zgglse - constrained least squares (LSE) problem
SUBROUTINE ZGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*) INTEGER M, N, P, LDA, LDB, LDWORK, INFO SUBROUTINE ZGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*) INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO F95 INTERFACE SUBROUTINE GGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) COMPLEX(8), DIMENSION(:) :: C, D, X, WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO SUBROUTINE GGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) COMPLEX(8), DIMENSION(:) :: C, D, X, WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO C INTERFACE #include <sunperf.h> void zgglse(int m, int n, int p, doublecomplex *a, int lda, doublecom- plex *b, int ldb, doublecomplex *c, doublecomplex *d, double- complex *x, int *info); void zgglse_64(long m, long n, long p, doublecomplex *a, long lda, dou- blecomplex *b, long ldb, doublecomplex *c, doublecomplex *d, doublecomplex *x, long *info);
Oracle Solaris Studio Performance Library zgglse(3P) NAME zgglse - solve the linear equality-constrained least squares (LSE) problem SYNOPSIS SUBROUTINE ZGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*) INTEGER M, N, P, LDA, LDB, LDWORK, INFO SUBROUTINE ZGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*) INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO F95 INTERFACE SUBROUTINE GGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) COMPLEX(8), DIMENSION(:) :: C, D, X, WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO SUBROUTINE GGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK, INFO) COMPLEX(8), DIMENSION(:) :: C, D, X, WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO C INTERFACE #include <sunperf.h> void zgglse(int m, int n, int p, doublecomplex *a, int lda, doublecom- plex *b, int ldb, doublecomplex *c, doublecomplex *d, double- complex *x, int *info); void zgglse_64(long m, long n, long p, doublecomplex *a, long lda, dou- blecomplex *b, long ldb, doublecomplex *c, doublecomplex *d, doublecomplex *x, long *info); PURPOSE zgglse solves the linear equality-constrained least squares (LSE) prob- lem: minimize || c - A*x ||_2 subject to B*x = d where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vec- tor, and d is a given P-vector. It is assumed that P <= N <= M+P, and rank(B) = P and rank( ( A ) ) = N. ( ( B ) ) These conditions ensure that the LSE problem has a unique solution, which is obtained using a GRQ factorization of the matrices B and A. ARGUMENTS M (input) The number of rows of the matrix A. M >= 0. N (input) The number of columns of the matrices A and B. N >= 0. P (input) The number of rows of the matrix B. 0 <= P <= N <= M+P. A (input/output) On entry, the M-by-N matrix A. On exit, A is destroyed. LDA (input) The leading dimension of the array A. LDA >= max(1,M). B (input/output) On entry, the P-by-N matrix B. On exit, B is destroyed. LDB (input) The leading dimension of the array B. LDB >= max(1,P). C (input/output) On entry, C contains the right hand side vector for the least squares part of the LSE problem. On exit, the residual sum of squares for the solution is given by the sum of squares of elements N-P+1 to M of vector C. D (input/output) On entry, D contains the right hand side vector for the con- strained equation. On exit, D is destroyed. X (output) On exit, X is the solution of the LSE problem. WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LDWORK. LDWORK (input) The dimension of the array WORK. LDWORK >= max(1,M+N+P). For optimum performance LDWORK >= P+min(M,N)+max(M,N)*NB, where NB is an upper bound for the optimal blocksizes for ZGEQRF, ZGERQF, ZUNMQR and ZUNMRQ. 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 zgglse(3P)