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SGGGLM(l)) SGGGLM(l)SGGGLM - solve a general Gauss-Markov linear model (GLM) problemNAMESUBROUTINE 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( * )SYNOPSISSGGGLM 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 A and B. 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.PURPOSEN (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. 0 <= M <= N. P (input) INTEGER The number of columns of the matrix B. P >= N-M. 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 destroyed. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). D (input/output) REAL array, dimension (N) On entry, D is the left hand side of the GLM equation. 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/output) 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 >= 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, SOR- MQR and SORMRQ. If LWORK =ARGUMENTS, 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 (output) INTEGER = 0: successful exit. < 0: if INFO =-1, the i-th argument had an illegal value.-iLAPACK version 3.015 June 2000 SGGGLM(l)

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