise: X, U1, U2, V1T, and V2T are stored in column-
+*> major order.
+*> \endverbatim
+*>
+*> \param[in] SIGNS
+*> \verbatim
+*> SIGNS is CHARACTER
+*> = 'O': The lower-left block is made nonpositive (the
+*> "other" convention);
+*> otherwise: The upper-right block is made nonpositive (the
+*> "default" convention).
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows and columns in X.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is INTEGER
+*> The number of rows in X11 and X12. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*> Q is INTEGER
+*> The number of columns in X11 and X21. 0 <= Q <=
+*> MIN(P,M-P,M-Q).
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*> X11 is COMPLEX*16 array, dimension (LDX11,Q)
+*> On entry, the top-left block of the unitary matrix to be
+*> reduced. On exit, the form depends on TRANS:
+*> If TRANS = 'N', then
+*> the columns of tril(X11) specify reflectors for P1,
+*> the rows of triu(X11,1) specify reflectors for Q1;
+*> else TRANS = 'T', and
+*> the rows of triu(X11) specify reflectors for P1,
+*> the columns of tril(X11,-1) specify reflectors for Q1.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*> LDX11 is INTEGER
+*> The leading dimension of X11. If TRANS = 'N', then LDX11 >=
+*> P; else LDX11 >= Q.
+*> \endverbatim
+*>
+*> \param[in,out] X12
+*> \verbatim
+*> X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
+*> On entry, the top-right block of the unitary matrix to
+*> be reduced. On exit, the form depends on TRANS:
+*> If TRANS = 'N', then
+*> the rows of triu(X12) specify the first P reflectors for
+*> Q2;
+*> else TRANS = 'T', and
+*> the columns of tril(X12) specify the first P reflectors
+*> for Q2.
+*> \endverbatim
+*>
+*> \param[in] LDX12
+*> \verbatim
+*> LDX12 is INTEGER
+*> The leading dimension of X12. If TRANS = 'N', then LDX12 >=
+*> P; else LDX11 >= M-Q.
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*> X21 is COMPLEX*16 array, dimension (LDX21,Q)
+*> On entry, the bottom-left block of the unitary matrix to
+*> be reduced. On exit, the form depends on TRANS:
+*> If TRANS = 'N', then
+*> the columns of tril(X21) specify reflectors for P2;
+*> else TRANS = 'T', and
+*> the rows of triu(X21) specify reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*> LDX21 is INTEGER
+*> The leading dimension of X21. If TRANS = 'N', then LDX21 >=
+*> M-P; else LDX21 >= Q.
+*> \endverbatim
+*>
+*> \param[in,out] X22
+*> \verbatim
+*> X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
+*> On entry, the bottom-right block of the unitary matrix to
+*> be reduced. On exit, the form depends on TRANS:
+*> If TRANS = 'N', then
+*> the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
+*> M-P-Q reflectors for Q2,
+*> else TRANS = 'T', and
+*> the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
+*> M-P-Q reflectors for P2.
+*> \endverbatim
+*>
+*> \param[in] LDX22
+*> \verbatim
+*> LDX22 is INTEGER
+*> The leading dimension of X22. If TRANS = 'N', then LDX22 >=
+*> M-P; else LDX22 >= M-Q.
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*> THETA is DOUBLE PRECISION array, dimension (Q)
+*> The entries of the bidiagonal blocks B11, B12, B21, B22 can
+*> be computed from the angles THETA and PHI. See Further
+*> Details.
+*> \endverbatim
+*>
+*> \param[out] PHI
+*> \verbatim
+*> PHI is DOUBLE PRECISION array, dimension (Q-1)
+*> The entries of the bidiagonal blocks B11, B12, B21, B22 can
+*> be computed from the angles THETA and PHI. See Further
+*> Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP1
+*> \verbatim
+*> TAUP1 is COMPLEX*16 array, dimension (P)
+*> The scalar factors of the elementary reflectors that define
+*> P1.
+*> \endverbatim
+*>
+*> \param[out] TAUP2
+*> \verbatim
+*> TAUP2 is COMPLEX*16 array, dimension (M-P)
+*> The scalar factors of the elementary reflectors that define
+*> P2.
+*> \endverbatim
+*>
+*> \param[out] TAUQ1
+*> \verbatim
+*> TAUQ1 is COMPLEX*16 array, dimension (Q)
+*> The scalar factors of the elementary reflectors that define
+*> Q1.
+*> \endverbatim
+*>
+*> \param[out] TAUQ2
+*> \verbatim
+*> TAUQ2 is COMPLEX*16 array, dimension (M-Q)
+*> The scalar factors of the elementary reflectors that define
+*> Q2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (LWORK)
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= M-Q.
+*>
+*> 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.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The bidiagonal blocks B11, B12, B21, and B22 are represented
+*> implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
+*> PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
+*> lower bidiagonal. Every entry in each bidiagonal band is a product
+*> of a sine or cosine of a THETA with a sine or cosine of a PHI. See
+*> [1] or ZUNCSD for details.
+*>
+*> P1, P2, Q1, and Q2 are represented as products of elementary
+*> reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
+*> using ZUNGQR and ZUNGLQ.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
+*>
+* =====================================================================
SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
$ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
- IMPLICIT NONE
-*
-* -- LAPACK routine ((version 3.3.0)) --
-*
-* -- Contributed by Brian Sutton of the Randolph-Macon College --
-* -- November 2010
*
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER SIGNS, TRANS
@@ -23,169 +304,6 @@
$ X21( LDX21, * ), X22( LDX22, * )
* ..
