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

/* 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  	)
{
/*  -- LAPACK routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    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|.   

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


       Decode and test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b2 = {1.,0.};
    static integer c__1 = 1;
    
    /* 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 */
    static integer i__, j, k, ii, ki, is;
    static doublereal ulp;
    static logical allv;
    static doublereal unfl, ovfl, smin;
    static logical over;
    static doublereal scale;
    extern logical lsame_(char *, char *);
    static doublereal remax;
    static logical leftv, bothv;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, doublecomplex *, integer *);
    static 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 *);
    static logical rightv;
    extern doublereal dzasum_(integer *, doublecomplex *, integer *);
    static doublereal smlnum;
    extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublereal *, doublereal *, integer *);


    --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_ */