572 lines
19 KiB
C++
572 lines
19 KiB
C++
#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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int dlaed4_(integer *n, integer *i__, doublereal *d__, doublereal *z__, doublereal *delta,
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doublereal *rho, doublereal *dlam, integer *info)
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{
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integer i__1;
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doublereal d__1;
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double sqrt(doublereal);
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doublereal a, b, c__;
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integer j;
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doublereal w;
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integer ii;
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doublereal dw, zz[3];
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integer ip1;
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doublereal del, eta, phi, eps, tau, psi;
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integer iim1, iip1;
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doublereal dphi, dpsi;
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integer iter;
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doublereal temp, prew, temp1, dltlb, dltub, midpt;
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integer niter;
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logical swtch;
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extern int dlaed5_(integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *),
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dlaed6_(integer *, logical *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *);
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logical swtch3;
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extern doublereal dlamch_(char *, ftnlen);
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logical orgati;
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doublereal erretm, rhoinv;
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--delta;
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--z__;
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--d__;
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*info = 0;
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if (*n == 1) {
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*dlam = d__[1] + *rho * z__[1] * z__[1];
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delta[1] = 1.;
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return 0;
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}
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if (*n == 2) {
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dlaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam);
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return 0;
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}
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eps = dlamch_((char *)"Epsilon", (ftnlen)7);
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rhoinv = 1. / *rho;
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if (*i__ == *n) {
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ii = *n - 1;
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niter = 1;
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midpt = *rho / 2.;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] = d__[j] - d__[*i__] - midpt;
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}
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psi = 0.;
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i__1 = *n - 2;
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for (j = 1; j <= i__1; ++j) {
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psi += z__[j] * z__[j] / delta[j];
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}
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c__ = rhoinv + psi;
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w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[*n];
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if (w <= 0.) {
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temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) +
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z__[*n] * z__[*n] / *rho;
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if (c__ <= temp) {
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tau = *rho;
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} else {
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del = d__[*n] - d__[*n - 1];
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a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n];
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b = z__[*n] * z__[*n] * del;
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if (a < 0.) {
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tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a);
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} else {
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tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.);
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}
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}
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dltlb = midpt;
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dltub = *rho;
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} else {
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del = d__[*n] - d__[*n - 1];
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a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n];
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b = z__[*n] * z__[*n] * del;
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if (a < 0.) {
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tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a);
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} else {
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tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.);
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}
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dltlb = 0.;
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dltub = midpt;
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] = d__[j] - d__[*i__] - tau;
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}
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dpsi = 0.;
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psi = 0.;
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erretm = 0.;
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i__1 = ii;
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for (j = 1; j <= i__1; ++j) {
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temp = z__[j] / delta[j];
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psi += z__[j] * temp;
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dpsi += temp * temp;
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erretm += psi;
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}
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erretm = abs(erretm);
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temp = z__[*n] / delta[*n];
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phi = z__[*n] * temp;
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dphi = temp * temp;
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erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi);
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w = rhoinv + phi + psi;
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if (abs(w) <= eps * erretm) {
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*dlam = d__[*i__] + tau;
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goto L250;
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}
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if (w <= 0.) {
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dltlb = max(dltlb, tau);
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} else {
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dltub = min(dltub, tau);
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}
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++niter;
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c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi;
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a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * (dpsi + dphi);
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b = delta[*n - 1] * delta[*n] * w;
