ztrevc.c

Go to the documentation of this file.

/* ztrevc.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"

/* Table of constant values */

static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;

/* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select, 
        integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, 
        integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer 
        *m, doublecomplex *work, doublereal *rwork, integer *info)
{
    /* System generated locals */
    integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, 
            i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double d_imag(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, j, k, ii, ki, is;
    doublereal ulp;
    logical allv;
    doublereal unfl, ovfl, smin;
    logical over;
    doublereal scale;
    extern logical lsame_(char *, char *);
    doublereal remax;
    logical leftv, bothv;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    logical somev;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
            integer *, doublereal *, doublecomplex *, integer *);
    extern integer izamax_(integer *, doublecomplex *, integer *);
    logical rightv;
    extern doublereal dzasum_(integer *, doublecomplex *, integer *);
    doublereal smlnum;
    extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *, 
            integer *, doublecomplex *, integer *, doublecomplex *, 
            doublereal *, doublereal *, integer *);


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

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

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

/*  ZTREVC computes some or all of the right and/or left eigenvectors of */
/*  a complex upper triangular matrix T. */
/*  Matrices of this type are produced by the Schur factorization of */
/*  a complex general matrix:  A = Q*T*Q**H, as computed by ZHSEQR. */

/*  The right eigenvector x and the left eigenvector y of T corresponding */
/*  to an eigenvalue w are defined by: */

/*               T*x = w*x,     (y**H)*T = w*(y**H) */

/*  where y**H denotes the conjugate transpose of the vector y. */
/*  The eigenvalues are not input to this routine, but are read directly */
/*  from the diagonal of T. */

/*  This routine returns the matrices X and/or Y of right and left */
/*  eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
/*  input matrix.  If Q is the unitary factor that reduces a matrix A to */
/*  Schur form T, then Q*X and Q*Y are the matrices of right and left */
/*  eigenvectors of A. */

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

/*  SIDE    (input) CHARACTER*1 */
/*          = 'R':  compute right eigenvectors only; */
/*          = 'L':  compute left eigenvectors only; */
/*          = 'B':  compute both right and left eigenvectors. */

/*  HOWMNY  (input) CHARACTER*1 */
/*          = 'A':  compute all right and/or left eigenvectors; */
/*          = 'B':  compute all right and/or left eigenvectors, */
/*                  backtransformed using the matrices supplied in */
/*                  VR and/or VL; */
/*          = 'S':  compute selected right and/or left eigenvectors, */
/*                  as indicated by the logical array SELECT. */

/*  SELECT  (input) LOGICAL array, dimension (N) */
/*          If HOWMNY = 'S', SELECT specifies the eigenvectors to be */
/*          computed. */
/*          The eigenvector corresponding to the j-th eigenvalue is */
/*          computed if SELECT(j) = .TRUE.. */
/*          Not referenced if HOWMNY = 'A' or 'B'. */

/*  N       (input) INTEGER */
/*          The order of the matrix T. N >= 0. */

/*  T       (input/output) COMPLEX*16 array, dimension (LDT,N) */
/*          The upper triangular matrix T.  T is modified, but restored */
/*          on exit. */

/*  LDT     (input) INTEGER */
/*          The leading dimension of the array T. LDT >= max(1,N). */

/*  VL      (input/output) COMPLEX*16 array, dimension (LDVL,MM) */
/*          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/*          contain an N-by-N matrix Q (usually the unitary matrix Q of */
/*          Schur vectors returned by ZHSEQR). */
/*          On exit, if SIDE = 'L' or 'B', VL contains: */
/*          if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
/*          if HOWMNY = 'B', the matrix Q*Y; */
/*          if HOWMNY = 'S', the left eigenvectors of T specified by */
/*                           SELECT, stored consecutively in the columns */
/*                           of VL, in the same order as their */
/*                           eigenvalues. */
/*          Not referenced if SIDE = 'R'. */

/*  LDVL    (input) INTEGER */
/*          The leading dimension of the array VL.  LDVL >= 1, and if */
/*          SIDE = 'L' or 'B', LDVL >= N. */

/*  VR      (input/output) COMPLEX*16 array, dimension (LDVR,MM) */
/*          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/*          contain an N-by-N matrix Q (usually the unitary matrix Q of */
/*          Schur vectors returned by ZHSEQR). */
/*          On exit, if SIDE = 'R' or 'B', VR contains: */
/*          if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
/*          if HOWMNY = 'B', the matrix Q*X; */
/*          if HOWMNY = 'S', the right eigenvectors of T specified by */
/*                           SELECT, stored consecutively in the columns */
/*                           of VR, in the same order as their */
/*                           eigenvalues. */
/*          Not referenced if SIDE = 'L'. */

/*  LDVR    (input) INTEGER */
/*          The leading dimension of the array VR.  LDVR >= 1, and if */
/*          SIDE = 'R' or 'B'; LDVR >= N. */

