/*  -- translated by f2c (version 20240504).
   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"

/* Table of constant values */

static integer c__1 = 1;

/* > \brief \b DGEBAL   

    =========== DOCUMENTATION ===========   

   Online html documentation available at   
              http://www.netlib.org/lapack/explore-html/   

   > \htmlonly   
   > Download DGEBAL + dependencies   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgebal.
f">   
   > [TGZ]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgebal.
f">   
   > [ZIP]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgebal.
f">   
   > [TXT]</a>   
   > \endhtmlonly   

    Definition:   
    ===========   

         SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )   

         CHARACTER          JOB   
         INTEGER            IHI, ILO, INFO, LDA, N   
         DOUBLE PRECISION   A( LDA, * ), SCALE( * )   


   > \par Purpose:   
    =============   
   >   
   > \verbatim   
   >   
   > DGEBAL balances a general real matrix A.  This involves, first,   
   > permuting A by a similarity transformation to isolate eigenvalues   
   > in the first 1 to ILO-1 and last IHI+1 to N elements on the   
   > diagonal; and second, applying a diagonal similarity transformation   
   > to rows and columns ILO to IHI to make the rows and columns as   
   > close in norm as possible.  Both steps are optional.   
   >   
   > Balancing may reduce the 1-norm of the matrix, and improve the   
   > accuracy of the computed eigenvalues and/or eigenvectors.   
   > \endverbatim   

    Arguments:   
    ==========   

   > \param[in] JOB   
   > \verbatim   
   >          JOB is CHARACTER*1   
   >          Specifies the operations to be performed on A:   
   >          = 'N':  none:  simply set ILO = 1, IHI = N, SCALE(I) = 1.0   
   >                  for i = 1,...,N;   
   >          = 'P':  permute only;   
   >          = 'S':  scale only;   
   >          = 'B':  both permute and scale.   
   > \endverbatim   
   >   
   > \param[in] N   
   > \verbatim   
   >          N is INTEGER   
   >          The order of the matrix A.  N >= 0.   
   > \endverbatim   
   >   
   > \param[in,out] A   
   > \verbatim   
   >          A is DOUBLE array, dimension (LDA,N)   
   >          On entry, the input matrix A.   
   >          On exit,  A is overwritten by the balanced matrix.   
   >          If JOB = 'N', A is not referenced.   
   >          See Further Details.   
   > \endverbatim   
   >   
   > \param[in] LDA   
   > \verbatim   
   >          LDA is INTEGER   
   >          The leading dimension of the array A.  LDA >= max(1,N).   
   > \endverbatim   
   >   
   > \param[out] ILO   
   > \verbatim   
   >          ILO is INTEGER   
   > \endverbatim   
   > \param[out] IHI   
   > \verbatim   
   >          IHI is INTEGER   
   >          ILO and IHI are set to integers such that on exit   
   >          A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.   
   >          If JOB = 'N' or 'S', ILO = 1 and IHI = N.   
   > \endverbatim   
   >   
   > \param[out] SCALE   
   > \verbatim   
   >          SCALE is DOUBLE array, dimension (N)   
   >          Details of the permutations and scaling factors applied to   
   >          A.  If P(j) is the index of the row and column interchanged   
   >          with row and column j and D(j) is the scaling factor   
   >          applied to row and column j, then   
   >          SCALE(j) = P(j)    for j = 1,...,ILO-1   
   >                   = D(j)    for j = ILO,...,IHI   
   >                   = P(j)    for j = IHI+1,...,N.   
   >          The order in which the interchanges are made is N to IHI+1,   
   >          then 1 to ILO-1.   
   > \endverbatim   
   >   
   > \param[out] INFO   
   > \verbatim   
   >          INFO is INTEGER   
   >          = 0:  successful exit.   
   >          < 0:  if INFO = -i, the i-th argument had an illegal value.   
   > \endverbatim   

    Authors:   
    ========   

   > \author Univ. of Tennessee   
   > \author Univ. of California Berkeley   
   > \author Univ. of Colorado Denver   
   > \author NAG Ltd.   

   > \date November 2013   

   > \ingroup doubleGEcomputational   

   > \par Further Details:   
    =====================   
   >   
   > \verbatim   
   >   
   >  The permutations consist of row and column interchanges which put   
   >  the matrix in the form   
   >   
   >             ( T1   X   Y  )   
   >     P A P = (  0   B   Z  )   
   >             (  0   0   T2 )   
   >   
   >  where T1 and T2 are upper triangular matrices whose eigenvalues lie   
   >  along the diagonal.  The column indices ILO and IHI mark the starting   
   >  and ending columns of the submatrix B. Balancing consists of applying   
   >  a diagonal similarity transformation inv(D) * B * D to make the   
   >  1-norms of each row of B and its corresponding column nearly equal.   
   >  The output matrix is   
   >   
   >     ( T1     X*D          Y    )   
   >     (  0  inv(D)*B*D  inv(D)*Z ).   
   >     (  0      0           T2   )   
   >   
   >  Information about the permutations P and the diagonal matrix D is   
   >  returned in the vector SCALE.   
   >   
   >  This subroutine is based on the EISPACK routine BALANC.   
   >   
   >  Modified by Tzu-Yi Chen, Computer Science Division, University of   
   >    California at Berkeley, USA   
   > \endverbatim   
   >   
    =====================================================================   
   Subroutine */ int igraphdgebal_(char *job, integer *n, doublereal *a, integer *
	lda, integer *ilo, integer *ihi, doublereal *scale, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Local variables */
    doublereal c__, f, g;
    integer i__, j, k, l, m;
    doublereal r__, s, ca, ra;
    integer ica, ira, iexc;
    extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern logical igraphlsame_(char *, char *);
    extern /* Subroutine */ int igraphdswap_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    doublereal sfmin1, sfmin2, sfmax1, sfmax2;
    extern doublereal igraphdlamch_(char *);
    extern integer igraphidamax_(integer *, doublereal *, integer *);
    extern logical igraphdisnan_(doublereal *);
    extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
    logical noconv;


/*  -- LAPACK computational routine (version 3.5.0) --   
    -- LAPACK is a software package provided by Univ. of Tennessee,    --   
    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   
       November 2013   


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


       Test the input parameters   

       Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --scale;

    /* Function Body */
    *info = 0;
    if (! igraphlsame_(job, "N") && ! igraphlsame_(job, "P") && ! igraphlsame_(job, "S") 
	    && ! igraphlsame_(job, "B")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*n)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	igraphxerbla_("DGEBAL", &i__1, (ftnlen)6);
	return 0;
    }

    k = 1;
    l = *n;

    if (*n == 0) {
	goto L210;
    }

    if (igraphlsame_(job, "N")) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    scale[i__] = 1.;
/* L10: */
	}
	goto L210;
    }

    if (igraphlsame_(job, "S")) {
	goto L120;
    }

/*     Permutation to isolate eigenvalues if possible */

    goto L50;

/*     Row and column exchange. */

L20:
    scale[m] = (doublereal) j;
    if (j == m) {
	goto L30;
    }

    igraphdswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
    i__1 = *n - k + 1;
    igraphdswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);

L30:
    switch (iexc) {
	case 1:  goto L40;
	case 2:  goto L80;
    }

/*     Search for rows isolating an eigenvalue and push them down. */

L40:
    if (l == 1) {
	goto L210;
    }
    --l;

L50:
    for (j = l; j >= 1; --j) {

	i__1 = l;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (i__ == j) {
		goto L60;
	    }
	    if (a[j + i__ * a_dim1] != 0.) {
		goto L70;
	    }
L60:
	    ;
	}

	m = l;
	iexc = 1;
	goto L20;
L70:
	;
    }

    goto L90;

/*     Search for columns isolating an eigenvalue and push them left. */

L80:
    ++k;