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if (c__ < 0.) {
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c__ = abs(c__);
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}
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if (c__ == 0.) {
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eta = -w / (dpsi + dphi);
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} else if (a >= 0.) {
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eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.);
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} else {
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eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))));
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}
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if (w * eta > 0.) {
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eta = -w / (dpsi + dphi);
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}
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temp = tau + eta;
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if (temp > dltub || temp < dltlb) {
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if (w < 0.) {
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eta = (dltub - tau) / 2.;
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} else {
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eta = (dltlb - tau) / 2.;
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}
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] -= eta;
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}
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tau += eta;
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dpsi = 0.;
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psi = 0.;
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erretm = 0.;
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i__1 = ii;
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for (j = 1; j <= i__1; ++j) {
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temp = z__[j] / delta[j];
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psi += z__[j] * temp;
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dpsi += temp * temp;
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erretm += psi;
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}
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erretm = abs(erretm);
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temp = z__[*n] / delta[*n];
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phi = z__[*n] * temp;
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dphi = temp * temp;
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erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi);
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w = rhoinv + phi + psi;
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iter = niter + 1;
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for (niter = iter; niter <= 30; ++niter) {
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if (abs(w) <= eps * erretm) {
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*dlam = d__[*i__] + tau;
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goto L250;
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}
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if (w <= 0.) {
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dltlb = max(dltlb, tau);
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} else {
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dltub = min(dltub, tau);
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}
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c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi;
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a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * (dpsi + dphi);
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b = delta[*n - 1] * delta[*n] * w;
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if (a >= 0.) {
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eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.);
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} else {
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eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))));
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}
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if (w * eta > 0.) {
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eta = -w / (dpsi + dphi);
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}
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temp = tau + eta;
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if (temp > dltub || temp < dltlb) {
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if (w < 0.) {
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eta = (dltub - tau) / 2.;
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} else {
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eta = (dltlb - tau) / 2.;
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}
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] -= eta;
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}
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tau += eta;
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dpsi = 0.;
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psi = 0.;
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erretm = 0.;
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i__1 = ii;
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for (j = 1; j <= i__1; ++j) {
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temp = z__[j] / delta[j];
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psi += z__[j] * temp;
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dpsi += temp * temp;
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erretm += psi;
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}
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erretm = abs(erretm);
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temp = z__[*n] / delta[*n];
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phi = z__[*n] * temp;
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dphi = temp * temp;
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erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi);
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w = rhoinv + phi + psi;
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}
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*info = 1;
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*dlam = d__[*i__] + tau;
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goto L250;
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} else {
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niter = 1;
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ip1 = *i__ + 1;
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del = d__[ip1] - d__[*i__];
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midpt = del / 2.;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] = d__[j] - d__[*i__] - midpt;
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}
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psi = 0.;
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i__1 = *i__ - 1;
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for (j = 1; j <= i__1; ++j) {
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psi += z__[j] * z__[j] / delta[j];
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}
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phi = 0.;
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i__1 = *i__ + 2;
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for (j = *n; j >= i__1; --j) {
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phi += z__[j] * z__[j] / delta[j];
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}
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c__ = rhoinv + psi + phi;
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w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / delta[ip1];
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if (w > 0.) {
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orgati = TRUE_;
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a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1];
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b = z__[*i__] * z__[*i__] * del;
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if (a > 0.) {
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tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))));
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} else {
