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

/* Subroutine */ int cgels_(char *trans, integer *m, integer *n, integer *
	nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex *
	work, integer *lwork, integer *info)
{
/*  -- LAPACK driver 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   
    =======   

    CGELS solves overdetermined or underdetermined complex linear systems   
    involving an M-by-N matrix A, or its conjugate-transpose, using a QR   
    or LQ factorization of A.  It is assumed that A has full rank.   

    The following options are provided:   

    1. If TRANS = 'N' and m >= n:  find the least squares solution of   
       an overdetermined system, i.e., solve the least squares problem   
                    minimize || B - A*X ||.   

    2. If TRANS = 'N' and m < n:  find the minimum norm solution of   
       an underdetermined system A * X = B.   

    3. If TRANS = 'C' and m >= n:  find the minimum norm solution of   
       an undetermined system A**H * X = B.   

    4. If TRANS = 'C' and m < n:  find the least squares solution of   
       an overdetermined system, i.e., solve the least squares problem   
                    minimize || B - A**H * X ||.   

    Several right hand side vectors b and solution vectors x can be   
    handled in a single call; they are stored as the columns of the   
    M-by-NRHS right hand side matrix B and the N-by-NRHS solution   
    matrix X.   

    Arguments   
    =========   

    TRANS   (input) CHARACTER   
            = 'N': the linear system involves A;   
            = 'C': the linear system involves A**H.   

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

    N       (input) INTEGER   
            The number of columns of the matrix A.  N >= 0.   

    NRHS    (input) INTEGER   
            The number of right hand sides, i.e., the number of   
            columns of the matrices B and X. NRHS >= 0.   

    A       (input/output) COMPLEX array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
              if M >= N, A is overwritten by details of its QR   
                         factorization as returned by CGEQRF;   
              if M <  N, A is overwritten by details of its LQ   
                         factorization as returned by CGELQF.   

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

    B       (input/output) COMPLEX array, dimension (LDB,NRHS)   
            On entry, the matrix B of right hand side vectors, stored   
            columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS   
            if TRANS = 'C'.   
            On exit, B is overwritten by the solution vectors, stored   
            columnwise:   
            if TRANS = 'N' and m >= n, rows 1 to n of B contain the least   
            squares solution vectors; the residual sum of squares for the   
            solution in each column is given by the sum of squares of   
            elements N+1 to M in that column;   
            if TRANS = 'N' and m < n, rows 1 to N of B contain the   
            minimum norm solution vectors;   
            if TRANS = 'C' and m >= n, rows 1 to M of B contain the   
            minimum norm solution vectors;   
            if TRANS = 'C' and m < n, rows 1 to M of B contain the   
            least squares solution vectors; the residual sum of squares   
            for the solution in each column is given by the sum of   
            squares of elements M+1 to N in that column.   

    LDB     (input) INTEGER   
            The leading dimension of the array B. LDB >= MAX(1,M,N).   

    WORK    (workspace/output) COMPLEX 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, MN + max( MN, NRHS ) ).   
            For optimal performance,   
            LWORK >= max( 1, MN + max( MN, NRHS )*NB ).   
            where MN = min(M,N) and NB is the optimum block size.   

            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   

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


       Test the input arguments.   

       Parameter adjustments */
    /* Table of constant values */
    static complex c_b1 = {0.f,0.f};
    static complex c_b2 = {1.f,0.f};
    static integer c__1 = 1;
    static integer c_n1 = -1;
    static integer c__0 = 0;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    real r__1;
    /* Local variables */
    static real anrm, bnrm;
    static integer brow;
    static logical tpsd;
    static integer i__, j, iascl, ibscl;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *);
    static integer wsize;
    static real rwork[1];
    static integer nb;
    extern /* Subroutine */ int slabad_(real *, real *);
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    static integer mn;
    extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, 
	    integer *, complex *, complex *, integer *, integer *), clascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
	    , complex *, integer *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, 
	    integer *, complex *, complex *, integer *, integer *), claset_(
	    char *, integer *, integer *, complex *, complex *, complex *, 
	    integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static integer scllen;
    static real bignum;
    extern /* Subroutine */ int cunmlq_(char *, char *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *, integer *), cunmqr_(char *, 
	    char *, integer *, integer *, integer *, complex *, integer *, 
	    complex *, complex *, integer *, complex *, integer *, integer *);
    static real smlnum;
    static logical lquery;
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]


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

    /* Function Body */
    *info = 0;
    mn = min(*m,*n);
    lquery = *lwork == -1;
    if (! (lsame_(trans, "N") || lsame_(trans, "C"))) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*lda < max(1,*m)) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*m);
	if (*ldb < max(i__1,*n)) {
	    *info = -8;
	} else /* if(complicated condition) */ {
/* Computing MAX */
	    i__1 = 1, i__2 = mn + max(mn,*nrhs);
	    if (*lwork < max(i__1,i__2) && ! lquery) {
		*info = -10;
	    }
	}
    }

