dggglm - Markov linear model (GLM) problem
SUBROUTINE DGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER N, M, P, LDA, LDB, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*) SUBROUTINE DGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*) F95 INTERFACE SUBROUTINE GGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO REAL(8), DIMENSION(:) :: D, X, Y, WORK REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO REAL(8), DIMENSION(:) :: D, X, Y, WORK REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dggglm(int n, int m, int p, double *a, int lda, double *b, int ldb, double *d, double *x, double *y, int *info); void dggglm_64(long n, long m, long p, double *a, long lda, double *b, long ldb, double *d, double *x, double *y, long *info);
Oracle Solaris Studio Performance Library dggglm(3P) NAME dggglm - solve a general Gauss-Markov linear model (GLM) problem SYNOPSIS SUBROUTINE DGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER N, M, P, LDA, LDB, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*) SUBROUTINE DGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*) F95 INTERFACE SUBROUTINE GGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO REAL(8), DIMENSION(:) :: D, X, Y, WORK REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, INFO) INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO REAL(8), DIMENSION(:) :: D, X, Y, WORK REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dggglm(int n, int m, int p, double *a, int lda, double *b, int ldb, double *d, double *x, double *y, int *info); void dggglm_64(long n, long m, long p, double *a, long lda, double *b, long ldb, double *d, double *x, double *y, long *info); PURPOSE dggglm 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. ARGUMENTS N (input) The number of rows of the matrices A and B. N >= 0. M (input) The number of columns of the matrix A. 0 <= M <= N. P (input) The number of columns of the matrix B. P >= N-M. A (input/output) On entry, the N-by-M matrix A. On exit, A is destroyed. LDA (input) The leading dimension of the array A. LDA >= max(1,N). B (input/output) On entry, the N-by-P matrix B. On exit, B is destroyed. LDB (input) The leading dimension of the array B. LDB >= max(1,N). D (input/output) On entry, D is the left hand side of the GLM equation. On exit, D is destroyed. X (output) On exit, X and Y are the solutions of the GLM problem. Y (output) See the description of X. WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LDWORK. LDWORK (input) The dimension of the array WORK. LDWORK >= max(1,N+M+P). For optimum performance, LDWORK >= M+min(N,P)+max(N,P)*NB, where NB is an upper bound for the optimal blocksizes for DGEQRF, DGERQF, DORMQR and DORMRQ. If LDWORK = -1, then a workspace query is assumed; the rou- tine 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 LDWORK is issued by XERBLA. INFO (output) = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. 7 Nov 2015 dggglm(3P)