dggbak.c

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/* dggbak.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"

/* Subroutine */ int dggbak_(char *job, char *side, integer *n, integer *ilo, 
        integer *ihi, doublereal *lscale, doublereal *rscale, integer *m, 
        doublereal *v, integer *ldv, integer *info)
{
    /* System generated locals */
    integer v_dim1, v_offset, i__1;

    /* Local variables */
    integer i__, k;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    logical leftv;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    logical rightv;


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

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

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

/*  DGGBAK forms the right or left eigenvectors of a real generalized */
/*  eigenvalue problem A*x = lambda*B*x, by backward transformation on */
/*  the computed eigenvectors of the balanced pair of matrices output by */
/*  DGGBAL. */

/*  Arguments */
/*  ========= */

/*  JOB     (input) CHARACTER*1 */
/*          Specifies the type of backward transformation required: */
/*          = 'N':  do nothing, return immediately; */
/*          = 'P':  do backward transformation for permutation only; */
/*          = 'S':  do backward transformation for scaling only; */
/*          = 'B':  do backward transformations for both permutation and */
/*                  scaling. */
/*          JOB must be the same as the argument JOB supplied to DGGBAL. */

/*  SIDE    (input) CHARACTER*1 */
/*          = 'R':  V contains right eigenvectors; */
/*          = 'L':  V contains left eigenvectors. */

/*  N       (input) INTEGER */
/*          The number of rows of the matrix V.  N >= 0. */

/*  ILO     (input) INTEGER */
/*  IHI     (input) INTEGER */
/*          The integers ILO and IHI determined by DGGBAL. */
/*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */

/*  LSCALE  (input) DOUBLE PRECISION array, dimension (N) */
/*          Details of the permutations and/or scaling factors applied */
/*          to the left side of A and B, as returned by DGGBAL. */

/*  RSCALE  (input) DOUBLE PRECISION array, dimension (N) */
/*          Details of the permutations and/or scaling factors applied */
/*          to the right side of A and B, as returned by DGGBAL. */

/*  M       (input) INTEGER */
/*          The number of columns of the matrix V.  M >= 0. */

/*  V       (input/output) DOUBLE PRECISION array, dimension (LDV,M) */
/*          On entry, the matrix of right or left eigenvectors to be */
/*          transformed, as returned by DTGEVC. */
/*          On exit, V is overwritten by the transformed eigenvectors. */

/*  LDV     (input) INTEGER */
/*          The leading dimension of the matrix V. LDV >= max(1,N). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

/*  Further Details */
/*  =============== */

/*  See R.C. Ward, Balancing the generalized eigenvalue problem, */
/*                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    --lscale;
    --rscale;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;

    /* Function Body */
    rightv = lsame_(side, "R");
    leftv = lsame_(side, "L");

    *info = 0;
    if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") 
            && ! lsame_(job, "B")) {
        *info = -1;
    } else if (! rightv && ! leftv) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*ilo < 1) {
        *info = -4;
    } else if (*n == 0 && *ihi == 0 && *ilo != 1) {
        *info = -4;
    } else if (*n > 0 && (*ihi < *ilo || *ihi > max(1,*n))) {
        *info = -5;
    } else if (*n == 0 && *ilo == 1 && *ihi != 0) {
        *info = -5;
    } else if (*m < 0) {
        *info = -8;
    } else if (*ldv < max(1,*n)) {
        *info = -10;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGGBAK", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }
    if (*m == 0) {
        return 0;
    }
    if (lsame_(job, "N")) {
        return 0;
    }

    if (*ilo == *ihi) {
        goto L30;
    }

/*     Backward balance */

    if (lsame_(job, "S") || lsame_(job, "B")) {

/*        Backward transformation on right eigenvectors */

        if (rightv) {
            i__1 = *ihi;
            for (i__ = *ilo; i__ <= i__1; ++i__) {
                dscal_(m, &rscale[i__], &v[i__ + v_dim1], ldv);
/* L10: */
            }
        }

/*        Backward transformation on left eigenvectors */

        if (leftv) {
            i__1 = *ihi;
            for (i__ = *ilo; i__ <= i__1; ++i__) {
                dscal_(m, &lscale[i__], &v[i__ + v_dim1], ldv);
/* L20: */
            }
        }
    }

/*     Backward permutation */

L30:
    if (lsame_(job, "P") || lsame_(job, "B")) {

/*        Backward permutation on right eigenvectors */

        if (rightv) {
            if (*ilo == 1) {
                goto L50;
            }

            for (i__ = *ilo - 1; i__ >= 1; --i__) {
                k = (integer) rscale[i__];
                if (k == i__) {
                    goto L40;
                }
                dswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L40:
                ;
            }

L50:
            if (*ihi == *n) {
                goto L70;
            }
            i__1 = *n;
            for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
                k = (integer) rscale[i__];
                if (k == i__) {
                    goto L60;
                }
                dswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L60:
                ;
            }
        }

/*        Backward permutation on left eigenvectors */

L70:
        if (leftv) {
            if (*ilo == 1) {
                goto L90;
            }
            for (i__ = *ilo - 1; i__ >= 1; --i__) {
                k = (integer) lscale[i__];
                if (k == i__) {
                    goto L80;
                }
                dswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L80:
                ;
            }

L90:
            if (*ihi == *n) {
                goto L110;
            }
            i__1 = *n;
            for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
                k = (integer) lscale[i__];
                if (k == i__) {
                    goto L100;
                }
                dswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
L100:
                ;
            }
        }
    }

L110:

    return 0;

/*     End of DGGBAK */

} /* dggbak_ */