/*     Figure out optimal block size */

    if (*info == 0 || *info == -10) {

	tpsd = TRUE_;
	if (lsame_(trans, "N")) {
	    tpsd = FALSE_;
	}

	if (*m >= *n) {
	    nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
		    (ftnlen)1);
	    if (tpsd) {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LN", m, nrhs, n, &
			c_n1, (ftnlen)6, (ftnlen)2);
		nb = max(i__1,i__2);
	    } else {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &
			c_n1, (ftnlen)6, (ftnlen)2);
		nb = max(i__1,i__2);
	    }
	} else {
	    nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
		    (ftnlen)1);
	    if (tpsd) {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LC", n, nrhs, m, &
			c_n1, (ftnlen)6, (ftnlen)2);
		nb = max(i__1,i__2);
	    } else {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LN", n, nrhs, m, &
			c_n1, (ftnlen)6, (ftnlen)2);
		nb = max(i__1,i__2);
	    }
	}

/* Computing MAX */
	i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
	wsize = max(i__1,i__2);
	r__1 = (real) wsize;
	work[1].r = r__1, work[1].i = 0.f;

    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CGELS ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible   

   Computing MIN */
    i__1 = min(*m,*n);
    if (min(i__1,*nrhs) == 0) {
	i__1 = max(*m,*n);
	claset_("Full", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
	return 0;
    }

/*     Get machine parameters */

    smlnum = slamch_("S") / slamch_("P");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Scale A, B if max element outside range [SMLNUM,BIGNUM] */

    anrm = clange_("M", m, n, &a[a_offset], lda, rwork);
    iascl = 0;
    if (anrm > 0.f && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.f) {

/*        Matrix all zero. Return zero solution. */

	i__1 = max(*m,*n);
	claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
	goto L50;
    }

    brow = *m;
    if (tpsd) {
	brow = *n;
    }
    bnrm = clange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
    ibscl = 0;
    if (bnrm > 0.f && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	clascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	clascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 2;
    }

    if (*m >= *n) {

/*        compute QR factorization of A */

	i__1 = *lwork - mn;
	cgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
		;

/*        workspace at least N, optimally N*NB */

	if (! tpsd) {

/*           Least-Squares Problem min || A * X - B ||   

             B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */

	    i__1 = *lwork - mn;
	    cunmqr_("Left", "Conjugate transpose", m, nrhs, n, &a[a_offset], 
		    lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, 
		    info);

/*           workspace at least NRHS, optimally NRHS*NB   

             B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */

	    ctrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &
		    c_b2, &a[a_offset], lda, &b[b_offset], ldb);

	    scllen = *n;

	} else {

/*           Overdetermined system of equations A' * X = B   

             B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */

	    ctrsm_("Left", "Upper", "Conjugate transpose", "Non-unit", n, 
		    nrhs, &c_b2, &a[a_offset], lda, &b[b_offset], ldb);

/*           B(N+1:M,1:NRHS) = ZERO */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *m;
		for (i__ = *n + 1; i__ <= i__2; ++i__) {
		    i__3 = b_subscr(i__, j);
		    b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L10: */
		}
/* L20: */
	    }

/*           B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */

	    i__1 = *lwork - mn;
	    cunmqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB */

	    scllen = *m;

	}

    } else {

/*        Compute LQ factorization of A */

	i__1 = *lwork - mn;
	cgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
		;

/*        workspace at least M, optimally M*NB. */

	if (! tpsd) {

/*           underdetermined system of equations A * X = B   

             B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */

	    ctrsm_("Left", "Lower", "No transpose", "Non-unit", m, nrhs, &
		    c_b2, &a[a_offset], lda, &b[b_offset], ldb);

/*           B(M+1:N,1:NRHS) = 0 */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n;
		for (i__ = *m + 1; i__ <= i__2; ++i__) {
		    i__3 = b_subscr(i__, j);
		    b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
		}
/* L40: */
	    }

/*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */

	    i__1 = *lwork - mn;
	    cunmlq_("Left", "Conjugate transpose", n, nrhs, m, &a[a_offset], 
		    lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, 
		    info);

/*           workspace at least NRHS, optimally NRHS*NB */

	    scllen = *n;

	} else {

/*           overdetermined system min || A' * X - B ||   

             B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */

	    i__1 = *lwork - mn;
	    cunmlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB   

             B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */

	    ctrsm_("Left", "Lower", "Conjugate transpose", "Non-unit", m, 
		    nrhs, &c_b2, &a[a_offset], lda, &b[b_offset], ldb);

	    scllen = *m;

	}

    }

/*     Undo scaling */

    if (iascl == 1) {
	clascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    } else if (iascl == 2) {
	clascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    }
    if (ibscl == 1) {
	clascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    } else if (ibscl == 2) {
	clascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
		, ldb, info);
    }

L50:
    r__1 = (real) wsize;
    work[1].r = r__1, work[1].i = 0.f;

    return 0;

/*     End of CGELS */

} /* cgels_ */

#undef b_ref
#undef b_subscr


