sggglm.f man page

sggglm.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

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

Purpose:

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

X

X is REAL array, dimension (M)

Y

Y is REAL array, dimension (P)

On exit, X and Y are the solutions of the GLM problem.

WORK

WORK is REAL 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
SGEQRF, SGERQF, SORMQR and SORMRQ.

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 sggglm.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sggglm(3) is an alias of sggglm.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK