zggglm (3)  Linux Manuals
NAME
zggglm.f 
SYNOPSIS
Functions/Subroutines
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
Function/Subroutine Documentation
subroutine zggglm (integerN, integerM, integerP, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )D, complex*16, dimension( * )X, complex*16, dimension( * )Y, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Purpose:

ZGGGLM solves a general GaussMarkov linear model (GLM) problem: minimize  y _2 subject to d = A*x + B*y x where A is an NbyM matrix, B is an NbyP matrix, and d is a given Nvector. 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 2norm 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)*(dA*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.
MM is INTEGER The number of columns of the matrix A. 0 <= M <= N.
PP is INTEGER The number of columns of the matrix B. P >= NM.
AA is COMPLEX*16 array, dimension (LDA,M) On entry, the NbyM matrix A. On exit, the upper triangular part of the array A contains the MbyM upper triangular matrix R.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
BB is COMPLEX*16 array, dimension (LDB,P) On entry, the NbyP matrix B. On exit, if N <= P, the upper triangle of the subarray B(1:N,PN+1:P) contains the NbyN upper triangular matrix T; if N > P, the elements on and above the (NP)th subdiagonal contain the NbyP upper trapezoidal matrix T.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
DD is COMPLEX*16 array, dimension (N) On entry, D is the left hand side of the GLM equation. On exit, D is destroyed.
XX is COMPLEX*16 array, dimension (M)
YY is COMPLEX*16 array, dimension (P) On exit, X and Y are the solutions of the GLM problem.
WORKWORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK 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.
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith 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 (NM) by (NM) 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.
Author
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