/*  MM      (input) INTEGER */
/*          The number of columns in the arrays VL and/or VR. MM >= M. */

/*  M       (output) INTEGER */
/*          The number of columns in the arrays VL and/or VR actually */
/*          used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M */
/*          is set to N.  Each selected eigenvector occupies one */
/*          column. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (2*N) */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */

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

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

/*  The algorithm used in this program is basically backward (forward) */
/*  substitution, with scaling to make the the code robust against */
/*  possible overflow. */

/*  Each eigenvector is normalized so that the element of largest */
/*  magnitude has magnitude 1; here the magnitude of a complex number */
/*  (x,y) is taken to be |x| + |y|. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and test the input parameters */

    /* Parameter adjustments */
    --select;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --work;
    --rwork;

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

    allv = lsame_(howmny, "A");
    over = lsame_(howmny, "B");
    somev = lsame_(howmny, "S");

/*     Set M to the number of columns required to store the selected */
/*     eigenvectors. */

    if (somev) {
        *m = 0;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (select[j]) {
                ++(*m);
            }
/* L10: */
        }
    } else {
        *m = *n;
    }

    *info = 0;
    if (! rightv && ! leftv) {
        *info = -1;
    } else if (! allv && ! over && ! somev) {
        *info = -2;
    } else if (*n < 0) {
        *info = -4;
    } else if (*ldt < max(1,*n)) {
        *info = -6;
    } else if (*ldvl < 1 || leftv && *ldvl < *n) {
        *info = -8;
    } else if (*ldvr < 1 || rightv && *ldvr < *n) {
        *info = -10;
    } else if (*mm < *m) {
        *info = -11;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZTREVC", &i__1);
        return 0;
    }

/*     Quick return if possible. */

    if (*n == 0) {
        return 0;
    }

/*     Set the constants to control overflow. */

    unfl = dlamch_("Safe minimum");
    ovfl = 1. / unfl;
    dlabad_(&unfl, &ovfl);
    ulp = dlamch_("Precision");
    smlnum = unfl * (*n / ulp);

/*     Store the diagonal elements of T in working array WORK. */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        i__2 = i__ + *n;
        i__3 = i__ + i__ * t_dim1;
        work[i__2].r = t[i__3].r, work[i__2].i = t[i__3].i;
/* L20: */
    }

/*     Compute 1-norm of each column of strictly upper triangular */
/*     part of T to control overflow in triangular solver. */

    rwork[1] = 0.;
    i__1 = *n;
    for (j = 2; j <= i__1; ++j) {
        i__2 = j - 1;
        rwork[j] = dzasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L30: */
    }

    if (rightv) {

/*        Compute right eigenvectors. */

        is = *m;
        for (ki = *n; ki >= 1; --ki) {

            if (somev) {
                if (! select[ki]) {
                    goto L80;
                }
            }
/* Computing MAX */
            i__1 = ki + ki * t_dim1;
            d__3 = ulp * ((d__1 = t[i__1].r, abs(d__1)) + (d__2 = d_imag(&t[
                    ki + ki * t_dim1]), abs(d__2)));
            smin = max(d__3,smlnum);

            work[1].r = 1., work[1].i = 0.;

/*           Form right-hand side. */

            i__1 = ki - 1;
            for (k = 1; k <= i__1; ++k) {
                i__2 = k;
                i__3 = k + ki * t_dim1;
                z__1.r = -t[i__3].r, z__1.i = -t[i__3].i;
                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L40: */
            }

/*           Solve the triangular system: */
/*              (T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK. */

            i__1 = ki - 1;
            for (k = 1; k <= i__1; ++k) {
                i__2 = k + k * t_dim1;
                i__3 = k + k * t_dim1;
                i__4 = ki + ki * t_dim1;
                z__1.r = t[i__3].r - t[i__4].r, z__1.i = t[i__3].i - t[i__4]
                        .i;
                t[i__2].r = z__1.r, t[i__2].i = z__1.i;
                i__2 = k + k * t_dim1;
                if ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[k + k * 
                        t_dim1]), abs(d__2)) < smin) {
                    i__3 = k + k * t_dim1;
                    t[i__3].r = smin, t[i__3].i = 0.;
                }
/* L50: */
            }

            if (ki > 1) {
                i__1 = ki - 1;
                zlatrs_("Upper", "No transpose", "Non-unit", "Y", &i__1, &t[
                        t_offset], ldt, &work[1], &scale, &rwork[1], info);
                i__1 = ki;
                work[i__1].r = scale, work[i__1].i = 0.;
            }

