/* ./src_f77/cgels.f -- translated by f2c (version 20030320).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include <punc/vf2c.h>

/* 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;

/* 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, ftnlen trans_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    real r__1;

    /* Local variables */
    static integer i__, j, nb, mn;
    static real anrm, bnrm;
    static integer brow;
    static logical tpsd;
    static integer iascl, ibscl;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *, ftnlen, ftnlen, ftnlen, ftnlen);
    static integer wsize;
    static real rwork[1];
    extern /* Subroutine */ int slabad_(real *, real *);
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *, ftnlen);
    extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, 
	    integer *, complex *, complex *, integer *, integer *), clascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
	    , complex *, integer *, integer *, ftnlen);
    extern doublereal slamch_(char *, ftnlen);
    extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, 
	    integer *, complex *, complex *, integer *, integer *), claset_(
	    char *, integer *, integer *, complex *, complex *, complex *, 
	    integer *, ftnlen), xerbla_(char *, integer *, ftnlen);
    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 *, ftnlen, ftnlen), cunmqr_(char *, 
	    char *, integer *, integer *, integer *, complex *, integer *, 
	    complex *, complex *, integer *, complex *, integer *, integer *, 
	    ftnlen, ftnlen);
    static real smlnum;
    static logical lquery;


/*  -- 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 */

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

/*  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 */

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

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

/*     Test the input arguments. */

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

    /* Function Body */
    *info = 0;
    mn = min(*m,*n);
    lquery = *lwork == -1;
    if (! (lsame_(trans, "N", (ftnlen)1, (ftnlen)1) || lsame_(trans, "C", (
	    ftnlen)1, (ftnlen)1))) {
	*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", (ftnlen)1, (ftnlen)1)) {
	    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, (ftnlen)6);
	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, (ftnlen)
		4);
	return 0;
    }

/*     Get machine parameters */

    smlnum = slamch_("S", (ftnlen)1) / slamch_("P", (ftnlen)1);
    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, (ftnlen)1);
    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, (ftnlen)1);
	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, (ftnlen)1);
	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, (ftnlen)1);
	goto L50;
    }

    brow = *m;
    if (tpsd) {
	brow = *n;
    }
    bnrm = clange_("M", &brow, nrhs, &b[b_offset], ldb, rwork, (ftnlen)1);
    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, (ftnlen)1);
	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, (ftnlen)1);
	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, (ftnlen)4, (ftnlen)19);

/*           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, (ftnlen)4, (
		    ftnlen)5, (ftnlen)12, (ftnlen)8);

	    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, (
		    ftnlen)4, (ftnlen)5, (ftnlen)19, (ftnlen)8);

/*           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 = i__ + j * b_dim1;
		    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, (
		    ftnlen)4, (ftnlen)12);

/*           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, (ftnlen)4, (
		    ftnlen)5, (ftnlen)12, (ftnlen)8);

/*           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 = i__ + j * b_dim1;
		    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, (ftnlen)4, (ftnlen)19);

/*           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, (
		    ftnlen)4, (ftnlen)12);

/*           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, (
		    ftnlen)4, (ftnlen)5, (ftnlen)19, (ftnlen)8);

	    scllen = *m;

	}

    }

/*     Undo scaling */

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

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

    return 0;

/*     End of CGELS */

} /* cgels_ */