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tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.);
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}
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dltlb = 0.;
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dltub = midpt;
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} else {
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orgati = FALSE_;
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a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1];
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b = z__[ip1] * z__[ip1] * del;
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if (a < 0.) {
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tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs(d__1))));
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} else {
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tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / (c__ * 2.);
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}
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dltlb = -midpt;
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dltub = 0.;
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}
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if (orgati) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] = d__[j] - d__[*i__] - tau;
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] = d__[j] - d__[ip1] - tau;
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}
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}
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if (orgati) {
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ii = *i__;
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} else {
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ii = *i__ + 1;
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}
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iim1 = ii - 1;
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iip1 = ii + 1;
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dpsi = 0.;
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psi = 0.;
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erretm = 0.;
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i__1 = iim1;
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for (j = 1; j <= i__1; ++j) {
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temp = z__[j] / delta[j];
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psi += z__[j] * temp;
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dpsi += temp * temp;
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erretm += psi;
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}
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erretm = abs(erretm);
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dphi = 0.;
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phi = 0.;
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i__1 = iip1;
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for (j = *n; j >= i__1; --j) {
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temp = z__[j] / delta[j];
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phi += z__[j] * temp;
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dphi += temp * temp;
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erretm += phi;
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}
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w = rhoinv + phi + psi;
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swtch3 = FALSE_;
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if (orgati) {
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if (w < 0.) {
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swtch3 = TRUE_;
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}
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} else {
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if (w > 0.) {
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swtch3 = TRUE_;
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}
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}
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if (ii == 1 || ii == *n) {
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swtch3 = FALSE_;
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}
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temp = z__[ii] / delta[ii];
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dw = dpsi + dphi + temp * temp;
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temp = z__[ii] * temp;
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w += temp;
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erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + abs(tau) * dw;
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if (abs(w) <= eps * erretm) {
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if (orgati) {
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*dlam = d__[*i__] + tau;
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} else {
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*dlam = d__[ip1] + tau;
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}
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goto L250;
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}
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if (w <= 0.) {
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dltlb = max(dltlb, tau);
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} else {
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dltub = min(dltub, tau);
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}
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++niter;
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if (!swtch3) {
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if (orgati) {
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d__1 = z__[*i__] / delta[*i__];
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c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * d__1);
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} else {
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d__1 = z__[ip1] / delta[ip1];
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c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * d__1);
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}
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a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * dw;
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b = delta[*i__] * delta[ip1] * w;
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if (c__ == 0.) {
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if (a == 0.) {
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if (orgati) {
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a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * (dpsi + dphi);
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} else {
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a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * (dpsi + dphi);
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}
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}
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eta = b / a;
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} else if (a <= 0.) {
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eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.);
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} else {
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eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))));
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}
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} else {
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temp = rhoinv + psi + phi;
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if (orgati) {
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temp1 = z__[iim1] / delta[iim1];
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temp1 *= temp1;
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c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * temp1;
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zz[0] = z__[iim1] * z__[iim1];
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zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi);
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} else {
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temp1 = z__[iip1] / delta[iip1];
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temp1 *= temp1;
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c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * temp1;
