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NAME SGGGLM - solve a generalized linear regression model (GLM) problem SYNOPSIS SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO ) INTEGER INFO, LDA, LDB, LWORK, M, N, P REAL A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ), Y( * ) PURPOSE SGGGLM solves a generalized linear regression model (GLM) problem: minimize y'*y subject to d = A*x + B*y x,y using a generalized QR factorization of A and B, where A is an N-by-M matrix, B is a given N-by-P matrix, and d is a given N vector. It is also 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. 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)*(b-A*x) || x where ||.|| is vector 2-norm, and inv(B) denotes the inverse of matrix B. ARGUMENTS N (input) INTEGER The number of rows of the matrices A and B. N >= 0. M (input) INTEGER The number of columns of the matrix A. M >= 0. P (input) INTEGER The number of columns of the matrix B. P >= 0. Assume that M <= N <= M+P. A (input/output) REAL array, dimension (LDA,M) On entry, the N-by-M matrix A. On exit, A is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max( 1,N ). B (input/output) REAL array, dimension (LDB,P) On entry, the N-by-P matrix B. On exit, B is des- troyed. LDB (input) INTEGER The leading dimension of the array B. LDB >= max( 1,N ). D (input) REAL array, dimension (N) On entry, D is the left hand side of the GLM equa- tion. On exit, D is destroyed. X (output) REAL array, dimension (M) Y (output) REAL array, dimension (P) On exit, X and Y are the solutions of the GLM problem. WORK (workspace) REAL array, dimension ( LWORK ) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= M+P+max(N,M,P). For optimum performance, LWORK >= M+P+max(N,M,P)*max(NB1,NB2), where NB1 is the optimal blocksize for the QR factorization of an N- by-M matrix A. NB2 is the optimal blocksize for the RQ factorization of an N-by-P matrix B. INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.