dgglse.c

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/* dgglse.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b31 = -1.;
static doublereal c_b33 = 1.;

/* Subroutine */ int dgglse_(integer *m, integer *n, integer *p, doublereal *
        a, integer *lda, doublereal *b, integer *ldb, doublereal *c__, 
        doublereal *d__, doublereal *x, doublereal *work, integer *lwork, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    integer nb, mn, nr, nb1, nb2, nb3, nb4, lopt;
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *), dcopy_(integer *, 
            doublereal *, integer *, doublereal *, integer *), daxpy_(integer 
            *, doublereal *, doublereal *, integer *, doublereal *, integer *)
            , dtrmv_(char *, char *, char *, integer *, doublereal *, integer 
            *, doublereal *, integer *), dggrqf_(
            integer *, integer *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, doublereal *, 
             integer *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    integer lwkmin;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, integer *), 
            dormrq_(char *, char *, integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *, 
            integer *, doublereal *, integer *, doublereal *, integer *, 
            integer *);


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DGGLSE 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (P) */
/*          On entry, D contains the right hand side vector for the */
/*          constrained equation. */
/*          On exit, D is destroyed. */

/*  X       (output) DOUBLE PRECISION array, dimension (N) */
/*          On exit, X is the solution of the LSE problem. */

/*  WORK    (workspace/output) DOUBLE PRECISION 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 */
/*          DGEQRF, SGERQF, DORMQR 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. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

    /* Parameter adjustments */
    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, "DGEQRF", " ", m, n, &c_n1, &c_n1);
            nb2 = ilaenv_(&c__1, "DGERQF", " ", m, n, &c_n1, &c_n1);
            nb3 = ilaenv_(&c__1, "DORMQR", " ", m, n, p, &c_n1);
            nb4 = ilaenv_(&c__1, "DORMRQ", " ", m, n, p, &c_n1);
/* 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] = (doublereal) lwkopt;

        if (*lwork < lwkmin && ! lquery) {
            *info = -12;
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGGLSE", &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;
    dggrqf_(p, m, n, &b[b_offset], ldb, &work[1], &a[a_offset], lda, &work[*p 
            + 1], &work[*p + mn + 1], &i__1, info);
    lopt = (integer) 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;
    dormqr_("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) {
        dtrtrs_("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 */

        dcopy_(p, &d__[1], &c__1, &x[*n - *p + 1], &c__1);

/*        Update c1 */

        i__1 = *n - *p;
        dgemv_("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;
        dtrtrs_("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 solutions in X */

        i__1 = *n - *p;
        dcopy_(&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;
            dgemv_("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) {
        dtrmv_("Upper", "No transpose", "Non unit", &nr, &a[*n - *p + 1 + (*n 
                - *p + 1) * a_dim1], lda, &d__[1], &c__1);
        daxpy_(&nr, &c_b31, &d__[1], &c__1, &c__[*n - *p + 1], &c__1);
    }

/*     Backward transformation x = Q'*x */

    i__1 = *lwork - *p - mn;
    dormrq_("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] = (doublereal) (*p + mn + max(i__1,i__2));

    return 0;

/*     End of DGGLSE */

} /* dgglse_ */