cggglm.f (3) Linux Manual Page

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

 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 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 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 array, dimension (N)

 On entry, D is the left hand side of the GLM equation.

 On exit, D is destroyed.

X

 X is COMPLEX array, dimension (M)

Y

 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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