#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgglse_(integer *m, integer *n, integer *p, real *a, integer *lda, real *b, integer *ldb, real *c__, real *d__, real *x, real *work, integer *lwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SGGLSE solves the linear equality-constrained least squares (LSE) problem: 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-vector, 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 generalized RQ factorization of the matrices (B, A) given by B = (0 R)*Q, A = Z*T*Q. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrices A and B. N >= 0. P (input) INTEGER The number of rows of the matrix B. 0 <= P <= N <= M+P. A (input/output) REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix T. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). B (input/output) REAL array, dimension (LDB,N) On entry, the P-by-N matrix B. On exit, the upper triangle of the subarray B(1:P,N-P+1:N) contains the P-by-P upper triangular matrix R. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,P). C (input/output) REAL array, dimension (M) 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) REAL array, dimension (P) On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed. X (output) REAL array, dimension (N) On exit, X is the solution of the LSE problem. WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,M+N+P). For optimum performance LWORK >= P+min(M,N)+max(M,N)*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 (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. = 1: the upper triangular factor R associated with B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) < P; the least squares solution could not be computed. = 2: the (N-P) by (N-P) part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that rank( (A) ) < N; the least squares solution could not ( (B) ) be computed. ===================================================================== Test the input parameters Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static real c_b31 = -1.f; static real c_b33 = 1.f; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; /* Local variables */ static integer nb, mn, nr, nb1, nb2, nb3, nb4, lopt; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, integer *), strmv_(char *, char *, char *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int sggrqf_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, real *, integer * , integer *); static integer lwkmin, lwkopt; static logical lquery; extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *), sormrq_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real * , integer *, real *, integer *, integer *), strtrs_(char *, char *, char *, integer *, integer *, real *, integer *, real *, integer *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --c__; --d__; --x; --work; /* Function Body */ *info = 0; mn = min(*m,*n); lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*p < 0 || *p > *n || *p < *n - *m) { *info = -3; } else if (*lda < max(1,*m)) { *info = -5; } else if (*ldb < max(1,*p)) { *info = -7; } /* Calculate workspace */ if (*info == 0) { if (*n == 0) { lwkmin = 1; lwkopt = 1; } else { nb1 = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); nb2 = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); nb3 = ilaenv_(&c__1, "SORMQR", " ", m, n, p, &c_n1, (ftnlen)6, ( ftnlen)1); nb4 = ilaenv_(&c__1, "SORMRQ", " ", m, n, p, &c_n1, (ftnlen)6, ( ftnlen)1); /* Computing MAX */ i__1 = max(nb1,nb2), i__1 = max(i__1,nb3); nb = max(i__1,nb4); lwkmin = *m + *n + *p; lwkopt = *p + mn + max(*m,*n) * nb; } work[1] = (real) lwkopt; if (*lwork < lwkmin && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("SGGLSE", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Compute the GRQ factorization of matrices B and A: B*Q' = ( 0 T12 ) P Z'*A*Q' = ( R11 R12 ) N-P N-P P ( 0 R22 ) M+P-N N-P P where T12 and R11 are upper triangular, and Q and Z are orthogonal. */ i__1 = *lwork - *p - mn; sggrqf_(p, m, n, &b[b_offset], ldb, &work[1], &a[a_offset], lda, &work[*p + 1], &work[*p + mn + 1], &i__1, info); lopt = work[*p + mn + 1]; /* Update c = Z'*c = ( c1 ) N-P ( c2 ) M+P-N */ i__1 = max(1,*m); i__2 = *lwork - *p - mn; sormqr_("Left", "Transpose", m, &c__1, &mn, &a[a_offset], lda, &work[*p + 1], &c__[1], &i__1, &work[*p + mn + 1], &i__2, info); /* Computing MAX */ i__1 = lopt, i__2 = (integer) work[*p + mn + 1]; lopt = max(i__1,i__2); /* Solve T12*x2 = d for x2 */ if (*p > 0) { strtrs_("Upper", "No transpose", "Non-unit", p, &c__1, &b[(*n - *p + 1) * b_dim1 + 1], ldb, &d__[1], p, info); if (*info > 0) { *info = 1; return 0; } /* Put the solution in X */ scopy_(p, &d__[1], &c__1, &x[*n - *p + 1], &c__1); /* Update c1 */ i__1 = *n - *p; sgemv_("No transpose", &i__1, p, &c_b31, &a[(*n - *p + 1) * a_dim1 + 1], lda, &d__[1], &c__1, &c_b33, &c__[1], &c__1); } /* Solve R11*x1 = c1 for x1 */ if (*n > *p) { i__1 = *n - *p; i__2 = *n - *p; strtrs_("Upper", "No transpose", "Non-unit", &i__1, &c__1, &a[ a_offset], lda, &c__[1], &i__2, info); if (*info > 0) { *info = 2; return 0; } /* Put the solution in X */ i__1 = *n - *p; scopy_(&i__1, &c__[1], &c__1, &x[1], &c__1); } /* Compute the residual vector: */ if (*m < *n) { nr = *m + *p - *n; if (nr > 0) { i__1 = *n - *m; sgemv_("No transpose", &nr, &i__1, &c_b31, &a[*n - *p + 1 + (*m + 1) * a_dim1], lda, &d__[nr + 1], &c__1, &c_b33, &c__[*n - *p + 1], &c__1); } } else { nr = *p; } if (nr > 0) { strmv_("Upper", "No transpose", "Non unit", &nr, &a[*n - *p + 1 + (*n - *p + 1) * a_dim1], lda, &d__[1], &c__1); saxpy_(&nr, &c_b31, &d__[1], &c__1, &c__[*n - *p + 1], &c__1); } /* Backward transformation x = Q'*x */ i__1 = *lwork - *p - mn; sormrq_("Left", "Transpose", n, &c__1, p, &b[b_offset], ldb, &work[1], &x[ 1], n, &work[*p + mn + 1], &i__1, info); /* Computing MAX */ i__1 = lopt, i__2 = (integer) work[*p + mn + 1]; work[1] = (real) (*p + mn + max(i__1,i__2)); return 0; /* End of SGGLSE */ } /* sgglse_ */