
NAMEzgglse.f SYNOPSISFunctions/Subroutinessubroutine zgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO) Function/Subroutine Documentationsubroutine zgglse (integerM, integerN, integerP, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )C, complex*16, dimension( * )D, complex*16, dimension( * )X, complex*16, dimension( * )WORK, integerLWORK, integerINFO)ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices Purpose:ZGGLSE solves the linear equalityconstrained least squares (LSE) problem: minimize  c  A*x _2 subject to B*x = d where A is an MbyN matrix, B is a PbyN matrix, c is a given Mvector, and d is a given Pvector. 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. M
Author:
M is INTEGER The number of rows of the matrix A. M >= 0.N N is INTEGER The number of columns of the matrices A and B. N >= 0.P P is INTEGER The number of rows of the matrix B. 0 <= P <= N <= M+P.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)byN upper trapezoidal matrix T.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B B is COMPLEX*16 array, dimension (LDB,N) On entry, the PbyN matrix B. On exit, the upper triangle of the subarray B(1:P,NP+1:N) contains the PbyP upper triangular matrix R.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,P).C 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 NP+1 to M of vector C.D 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.X X is COMPLEX*16 array, dimension (N) On exit, X is the solution of the LSE problem.WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK 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.INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith 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 (NP) by (NP) 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 180 of file zgglse.f.
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