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zggglm.f(3) LAPACK zggglm.f(3)

zggglm.f -


subroutine zggglm (N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO)
 
ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Purpose:
 ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by
A = Q*(R), B = Q*T*Z. (0)
In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem
minimize || inv(B)*(d-A*x) ||_2 x
where inv(B) denotes the inverse of B.
Parameters:
N
          N is INTEGER
          The number of rows of the matrices A and B.  N >= 0.
M
          M is INTEGER
          The number of columns of the matrix A.  0 <= M <= N.
P
          P is INTEGER
          The number of columns of the matrix B.  P >= N-M.
A
          A is COMPLEX*16 array, dimension (LDA,M)
          On entry, the N-by-M matrix A.
          On exit, the upper triangular part of the array A contains
          the M-by-M upper triangular matrix R.
LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
B
          B is COMPLEX*16 array, dimension (LDB,P)
          On entry, the N-by-P matrix B.
          On exit, if N <= P, the upper triangle of the subarray
          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
          if N > P, the elements on and above the (N-P)th subdiagonal
          contain the N-by-P upper trapezoidal matrix T.
LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
D
          D is COMPLEX*16 array, dimension (N)
          On entry, D is the left hand side of the GLM equation.
          On exit, D is destroyed.
X
          X is COMPLEX*16 array, dimension (M)
Y
          Y is COMPLEX*16 array, dimension (P)
On exit, X and Y are the solutions of the GLM 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,N+M+P).
          For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,
          where NB is an upper bound for the optimal blocksizes for
          ZGEQRF, ZGERQF, ZUNMQR and ZUNMRQ.
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 i-th argument had an illegal value.
          = 1:  the upper triangular factor R associated with A in the
                generalized QR factorization of the pair (A, B) is
                singular, so that rank(A) < M; the least squares
                solution could not be computed.
          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
                factor T associated with B in the generalized QR
                factorization of the pair (A, B) is singular, so that
                rank( A B ) < N; the least squares solution could not
                be computed.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 185 of file zggglm.f.

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