/*           Copy the vector x or Q*x to VR and normalize. */

            if (! over) {
                zcopy_(&ki, &work[1], &c__1, &vr[is * vr_dim1 + 1], &c__1);

                ii = izamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
                i__1 = ii + is * vr_dim1;
                remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
                        &vr[ii + is * vr_dim1]), abs(d__2)));
                zdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);

                i__1 = *n;
                for (k = ki + 1; k <= i__1; ++k) {
                    i__2 = k + is * vr_dim1;
                    vr[i__2].r = 0., vr[i__2].i = 0.;
/* L60: */
                }
            } else {
                if (ki > 1) {
                    i__1 = ki - 1;
                    z__1.r = scale, z__1.i = 0.;
                    zgemv_("N", n, &i__1, &c_b2, &vr[vr_offset], ldvr, &work[
                            1], &c__1, &z__1, &vr[ki * vr_dim1 + 1], &c__1);
                }

                ii = izamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
                i__1 = ii + ki * vr_dim1;
                remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
                        &vr[ii + ki * vr_dim1]), abs(d__2)));
                zdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
            }

/*           Set back the original diagonal elements of T. */

            i__1 = ki - 1;
            for (k = 1; k <= i__1; ++k) {
                i__2 = k + k * t_dim1;
                i__3 = k + *n;
                t[i__2].r = work[i__3].r, t[i__2].i = work[i__3].i;
/* L70: */
            }

            --is;
L80:
            ;
        }
    }

    if (leftv) {

/*        Compute left eigenvectors. */

        is = 1;
        i__1 = *n;
        for (ki = 1; ki <= i__1; ++ki) {

            if (somev) {
                if (! select[ki]) {
                    goto L130;
                }
            }
/* Computing MAX */
            i__2 = ki + ki * t_dim1;
            d__3 = ulp * ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[
                    ki + ki * t_dim1]), abs(d__2)));
            smin = max(d__3,smlnum);

            i__2 = *n;
            work[i__2].r = 1., work[i__2].i = 0.;

/*           Form right-hand side. */

            i__2 = *n;
            for (k = ki + 1; k <= i__2; ++k) {
                i__3 = k;
                d_cnjg(&z__2, &t[ki + k * t_dim1]);
                z__1.r = -z__2.r, z__1.i = -z__2.i;
                work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* L90: */
            }

/*           Solve the triangular system: */
/*              (T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK. */

            i__2 = *n;
            for (k = ki + 1; k <= i__2; ++k) {
                i__3 = k + k * t_dim1;
                i__4 = k + k * t_dim1;
                i__5 = ki + ki * t_dim1;
                z__1.r = t[i__4].r - t[i__5].r, z__1.i = t[i__4].i - t[i__5]
                        .i;
                t[i__3].r = z__1.r, t[i__3].i = z__1.i;
                i__3 = k + k * t_dim1;
                if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[k + k * 
                        t_dim1]), abs(d__2)) < smin) {
                    i__4 = k + k * t_dim1;
                    t[i__4].r = smin, t[i__4].i = 0.;
                }
/* L100: */
            }

            if (ki < *n) {
                i__2 = *n - ki;
                zlatrs_("Upper", "Conjugate transpose", "Non-unit", "Y", &
                        i__2, &t[ki + 1 + (ki + 1) * t_dim1], ldt, &work[ki + 
                        1], &scale, &rwork[1], info);
                i__2 = ki;
                work[i__2].r = scale, work[i__2].i = 0.;
            }

/*           Copy the vector x or Q*x to VL and normalize. */

            if (! over) {
                i__2 = *n - ki + 1;
                zcopy_(&i__2, &work[ki], &c__1, &vl[ki + is * vl_dim1], &c__1)
                        ;

                i__2 = *n - ki + 1;
                ii = izamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 1;
                i__2 = ii + is * vl_dim1;
                remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
                        &vl[ii + is * vl_dim1]), abs(d__2)));
                i__2 = *n - ki + 1;
                zdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);

                i__2 = ki - 1;
                for (k = 1; k <= i__2; ++k) {
                    i__3 = k + is * vl_dim1;
                    vl[i__3].r = 0., vl[i__3].i = 0.;
/* L110: */
                }
            } else {
                if (ki < *n) {
                    i__2 = *n - ki;
                    z__1.r = scale, z__1.i = 0.;
                    zgemv_("N", n, &i__2, &c_b2, &vl[(ki + 1) * vl_dim1 + 1], 
                            ldvl, &work[ki + 1], &c__1, &z__1, &vl[ki * 
                            vl_dim1 + 1], &c__1);
                }

                ii = izamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
                i__2 = ii + ki * vl_dim1;
                remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
                        &vl[ii + ki * vl_dim1]), abs(d__2)));
                zdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
            }

/*           Set back the original diagonal elements of T. */

            i__2 = *n;
            for (k = ki + 1; k <= i__2; ++k) {
                i__3 = k + k * t_dim1;
                i__4 = k + *n;
                t[i__3].r = work[i__4].r, t[i__3].i = work[i__4].i;
/* L120: */
            }

            ++is;
L130:
            ;
        }
    }

    return 0;

/*     End of ZTREVC */

} /* ztrevc_ */