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

/* Subroutine */ int dggrqf_(integer *m, integer *p, integer *n, doublereal *
	a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, 
	doublereal *taub, doublereal *work, integer *lwork, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    DGGRQF computes a generalized RQ factorization of an M-by-N matrix A   
    and a P-by-N matrix B:   

                A = R*Q,        B = Z*T*Q,   

    where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal   
    matrix, and R and T assume one of the forms:   

    if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,   
                     N-M  M                           ( R21 ) N   
                                                         N   

    where R12 or R21 is upper triangular, and   

    if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,   
                    (  0  ) P-N                         P   N-P   
                       N   

    where T11 is upper triangular.   

    In particular, if B is square and nonsingular, the GRQ factorization   
    of A and B implicitly gives the RQ factorization of A*inv(B):   

                 A*inv(B) = (R*inv(T))*Z'   

    where inv(B) denotes the inverse of the matrix B, and Z' denotes the   
    transpose of the matrix Z.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix A.  M >= 0.   

    P       (input) INTEGER   
            The number of rows of the matrix B.  P >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrices A and B. N >= 0.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, if M <= N, the upper triangle of the subarray   
            A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;   
            if M > N, the elements on and above the (M-N)-th subdiagonal   
            contain the M-by-N upper trapezoidal matrix R; the remaining   
            elements, with the array TAUA, represent the orthogonal   
            matrix Q as a product of elementary reflectors (see Further   
            Details).   

    LDA     (input) INTEGER   
            The leading dimension of the array A. LDA >= max(1,M).   

    TAUA    (output) DOUBLE PRECISION array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors which   
            represent the orthogonal matrix Q (see Further Details).   

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)   
            On entry, the P-by-N matrix B.   
            On exit, the elements on and above the diagonal of the array   
            contain the min(P,N)-by-N upper trapezoidal matrix T (T is   
            upper triangular if P >= N); the elements below the diagonal,   
            with the array TAUB, represent the orthogonal matrix Z as a   
            product of elementary reflectors (see Further Details).   

    LDB     (input) INTEGER   
            The leading dimension of the array B. LDB >= max(1,P).   

    TAUB    (output) DOUBLE PRECISION array, dimension (min(P,N))   
            The scalar factors of the elementary reflectors which   
            represent the orthogonal matrix Z (see Further Details).   

    WORK    (workspace/output) DOUBLE PRECISION 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 >= max(N,M,P)*max(NB1,NB2,NB3),   
            where NB1 is the optimal blocksize for the RQ factorization   
            of an M-by-N matrix, NB2 is the optimal blocksize for the   
            QR factorization of a P-by-N matrix, and NB3 is the optimal   
            blocksize for a call of DORMRQ.   

            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 INF0= -i, the i-th argument had an illegal value.   

    Further Details   
    ===============   

    The matrix Q is represented as a product of elementary reflectors   

       Q = H(1) H(2) . . . H(k), where k = min(m,n).   

    Each H(i) has the form   

       H(i) = I - taua * v * v'   

    where taua is a real scalar, and v is a real vector with   
    v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in   
    A(m-k+i,1:n-k+i-1), and taua in TAUA(i).   
    To form Q explicitly, use LAPACK subroutine DORGRQ.   
    To use Q to update another matrix, use LAPACK subroutine DORMRQ.   

    The matrix Z is represented as a product of elementary reflectors   

       Z = H(1) H(2) . . . H(k), where k = min(p,n).   

    Each H(i) has the form   

       H(i) = I - taub * v * v'   

    where taub is a real scalar, and v is a real vector with   
    v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),   
    and taub in TAUB(i).   
    To form Z explicitly, use LAPACK subroutine DORGQR.   
    To use Z to update another matrix, use LAPACK subroutine DORMQR.   

    =====================================================================   


       Test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    /* Local variables */
    static integer lopt, nb;
    extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dgerqf_(integer *, integer *, doublereal *, integer *, doublereal 
	    *, doublereal *, integer *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static integer nb1, nb2, nb3;
    extern /* Subroutine */ int dormrq_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer lwkopt;
    static logical lquery;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --taua;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --taub;
    --work;

    /* Function Body */
    *info = 0;
    nb1 = ilaenv_(&c__1, "DGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb2 = ilaenv_(&c__1, "DGEQRF", " ", p, n, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb3 = ilaenv_(&c__1, "DORMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
    i__1 = max(nb1,nb2);
    nb = max(i__1,nb3);
/* Computing MAX */
    i__1 = max(*n,*m);
    lwkopt = max(i__1,*p) * nb;
    work[1] = (doublereal) lwkopt;
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*p < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,*p)) {
	*info = -8;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*m), i__1 = max(i__1,*p);
	if (*lwork < max(i__1,*n) && ! lquery) {
	    *info = -11;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGGRQF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     RQ factorization of M-by-N matrix A: A = R*Q */

    dgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
    lopt = (integer) work[1];

/*     Update B := B*Q'   

   Computing MAX */
    i__1 = 1, i__2 = *m - *n + 1;
    i__3 = min(*m,*n);
    dormrq_("Right", "Transpose", p, n, &i__3, &a_ref(max(i__1,i__2), 1), lda,
	     &taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    lopt = max(i__1,i__2);

/*     QR factorization of P-by-N matrix B: B = Z*T */

    dgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    work[1] = (doublereal) max(i__1,i__2);

    return 0;

/*     End of DGGRQF */

} /* dggrqf_ */

#undef a_ref


