--- rpl/lapack/lapack/zgglse.f 2011/07/22 07:38:14 1.8 +++ 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 3.3.1) -- +* -- 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..-- -* -- April 2011 -- +* 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 ..