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zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1));
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zz[2] = z__[iip1] * z__[iip1];
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}
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zz[1] = z__[ii] * z__[ii];
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dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info);
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if (*info != 0) {
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goto L250;
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}
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}
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if (w * eta >= 0.) {
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eta = -w / dw;
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}
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temp = tau + eta;
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if (temp > dltub || temp < dltlb) {
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if (w < 0.) {
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eta = (dltub - tau) / 2.;
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} else {
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eta = (dltlb - tau) / 2.;
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}
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}
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prew = w;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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delta[j] -= eta;
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}
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dpsi = 0.;
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psi = 0.;
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erretm = 0.;
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i__1 = iim1;
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for (j = 1; j <= i__1; ++j) {
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temp = z__[j] / delta[j];
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psi += z__[j] * temp;
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dpsi += temp * temp;
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erretm += psi;
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}
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erretm = abs(erretm);
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dphi = 0.;
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phi = 0.;
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i__1 = iip1;
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for (j = *n; j >= i__1; --j) {
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temp = z__[j] / delta[j];
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phi += z__[j] * temp;
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dphi += temp * temp;
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erretm += phi;
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}
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temp = z__[ii] / delta[ii];
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dw = dpsi + dphi + temp * temp;
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temp = z__[ii] * temp;
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w = rhoinv + phi + psi + temp;
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erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. +
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(d__1 = tau + eta, abs(d__1)) * dw;
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swtch = FALSE_;
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if (orgati) {
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if (-w > abs(prew) / 10.) {
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swtch = TRUE_;
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}
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} else {
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if (w > abs(prew) / 10.) {
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swtch = TRUE_;
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}
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}
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tau += eta;
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iter = niter + 1;
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for (niter = iter; niter <= 30; ++niter) {
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if (abs(w) <= eps * erretm) {
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if (orgati) {
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*dlam = d__[*i__] + tau;
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} else {
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*dlam = d__[ip1] + tau;
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}
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goto L250;
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}
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if (w <= 0.) {
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dltlb = max(dltlb, tau);
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} else {
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dltub = min(dltub, tau);
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}
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if (!swtch3) {
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if (!swtch) {
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if (orgati) {
|
|
d__1 = z__[*i__] / delta[*i__];
|
|
c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * d__1);
|
|
} else {
|
|
d__1 = z__[ip1] / delta[ip1];
|
|
c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * d__1);
|
|
}
|
|
} else {
|
|
temp = z__[ii] / delta[ii];
|
|
if (orgati) {
|
|
dpsi += temp * temp;
|
|
} else {
|
|
dphi += temp * temp;
|
|
}
|
|
c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi;
|
|
}
|
|
a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * dw;
|
|
b = delta[*i__] * delta[ip1] * w;
|
|
if (c__ == 0.) {
|
|
if (a == 0.) {
|
|
if (!swtch) {
|
|
if (orgati) {
|
|
a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * (dpsi + dphi);
|
|
} else {
|
|
a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * (dpsi + dphi);
|
|
}
|
|
} else {
|
|
a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] * delta[ip1] * dphi;
|
|
}
|
|
}
|
|
eta = b / a;
|
|
} else if (a <= 0.) {
|
|
eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.);
|
|
} else {
|
|
eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))));
|
|
}
|
|
} else {
|
|
temp = rhoinv + psi + phi;
|
|
if (swtch) {
|
|
c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi;
|
|
zz[0] = delta[iim1] * delta[iim1] * dpsi;
|
|
zz[2] = delta[iip1] * delta[iip1] * dphi;
|
|
} else {
|
|
if (orgati) {
|
|
temp1 = z__[iim1] / delta[iim1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * temp1;
|
|
zz[0] = z__[iim1] * z__[iim1];
|
|
zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi);
|
|
} else {
|
|
temp1 = z__[iip1] / delta[iip1];
|
|
temp1 *= temp1;
|
|
c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * temp1;
|
|
zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1));
|
|
zz[2] = z__[iip1] * z__[iip1];
|
|
}
|
|
}
|
|
dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info);
|
|
if (*info != 0) {
|
|
goto L250;
|
|
}
|
|
}
|
|
if (w * eta >= 0.) {
|
|
eta = -w / dw;
|
|
}
|
|
temp = tau + eta;
|
|
if (temp > dltub || temp < dltlb) {
|
|
if (w < 0.) {
|
|
eta = (dltub - tau) / 2.;
|
|
} else {
|
|
eta = (dltlb - tau) / 2.;
|
|
}
|
|
}
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
delta[j] -= eta;
|
|
}
|
|
tau += eta;
|
|
prew = w;
|
|
dpsi = 0.;
|
|
psi = 0.;
|
|
erretm = 0.;
|
|
i__1 = iim1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = z__[j] / delta[j];
|
|
psi += z__[j] * temp;
|
|
dpsi += temp * temp;
|
|
erretm += psi;
|
|
}
|
|
erretm = abs(erretm);
|
|
dphi = 0.;
|
|
phi = 0.;
|
|
i__1 = iip1;
|
|
for (j = *n; j >= i__1; --j) {
|
|
temp = z__[j] / delta[j];
|
|
phi += z__[j] * temp;
|
|
dphi += temp * temp;
|
|
erretm += phi;
|
|
}
|
|
temp = z__[ii] / delta[ii];
|
|
dw = dpsi + dphi + temp * temp;
|
|
temp = z__[ii] * temp;
|
|
w = rhoinv + phi + psi + temp;
|
|
erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + abs(tau) * dw;
|
|
if (w * prew > 0. && abs(w) > abs(prew) / 10.) {
|
|
swtch = !swtch;
|
|
}
|
|
}
|
|
*info = 1;
|
|
if (orgati) {
|
|
*dlam = d__[*i__] + tau;
|
|
} else {
|
|
*dlam = d__[ip1] + tau;
|
|
}
|
|
}
|
|
L250:
|
|
return 0;
|
|
}
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|