--- rpl/lapack/lapack/zgglse.f 2010/08/13 21:04:04 1.6
+++ rpl/lapack/lapack/zgglse.f 2011/11/21 20:43:10 1.9
@@ -1,10 +1,189 @@
+*> \brief ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGGLSE + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
+* INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LDB, LWORK, M, N, P
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( * ), D( * ),
+* $ WORK( * ), X( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGGLSE solves the linear equality-constrained least squares (LSE)
+*> problem:
+*>
+*> minimize || c - A*x ||_2 subject to B*x = d
+*>
+*> where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
+*> M-vector, and d is a given P-vector. It is assumed that
+*> P <= N <= M+P, and
+*>
+*> rank(B) = P and rank( (A) ) = N.
+*> ( (B) )
+*>
+*> These conditions ensure that the LSE problem has a unique solution,
+*> which is obtained using a generalized RQ factorization of the
+*> matrices (B, A) given by
+*>
+*> B = (0 R)*Q, A = Z*T*Q.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrices A and B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is INTEGER
+*> The number of rows of the matrix B. 0 <= P <= N <= M+P.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the M-by-N matrix A.
+*> On exit, the elements on and above the diagonal of the array
+*> contain the min(M,N)-by-N upper trapezoidal matrix T.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,N)
+*> On entry, the P-by-N matrix B.
+*> On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
+*> contains the P-by-P upper triangular matrix R.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,P).
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is COMPLEX*16 array, dimension (M)
+*> On entry, C contains the right hand side vector for the
+*> least squares part of the LSE problem.
+*> On exit, the residual sum of squares for the solution
+*> is given by the sum of squares of elements N-P+1 to M of
+*> vector C.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is COMPLEX*16 array, dimension (P)
+*> On entry, D contains the right hand side vector for the
+*> constrained equation.
+*> On exit, D is destroyed.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (N)
+*> On exit, X is the solution of the LSE problem.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= max(1,M+N+P).
+*> For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
+*> where NB is an upper bound for the optimal blocksizes for
+*> ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.
+*>
+*> 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.
+*> = 1: the upper triangular factor R associated with B in the
+*> generalized RQ factorization of the pair (B, A) is
+*> singular, so that rank(B) < P; the least squares
+*> solution could not be computed.
+*> = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
+*> T associated with A in the generalized RQ factorization
+*> of the pair (B, A) is singular, so that
+*> rank( (A) ) < N; the least squares solution could not
+*> ( (B) )
+*> be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERsolve
+*
+* =====================================================================
SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
$ INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver 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..--
-* February 2007
+* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, P
@@ -14,98 +193,6 @@
$ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
-*
-* ZGGLSE solves the linear equality-constrained least squares (LSE)
-* problem:
-*
-* minimize || c - A*x ||_2 subject to B*x = d
-*
-* where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
-* M-vector, and d is a given P-vector. It is assumed that
-* P <= N <= M+P, and
-*
-* rank(B) = P and rank( ( A ) ) = N.
-* ( ( B ) )
-*
-* These conditions ensure that the LSE problem has a unique solution,
-* which is obtained using a generalized RQ factorization of the
-* matrices (B, A) given by
-*
-* B = (0 R)*Q, A = Z*T*Q.
-*
-* Arguments
-* =========
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrices A and B. N >= 0.
-*
-* P (input) INTEGER
-* The number of rows of the matrix B. 0 <= P <= N <= M+P.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the M-by-N matrix A.
-* On exit, the elements on and above the diagonal of the array
-* contain the min(M,N)-by-N upper trapezoidal matrix T.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB,N)
-* On entry, the P-by-N matrix B.
-* On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
-* contains the P-by-P upper triangular matrix R.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,P).
-*
-* C (input/output) COMPLEX*16 array, dimension (M)
-* On entry, C contains the right hand side vector for the
-* least squares part of the LSE problem.
-* On exit, the residual sum of squares for the solution
-* is given by the sum of squares of elements N-P+1 to M of
-* vector C.
-*
-* D (input/output) COMPLEX*16 array, dimension (P)
-* On entry, D contains the right hand side vector for the
-* constrained equation.
-* On exit, D is destroyed.
-*
-* X (output) COMPLEX*16 array, dimension (N)
-* On exit, X is the solution of the LSE problem.
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= max(1,M+N+P).
-* For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
-* where NB is an upper bound for the optimal blocksizes for
-* ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.
-*
-* 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.
-* = 1: the upper triangular factor R associated with B in the
-* generalized RQ factorization of the pair (B, A) is
-* singular, so that rank(B) < P; the least squares
-* solution could not be computed.
-* = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
-* T associated with A in the generalized RQ factorization
-* of the pair (B, A) is singular, so that
-* rank( (A) ) < N; the least squares solution could not
-* ( (B) )
-* be computed.
-*
* =====================================================================
*
* .. Parameters ..
@@ -183,9 +270,9 @@
*
* Compute the GRQ factorization of matrices B and A:
*
-* B*Q' = ( 0 T12 ) P Z'*A*Q' = ( R11 R12 ) N-P
-* N-P P ( 0 R22 ) M+P-N
-* N-P P
+* B*Q**H = ( 0 T12 ) P Z**H*A*Q**H = ( R11 R12 ) N-P
+* N-P P ( 0 R22 ) M+P-N
+* N-P P
*
* where T12 and R11 are upper triangular, and Q and Z are
* unitary.
@@ -194,7 +281,7 @@
$ WORK( P+MN+1 ), LWORK-P-MN, INFO )
LOPT = WORK( P+MN+1 )
*
-* Update c = Z'*c = ( c1 ) N-P
+* Update c = Z**H *c = ( c1 ) N-P
* ( c2 ) M+P-N
*
CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, 1, MN, A, LDA,
@@ -255,7 +342,7 @@
CALL ZAXPY( NR, -CONE, D, 1, C( N-P+1 ), 1 )
END IF
*
-* Backward transformation x = Q'*x
+* Backward transformation x = Q**H*x
*
CALL ZUNMRQ( 'Left', 'Conjugate Transpose', N, 1, P, B, LDB,
$ WORK( 1 ), X, N, WORK( P+MN+1 ), LWORK-P-MN, INFO )