cggglm(3)

NAME

cggglm.f –

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine cggglm (integerN, integerM, integerP, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )D, complex, dimension( * )X, complex, dimension( * )Y, complex, dimension( * )WORK, integerLWORK, integerINFO)

CGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:


CGGGLM 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 is INTEGER
          The number of rows of the matrices A and B.  N >= 0.

          M is INTEGER
          The number of columns of the matrix A.  0 <= M <= N.

          P is INTEGER
          The number of columns of the matrix B.  P >= N-M.

          A is COMPLEX 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 is COMPLEX 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 is COMPLEX array, dimension (N)
          On entry, D is the left hand side of the GLM equation.
          On exit, D is destroyed.

          X is COMPLEX array, dimension (M)

          Y is COMPLEX array, dimension (P)
          On exit, X and Y are the solutions of the GLM problem.

WORK

          WORK is COMPLEX 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
CGEQRF, CGERQF, CUNMQR 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 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 cggglm.f.

Author

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