L90:
    i__1 = l;
    for (j = k; j <= i__1; ++j) {

	i__2 = l;
	for (i__ = k; i__ <= i__2; ++i__) {
	    if (i__ == j) {
		goto L100;
	    }
	    if (a[i__ + j * a_dim1] != 0.) {
		goto L110;
	    }
L100:
	    ;
	}

	m = k;
	iexc = 2;
	goto L20;
L110:
	;
    }

L120:
    i__1 = l;
    for (i__ = k; i__ <= i__1; ++i__) {
	scale[i__] = 1.;
/* L130: */
    }

    if (igraphlsame_(job, "P")) {
	goto L210;
    }

/*     Balance the submatrix in rows K to L.   

       Iterative loop for norm reduction */

    sfmin1 = igraphdlamch_("S") / igraphdlamch_("P");
    sfmax1 = 1. / sfmin1;
    sfmin2 = sfmin1 * 2.;
    sfmax2 = 1. / sfmin2;

L140:
    noconv = FALSE_;

    i__1 = l;
    for (i__ = k; i__ <= i__1; ++i__) {

	i__2 = l - k + 1;
	c__ = igraphdnrm2_(&i__2, &a[k + i__ * a_dim1], &c__1);
	i__2 = l - k + 1;
	r__ = igraphdnrm2_(&i__2, &a[i__ + k * a_dim1], lda);
	ica = igraphidamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
	ca = (d__1 = a[ica + i__ * a_dim1], abs(d__1));
	i__2 = *n - k + 1;
	ira = igraphidamax_(&i__2, &a[i__ + k * a_dim1], lda);
	ra = (d__1 = a[i__ + (ira + k - 1) * a_dim1], abs(d__1));

/*        Guard against zero C or R due to underflow. */

	if (c__ == 0. || r__ == 0.) {
	    goto L200;
	}
	g = r__ / 2.;
	f = 1.;
	s = c__ + r__;
L160:
/* Computing MAX */
	d__1 = max(f,c__);
/* Computing MIN */
	d__2 = min(r__,g);
	if (c__ >= g || max(d__1,ca) >= sfmax2 || min(d__2,ra) <= sfmin2) {
	    goto L170;
	}
	d__1 = c__ + f + ca + r__ + g + ra;
	if (igraphdisnan_(&d__1)) {

/*           Exit if NaN to avoid infinite loop */

	    *info = -3;
	    i__2 = -(*info);
	    igraphxerbla_("DGEBAL", &i__2, (ftnlen)6);
	    return 0;
	}
	f *= 2.;
	c__ *= 2.;
	ca *= 2.;
	r__ /= 2.;
	g /= 2.;
	ra /= 2.;
	goto L160;

L170:
	g = c__ / 2.;
L180:
/* Computing MIN */
	d__1 = min(f,c__), d__1 = min(d__1,g);
	if (g < r__ || max(r__,ra) >= sfmax2 || min(d__1,ca) <= sfmin2) {
	    goto L190;
	}
	f /= 2.;
	c__ /= 2.;
	g /= 2.;
	ca /= 2.;
	r__ *= 2.;
	ra *= 2.;
	goto L180;

/*        Now balance. */

L190:
	if (c__ + r__ >= s * .95) {
	    goto L200;
	}
	if (f < 1. && scale[i__] < 1.) {
	    if (f * scale[i__] <= sfmin1) {
		goto L200;
	    }
	}
	if (f > 1. && scale[i__] > 1.) {
	    if (scale[i__] >= sfmax1 / f) {
		goto L200;
	    }
	}
	g = 1. / f;
	scale[i__] *= f;
	noconv = TRUE_;

	i__2 = *n - k + 1;
	igraphdscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
	igraphdscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);

L200:
	;
    }

    if (noconv) {
	goto L140;
    }

L210:
    *ilo = k;
    *ihi = l;

    return 0;

/*     End of DGEBAL */

} /* igraphdgebal_ */

