#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static integer c__1 = 1; int dlahqr_(logical *wantt, logical *wantz, integer *n, integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz, integer *info) { integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3, d__4; double sqrt(doublereal); integer i__, j, k, l, m; doublereal s, v[3]; integer i1, i2; doublereal t1, t2, t3, v2, v3, aa, ab, ba, bb, h11, h12, h21, h22, cs; integer nh; doublereal sn; integer nr; doublereal tr; integer nz; doublereal det, h21s; integer its; doublereal ulp, sum, tst, rt1i, rt2i, rt1r, rt2r; extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer kdefl; extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer itmax; extern int dlanv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); extern int dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *); doublereal safmin, safmax, rtdisc, smlnum; h_dim1 = *ldh; h_offset = 1 + h_dim1; h__ -= h_offset; --wr; --wi; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; *info = 0; if (*n == 0) { return 0; } if (*ilo == *ihi) { wr[*ilo] = h__[*ilo + *ilo * h_dim1]; wi[*ilo] = 0.; return 0; } i__1 = *ihi - 3; for (j = *ilo; j <= i__1; ++j) { h__[j + 2 + j * h_dim1] = 0.; h__[j + 3 + j * h_dim1] = 0.; } if (*ilo <= *ihi - 2) { h__[*ihi + (*ihi - 2) * h_dim1] = 0.; } nh = *ihi - *ilo + 1; nz = *ihiz - *iloz + 1; safmin = dlamch_((char *)"SAFE MINIMUM", (ftnlen)12); safmax = 1. / safmin; ulp = dlamch_((char *)"PRECISION", (ftnlen)9); smlnum = safmin * ((doublereal)nh / ulp); if (*wantt) { i1 = 1; i2 = *n; } itmax = max(10, nh) * 30; kdefl = 0; i__ = *ihi; L20: l = *ilo; if (i__ < *ilo) { goto L160; } i__1 = itmax; for (its = 0; its <= i__1; ++its) { i__2 = l + 1; for (k = i__; k >= i__2; --k) { if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= smlnum) { goto L40; } tst = (d__1 = h__[k - 1 + (k - 1) * h_dim1], abs(d__1)) + (d__2 = h__[k + k * h_dim1], abs(d__2)); if (tst == 0.) { if (k - 2 >= *ilo) { tst += (d__1 = h__[k - 1 + (k - 2) * h_dim1], abs(d__1)); } if (k + 1 <= *ihi) { tst += (d__1 = h__[k + 1 + k * h_dim1], abs(d__1)); } } if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= ulp * tst) { d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (d__2 = h__[k - 1 + k * h_dim1], abs(d__2)); ab = max(d__3, d__4); d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (d__2 = h__[k - 1 + k * h_dim1], abs(d__2)); ba = min(d__3, d__4); d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 = h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1], abs(d__2)); aa = max(d__3, d__4); d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 = h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1], abs(d__2)); bb = min(d__3, d__4); s = aa + ab; d__1 = smlnum, d__2 = ulp * (bb * (aa / s)); if (ba * (ab / s) <= max(d__1, d__2)) { goto L40; } } } L40: l = k; if (l > *ilo) { h__[l + (l - 1) * h_dim1] = 0.; } if (l >= i__ - 1) { goto L150; } ++kdefl; if (!(*wantt)) { i1 = l; i2 = i__; } if (kdefl % 20 == 0) { s = (d__1 = h__[i__ + (i__ - 1) * h_dim1], abs(d__1)) + (d__2 = h__[i__ - 1 + (i__ - 2) * h_dim1], abs(d__2)); h11 = s * .75 + h__[i__ + i__ * h_dim1]; h12 = s * -.4375; h21 = s; h22 = h11; } else if (kdefl % 10 == 0) { s = (d__1 = h__[l + 1 + l * h_dim1], abs(d__1)) + (d__2 = h__[l + 2 + (l + 1) * h_dim1], abs(d__2)); h11 = s * .75 + h__[l + l * h_dim1]; h12 = s * -.4375; h21 = s; h22 = h11; } else { h11 = h__[i__ - 1 + (i__ - 1) * h_dim1]; h21 = h__[i__ + (i__ - 1) * h_dim1]; h12 = h__[i__ - 1 + i__ * h_dim1]; h22 = h__[i__ + i__ * h_dim1]; } s = abs(h11) + abs(h12) + abs(h21) + abs(h22); if (s == 0.) { rt1r = 0.; rt1i = 0.; rt2r = 0.; rt2i = 0.; } else { h11 /= s; h21 /= s; h12 /= s; h22 /= s; tr = (h11 + h22) / 2.; det = (h11 - tr) * (h22 - tr) - h12 * h21; rtdisc = sqrt((abs(det))); if (det >= 0.) { rt1r = tr * s; rt2r = rt1r; rt1i = rtdisc * s; rt2i = -rt1i; } else { rt1r = tr + rtdisc; rt2r = tr - rtdisc; if ((d__1 = rt1r - h22, abs(d__1)) <= (d__2 = rt2r - h22, abs(d__2))) { rt1r *= s; rt2r = rt1r; } else { rt2r *= s; rt1r = rt2r; } rt1i = 0.; rt2i = 0.; } } i__2 = l; for (m = i__ - 2; m >= i__2; --m) { h21s = h__[m + 1 + m * h_dim1]; s = (d__1 = h__[m + m * h_dim1] - rt2r, abs(d__1)) + abs(rt2i) + abs(h21s); h21s = h__[m + 1 + m * h_dim1] / s; v[0] = h21s * h__[m + (m + 1) * h_dim1] + (h__[m + m * h_dim1] - rt1r) * ((h__[m + m * h_dim1] - rt2r) / s) - rt1i * (rt2i / s); v[1] = h21s * (h__[m + m * h_dim1] + h__[m + 1 + (m + 1) * h_dim1] - rt1r - rt2r); v[2] = h21s * h__[m + 2 + (m + 1) * h_dim1]; s = abs(v[0]) + abs(v[1]) + abs(v[2]); v[0] /= s; v[1] /= s; v[2] /= s; if (m == l) { goto L60; } if ((d__1 = h__[m + (m - 1) * h_dim1], abs(d__1)) * (abs(v[1]) + abs(v[2])) <= ulp * abs(v[0]) * ((d__2 = h__[m - 1 + (m - 1) * h_dim1], abs(d__2)) + (d__3 = h__[m + m * h_dim1], abs(d__3)) + (d__4 = h__[m + 1 + (m + 1) * h_dim1], abs(d__4)))) { goto L60; } } L60: i__2 = i__ - 1; for (k = m; k <= i__2; ++k) { i__3 = 3, i__4 = i__ - k + 1; nr = min(i__3, i__4); if (k > m) { dcopy_(&nr, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1); } dlarfg_(&nr, v, &v[1], &c__1, &t1); if (k > m) { h__[k + (k - 1) * h_dim1] = v[0]; h__[k + 1 + (k - 1) * h_dim1] = 0.; if (k < i__ - 1) { h__[k + 2 + (k - 1) * h_dim1] = 0.; } } else if (m > l) { h__[k + (k - 1) * h_dim1] *= 1. - t1; } v2 = v[1]; t2 = t1 * v2; if (nr == 3) { v3 = v[2]; t3 = t1 * v3; i__3 = i2; for (j = k; j <= i__3; ++j) { sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1] + v3 * h__[k + 2 + j * h_dim1]; h__[k + j * h_dim1] -= sum * t1; h__[k + 1 + j * h_dim1] -= sum * t2; h__[k + 2 + j * h_dim1] -= sum * t3; } i__4 = k + 3; i__3 = min(i__4, i__); for (j = i1; j <= i__3; ++j) { sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1] + v3 * h__[j + (k + 2) * h_dim1]; h__[j + k * h_dim1] -= sum * t1; h__[j + (k + 1) * h_dim1] -= sum * t2; h__[j + (k + 2) * h_dim1] -= sum * t3; } if (*wantz) { i__3 = *ihiz; for (j = *iloz; j <= i__3; ++j) { sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) * z_dim1] + v3 * z__[j + (k + 2) * z_dim1]; z__[j + k * z_dim1] -= sum * t1; z__[j + (k + 1) * z_dim1] -= sum * t2; z__[j + (k + 2) * z_dim1] -= sum * t3; } } } else if (nr == 2) { i__3 = i2; for (j = k; j <= i__3; ++j) { sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1]; h__[k + j * h_dim1] -= sum * t1; h__[k + 1 + j * h_dim1] -= sum * t2; } i__3 = i__; for (j = i1; j <= i__3; ++j) { sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]; h__[j + k * h_dim1] -= sum * t1; h__[j + (k + 1) * h_dim1] -= sum * t2; } if (*wantz) { i__3 = *ihiz; for (j = *iloz; j <= i__3; ++j) { sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) * z_dim1]; z__[j + k * z_dim1] -= sum * t1; z__[j + (k + 1) * z_dim1] -= sum * t2; } } } } } *info = i__; return 0; L150: if (l == i__) { wr[i__] = h__[i__ + i__ * h_dim1]; wi[i__] = 0.; } else if (l == i__ - 1) { dlanv2_(&h__[i__ - 1 + (i__ - 1) * h_dim1], &h__[i__ - 1 + i__ * h_dim1], &h__[i__ + (i__ - 1) * h_dim1], &h__[i__ + i__ * h_dim1], &wr[i__ - 1], &wi[i__ - 1], &wr[i__], &wi[i__], &cs, &sn); if (*wantt) { if (i2 > i__) { i__1 = i2 - i__; drot_(&i__1, &h__[i__ - 1 + (i__ + 1) * h_dim1], ldh, &h__[i__ + (i__ + 1) * h_dim1], ldh, &cs, &sn); } i__1 = i__ - i1 - 1; drot_(&i__1, &h__[i1 + (i__ - 1) * h_dim1], &c__1, &h__[i1 + i__ * h_dim1], &c__1, &cs, &sn); } if (*wantz) { drot_(&nz, &z__[*iloz + (i__ - 1) * z_dim1], &c__1, &z__[*iloz + i__ * z_dim1], &c__1, &cs, &sn); } } kdefl = 0; i__ = l - 1; goto L20; L160: return 0; } #ifdef __cplusplus } #endif