*
-* Purpose
-* =======
-*
-* ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
-* partitioned unitary matrix X:
-*
-* [ B11 | B12 0 0 ]
-* [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
-* X = [-----------] = [---------] [----------------] [---------] .
-* [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
-* [ 0 | 0 0 I ]
-*
-* X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
-* not the case, then X must be transposed and/or permuted. This can be
-* done in constant time using the TRANS and SIGNS options. See ZUNCSD
-* for details.)
-*
-* The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
-* (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
-* represented implicitly by Householder vectors.
-*
-* B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
-* implicitly by angles THETA, PHI.
-*
-* Arguments
-* =========
-*
-* TRANS (input) CHARACTER
-* = 'T': X, U1, U2, V1T, and V2T are stored in row-major
-* order;
-* otherwise: X, U1, U2, V1T, and V2T are stored in column-
-* major order.
-*
-* SIGNS (input) CHARACTER
-* = 'O': The lower-left block is made nonpositive (the
-* "other" convention);
-* otherwise: The upper-right block is made nonpositive (the
-* "default" convention).
-*
-* M (input) INTEGER
-* The number of rows and columns in X.
-*
-* P (input) INTEGER
-* The number of rows in X11 and X12. 0 <= P <= M.
-*
-* Q (input) INTEGER
-* The number of columns in X11 and X21. 0 <= Q <=
-* MIN(P,M-P,M-Q).
-*
-* X11 (input/output) COMPLEX*16 array, dimension (LDX11,Q)
-* On entry, the top-left block of the unitary matrix to be
-* reduced. On exit, the form depends on TRANS:
-* If TRANS = 'N', then
-* the columns of tril(X11) specify reflectors for P1,
-* the rows of triu(X11,1) specify reflectors for Q1;
-* else TRANS = 'T', and
-* the rows of triu(X11) specify reflectors for P1,
-* the columns of tril(X11,-1) specify reflectors for Q1.
-*
-* LDX11 (input) INTEGER
-* The leading dimension of X11. If TRANS = 'N', then LDX11 >=
-* P; else LDX11 >= Q.
-*
-* X12 (input/output) COMPLEX*16 array, dimension (LDX12,M-Q)
-* On entry, the top-right block of the unitary matrix to
-* be reduced. On exit, the form depends on TRANS:
-* If TRANS = 'N', then
-* the rows of triu(X12) specify the first P reflectors for
-* Q2;
-* else TRANS = 'T', and
-* the columns of tril(X12) specify the first P reflectors
-* for Q2.
-*
-* LDX12 (input) INTEGER
-* The leading dimension of X12. If TRANS = 'N', then LDX12 >=
-* P; else LDX11 >= M-Q.
-*
-* X21 (input/output) COMPLEX*16 array, dimension (LDX21,Q)
-* On entry, the bottom-left block of the unitary matrix to
-* be reduced. On exit, the form depends on TRANS:
-* If TRANS = 'N', then
-* the columns of tril(X21) specify reflectors for P2;
-* else TRANS = 'T', and
-* the rows of triu(X21) specify reflectors for P2.
-*
-* LDX21 (input) INTEGER
-* The leading dimension of X21. If TRANS = 'N', then LDX21 >=
-* M-P; else LDX21 >= Q.
-*
-* X22 (input/output) COMPLEX*16 array, dimension (LDX22,M-Q)
-* On entry, the bottom-right block of the unitary matrix to
-* be reduced. On exit, the form depends on TRANS:
-* If TRANS = 'N', then
-* the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
-* M-P-Q reflectors for Q2,
-* else TRANS = 'T', and
-* the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
-* M-P-Q reflectors for P2.
-*
-* LDX22 (input) INTEGER
-* The leading dimension of X22. If TRANS = 'N', then LDX22 >=
-* M-P; else LDX22 >= M-Q.
-*
-* THETA (output) DOUBLE PRECISION array, dimension (Q)
-* The entries of the bidiagonal blocks B11, B12, B21, B22 can
-* be computed from the angles THETA and PHI. See Further
-* Details.
-*
-* PHI (output) DOUBLE PRECISION array, dimension (Q-1)
-* The entries of the bidiagonal blocks B11, B12, B21, B22 can
-* be computed from the angles THETA and PHI. See Further
-* Details.
-*
-* TAUP1 (output) COMPLEX*16 array, dimension (P)
-* The scalar factors of the elementary reflectors that define
-* P1.
-*
-* TAUP2 (output) COMPLEX*16 array, dimension (M-P)
-* The scalar factors of the elementary reflectors that define
-* P2.
-*
-* TAUQ1 (output) COMPLEX*16 array, dimension (Q)
-* The scalar factors of the elementary reflectors that define
-* Q1.
-*
-* TAUQ2 (output) COMPLEX*16 array, dimension (M-Q)
-* The scalar factors of the elementary reflectors that define
-* Q2.
-*
-* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= M-Q.
-*
-* 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.
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* Further Details
-* ===============
-*
-* The bidiagonal blocks B11, B12, B21, and B22 are represented
-* implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
-* PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
-* lower bidiagonal. Every entry in each bidiagonal band is a product
-* of a sine or cosine of a THETA with a sine or cosine of a PHI. See
-* [1] or ZUNCSD for details.
-*
-* P1, P2, Q1, and Q2 are represented as products of elementary
-* reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
-* using ZUNGQR and ZUNGLQ.
-*
-* Reference
-* =========
-*
-* [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-* Algorithms, 50(1):33-65, 2009.
-*
* ====================================================================
*
* .. Parameters ..